Finite Group Databasebeta

← #25304365

Subgroups — #25304365

Order 11008.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142932C211yesmaximal, characteristic, complemented
2#19142903C211yesmaximal, characteristic, complemented
3#19142548C211yesmaximal, characteristic, complemented
4#19142541C211yesmaximal, characteristic
5#19142365C211yesmaximal, characteristic, complemented
6#19142342C211yesmaximal, characteristic, complemented
7#19142338C211yesmaximal, characteristic, complemented
8#19142296C211yesmaximal, characteristic
9#19142244C211yesmaximal, characteristic
10#19142154C211yesmaximal, characteristic, complemented
11#19142011C211yesmaximal, characteristic, complemented
12#19142011C211yesmaximal, characteristic, complemented
13#19141903C211yesmaximal, characteristic, complemented
14#19141721C211yesmaximal, characteristic, complemented
15#19141574C211yesmaximal, characteristic, complemented
16#19141472C211yesmaximal, characteristic, complemented
17#19141373C211yesmaximal, characteristic, complemented
18#19141088C211yesmaximal, characteristic
19#19140768C211yesmaximal, characteristic, complemented
20#19140767C211yesmaximal, characteristic, complemented
21#19140298C211yesmaximal, characteristic, complemented
22#19140260C211yesmaximal, characteristic, complemented
23#19140243C211yesmaximal, characteristic, complemented
24#19140238C211yesmaximal, characteristic, complemented
25#19139829C211yesmaximal, characteristic, complemented
26#19139820C211yesmaximal, characteristic, complemented
27#19138287C211yesmaximal, characteristic, complemented
28#19138273C211yesmaximal, characteristic, complemented
29#19137228C211yesmaximal, characteristic
30#19137040C211yesmaximal, characteristic
31C43×#2319C211yesmaximal, characteristic
32C2×#13063324C2211yescharacteristic
33C2×#13063316C2211yescharacteristic
34C2×#13063302C2211yescharacteristic
35C2×#13063302C2211yescharacteristic
36C2×#13063284C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38#14582841C2211yescharacteristic
39#14582841C2211yescharacteristic
40#14582841C2211yescharacteristic
41#14582841C2211yescharacteristic
42#14582841C2211yescharacteristic
43#14582841C2211yescharacteristic
44#14582838C2211yescharacteristic
45#14582838C2211yescharacteristic
46#14582838C2211yescharacteristic
47#14582838C2211yescharacteristic
48#14582838C2211yescharacteristic
49#14582838C2211yescharacteristic
50#14582838C2211yescharacteristic
51#14582838C2211yescharacteristic
52#14582835C2211yescharacteristic
53#14582835C2211yescharacteristic
54#14582833C2211yescharacteristic
55#14582833C2211yescharacteristic
56#14582832C2211yescharacteristic
57#14582832C2211yescharacteristic
58#14582832C2211yescharacteristic
59#14582832C2211yescharacteristic
60#14582831C2211yescharacteristic
61#14582831C2211yescharacteristic
62#14582822C2211yescharacteristic
63#14582822C2211yescharacteristic
64#14582822C2211yescharacteristic
65#14582822C2211yescharacteristic
66#14582822C2211yescharacteristic
67#14582822C2211yescharacteristic
68#14582820C2211yescharacteristic
69#14582820C2211yescharacteristic
70#14582820C2211yescharacteristic
71#14582820C2211yescharacteristic
72#14582820C2211yescharacteristic
73#14582820C2211yescharacteristic
74#14582819C2211yescharacteristic
75#14582819C2211yescharacteristic
76#14582819C2211yescharacteristic
77#14582819C2211yescharacteristic
78#14582811C2211yescharacteristic
79#14582811C2211yescharacteristic
80#14582811C2211yescharacteristic
81#14582811C2211yescharacteristic
82#14582811C2211yescharacteristic
83#14582811C2211yescharacteristic
84#14582811C2211yescharacteristic
85#14582811C2211yescharacteristic
86#14582805C2211yescharacteristic
87#14582805C2211yescharacteristic
88#14582805C2211yescharacteristic
89#14582805C2211yescharacteristic
90#14582805C2211yescharacteristic
91#14582803C2211yescharacteristic
92#14582803C2211yescharacteristic
93#14582803C2211yescharacteristic
94#14582803C2211yescharacteristic
95#14582803C2211yescharacteristic
96#14582803C2211yescharacteristic
97#14582803C2211yescharacteristic
