Finite Group Databasebeta

← #25304420

Subgroups — #25304420

Order 11008.

1496 conjugacy classes of subgroups.

The subgroup lattice has 1330 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#19142560C211yesmaximal, characteristic, complemented
4#19142515C211yesmaximal, characteristic, complemented
5#19142373C211yesmaximal, characteristic, complemented
6#19142370C211yesmaximal, characteristic, complemented
7#19142367C211yesmaximal, characteristic, complemented
8#19142250C211yesmaximal, characteristic
9#19142236C211yesmaximal, characteristic
10#19142080C211yesmaximal, characteristic, complemented
11#19142077C211yesmaximal, characteristic, complemented
12#19142074C211yesmaximal, characteristic, complemented
13#19141907C211yesmaximal, characteristic, complemented
14#19141809C211yesmaximal, characteristic
15#19141617C211yesmaximal, characteristic
16#19141543C211yesmaximal, characteristic, complemented
17#19141481C211yesmaximal, characteristic, complemented
18#19141252C211yesmaximal, characteristic, complemented
19#19140789C211yesmaximal, characteristic, complemented
20#19140305C211yesmaximal, characteristic, complemented
21#19140263C211yesmaximal, characteristic, complemented
22#19140250C211yesmaximal, characteristic, complemented
23#19140249C211yesmaximal, characteristic, complemented
24#19139826C211yesmaximal, characteristic, complemented
25#19139818C211yesmaximal, characteristic, complemented
26#19138305C211yesmaximal, characteristic, complemented
27#19138276C211yesmaximal, characteristic, complemented
28#19137237C211yesmaximal, characteristic
29#19137224C211yesmaximal, characteristic
30#19137034C211yesmaximal, characteristic
31C43×#2667C211yesmaximal, characteristic, complemented
32C2×#13063316C2211yescharacteristic
33C2×#13063315C2211yescharacteristic
34C2×#13063305C2211yescharacteristic
35C2×#13063302C2211yescharacteristic
36C2×C4×C22⋊D43C2211yescharacteristic
37C2×#13063282C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39#14582840C2211yescharacteristic
40#14582840C2211yescharacteristic
41#14582840C2211yescharacteristic
42#14582839C2211yescharacteristic
43#14582839C2211yescharacteristic
44#14582837C2211yescharacteristic
45#14582835C2211yescharacteristic
46#14582835C2211yescharacteristic
47#14582834C2211yescharacteristic
48#14582834C2211yescharacteristic
49#14582833C2211yescharacteristic
50#14582833C2211yescharacteristic
51#14582833C2211yescharacteristic
52#14582833C2211yescharacteristic
53#14582832C2211yescharacteristic
54#14582832C2211yescharacteristic
55#14582832C2211yescharacteristic
56#14582832C2211yescharacteristic
57#14582832C2211yescharacteristic
58#14582831C2211yescharacteristic
59#14582831C2211yescharacteristic
60#14582830C2211yescharacteristic
61#14582830C2211yescharacteristic
62#14582830C2211yescharacteristic
63#14582830C2211yescharacteristic
64#14582829C2211yescharacteristic
65#14582829C2211yescharacteristic
66#14582829C2211yescharacteristic
67#14582829C2211yescharacteristic
68#14582829C2211yescharacteristic
69#14582822C2211yescharacteristic
70#14582822C2211yescharacteristic
71#14582821C2211yescharacteristic
