Finite Group Databasebeta

← #25305104

Subgroups — #25305104

Order 11008.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142912C211yesmaximal, characteristic
2#19142901C211yesmaximal, characteristic, complemented
3#19142283C211yesmaximal, characteristic, complemented
4#19142283C211yesmaximal, characteristic, complemented
5#19142178C211yesmaximal, characteristic, complemented
6#19142178C211yesmaximal, characteristic, complemented
7#19142123C211yesmaximal, characteristic, complemented
8#19142088C211yesmaximal, characteristic, complemented
9#19142047C211yesmaximal, characteristic, complemented
10#19142045C211yesmaximal, characteristic, complemented
11#19141999C211yesmaximal, characteristic, complemented
12#19141999C211yesmaximal, characteristic, complemented
13#19141796C211yesmaximal, characteristic, complemented
14#19141756C211yesmaximal, characteristic, complemented
15#19141535C211yesmaximal, characteristic, complemented
16#19141460C211yesmaximal, characteristic, complemented
17#19141060C211yesmaximal, characteristic, complemented
18#19141045C211yesmaximal, characteristic, complemented
19#19140567C211yesmaximal, characteristic, complemented
20#19140551C211yesmaximal, characteristic
21#19139942C211yesmaximal, characteristic
22#19139161C211yesmaximal, characteristic
23#19139161C211yesmaximal, characteristic
24#19139094C211yesmaximal, characteristic, complemented
25#19139094C211yesmaximal, characteristic, complemented
26#19138319C211yesmaximal, characteristic, complemented
27#19138047C211yesmaximal, characteristic
28#19137330C211yesmaximal, characteristic, complemented
29#19137222C211yesmaximal, characteristic
30C2×#14582785C211yesmaximal, characteristic, complemented
31C43×#2583C211yesmaximal, characteristic, complemented
32C2×#13063320C2211yescharacteristic
33C2×#13063317C2211yescharacteristic
34C2×#13063315C2211yescharacteristic
35C2×#13063301C2211yescharacteristic
36C2×C4×C22⋊D43C2211yescharacteristic
37C22×C4⋊Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C43⋊#401C2211yescharacteristic
40C43⋊#401C2211yescharacteristic
41C43⋊#401C2211yescharacteristic
42#14582841C2211yescharacteristic
43#14582841C2211yescharacteristic
44#14582841C2211yescharacteristic
45#14582840C2211yescharacteristic
46#14582840C2211yescharacteristic
47#14582840C2211yescharacteristic
48#14582840C2211yescharacteristic
49#14582840C2211yescharacteristic
50#14582840C2211yescharacteristic
51#14582839C2211yescharacteristic
52#14582838C2211yescharacteristic
53#14582837C2211yescharacteristic
54#14582837C2211yescharacteristic
55#14582837C2211yescharacteristic
56#14582837C2211yescharacteristic
57#14582837C2211yescharacteristic
58#14582837C2211yescharacteristic
59#14582833C2211yescharacteristic
60#14582833C2211yescharacteristic
61#14582833C2211yescharacteristic
62#14582832C2211yescharacteristic
63#14582832C2211yescharacteristic
64#14582832C2211yescharacteristic
65#14582832C2211yescharacteristic