98#14582803C2211yescharacteristic
99#14582798C2211yescharacteristic
100#14582798C2211yescharacteristic
101#14582797C2211yescharacteristic
102#14582797C2211yescharacteristic
103#14582797C2211yescharacteristic
104#14582796C2211yescharacteristic
105#14582796C2211yescharacteristic
106#14582795C2211yescharacteristic
107#14582795C2211yescharacteristic
108#14582792C2211yescharacteristic
109#14582792C2211yescharacteristic
110#14582792C2211yescharacteristic
111#14582792C2211yescharacteristic
112#14582786C2211yescharacteristic
113#14582786C2211yescharacteristic
114#14582786C2211yescharacteristic
115#14582786C2211yescharacteristic
116#14582786C2211yescharacteristic
117#14582786C2211yescharacteristic
118#14582786C2211yescharacteristic
119#14582786C2211yescharacteristic
120#14582785C2211yescharacteristic
121#14582785C2211yescharacteristic
122#14582785C2211yescharacteristic
123#14582785C2211yescharacteristic
124#14582783C2211yescharacteristic
125#14582783C2211yescharacteristic
126#14582783C2211yescharacteristic
127#14582783C2211yescharacteristic
128#14582783C2211yescharacteristic
129#14582783C2211yescharacteristic
130#14582782C2211yescharacteristic
131#14582782C2211yescharacteristic
132#14582782C2211yescharacteristic
133#14582782C2211yescharacteristic
134#14582782C2211yescharacteristic
135#14582782C2211yescharacteristic
136#14582779C2211yescharacteristic
137#14582779C2211yescharacteristic
138#14582779C2211yescharacteristic
139#14582779C2211yescharacteristic
140#14582774C2211yescharacteristic
141#14582774C2211yescharacteristic
142#14582774C2211yescharacteristic
143#14582774C2211yescharacteristic
144#14582774C2211yescharacteristic
145#14582774C2211yescharacteristic
146#14582774C2211yescharacteristic
147#14582774C2211yescharacteristic
148#14582774C2211yescharacteristic
149#14582774C2211yescharacteristic
150#14582771C2211yescharacteristic
151#14582771C2211yescharacteristic
152#14582771C2211yescharacteristic
153#14582771C2211yescharacteristic
154#14582769C2211yescharacteristic
155#14582767C2211yescharacteristic
156#14582765C2211yescharacteristic
157#14582765C2211yescharacteristic
158#14582764C2211yescharacteristic
159#14582764C2211yescharacteristic
160#14582762C2211yescharacteristic
161#14582759C2211yescharacteristic
162#14582757C2211yescharacteristic
163#14582757C2211yescharacteristic
164#14582757C2211yescharacteristic
165#14582757C2211yescharacteristic
166C4×C4⋊Dic43C2211yescharacteristic
167C4×C22⋊Dic43C2211yescharacteristic
168C4×C22⋊Dic43C2211yescharacteristic
169C4×C22⋊Dic43C2211yescharacteristic
170#14582745C2211yescharacteristic
171C2×C43⋊#95C2211yescharacteristic
172C2×C4×D4×C43C2211yescharacteristic
173C43×#390C2211yescharacteristic
174C43×#390C2211yescharacteristic
175C43×#389C2211yescharacteristic
176C43×#389C2211yescharacteristic
177C43×#388C2211yescharacteristic
178C43×#388C2211yescharacteristic
179C43×#388C2211yescharacteristic
180C43×#388C2211yescharacteristic
181C43×#381C2211yescharacteristic
182C43×#381C2211yescharacteristic
183C43×#380C2211yescharacteristic
184C43×#380C2211yescharacteristic
185C4×C4⋊C4×C43C2211yescharacteristic
186C43×#376C2211yescharacteristic
187C22×Dic86C2311yescharacteristic
188C22×Dic86C2311yescharacteristic
189C22×Dic86C2311yescharacteristic
190C22×Dic86C2311yescharacteristic
191C22×Dic86C2311yescharacteristic
192C23×Dic43C2311yescharacteristic
193C23×Dic43C2311yescharacteristic
194C23×Dic43C2311yescharacteristic
195C23×Dic43C2311yescharacteristic
196#13063324—42no—
197#13063316—42no—
198#13063302—42no—
199#13063302—42no—
200#13063284—42no—
201C2×C4⋊Dic43C2311yescharacteristic
202C2×C4⋊Dic43C2311yescharacteristic
203C2×C4⋊Dic43C2311yescharacteristic
204C2×C4⋊Dic43C2311yescharacteristic
205C2×C4⋊Dic43C2311yescharacteristic
206C2×C4⋊Dic43C2311yescharacteristic
207C2×C4⋊Dic43C2311yescharacteristic
208C2×C4⋊Dic43C2311yescharacteristic
209C2×C4⋊Dic43C2311yescharacteristic
210C2×C4⋊Dic43C2311yescharacteristic
211C2×C4⋊Dic43C2311yescharacteristic
212C2×C4⋊Dic43C2311yescharacteristic
213C2×C4⋊Dic43C2311yescharacteristic
214C2×C4⋊Dic43C2311yescharacteristic