72#14582821C2211yescharacteristic
73#14582821C2211yescharacteristic
74#14582821C2211yescharacteristic
75#14582821C2211yescharacteristic
76#14582821C2211yescharacteristic
77#14582820C2211yescharacteristic
78#14582819C2211yescharacteristic
79#14582803C2211yescharacteristic
80#14582803C2211yescharacteristic
81#14582803C2211yescharacteristic
82#14582799C2211yescharacteristic
83#14582799C2211yescharacteristic
84#14582798C2211yescharacteristic
85#14582798C2211yescharacteristic
86#14582798C2211yescharacteristic
87#14582797C2211yescharacteristic
88#14582797C2211yescharacteristic
89#14582796C2211yescharacteristic
90#14582796C2211yescharacteristic
91#14582796C2211yescharacteristic
92#14582795C2211yescharacteristic
93#14582795C2211yescharacteristic
94#14582795C2211yescharacteristic
95#14582794C2211yescharacteristic
96#14582794C2211yescharacteristic
97#14582794C2211yescharacteristic
98#14582794C2211yescharacteristic
99#14582794C2211yescharacteristic
100#14582794C2211yescharacteristic
101#14582794C2211yescharacteristic
102#14582794C2211yescharacteristic
103#14582789C2211yescharacteristic
104#14582789C2211yescharacteristic
105#14582788C2211yescharacteristic
106#14582788C2211yescharacteristic
107#14582787C2211yescharacteristic
108#14582787C2211yescharacteristic
109#14582787C2211yescharacteristic
110#14582787C2211yescharacteristic
111#14582786C2211yescharacteristic
112#14582786C2211yescharacteristic
113#14582786C2211yescharacteristic
114#14582786C2211yescharacteristic
115#14582786C2211yescharacteristic
116#14582786C2211yescharacteristic
117#14582785C2211yescharacteristic
118#14582785C2211yescharacteristic
119#14582785C2211yescharacteristic
120#14582785C2211yescharacteristic
121#14582784C2211yescharacteristic
122#14582783C2211yescharacteristic
123#14582783C2211yescharacteristic
124#14582782C2211yescharacteristic
125#14582782C2211yescharacteristic
126#14582782C2211yescharacteristic
127#14582782C2211yescharacteristic
128#14582781C2211yescharacteristic
129#14582781C2211yescharacteristic
130#14582780C2211yescharacteristic
131#14582780C2211yescharacteristic
132#14582780C2211yescharacteristic
133#14582776C2211yescharacteristic
134#14582776C2211yescharacteristic
135#14582775C2211yescharacteristic
136#14582775C2211yescharacteristic
137#14582774C2211yescharacteristic
138#14582774C2211yescharacteristic
139#14582774C2211yescharacteristic
140#14582773C2211yescharacteristic
141#14582773C2211yescharacteristic
142#14582773C2211yescharacteristic
143#14582773C2211yescharacteristic
144#14582771C2211yescharacteristic
145#14582771C2211yescharacteristic
146#14582771C2211yescharacteristic
147#14582771C2211yescharacteristic
148#14582771C2211yescharacteristic
149#14582770C2211yescharacteristic
150#14582770C2211yescharacteristic
151#14582768C2211yescharacteristic
152#14582768C2211yescharacteristic
153#14582766C2211yescharacteristic
154#14582764C2211yescharacteristic
155#14582763C2211yescharacteristic
156#14582763C2211yescharacteristic
157#14582762C2211yescharacteristic
158#14582761C2211yescharacteristic
159#14582759C2211yescharacteristic
160#14582758C2211yescharacteristic