66#14582832C2211yescharacteristic
67#14582830C2211yescharacteristic
68#14582830C2211yescharacteristic
69#14582830C2211yescharacteristic
70#14582829C2211yescharacteristic
71#14582828C2211yescharacteristic
72#14582828C2211yescharacteristic
73#14582828C2211yescharacteristic
74#14582826C2211yescharacteristic
75#14582825C2211yescharacteristic
76#14582825C2211yescharacteristic
77#14582825C2211yescharacteristic
78#14582821C2211yescharacteristic
79#14582821C2211yescharacteristic
80#14582821C2211yescharacteristic
81#14582821C2211yescharacteristic
82#14582821C2211yescharacteristic
83#14582806C2211yescharacteristic
84#14582806C2211yescharacteristic
85#14582806C2211yescharacteristic
86#14582798C2211yescharacteristic
87#14582798C2211yescharacteristic
88#14582797C2211yescharacteristic
89#14582797C2211yescharacteristic
90#14582796C2211yescharacteristic
91#14582795C2211yescharacteristic
92#14582794C2211yescharacteristic
93#14582794C2211yescharacteristic
94#14582794C2211yescharacteristic
95#14582791C2211yescharacteristic
96#14582790C2211yescharacteristic
97#14582790C2211yescharacteristic
98#14582789C2211yescharacteristic
99#14582789C2211yescharacteristic
100#14582789C2211yescharacteristic
101#14582788C2211yescharacteristic
102#14582788C2211yescharacteristic
103#14582788C2211yescharacteristic
104#14582785C2211yescharacteristic
105#14582785C2211yescharacteristic
106#14582785C2211yescharacteristic
107#14582785C2211yescharacteristic
108#14582785C2211yescharacteristic
109#14582785C2211yescharacteristic
110#14582785C2211yescharacteristic
111#14582785C2211yescharacteristic
112#14582785C2211yescharacteristic
113#14582785C2211yescharacteristic
114#14582785C2211yescharacteristic
115#14582785C2211yescharacteristic
116#14582785C2211yescharacteristic
117#14582785C2211yescharacteristic
118#14582784C2211yescharacteristic
119#14582783C2211yescharacteristic
120#14582783C2211yescharacteristic
121#14582782C2211yescharacteristic
122#14582781C2211yescharacteristic
123#14582781C2211yescharacteristic
124#14582781C2211yescharacteristic
125#14582780C2211yescharacteristic
126#14582780C2211yescharacteristic
127#14582780C2211yescharacteristic
128#14582780C2211yescharacteristic
129#14582780C2211yescharacteristic
130#14582780C2211yescharacteristic
131#14582780C2211yescharacteristic
132#14582780C2211yescharacteristic
133#14582778C2211yescharacteristic
134#14582778C2211yescharacteristic
135#14582776C2211yescharacteristic
136#14582776C2211yescharacteristic
137#14582776C2211yescharacteristic
138#14582776C2211yescharacteristic
139#14582774C2211yescharacteristic
140#14582774C2211yescharacteristic
141#14582772C2211yescharacteristic
142#14582772C2211yescharacteristic
143#14582771C2211yescharacteristic
144#14582771C2211yescharacteristic
145#14582771C2211yescharacteristic
146#14582771C2211yescharacteristic
147#14582770C2211yescharacteristic
148#14582770C2211yescharacteristic