215C2×C4⋊Dic43C2311yescharacteristic
216C2×C4⋊Dic43C2311yescharacteristic
217C2×C4⋊Dic43C2311yescharacteristic
218C2×C4⋊Dic43C2311yescharacteristic
219C2×C4⋊Dic43C2311yescharacteristic
220C2×Dic43⋊C4C2311yescharacteristic
221C2×Dic43⋊C4C2311yescharacteristic
222C2×Dic43⋊C4C2311yescharacteristic
223C2×Dic43⋊C4C2311yescharacteristic
224C2×Dic43⋊C4C2311yescharacteristic
225C2×Dic43⋊C4C2311yescharacteristic
226C2×Dic43⋊C4C2311yescharacteristic
227C2×Dic43⋊C4C2311yescharacteristic
228C2×Dic43⋊C4C2311yescharacteristic
229C2×Dic43⋊C4C2311yescharacteristic
230C2×Dic43⋊C4C2311yescharacteristic
231C2×Dic43⋊C4C2311yescharacteristic
232C2×Dic43⋊C4C2311yescharacteristic
233C2×Dic43⋊C4C2311yescharacteristic
234C2×Dic43⋊C4C2311yescharacteristic
235C2×Dic43⋊C4C2311yescharacteristic
236C2×Dic43⋊C4C2311yescharacteristic
237C2×Dic43⋊C4C2311yescharacteristic
238C2×C22⋊Dic43C2311yescharacteristic
239C2×C22⋊Dic43C2311yescharacteristic
240C2×C22⋊Dic43C2311yescharacteristic
241C2×C22⋊Dic43C2311yescharacteristic
242C2×C22⋊Dic43C2311yescharacteristic
243C2×C22⋊Dic43C2311yescharacteristic
244C2×C22⋊Dic43C2311yescharacteristic
245C2×C22⋊Dic43C2311yescharacteristic
246C2×C22⋊Dic43C2311yescharacteristic
247C2×C22⋊Dic43C2311yescharacteristic
248C2×C22⋊Dic43C2311yescharacteristic
249C2×C22⋊Dic43C2311yescharacteristic
250C2×C4×Dic43—42no—
251C2×C4×Dic43C2311yescharacteristic
252C2×C4×Dic43C2311yescharacteristic
253C2×C4×Dic43C2311yescharacteristic
254C2×C4×Dic43C2311yescharacteristic
255C2×C4×Dic43C2311yescharacteristic
256C2×C4×Dic43C2311yescharacteristic
257C2×C4×Dic43C2311yescharacteristic
258C2×C4×Dic43C2311yescharacteristic
259C43⋊#95C2311yescharacteristic
260C43⋊#95C2311yescharacteristic
261C43⋊#95C2311yescharacteristic
262C43⋊#95C2311yescharacteristic
263C43⋊#95C2311yescharacteristic
264C43⋊#95C2311yescharacteristic
265C43⋊#95C2311yescharacteristic
266C43⋊#95C2311yescharacteristic
267C43⋊#95C2311yescharacteristic
268C43⋊#95C2311yescharacteristic
269C43⋊#95C2311yescharacteristic
270C43⋊#95C2311yescharacteristic
271C43⋊#95C2311yescharacteristic
272C43⋊#95C2311yescharacteristic
273C43⋊#95C2311yescharacteristic
274C43⋊#95C2311yescharacteristic
275C43⋊#95C2311yescharacteristic
276C43⋊#95C2311yescharacteristic
277C43⋊#95C2311yescharacteristic
278C43⋊#95C2311yescharacteristic
279C43⋊#95C2311yescharacteristic
280C43⋊#95C2311yescharacteristic
281C43⋊#95C2311yescharacteristic
282C43⋊#95C2311yescharacteristic
283C43⋊#95C2311yescharacteristic
284C43⋊#95C2311yescharacteristic
285C43⋊#95C2311yescharacteristic
286C43⋊#95C2311yescharacteristic
287C43⋊#95C2311yescharacteristic
288C43⋊#95C2311yescharacteristic
289C43⋊#95C2311yescharacteristic
290C43⋊#95C2311yescharacteristic
291C43⋊#95C2311yescharacteristic
292C43⋊#95C2311yescharacteristic
293C43⋊#95C2311yescharacteristic
294C43⋊#95C2311yescharacteristic
295C43⋊#95C2311yescharacteristic
296C43⋊#95C2311yescharacteristic
297C43⋊#95C2311yescharacteristic
298C43⋊#95C2311yescharacteristic
299C43⋊#95C2311yescharacteristic
300C43⋊#95C2311yescharacteristic
301C43⋊#95C2311yescharacteristic
302C43⋊#95C2311yescharacteristic
303C43⋊#95C2311yescharacteristic
304C43⋊#95C2311yescharacteristic
305C43⋊#95C2311yescharacteristic
306C43⋊#95C2311yescharacteristic
307C43⋊#95C2311yescharacteristic
308C43⋊#95C2311yescharacteristic
309C43⋊#95C2311yescharacteristic
310C43⋊#95C2311yescharacteristic
311C43⋊#95C2311yescharacteristic
312C43⋊#95C2311yescharacteristic
313C22×D4×C43C2311yescharacteristic
314C23×C4×C43C2311yescharacteristic
315C23×C4×C43C2311yescharacteristic
316C4×D4×C43Q818yescomplemented
317C2×C4⋊C4×C43C2311yescharacteristic
318C2×C4⋊C4×C43C2311yescharacteristic
319C2×C4⋊C4×C43C2311yescharacteristic
320C2×C4⋊C4×C43C2311yescharacteristic
321C2×C4⋊C4×C43C2311yescharacteristic
322C2×C4⋊C4×C43C2311yescharacteristic
323C2×C4⋊C4×C43C2311yescharacteristic
324C2×C22⋊C4×C43C2311yescharacteristic
325C2×C22⋊C4×C43C2311yescharacteristic
326C2×C22⋊C4×C43C2311yescharacteristic
327C2×C22⋊C4×C43C2311yescharacteristic
328C2×C22⋊C4×C43C2311yescharacteristic