161#14582758C2211yescharacteristic
162#14582758C2211yescharacteristic
163#14582757C2211yescharacteristic
164#14582756C2211yescharacteristic
165C4×Dic43⋊C4C2211yescharacteristic
166#14582750C2211yescharacteristic
167C4×(C2×D43)⋊C4C2211yescharacteristic
168#14582746C2211yescharacteristic
169#14582745C2211yescharacteristic
170#14582744C2211yescharacteristic
171#95×D43C2211yescharacteristic
172C43×#399C2211yescharacteristic
173C43×#399C2211yescharacteristic
174C43×#398C2211yescharacteristic
175C43×#398C2211yescharacteristic
176C43×#398C2211yescharacteristic
177C43×#398C2211yescharacteristic
178C43×#396C2211yescharacteristic
179C43×#396C2211yescharacteristic
180C43×#389C2211yescharacteristic
181C43×#389C2211yescharacteristic
182C43×#387C2211yescharacteristic
183C43×#387C2211yescharacteristic
184C43×#381C2211yescharacteristic
185C43×#380C2211yescharacteristic
186C4×C22⋊C4×C43C2211yescharacteristic
187C22×Dic86C2311yescharacteristic
188C22×C22⋊D43C2311yescharacteristic
189C23×Dic43C2311yescharacteristic
190C23×Dic43C2311yescharacteristic
191C22×C4×D43C2311yescharacteristic
192C22×C4×D43C2311yescharacteristic
193C22×C4×D43C2311yescharacteristic
194#13063316—42no—
195#13063315—42no—
196#13063305—42no—
197#13063302—42no—
198C4×C22⋊D43Q818yescomplemented
199#13063282—42no—
200C2×C4⋊Dic43C2311yescharacteristic
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×Dic43⋊C4C2311yescharacteristic
214C2×Dic43⋊C4C2311yescharacteristic
215C2×Dic43⋊C4C2311yescharacteristic
216C2×Dic43⋊C4C2311yescharacteristic
217C2×Dic43⋊C4C2311yescharacteristic
218C2×Dic43⋊C4C2311yescharacteristic
219C2×Dic43⋊C4C2311yescharacteristic
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×Dic43⋊C4C2311yescharacteristic
239C2×Dic43⋊C4C2311yescharacteristic
240C2×Dic43⋊C4C2311yescharacteristic
241C2×Dic43⋊C4C2311yescharacteristic
242C2×C22⋊Dic43C2311yescharacteristic
243C2×C22⋊Dic43C2311yescharacteristic
244C2×C22⋊Dic43C2311yescharacteristic
245C2×C22⋊Dic43C2311yescharacteristic
246C2×C22⋊Dic43C2311yescharacteristic
247C2×(C2×D43)⋊C4C2311yescharacteristic
248C2×(C2×D43)⋊C4C2311yescharacteristic
249C2×(C2×D43)⋊C4C2311yescharacteristic
250C2×(C2×D43)⋊C4C2311yescharacteristic
251C2×(C2×D43)⋊C4C2311yescharacteristic
252C2×(C2×D43)⋊C4C2311yescharacteristic
253C2×(C2×D43)⋊C4C2311yescharacteristic
254C2×(C2×D43)⋊C4C2311yescharacteristic
255C2×(C2×D43)⋊C4C2311yescharacteristic
256C2×(C2×D43)⋊C4C2311yescharacteristic
257C2×(C2×D43)⋊C4C2311yescharacteristic
258C2×C4×Dic43—42no—
259C2×C4×Dic43C2311yescharacteristic
260C2×C4×Dic43C2311yescharacteristic
261C2×C4×Dic43C2311yescharacteristic
262C2×C4×Dic43C2311yescharacteristic
263C2×C4×Dic43C2311yescharacteristic
264C2×C4×Dic43C2311yescharacteristic
265C2×C4×Dic43C2311yescharacteristic
266C2×C4×Dic43C2311yescharacteristic
267C2×C4×Dic43C2311yescharacteristic
268C2×C4×Dic43C2311yescharacteristic
269C2×C4×Dic43C2311yescharacteristic
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
313C43⋊#95C2311yescharacteristic
314C23×C4×C43C2311yescharacteristic
315C2×C4⋊C4×C43C2311yescharacteristic
316C2×C4⋊C4×C43C2311yescharacteristic