149#14582766C2211yescharacteristic
150#14582766C2211yescharacteristic
151#14582766C2211yescharacteristic
152#14582766C2211yescharacteristic
153#14582765C2211yescharacteristic
154#14582763C2211yescharacteristic
155#14582763C2211yescharacteristic
156#14582763C2211yescharacteristic
157#14582763C2211yescharacteristic
158#14582761C2211yescharacteristic
159#14582759C2211yescharacteristic
160#14582758C2211yescharacteristic
161#14582757C2211yescharacteristic
162#14582757C2211yescharacteristic
163#14582757C2211yescharacteristic
164#14582757C2211yescharacteristic
165#14582756C2211yescharacteristic
166C22⋊C4×Dic43C2211yescharacteristic
167C22⋊C4×Dic43C2211yescharacteristic
168C2×C43⋊#95C2211yescharacteristic
169C2×C43⋊#95C2211yescharacteristic
170C2×C43⋊#95C2211yescharacteristic
171C2×C43⋊#95C2211yescharacteristic
172C2×C22⋊Q8×C43C2211yescharacteristic
173C22×C4⋊C4×C43C2211yescharacteristic
174C43×#398C2211yescharacteristic
175C43×#398C2211yescharacteristic
176C43×#395C2211yescharacteristic
177C43×#395C2211yescharacteristic
178C43×#389C2211yescharacteristic
179C43×#389C2211yescharacteristic
180C43×#389C2211yescharacteristic
181C43×#389C2211yescharacteristic
182C43×#385C2211yescharacteristic
183C43×#385C2211yescharacteristic
184C43×#385C2211yescharacteristic
185C43×#385C2211yescharacteristic
186C4×C22⋊C4×C43C2211yescharacteristic
187C22×C22⋊D43C2311yescharacteristic
188C23×Dic43C2311yescharacteristic
189C23×Dic43C2311yescharacteristic
190C23×Dic43C2311yescharacteristic
191C23×Dic43C2311yescharacteristic
192C22×C4×D43C2311yescharacteristic
193#13063320—42no—
194#13063317—42no—
195#13063315—42no—
196#13063301—42no—
197C4×C22⋊D43—24no—
198C2×C4⋊Dic43—42no—
199C2×C4⋊Dic43C2311yescharacteristic
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×Dic43⋊C4C2311yescharacteristic
210C2×Dic43⋊C4C2311yescharacteristic
211C2×Dic43⋊C4C2311yescharacteristic
212C2×Dic43⋊C4C2311yescharacteristic
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×C22⋊Dic43C2311yescharacteristic
231C2×C22⋊Dic43C2311yescharacteristic
232C2×C22⋊Dic43C2311yescharacteristic
233C2×(C2×D43)⋊C4C2311yescharacteristic
234C2×(C2×D43)⋊C4C2311yescharacteristic
235C2×(C2×D43)⋊C4C2311yescharacteristic
236C2×(C2×D43)⋊C4C2311yescharacteristic
237C2×(C2×D43)⋊C4C2311yescharacteristic
238C2×(C2×D43)⋊C4C2311yescharacteristic
239C2×(C2×D43)⋊C4C2311yescharacteristic
240C2×(C2×D43)⋊C4C2311yescharacteristic
241C2×(C2×D43)⋊C4C2311yescharacteristic
242C2×(C2×D43)⋊C4C2311yescharacteristic
243C2×(C2×D43)⋊C4C2311yescharacteristic
244C2×(C2×D43)⋊C4C2311yescharacteristic
245C2×(C2×D43)⋊C4C2311yescharacteristic
246C2×C4×Dic43—42no—
247C2×C4×Dic43C2311yescharacteristic
248C2×C4×Dic43C2311yescharacteristic
249C2×C4×Dic43C2311yescharacteristic
250C2×C4×Dic43C2311yescharacteristic
251C2×C4×Dic43C2311yescharacteristic
252C2×C4×Dic43C2311yescharacteristic
253C2×C4×Dic43C2311yescharacteristic
254C2×C4×Dic43C2311yescharacteristic