329C2×C22⋊C4×C43C2311yescharacteristic
330C2×C22⋊C4×C43C2311yescharacteristic
331C2×C22⋊C4×C43C2311yescharacteristic
332C2×C22⋊C4×C43C2311yescharacteristic
333C2×C22⋊C4×C43C2311yescharacteristic
334C2×C42×C43C2311yescharacteristic
335C2×C42×C43C2311yescharacteristic
336C2×C42×C43C2311yescharacteristic
337C2×C42×C43C2311yescharacteristic
338C2×C42×C43C2311yescharacteristic
339#95×C43C2311yescharacteristic
340#95×C43C2311yescharacteristic
341#95×C43C2311yescharacteristic
342#95×C43C2311yescharacteristic
343#95×C43C2311yescharacteristic
344#95×C43C2311yescharacteristic
345#95×C43C2311yescharacteristic
346#95×C43C2311yescharacteristic
347#95×C43C2311yescharacteristic
348#95×C43C2311yescharacteristic
349C24×C43C2411yescharacteristic
350C24×C43C2411yescharacteristic
351C2×D4×C43—41no—
352C2×D4×C43—41no—
353C2×D4×C43C2×Q814yes—
354C22×C4×C43—41no—
355C22×C4×C43—41no—
356C22×C4×C43—41no—
357C22×C4×C43—41no—
358C22×C4×C43C2×Q814yes—
359C22×C4×C43C2×Q814yes—
360C22×C4×C43C2411yescharacteristic
361C22×C4×C43C2411yescharacteristic
362C22×C4×C43C2411yescharacteristic
363C22×C4×C43C2411yescharacteristic
364C22×C4×C43C2411yescharacteristic
365C22×C4×C43C2411yescharacteristic
366C22×C4×C43C2411yescharacteristic
367C22×C4×C43C2411yescharacteristic
368C22×C4×C43C2411yescharacteristic
369C22×C4×C43C2411yescharacteristic
370C22×C4×C43C2411yescharacteristic
371C22×C4×C43C2411yescharacteristic
372C22×C4×C43C2411yescharacteristic
373C22×Dic43—22no—
374C22×Dic43—41no—
375C22×Dic43—41no—
376C22×Dic43—41no—
377C22×Dic43—41no—
378C22×Dic43—41no—
379C22×Dic43—41no—
380C22×Dic43—41no—
381C22×Dic43—41no—
382C22×Dic43—41no—
383C22×Dic43—41no—
384C22×Dic43—41no—
385C22×Dic43C2411yescharacteristic
386C22×Dic43C2411yescharacteristic
387C22×Dic43C2411yescharacteristic
388C22×Dic43C2411yescharacteristic
389C22×Dic43C2411yescharacteristic
390C22×Dic43C2411yescharacteristic
391C22×Dic43C2411yescharacteristic
392C22×Dic43C2411yescharacteristic
393C22×Dic43C2411yescharacteristic
394C22×Dic43C2411yescharacteristic
395C22×Dic43C2411yescharacteristic
396C22×Dic43C2411yescharacteristic
397C22×Dic43C2411yescharacteristic
398C22×Dic43C2411yescharacteristic
399C22×Dic43C2411yescharacteristic
400C22×Dic43C2411yescharacteristic
401C2×Dic86—22no—
402C2×Dic86—41no—
403C2×Dic86—41no—
404C2×Dic86—41no—
405C2×Dic86—41no—
406C2×Dic86—41no—
407C2×Dic86—41no—
408C2×Dic86—41no—
409C2×Dic86—41no—
410C2×Dic86—41no—
411C2×Dic86—41no—
412C2×Dic86—41no—
413C2×Dic86—41no—
414C2×Dic86—41no—
415C2×Dic86—41no—
416C4⋊C4×C43—41no—
417C4⋊C4×C43—41no—
418C4⋊C4×C43—41no—
419C4⋊C4×C43—41no—
420C4⋊C4×C43—41no—
421C4⋊C4×C43—41no—
422C4⋊C4×C43C2×Q814yes—
423C22⋊C4×C43—41no—
424C22⋊C4×C43—41no—
425C22⋊C4×C43—41no—
426C22⋊C4×C43—41no—
427C22⋊C4×C43—41no—
428C22⋊C4×C43—41no—
429C22⋊C4×C43—41no—
430C22⋊C4×C43—41no—
431C22⋊C4×C43C2×Q814yes—
432C22⋊C4×C43C2×Q814yes—
433C42×C43—41no—
434C42×C43—41no—
435C42×C43—41no—
436C42×C43—41no—
437C42×C43C2×Q814yes—
438C22⋊Dic43—22no—
439C22⋊Dic43—41no—
440C22⋊Dic43—41no—
441C22⋊Dic43—41no—
442C22⋊Dic43—41no—
443C22⋊Dic43—41no—
444C22⋊Dic43—41no—
445C22⋊Dic43—41no—
446C22⋊Dic43—41no—
447C22⋊Dic43—41no—
448C22⋊Dic43—41no—
449C22⋊Dic43—41no—
450C4⋊Dic43—22no—
451C4⋊Dic43—41no—
452C4⋊Dic43—41no—
453C4⋊Dic43—41no—
454C4⋊Dic43—41no—
455C4⋊Dic43—41no—
456C4⋊Dic43—41no—
457C4⋊Dic43—41no—
458C4⋊Dic43—41no—
459C4⋊Dic43—41no—
460C4⋊Dic43—41no—
461C4⋊Dic43—41no—
462C4⋊Dic43—41no—
463C4⋊Dic43—41no—
464C4⋊Dic43—41no—
465C4⋊Dic43—41no—
466C4⋊Dic43—41no—
467C4⋊Dic43—41no—
468C4⋊Dic43—41no—
469Dic43⋊C4—22no—
470Dic43⋊C4—22no—
471Dic43⋊C4—22no—
472Dic43⋊C4—41no—
473Dic43⋊C4—41no—
474Dic43⋊C4—41no—
475Dic43⋊C4—41no—
476Dic43⋊C4—41no—
477Dic43⋊C4—41no—
478Dic43⋊C4—41no—
479Dic43⋊C4—41no—
480Dic43⋊C4—41no—
481Dic43⋊C4—41no—
482Dic43⋊C4—41no—
483Dic43⋊C4—41no—
484Dic43⋊C4—41no—
485Dic43⋊C4—41no—
486Dic43⋊C4—41no—
487C4×Dic43—22no—
488C4×Dic43—22no—
489C4×Dic43—41no—
490C4×Dic43—41no—
491C4×Dic43—41no—
492C4×Dic43—41no—
493C4×Dic43—41no—
494C4×Dic43—41no—
495C23×C43—21no—
496C23×C43—21no—
497C23×C43—21no—
498C23×C43—21no—