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×C4⋊C4×C43C2311yescharacteristic
325C2×C4⋊C4×C43C2311yescharacteristic
326C2×C4⋊C4×C43C2311yescharacteristic
327C2×C4⋊C4×C43C2311yescharacteristic
328C2×C4⋊C4×C43C2311yescharacteristic
329C2×C22⋊C4×C43C2311yescharacteristic
330C2×C22⋊C4×C43C2311yescharacteristic
331C2×C22⋊C4×C43C2311yescharacteristic
332C2×C22⋊C4×C43C2311yescharacteristic
333C2×C22⋊C4×C43C2311yescharacteristic
334C2×C22⋊C4×C43C2311yescharacteristic
335C2×C42×C43C2311yescharacteristic
336C2×C42×C43C2311yescharacteristic
337#95×C43C2311yescharacteristic
338#95×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
350C23×D43C2411yescharacteristic
351C22×C4×C43—41no—
352C22×C4×C43—41no—
353C22×C4×C43C2×Q814yes—
354C22×C4×C43C2411yescharacteristic
355C22×C4×C43C2411yescharacteristic
356C22×C4×C43C2411yescharacteristic
357C22×C4×C43C2411yescharacteristic
358C22×C4×C43C2411yescharacteristic
359C22×C4×C43C2411yescharacteristic
360C22×C4×C43C2411yescharacteristic
361C22×C4×C43C2411yescharacteristic
362C22×C4×C43C2411yescharacteristic
363C22×C4×C43C2411yescharacteristic
364C22×C4×C43C2411yescharacteristic
365C22×C4×C43C2411yescharacteristic
366C22×C4×C43C2411yescharacteristic
367C22×C4×C43C2411yescharacteristic
368C2×C22⋊D43—41no—
369C2×C22⋊D43—41no—
370C2×C22⋊D43C2×Q814yes—
371C22×Dic43—22no—
372C22×Dic43—41no—
373C22×Dic43—41no—
374C22×Dic43—41no—
375C22×Dic43—41no—
376C22×Dic43—41no—
377C22×Dic43C2411yescharacteristic
378C22×Dic43C2411yescharacteristic
379C22×Dic43C2411yescharacteristic
380C22×Dic43C2411yescharacteristic
381C22×Dic43C2411yescharacteristic
382C22×Dic43C2411yescharacteristic
383C22×Dic43C2411yescharacteristic
384C22×Dic43C2411yescharacteristic
385C22×Dic43C2411yescharacteristic
386C22×Dic43C2411yescharacteristic
387C22×Dic43C2411yescharacteristic
388C22×Dic43C2411yescharacteristic
389C22×Dic43C2411yescharacteristic
390C22×Dic43C2411yescharacteristic
391C22×Dic43C2411yescharacteristic
392C2×C4×D43—41no—
393C2×C4×D43—41no—
394C2×C4×D43—41no—
395C2×C4×D43—41no—
396C2×C4×D43—41no—
397C2×C4×D43—41no—
398C2×C4×D43—41no—
399C2×C4×D43—41no—
400C2×C4×D43C2×Q814yes—
401C2×Dic86—22no—
402C2×Dic86—41no—
403C2×Dic86—41no—
404C4⋊C4×C43—41no—
405C4⋊C4×C43—41no—
406C4⋊C4×C43—41no—
407C4⋊C4×C43—41no—
408C4⋊C4×C43—41no—
409C4⋊C4×C43—41no—
410C4⋊C4×C43—41no—
411C4⋊C4×C43—41no—
412C4⋊C4×C43—41no—
413C4⋊C4×C43—41no—
414C4⋊C4×C43—41no—
415C4⋊C4×C43—41no—
416C4⋊C4×C43—41no—
417C4⋊C4×C43—41no—
418C22⋊C4×C43—41no—
419C22⋊C4×C43—41no—
420C22⋊C4×C43—41no—
421C22⋊C4×C43—41no—
422C22⋊C4×C43—41no—
423C22⋊C4×C43—41no—
424C42×C43—41no—
425C42×C43—41no—
426C22⋊Dic43—41no—
427C22⋊Dic43—41no—
428C22⋊Dic43—41no—
429C22⋊Dic43—41no—
430C22⋊Dic43C2×Q814yes—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—41no—
433(C2×D43)⋊C4—41no—
434(C2×D43)⋊C4—41no—
435(C2×D43)⋊C4—41no—
436(C2×D43)⋊C4—41no—
437(C2×D43)⋊C4—41no—
438(C2×D43)⋊C4—41no—
439(C2×D43)⋊C4—41no—
440(C2×D43)⋊C4—41no—
441(C2×D43)⋊C4C2×Q814yes—
442C4⋊Dic43—22no—
443C4⋊Dic43—22no—
444C4⋊Dic43—41no—
445C4⋊Dic43—41no—
446C4⋊Dic43—41no—
447C4⋊Dic43—41no—
448C4⋊Dic43—41no—
449C4⋊Dic43—41no—