255C2×C4×Dic43C2311yescharacteristic
256C43⋊#95C2311yescharacteristic
257C43⋊#95C2311yescharacteristic
258C43⋊#95C2311yescharacteristic
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
313C43⋊#95C2311yescharacteristic
314C22×Q8×C43C2311yescharacteristic
315C23×C4×C43C2311yescharacteristic
316C23×C4×C43C2311yescharacteristic
317C23×C4×C43C2311yescharacteristic
318C22⋊Q8×C43—24no—
319C2×C4⋊C4×C43—24no—
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×C4⋊C4×C43C2311yescharacteristic
330C2×C4⋊C4×C43C2311yescharacteristic
331C2×C4⋊C4×C43C2311yescharacteristic
332C2×C4⋊C4×C43C2311yescharacteristic
333C2×C4⋊C4×C43C2311yescharacteristic
334C2×C4⋊C4×C43C2311yescharacteristic
335C2×C22⋊C4×C43C2311yescharacteristic
336C2×C22⋊C4×C43C2311yescharacteristic
337C2×C22⋊C4×C43C2311yescharacteristic
338C2×C22⋊C4×C43C2311yescharacteristic
339C2×C42×C43C2311yescharacteristic
340C2×C42×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
349#95×C43C2311yescharacteristic
350#95×C43C2311yescharacteristic
351C24×C43C2411yescharacteristic
352C23×D43C2411yescharacteristic
353C2×Q8×C43—22no—
354C2×Q8×C43—41no—
355C2×Q8×C43—41no—
356C22×C4×C43—22no—
357C22×C4×C43—22no—
358C22×C4×C43—41no—
359C22×C4×C43—41no—
360C22×C4×C43—41no—
361C22×C4×C43—41no—
362C22×C4×C43—41no—
363C22×C4×C43—41no—
364C22×C4×C43#4114yes—
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×C4×C43C2411yescharacteristic
374C22×C4×C43C2411yescharacteristic
375C22×C4×C43C2411yescharacteristic
376C22×C4×C43C2411yescharacteristic
377C22×C4×C43C2411yescharacteristic
378C22×C4×C43C2411yescharacteristic
379C2×C22⋊D43—22no—
380C2×C22⋊D43—22no—
381C2×C22⋊D43—22no—
382C22×Dic43—22no—
383C22×Dic43—22no—
384C22×Dic43—22no—
385C22×Dic43—22no—
386C22×Dic43—22no—
387C22×Dic43—41no—
388C22×Dic43—41no—
389C22×Dic43—41no—
390C22×Dic43—41no—
391C22×Dic43—41no—
392C22×Dic43—41no—
393C22×Dic43—41no—
394C22×Dic43C2411yescharacteristic
395C22×Dic43C2411yescharacteristic
396C22×Dic43C2411yescharacteristic
397C22×Dic43C2411yescharacteristic
398C22×Dic43C2411yescharacteristic
399C22×Dic43C2411yescharacteristic
400C22×Dic43C2411yescharacteristic
401C22×Dic43C2411yescharacteristic
402C22×Dic43C2411yescharacteristic
403C22×Dic43C2411yescharacteristic
404C22×Dic43C2411yescharacteristic
405C22×Dic43C2411yescharacteristic
406C22×Dic43C2411yescharacteristic
407C22×Dic43C2411yescharacteristic
408C22×Dic43C2411yescharacteristic
409C2×C4×D43—22no—
410C2×C4×D43—41no—
411C2×C4×D43—41no—
412C4⋊C4×C43—22no—
413C4⋊C4×C43—22no—
414C4⋊C4×C43—22no—
415C4⋊C4×C43—22no—
416C4⋊C4×C43—22no—
417C4⋊C4×C43—22no—
418C4⋊C4×C43—22no—
419C4⋊C4×C43—41no—
420C4⋊C4×C43—41no—
421C4⋊C4×C43—41no—
422C4⋊C4×C43—41no—
423C4⋊C4×C43—41no—
424C4⋊C4×C43—41no—
425C4⋊C4×C43—41no—
426C4⋊C4×C43—41no—
427C22⋊C4×C43—22no—
428C22⋊C4×C43—22no—
429C22⋊C4×C43—22no—
430C22⋊C4×C43—22no—
431C42×C43—41no—
432C42×C43—41no—
433C22⋊Dic43—22no—
434C22⋊Dic43—22no—