499C23×C43—21no—
500C23×C43—21no—
501C23×C43—21no—
502C23×C43—21no—
503C23×C43—21no—
504C23×C43—21no—
505C23×C43—21no—
506C23×C43—21no—
507C23×C43C22×Q812yes—
508C23×C43C22×Q812yes—
509C23×C43C2511yescharacteristic
510D4×C43—44no—
511C2×C4×C43—21no—
512C2×C4×C43—21no—
513C2×C4×C43—21no—
514C2×C4×C43—21no—
515C2×C4×C43—21no—
516C2×C4×C43—21no—
517C2×C4×C43—21no—
518C2×C4×C43—21no—
519C2×C4×C43—21no—
520C2×C4×C43—21no—
521C2×C4×C43—21no—
522C2×C4×C43—21no—
523C2×C4×C43—21no—
524C2×C4×C43—21no—
525C2×C4×C43—21no—
526C2×C4×C43—21no—
527C2×C4×C43—21no—
528C2×C4×C43—21no—
529C2×C4×C43—21no—
530C2×C4×C43—21no—
531C2×C4×C43—21no—
532C2×C4×C43—21no—
533C2×C4×C43—21no—
534C2×C4×C43—21no—
535C2×C4×C43—21no—
536C2×C4×C43—21no—
537C2×C4×C43—21no—
538C2×C4×C43—21no—
539C2×C4×C43—21no—
540C2×C4×C43—21no—
541C2×C4×C43—21no—
542C2×C4×C43—21no—
543C2×C4×C43—21no—
544C2×C4×C43—21no—
545C2×C4×C43—44no—
546C2×C4×C43—44no—
547C2×C4×C43C22×Q812yes—
548C2×C4×C43C22×Q812yes—
549C2×C4×C43C22×Q812yes—
550C2×C4×C43C22×Q812yes—
551C2×C4×C43C22×Q812yes—
552C2×Dic43—21no—
553C2×Dic43—21no—
554C2×Dic43—21no—
555C2×Dic43—21no—
556C2×Dic43—21no—
557C2×Dic43—21no—
558C2×Dic43—21no—
559C2×Dic43—21no—
560C2×Dic43—21no—
561C2×Dic43—21no—
562C2×Dic43—21no—
563C2×Dic43—21no—
564C2×Dic43—21no—
565C2×Dic43—21no—
566C2×Dic43—21no—
567C2×Dic43—21no—
568C2×Dic43—21no—
569C2×Dic43—21no—
570C2×Dic43—21no—
571C2×Dic43—21no—
572C2×Dic43—21no—
573C2×Dic43—21no—
574C2×Dic43—21no—
575C2×Dic43—21no—
576C2×Dic43—21no—
577C2×Dic43—21no—
578C2×Dic43—21no—
579C2×Dic43—21no—
580C2×Dic43—21no—
581C2×Dic43—21no—
582C2×Dic43—21no—
583C2×Dic43—21no—
584C2×Dic43—21no—
585C2×Dic43—21no—
586C2×Dic43—21no—
587C2×Dic43—21no—
588C2×Dic43—21no—
589C2×Dic43—21no—
590C2×Dic43—21no—
591C2×Dic43—21no—
592C2×Dic43—21no—
593C2×Dic43—21no—
594C2×Dic43—21no—
595C2×Dic43—21no—
596C2×Dic43—21no—
597C2×Dic43—21no—
598C2×Dic43—21no—
599C2×Dic43—44no—
600C2×Dic43—44no—
601C2×Dic43—82no—
602C2×Dic43—82no—
603C2×Dic43H(5,𝔽2)12yes—
604Dic86—82no—
605Dic86—82no—
606Dic86—82no—
607Dic86—82no—
608Dic86—82no—
609#36755—431nomaximal, Sylow
610C22×C43—22no—
611C22×C43—22no—
612C22×C43—22no—
613C22×C43—22no—
614C22×C43—22no—
615C22×C43—22no—
616C22×C43—41no—
617C22×C43—41no—
618C22×C43—41no—
619C22×C43—41no—
620C22×C43—41no—
621C22×C43—41no—
622C22×C43—41no—
623C22×C43—41no—
624C22×C43C23×Q811yescharacteristic
625C22×C43C2×H(5,𝔽2)11yescharacteristic
626C22×C43#58511yescharacteristic
627C22×C43#58511yescharacteristic
628C22×C43#58511yescharacteristic
629C22×C43#58511yescharacteristic
630C22×C43#58511yescharacteristic
631C4×C43—22no—
632C4×C43—22no—
633C4×C43—22no—
634C4×C43—22no—
635C4×C43—22no—
636C4×C43—41no—
637C4×C43—41no—
638C4×C43—41no—
639C4×C43—41no—
640C4×C43—41no—
641C4×C43—41no—
642C4×C43—41no—
643C4×C43—41no—
644Dic43—22no—
645Dic43—41no—
646Dic43—41no—
647Dic43—41no—
648Dic43—41no—
649Dic43—41no—
650Dic43—41no—
651Dic43—41no—
652Dic43—41no—
653Dic43—41no—
654Dic43—41no—
655Dic43—41no—
656Dic43—41no—
657Dic43—41no—
658Dic43—41no—
659Dic43—41no—
660#2855—431no—
661#2851—431no—
662#2805—431no—
663#2804—431no—
664#2790—431no—
665#2788—431no—
666#2788—431no—
667#2784—431no—
668#2780—431no—
669#2774—431no—
670#2763—431no—
671#2763—431no—
672#2755—431no—
673#2742—431no—
674#2729—431no—
675#2720—431no—
676#2713—431no—
677#2692—431no—
678#2665—431no—
679#2665—431no—
680#2612—431no—
681#2607—431no—
682#2605—431no—
683#2605—431no—
684#2570—431no—
685#2569—431no—
686#2439—431no—
687#2438—431no—
688#2319D4311yescharacteristic
689#2318—431no—
690#2290—431no—
691C2×C43—42no—
692C2×C43—42no—
693C2×C43#345811yescharacteristic
694C2×C43#350111yescharacteristic
695C2×C43#350411yescharacteristic
696C2×C43#353311yescharacteristic
697C2×C43#354011yescharacteristic
698C2×C43#356611yescharacteristic
699C2×C43#356811yescharacteristic
700C2×C4⋊Q8—431no—
701C2×#125—431no—
702C2×C22⋊Q8—431no—
703C2×C22⋊Q8—431no—
704C2×C4×D4C2×D4311yescharacteristic
705C2×#117—431no—
706C22×C42—431no—
707#400—431no—
708#400—431no—
709#400—431no—
710#400—431no—
711#400—431no—