450C4⋊Dic43—41no—
451C4⋊Dic43—41no—
452C4⋊Dic43—41no—
453C4⋊Dic43—41no—
454C4⋊Dic43—41no—
455Dic43⋊C4—22no—
456Dic43⋊C4—22no—
457Dic43⋊C4—41no—
458Dic43⋊C4—41no—
459Dic43⋊C4—41no—
460Dic43⋊C4—41no—
461Dic43⋊C4—41no—
462Dic43⋊C4—41no—
463Dic43⋊C4—41no—
464Dic43⋊C4—41no—
465Dic43⋊C4—41no—
466Dic43⋊C4—41no—
467Dic43⋊C4—41no—
468Dic43⋊C4—41no—
469Dic43⋊C4—41no—
470Dic43⋊C4—41no—
471Dic43⋊C4—41no—
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⋊C4C2×Q814yes—
484C4×Dic43—22no—
485C4×Dic43—22no—
486C4×Dic43—41no—
487C4×Dic43—41no—
488C4×Dic43—41no—
489C4×Dic43—41no—
490C4×Dic43—41no—
491C4×Dic43—41no—
492C4×Dic43—41no—
493C4×Dic43—41no—
494C4×Dic43C2×Q814yes—
495C23×C43—21no—
496C23×C43—21no—
497C23×C43—21no—
498C23×C43—21no—
499C23×C43—21no—
500C23×C43—21no—
501C23×C43C22×Q812yes—
502C23×C43C2511yescharacteristic
503C22×D43—21no—
504C22×D43—21no—
505C22×D43—21no—
506C22×D43—21no—
507C22×D43—21no—
508C22×D43—21no—
509C22×D43C22×Q812yes—
510C2×C4×C43—21no—
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—21no—
546C2×C4×C43—21no—
547C2×C4×C43—21no—
548C2×C4×C43—21no—
549C2×C4×C43—21no—
550C2×C4×C43—44no—
551C2×C4×C43C22×Q812yes—
552C2×C4×C43C22×Q812yes—
553C22⋊D43—44no—
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—44no—
596C2×Dic43—44no—
597C2×Dic43C22×Q812yes—
598C2×Dic43C22×Q812yes—
599C2×Dic43C22×Q812yes—
600C2×Dic43H(5,𝔽2)12yes—
601C4×D43—44no—
602C4×D43—82no—
603C4×D43—82no—
604Dic86—82no—
605#36756—431nomaximal, Sylow
606C22×C43—22no—
607C22×C43—22no—
608C22×C43—22no—
609C22×C43—41no—
610C22×C43—41no—
611C22×C43—41no—
612C22×C43—41no—
613C22×C43C23×Q811yescharacteristic
614C22×C43C2×H(5,𝔽2)11yescharacteristic
615C22×C43#58511yescharacteristic
616C22×C43#58511yescharacteristic
617C22×C43#58511yescharacteristic
618C22×C43#58511yescharacteristic
619C22×C43#58511yescharacteristic
620C2×D43—22no—
621C2×D43—22no—
622C2×D43—22no—
623C2×D43—41no—
624C2×D43—41no—
625C2×D43—41no—
626C2×D43—41no—
627C4×C43—22no—
628C4×C43—22no—
629C4×C43—41no—
630C4×C43—41no—
631C4×C43—41no—
632C4×C43—41no—
633C4×C43—41no—
634C4×C43—41no—
635C4×C43—41no—
636C4×C43—41no—
637C4×C43—41no—
638C4×C43—41no—
639C4×C43—41no—
640C4×C43—41no—
641Dic43—22no—
642Dic43—22no—
643Dic43—22no—
644Dic43—22no—
645Dic43—41no—
646Dic43—41no—
647Dic43—41no—
648Dic43—41no—
649Dic43—41no—
650Dic43—41no—
651Dic43—41no—
652Dic43—41no—
653Dic43—41no—
654Dic43—41no—
655Dic43—41no—
656#2855—431no—
657#2851—431no—
658#2807—431no—
659#2802—431no—
660#2791—431no—
661#2790—431no—
662#2790—431no—
663#2780—431no—
664#2780—431no—
665#2768—431no—
666#2768—431no—
667#2768—431no—
668#2755—431no—
669#2748—431no—
670#2732—431no—
671#2726—431no—
672#2720—431no—
673#2704—431no—
674#2667—431no—
675#2667D4311yescharacteristic, complemented
676#2612—431no—
677#2608—431no—
678#2606—431no—
679#2606—431no—
680#2570—431no—
681#2569—431no—
682#2441—431no—
683#2438—431no—
684#2319—431no—
685#2318—431no—
686#2290—431no—
687C2×C43—42no—
688C2×C43#345811yescharacteristic
689C2×C43#350111yescharacteristic
690C2×C43#350411yescharacteristic
691C2×C43#353311yescharacteristic
692C2×C43#353911yescharacteristic