712#400—431no—
713#400—431no—
714#400—431no—
715#400—431no—
716#400—431no—
717#400—431no—
718#400—431no—
719#400—431no—
720#400—431no—
721#399—431no—
722#399—431no—
723#398—431no—
724#398—431no—
725#398—431no—
726#398—431no—
727#398—431no—
728#398—431no—
729#398—431no—
730#398—431no—
731#396—431no—
732#396—431no—
733#396—431no—
734#396—431no—
735#396—431no—
736#396—431no—
737#395—431no—
738#395—431no—
739#395—431no—
740#395—431no—
741#395—431no—
742#395—431no—
743#395—431no—
744#395—431no—
745#395—431no—
746#395—431no—
747#393—431no—
748#393—431no—
749#393—431no—
750#393—431no—
751#393—431no—
752#393—431no—
753#393—431no—
754#393—431no—
755#391—431no—
756#391—431no—
757#391—431no—
758#391—431no—
759#391—431no—
760#391—431no—
761#391—431no—
762#391—431no—
763#391—431no—
764#391—431no—
765#391—431no—
766#391—431no—
767#391—431no—
768#390C2×D4311yescharacteristic
769#390C2×D4311yescharacteristic
770#389—431no—
771#389—431no—
772#389—431no—
773#389—431no—
774#389—431no—
775#389—431no—
776#389—431no—
777#389—431no—
778#389—431no—
779#389C2×D4311yescharacteristic
780#389C2×D4311yescharacteristic
781#388—431no—
782#388—431no—
783#388—431no—
784#388—431no—
785#388C2×D4311yescharacteristic
786#388C2×D4311yescharacteristic
787#388C2×D4311yescharacteristic
788#388C2×D4311yescharacteristic
789#387—431no—
790#387—431no—
791#387—431no—
792#387—431no—
793#387—431no—
794#387—431no—
795#387—431no—
796#387—431no—
797#387—431no—
798#387—431no—
799#387—431no—
800#387—431no—
801#387—431no—
802#387—431no—
803#387—431no—
804#387—431no—
805#387—431no—
806#387—431no—
807#387—431no—
808#387—431no—
809#387—431no—
810#387—431no—
811#387—431no—
812#387—431no—
813#386—431no—
814#386—431no—
815#386—431no—
816#386—431no—
817#385—431no—
818#385—431no—
819#385—431no—
820#385—431no—
821#385—431no—
822#385—431no—
823#385—431no—
824#385—431no—
825#385—431no—
826#385—431no—
827#385—431no—
828#385—431no—
829#385—431no—
830#385—431no—
831#384—431no—
832#383—431no—
833#382—431no—
834#382—431no—
835#382—431no—
836#382—431no—
837#381—431no—
838#381C2×D4311yescharacteristic
839#381C2×D4311yescharacteristic
840#380—431no—
841#380—431no—
842#380—431no—
843#380—431no—
844#380—431no—
845#380C2×D4311yescharacteristic
846#380C2×D4311yescharacteristic
847C4×C4⋊C4—431no—
848C4×C4⋊C4C2×D4311yescharacteristic
849C4×C22⋊C4—431no—
850C4×C22⋊C4—431no—
851C4×C22⋊C4—431no—
852#376—431no—
853#376C2×D4311yescharacteristic
854C2×#95—431no—
855C43#3675511yescharacteristic, complemented, Sylow
856C22×Q8—431no—
857C22×Q8—431no—
858C22×Q8—431no—
859C22×Q8—431no—
860C22×Q8—431no—
861C22×D4C22×D4311yescharacteristic
862C23×C4—431no—
863C23×C4—431no—
864C23×C4—431no—
865C23×C4—431no—
866C23×C4C22×D4311yescharacteristic
867C23×C4C22×D4311yescharacteristic
868C4⋊Q8—1722no—
869#125—1722no—
870C22⋊Q8—1722no—
871C22⋊Q8—1722no—
872C4×D4Dic8618yescomplemented
873#117—1722no—
874C2×C4⋊C4—431no—
875C2×C4⋊C4—431no—
876C2×C4⋊C4—431no—
877C2×C4⋊C4—431no—
878C2×C4⋊C4—431no—
879C2×C4⋊C4—431no—
880C2×C4⋊C4—431no—
881C2×C4⋊C4—431no—
882C2×C4⋊C4—431no—
883C2×C4⋊C4—431no—
884C2×C4⋊C4—431no—
885C2×C4⋊C4—431no—
886C2×C4⋊C4—431no—
887C2×C4⋊C4—431no—
888C2×C4⋊C4—431no—
889C2×C4⋊C4—431no—
890C2×C4⋊C4—431no—
891C2×C4⋊C4—431no—
892C2×C4⋊C4—431no—
893C2×C4⋊C4—431no—
894C2×C4⋊C4—431no—
895C2×C4⋊C4—431no—
896C2×C4⋊C4—431no—
897C2×C4⋊C4—431no—
898C2×C4⋊C4—431no—
899C2×C4⋊C4—431no—
900C2×C4⋊C4—431no—
901C2×C4⋊C4—431no—
902C2×C4⋊C4—431no—
903C2×C4⋊C4—431no—
904C2×C4⋊C4—431no—
905C2×C4⋊C4—431no—
906C2×C4⋊C4—431no—
907C2×C4⋊C4—431no—
908C2×C4⋊C4—431no—
909C2×C4⋊C4—431no—
910C2×C4⋊C4—431no—
911C2×C4⋊C4C22×D4311yescharacteristic
912C2×C4⋊C4C22×D4311yescharacteristic
913C2×C4⋊C4C22×D4311yescharacteristic
914C2×C4⋊C4C22×D4311yescharacteristic
915C2×C4⋊C4C22×D4311yescharacteristic
916C2×C4⋊C4C22×D4311yescharacteristic
917C2×C4⋊C4C22×D4311yescharacteristic
918C2×C22⋊C4—431no—
919C2×C22⋊C4—431no—
920C2×C22⋊C4—431no—
921C2×C22⋊C4—431no—
922C2×C22⋊C4—431no—
923C2×C22⋊C4—431no—
924C2×C22⋊C4—431no—
925C2×C22⋊C4—431no—
926C2×C22⋊C4—431no—
927C2×C22⋊C4—431no—