693C2×C43#356611yescharacteristic
694C2×C43#356711yescharacteristic
695D43—42no—
696C2×#125—431no—
697C2×#125—431no—
698C2×C22⋊Q8—431no—
699C2×C22⋊Q8—431no—
700C2×C4×D4—431no—
701C2×#117—431no—
702C22×C42—431no—
703#400—431no—
704#400—431no—
705#400—431no—
706#400—431no—
707#400—431no—
708#400—431no—
709#399—431no—
710#399—431no—
711#399—431no—
712#399—431no—
713#399C2×D4311yescharacteristic
714#399C2×D4311yescharacteristic
715#398—431no—
716#398—431no—
717#398—431no—
718#398—431no—
719#398—431no—
720#398—431no—
721#398—431no—
722#398—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#398—431no—
732#398—431no—
733#398—431no—
734#398—431no—
735#398C2×D4311yescharacteristic
736#398C2×D4311yescharacteristic
737#398C2×D4311yescharacteristic
738#398C2×D4311yescharacteristic
739#396—431no—
740#396—431no—
741#396—431no—
742#396—431no—
743#396—431no—
744#396—431no—
745#396—431no—
746#396—431no—
747#396C2×D4311yescharacteristic
748#396C2×D4311yescharacteristic
749#395—431no—
750#395—431no—
751#391—431no—
752#391—431no—
753#391—431no—
754#390—431no—
755#390—431no—
756#389—431no—
757#389—431no—
758#389—431no—
759#389—431no—
760#389—431no—
761#389—431no—
762#389—431no—
763#389—431no—
764#389—431no—
765#389—431no—
766#389—431no—
767#389—431no—
768#389—431no—
769#389—431no—
770#389—431no—
771#389—431no—
772#389—431no—
773#389—431no—
774#389—431no—
775#389C2×D4311yescharacteristic
776#389C2×D4311yescharacteristic
777#388—431no—
778#388—431no—
779#388—431no—
780#388—431no—
781#388—431no—
782#388—431no—
783#388—431no—
784#388—431no—
785#387—431no—
786#387—431no—
787#387—431no—
788#387—431no—
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#387C2×D4311yescharacteristic
808#387C2×D4311yescharacteristic
809#386—431no—
810#386—431no—
811#386—431no—
812#386—431no—
813#385—431no—
814#385—431no—
815#385—431no—
816#385—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#384—431no—
828#384—431no—
829#383—431no—
830#382—431no—
831#382—431no—
832#382—431no—
833#381—431no—
834#381—431no—
835#381C2×D4311yescharacteristic
836#380—431no—
837#380—431no—
838#380—431no—
839#380—431no—
840#380—431no—
841#380—431no—
842#380C2×D4311yescharacteristic
843C4×C4⋊C4—431no—
844C4×C4⋊C4—431no—
845C4×C22⋊C4—431no—
846C4×C22⋊C4—431no—
847C4×C22⋊C4C2×D4311yescharacteristic
848#376—431no—
849#376—431no—
850C2×#95—431no—
851C43#3675611yescharacteristic, complemented, Sylow
852C22×Q8—431no—
853C22×D4—431no—
854C23×C4—431no—
855C23×C4—431no—
856C23×C4—431no—
857C23×C4—431no—
858C23×C4—431no—
859C23×C4C22×D4311yescharacteristic
860#125—1722no—
861#125—1722no—
862C22⋊Q8—1722no—
863C22⋊Q8—1722no—
864C4×D4—438no—
865#117—1722no—
866C2×C4⋊C4—431no—
867C2×C4⋊C4—431no—
868C2×C4⋊C4—431no—
869C2×C4⋊C4—431no—
870C2×C4⋊C4—431no—
871C2×C4⋊C4—431no—
872C2×C4⋊C4—431no—
873C2×C4⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
909C2×C4⋊C4C22×D4311yescharacteristic
910C2×C4⋊C4C22×D4311yescharacteristic
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×C4⋊C4C22×D4311yescharacteristic
919C2×C4⋊C4C22×D4311yescharacteristic
920C2×C4⋊C4C22×D4311yescharacteristic