928C2×C22⋊C4—431no—
929C2×C22⋊C4—431no—
930C2×C22⋊C4C22×D4311yescharacteristic
931C2×C22⋊C4C22×D4311yescharacteristic
932C2×C22⋊C4C22×D4311yescharacteristic
933C2×C22⋊C4C22×D4311yescharacteristic
934C2×C22⋊C4C22×D4311yescharacteristic
935C2×C22⋊C4C22×D4311yescharacteristic
936C2×C22⋊C4C22×D4311yescharacteristic
937C2×C22⋊C4C22×D4311yescharacteristic
938C2×C22⋊C4C22×D4311yescharacteristic
939C2×C22⋊C4C22×D4311yescharacteristic
940C2×C42—431no—
941C2×C42—431no—
942C2×C42—431no—
943C2×C42—431no—
944C2×C42—431no—
945C2×C42—431no—
946C2×C42—431no—
947C2×C42—431no—
948C2×C42—1722no—
949C2×C42C22×D4311yescharacteristic
950C2×C42C22×D4311yescharacteristic
951C2×C42C22×D4311yescharacteristic
952C2×C42C22×D4311yescharacteristic
953C2×C42C22×D4311yescharacteristic
954#95—431no—
955#95—431no—
956#95—431no—
957#95—431no—
958#95—431no—
959#95—431no—
960#95—431no—
961#95—431no—
962#95—431no—
963#95—431no—
964#95—431no—
965#95—431no—
966#95—431no—
967#95—431no—
968#95—431no—
969#95—431no—
970#95—431no—
971#95—431no—
972#95—431no—
973#95—431no—
974#95—431no—
975#95—431no—
976#95—431no—
977#95—431no—
978#95—431no—
979#95—431no—
980#95—431no—
981#95—431no—
982#95—431no—
983#95—431no—
984#95—431no—
985#95—431no—
986#95—431no—
987#95—431no—
988#95—431no—
989#95—431no—
990#95—431no—
991#95—431no—
992#95—431no—
993#95—431no—
994#95—431no—
995#95—431no—
996#95—431no—
997#95—431no—
998#95—431no—
999#95—431no—
1000#95—431no—
1001#95—431no—
1002#95—431no—
1003#95—431no—
1004#95—431no—
1005#95—431no—
1006#95—431no—
1007#95—431no—
1008#95C22×D4311yescharacteristic
1009#95C22×D4311yescharacteristic
1010#95C22×D4311yescharacteristic
1011#95C22×D4311yescharacteristic
1012#95C22×D4311yescharacteristic
1013#95C22×D4311yescharacteristic
1014#95C22×D4311yescharacteristic
1015#95C22×D4311yescharacteristic
1016#95C22×D4311yescharacteristic
1017#95C22×D4311yescharacteristic
1018C24C23×D4311yescharacteristic
1019C24C23×D4311yescharacteristic
1020C2×Q8—862no—
1021C2×Q8—1721no—
1022C2×Q8—1721no—
1023C2×Q8—1721no—
1024C2×Q8—1721no—
1025C2×Q8—1721no—
1026C2×Q8—1721no—
1027C2×Q8—1721no—
1028C2×Q8—1721no—
1029C2×Q8—1721no—
1030C2×Q8—1721no—
1031C2×Q8—1721no—
1032C2×Q8—1721no—
1033C2×Q8—1721no—
1034C2×Q8—1721no—
1035C2×D4—41no—
1036C2×D4—41no—
1037C2×D4C2×Dic8614yes—
1038C22×C4—41no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—41no—
1042C22×C4—431no—
1043C22×C4—431no—
1044C22×C4—431no—
1045C22×C4—431no—
1046C22×C4—431no—
1047C22×C4—431no—
1048C22×C4—431no—
1049C22×C4—431no—
1050C22×C4—431no—
1051C22×C4—431no—
1052C22×C4—431no—
1053C22×C4—431no—
1054C22×C4—431no—
1055C22×C4—431no—
1056C22×C4—431no—
1057C22×C4—431no—
1058C22×C4—862no—
1059C22×C4—1721no—
1060C22×C4—1721no—
1061C22×C4—1721no—
1062C22×C4—1721no—
1063C22×C4—1721no—
1064C22×C4—1721no—
1065C22×C4—1721no—
1066C22×C4—1721no—
1067C22×C4—1721no—
1068C22×C4—1721no—
1069C22×C4—1721no—
1070C22×C4C2×Dic8614yes—
1071C22×C4C2×Dic8614yes—
1072C22×C4C23×D4311yescharacteristic
1073C22×C4C23×D4311yescharacteristic
1074C22×C4C23×D4311yescharacteristic
1075C22×C4C23×D4311yescharacteristic
1076C22×C4C23×D4311yescharacteristic
1077C22×C4C23×D4311yescharacteristic
1078C22×C4C23×D4311yescharacteristic
1079C22×C4C23×D4311yescharacteristic
1080C22×C4C23×D4311yescharacteristic
1081C22×C4C23×D4311yescharacteristic
1082C22×C4C23×D4311yescharacteristic
1083C22×C4C23×D4311yescharacteristic
1084C22×C4C23×D4311yescharacteristic
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—862no—
1092C4⋊C4—862no—
1093C4⋊C4—862no—
1094C4⋊C4—862no—
1095C4⋊C4—1721no—
1096C4⋊C4—1721no—
1097C4⋊C4—1721no—
1098C4⋊C4—1721no—
1099C4⋊C4—1721no—
1100C4⋊C4—1721no—
1101C4⋊C4—1721no—
1102C4⋊C4—1721no—
1103C4⋊C4—1721no—
1104C4⋊C4—1721no—
1105C4⋊C4—1721no—
1106C4⋊C4—1721no—
1107C4⋊C4—1721no—
1108C4⋊C4—1721no—
1109C4⋊C4—1721no—
1110C4⋊C4—1721no—
1111C4⋊C4—1721no—
1112C4⋊C4—1721no—
1113C4⋊C4—1721no—
1114C4⋊C4—1721no—
1115C4⋊C4—1721no—
1116C4⋊C4—1721no—
1117C4⋊C4—1721no—
1118C4⋊C4—1721no—
1119C4⋊C4—1721no—
1120C4⋊C4—1721no—
1121C4⋊C4—1721no—
1122C4⋊C4—1721no—
1123C4⋊C4—1721no—
1124C4⋊C4—1721no—
1125C4⋊C4—1721no—
1126C4⋊C4—1721no—
1127C4⋊C4—1721no—
1128C4⋊C4C2×Dic8614yes—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—862no—
1138C22⋊C4—1721no—
1139C22⋊C4—1721no—
1140C22⋊C4—1721no—
1141C22⋊C4—1721no—
1142C22⋊C4—1721no—
1143C22⋊C4—1721no—
1144C22⋊C4—1721no—
1145C22⋊C4—1721no—
1146C22⋊C4—1721no—
1147C22⋊C4—1721no—
1148C22⋊C4—1721no—
1149C22⋊C4C2×Dic8614yes—
1150C22⋊C4C2×Dic8614yes—
1151C42—41no—
1152C42—41no—
1153C42—41no—
1154C42—41no—
1155C42—862no—
1156C42—862no—
1157C42—1721no—
1158C42—1721no—
1159C42—1721no—
1160C42—1721no—
1161C42—1721no—
1162C42—1721no—
1163C42C2×Dic8614yes—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23C22×Dic8612yes—
1177C23C22×Dic8612yes—
1178C23C24×D4311yescharacteristic
1179Q8—3442no—
1180Q8—3442no—
1181Q8—3442no—
1182Q8—3442no—
1183Q8—3442no—
1184D4—44no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—432no—
1222C2×C4—861no—
1223C2×C4—861no—
1224C2×C4—861no—
1225C2×C4—861no—
1226C2×C4—861no—
1227C2×C4—861no—
1228C2×C4—861no—
1229C2×C4—861no—
1230C2×C4—861no—
1231C2×C4—861no—
1232C2×C4—861no—
1233C2×C4—861no—
1234C2×C4—861no—
1235C2×C4—861no—
1236C2×C4—861no—
1237C2×C4—861no—
1238C2×C4—861no—
1239C2×C4—861no—
1240C2×C4—861no—
1241C2×C4—861no—
1242C2×C4—861no—
1243C2×C4—861no—
1244C2×C4—861no—
1245C2×C4—861no—
1246C2×C4—861no—
1247C2×C4—861no—
1248C2×C4—861no—
1249C2×C4—861no—
1250C2×C4—861no—
1251C2×C4—861no—
1252C2×C4—861no—
1253C2×C4—861no—
1254C2×C4—861no—
1255C2×C4—861no—
1256C2×C4—861no—
1257C2×C4—861no—
1258C2×C4—861no—
1259C2×C4—861no—
1260C2×C4—861no—
1261C2×C4—861no—
1262C2×C4—861no—
1263C2×C4—861no—
1264C2×C4—861no—
1265C2×C4—861no—
1266C2×C4—861no—
1267C2×C4—861no—
1268C2×C4—861no—
1269C2×C4—3442no—
1270C2×C4—3442no—
1271C2×C4—1724no—
1272C2×C4—1724no—
1273C2×C4C22×Dic8612yes—
1274C2×C4C22×Dic8612yes—
1275C2×C4C22×Dic8612yes—
1276C2×C4C22×Dic8612yes—
1277C2×C4C22×Dic8612yes—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22C23×Dic8611yescharacteristic
1293C22H(5,𝔽2)×D4311yescharacteristic
1294C22#1458373411yescharacteristic
1295C22#1458373411yescharacteristic
1296C22#1458373511yescharacteristic
1297C22#1458373511yescharacteristic
1298C22#1458373611yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—862no—
1313C4—1721no—
1314C4—1721no—
1315C4—1721no—
1316C4—1721no—
1317C4—1721no—
1318C4—1721no—
1319C4—1721no—
1320C4—1721no—
1321C4—1721no—
1322C4—1721no—
1323C4—1721no—
1324C4—1721no—
1325C4—1721no—
1326C4—1721no—
1327C4—1721no—
1328C2—42no—
1329C2—42no—
1330C2#1914800011yescharacteristic
1331C2#1914839311yescharacteristic
1332C2#1914841711yescharacteristic
1333C2#1914875511yescharacteristic
1334C2#1914886011yescharacteristic
1335C2#1914926711yescharacteristic
1336C2#1914928711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2319C2
prime radicalC22×D4×C43C23
hypercenter#2319D43
hypocenterC43#36755
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2319

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19142932C2semidirect
2. #19142903C2semidirect
3. #19142548C2semidirect
5. #19142365C2semidirect
6. #19142342C2semidirect
7. #19142338C2semidirect
10. #19142154C2semidirect
11. #19142011C2semidirect
12. #19142011C2semidirect
13. #19141903C2semidirect
14. #19141721C2semidirect
15. #19141574C2semidirect
16. #19141472C2semidirect
17. #19141373C2semidirect
19. #19140768C2semidirect
20. #19140767C2semidirect
21. #19140298C2semidirect
22. #19140260C2semidirect
23. #19140243C2semidirect
24. #19140238C2semidirect
25. #19139829C2semidirect
26. #19139820C2semidirect
27. #19138287C2semidirect
28. #19138273C2semidirect
316. C4×D4×C43Q8semidirect
855. C43#36755semidirect
872. C4×D4Dic86semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191429322
#191429032
#191425482
#191425412
#191423652
#191423422
#191423382
#191422962
#191422442
#191421542
#191420112
#191419032
#191417212
#191415742
#191414722
#191413732
#191410882
#191407682
#191407672
#191402982
#191402602
#191402432
#191402382
#191398292
#191398202
#191382872
#191382732
#191372282
#191370402
C43×#23192
#3675543