921C2×C4⋊C4C22×D4311yescharacteristic
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⋊C4—431no—
931C2×C22⋊C4—431no—
932C2×C22⋊C4—431no—
933C2×C22⋊C4—431no—
934C2×C22⋊C4—431no—
935C2×C22⋊C4—431no—
936C2×C22⋊C4—431no—
937C2×C22⋊C4—431no—
938C2×C22⋊C4C22×D4311yescharacteristic
939C2×C22⋊C4C22×D4311yescharacteristic
940C2×C22⋊C4C22×D4311yescharacteristic
941C2×C22⋊C4C22×D4311yescharacteristic
942C2×C22⋊C4C22×D4311yescharacteristic
943C2×C22⋊C4C22×D4311yescharacteristic
944C2×C42—431no—
945C2×C42—431no—
946C2×C42—431no—
947C2×C42—431no—
948C2×C42—431no—
949C2×C42—431no—
950C2×C42—431no—
951C2×C42—431no—
952C2×C42—431no—
953C2×C42—431no—
954C2×C42—431no—
955C2×C42—1722no—
956C2×C42C22×D4311yescharacteristic
957C2×C42C22×D4311yescharacteristic
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#95C22×D4311yescharacteristic
1003#95C22×D4311yescharacteristic
1004#95C22×D4311yescharacteristic
1005#95C22×D4311yescharacteristic
1006#95C22×D4311yescharacteristic
1007#95C22×D4311yescharacteristic
1008#95C22×D4311yescharacteristic
1009#95C22×D4311yescharacteristic
1010#95C22×D4311yescharacteristic
1011#95C22×D4311yescharacteristic
1012#95C22×D4311yescharacteristic
1013#95C22×D4311yescharacteristic
1014C24—431no—
1015C24C23×D4311yescharacteristic
1016C2×Q8—862no—
1017C2×Q8—1721no—
1018C2×Q8—1721no—
1019C2×D4—434no—
1020C2×D4—1721no—
1021C2×D4—1721no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—431no—
1025C22×C4—431no—
1026C22×C4—431no—
1027C22×C4—431no—
1028C22×C4—434no—
1029C22×C4—431no—
1030C22×C4—431no—
1031C22×C4—431no—
1032C22×C4—431no—
1033C22×C4—431no—
1034C22×C4—431no—
1035C22×C4—431no—
1036C22×C4—431no—
1037C22×C4—431no—
1038C22×C4—431no—
1039C22×C4—431no—
1040C22×C4—862no—
1041C22×C4—1721no—
1042C22×C4—1721no—
1043C22×C4—1721no—
1044C22×C4—1721no—
1045C22×C4—1721no—
1046C22×C4—1721no—
1047C22×C4—1721no—
1048C22×C4—1721no—
1049C22×C4—1721no—
1050C22×C4—1721no—
1051C22×C4—1721no—
1052C22×C4—1721no—
1053C22×C4—1721no—
1054C22×C4Q8×D4314yes—
1055C22×C4C23×D4311yescharacteristic
1056C22×C4C23×D4311yescharacteristic
1057C22×C4C23×D4311yescharacteristic
1058C22×C4C23×D4311yescharacteristic
1059C22×C4C23×D4311yescharacteristic
1060C22×C4C23×D4311yescharacteristic
1061C22×C4C23×D4311yescharacteristic
1062C22×C4C23×D4311yescharacteristic
1063C22×C4C23×D4311yescharacteristic
1064C22×C4C23×D4311yescharacteristic
1065C22×C4C23×D4311yescharacteristic
1066C22×C4C23×D4311yescharacteristic
1067C22×C4C23×D4311yescharacteristic
1068C22×C4C23×D4311yescharacteristic
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—434no—
1084C4⋊C4—862no—
1085C4⋊C4—862no—
1086C4⋊C4—862no—
1087C4⋊C4—862no—
1088C4⋊C4—1721no—
1089C4⋊C4—1721no—
1090C4⋊C4—1721no—
1091C4⋊C4—1721no—
1092C4⋊C4—1721no—
1093C4⋊C4—1721no—
1094C4⋊C4—1721no—
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—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—434no—
1132C22⋊C4—434no—
1133C22⋊C4—862no—
1134C22⋊C4—1721no—
1135C22⋊C4—1721no—
1136C22⋊C4—1721no—
1137C22⋊C4—1721no—
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—
1147C42—41no—
1148C42—41no—
1149C42—434no—
1150C42—862no—
1151C42—862no—
1152C42—1721no—
1153C42—1721no—
1154C42—1721no—
1155C42—1721no—
1156C42—1721no—
1157C42—1721no—
1158C42—1721no—
1159C42—1721no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—432no—
1167C23—861no—
1168C23—861no—
1169C23—861no—
1170C23—861no—
1171C23—861no—
1172C23—861no—
1173C23C2×Q8×D4312yes—
1174C23C24×D4311yescharacteristic
1175Q8—3442no—
1176D4—1724no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
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—44no—
1218C2×C4—432no—
1219C2×C4—432no—
1220C2×C4—432no—
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—3442no—
1264C2×C4—3442no—
1265C2×C4—1724no—
1266C2×C4—1724no—
1267C2×C4—1724no—
1268C2×C4C2×Q8×D4312yes—
1269C2×C4C2×Q8×D4312yes—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—862no—
1278C22—862no—
1279C22—862no—
1280C22—1721no—
1281C22—1721no—
1282C22—1721no—
1283C22—1721no—
1284C22C22×Q8×D4311yescharacteristic
1285C22H(5,𝔽2)×D4311yescharacteristic
1286C22#1458373411yescharacteristic
1287C22#1458373411yescharacteristic
1288C22#1458373511yescharacteristic
1289C22#1458373511yescharacteristic
1290C22#1458373611yescharacteristic
1291C4—22no—
1292C4—22no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—862no—
1306C4—862no—
1307C4—862no—
1308C4—862no—
1309C4—1721no—
1310C4—1721no—
1311C4—1721no—
1312C4—1721no—
1313C4—1721no—
1314C4—1721no—
1315C4—1721no—
1316C4—1721no—
1317C4—1721no—
1318C4—1721no—
1319C4—1721no—
1320C2—42no—
1321C2—1722no—
1322C2#1914799811yescharacteristic
1323C2#1914839511yescharacteristic
1324C2#1914841811yescharacteristic
1325C2#1914877011yescharacteristic
1326C2#1914884711yescharacteristic
1327C2#1914925111yescharacteristic
1328C2#1914928011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2667C2
prime radicalC22×C22⋊D43C23
hypercenter#2667D43
hypocenterC43#36756
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2667

Complements

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

NH ≅ G/Ntype
1. #19142932C2semidirect
2. #19142903C2semidirect
3. #19142560C2semidirect
4. #19142515C2semidirect
5. #19142373C2semidirect
6. #19142370C2semidirect
7. #19142367C2semidirect
10. #19142080C2semidirect
11. #19142077C2semidirect
12. #19142074C2semidirect
13. #19141907C2semidirect
16. #19141543C2semidirect
17. #19141481C2semidirect
18. #19141252C2semidirect
19. #19140789C2semidirect
20. #19140305C2semidirect
21. #19140263C2semidirect
22. #19140250C2semidirect
23. #19140249C2semidirect
24. #19139826C2semidirect
25. #19139818C2semidirect
26. #19138305C2semidirect
27. #19138276C2semidirect
31. C43×#2667C2semidirect
198. C4×C22⋊D43Q8semidirect
675. #2667D43semidirect
851. C43#36756semidirect

Maximal subgroups

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

subgroupindex
#191429322
#191429032
#191425602
#191425152
#191423732
#191423702
#191423672
#191422502
#191422362
#191420802
#191420772
#191420742
#191419072
#191418092
#191416172
#191415432
#191414812
#191412522
#191407892
#191403052
#191402632
#191402502
#191402492
#191398262
#191398182
#191383052
#191382762
#191372372
#191372242
#191370342
C43×#26672
#3675643