435C22⋊Dic43—22no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—41no—
439(C2×D43)⋊C4—41no—
440(C2×D43)⋊C4—41no—
441(C2×D43)⋊C4—41no—
442(C2×D43)⋊C4—41no—
443(C2×D43)⋊C4—41no—
444(C2×D43)⋊C4—41no—
445(C2×D43)⋊C4—41no—
446(C2×D43)⋊C4—41no—
447(C2×D43)⋊C4—41no—
448(C2×D43)⋊C4—41no—
449C4⋊Dic43—22no—
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—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462Dic43⋊C4—22no—
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—
480C4×Dic43—22no—
481C4×Dic43—22no—
482C4×Dic43—22no—
483C4×Dic43—41no—
484C4×Dic43—41no—
485C4×Dic43—41no—
486C4×Dic43—41no—
487C4×Dic43—41no—
488C4×Dic43—41no—
489C23×C43—21no—
490C23×C43—21no—
491C23×C43—21no—
492C23×C43—21no—
493C23×C43C2×#4112yes—
494C23×C432−1+412yes—
495C23×C432−1+412yes—
496C23×C43C2511yescharacteristic
497C22×D43—21no—
498C22×D43—21no—
499C22×D43—21no—
500C22×D43—21no—
501C22×D43—21no—
502C22×D43—21no—
503C22×D43—21no—
504Q8×C43—82no—
505C2×C4×C43—21no—
506C2×C4×C43—21no—
507C2×C4×C43—21no—
508C2×C4×C43—21no—
509C2×C4×C43—21no—
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—44no—
546C2×C4×C43—44no—
547C2×C4×C43—44no—
548C2×C4×C43C2×#4112yes—
549C2×C4×C43C2×#4112yes—
550C22⋊D43—44no—
551C2×Dic43—21no—
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—44no—
596C2×Dic43—44no—
597C2×Dic43—82no—
598C2×Dic43—82no—
599C2×Dic43H(5,𝔽2)12yes—
600C4×D43—82no—
601#36782—431nomaximal, Sylow
602C22×C43—22no—
603C22×C43—22no—
604C22×C43—22no—
605C22×C43—22no—
606C22×C43—22no—
607C22×C43—22no—
608C22×C43#54114yes—
609C22×C43C22×#4111yescharacteristic
610C22×C43C2×H(5,𝔽2)11yescharacteristic
611C22×C43C2×2−1+411yescharacteristic
612C22×C43C2×2−1+411yescharacteristic
613C22×C43#58511yescharacteristic
614C22×C43#58511yescharacteristic
615C22×C43#58511yescharacteristic
616C2×D43—41no—
617C2×D43—41no—
618C2×D43—41no—
619C2×D43—41no—
620C2×D43—41no—
621C2×D43—41no—
622C2×D43—41no—
623C4×C43—22no—
624C4×C43—22no—
625C4×C43—41no—
626C4×C43—41no—
627C4×C43—41no—
628C4×C43—41no—
629C4×C43—41no—
630C4×C43—41no—
631C4×C43—41no—
632C4×C43—41no—
633C4×C43—41no—
634C4×C43—41no—
635C4×C43—41no—
636C4×C43—41no—
637Dic43—22no—
638Dic43—41no—
639Dic43—41no—
640Dic43—41no—
641Dic43—41no—
642Dic43—41no—
643Dic43—41no—
644Dic43—41no—
645Dic43—41no—
646Dic43—41no—
647Dic43—41no—
648Dic43—41no—
649Dic43—41no—
650Dic43—41no—
651Dic43—41no—
652#2852—431no—
653#2851—431no—
654#2783—431no—
655#2783—431no—
656#2776—431no—
657#2776—431no—
658#2772—431no—
659#2769—431no—
660#2766—431no—
661#2766—431no—
662#2762—431no—
663#2762—431no—
664#2747—431no—
665#2744—431no—
666#2725—431no—
667#2719—431no—
668#2690—431no—
669#2689—431no—
670#2646—431no—
671#2643—431no—
672#2583D4311yescharacteristic, complemented
673#2579—431no—
674#2510—431no—
675#2510—431no—
676#2505—431no—
677#2505—431no—
678#2442—431no—
679#2417—431no—
680#2329—431no—
681#2318—431no—
682C2×#387—431no—
683C2×C43—24no—
684C2×C43C2×#54111yescharacteristic
685C2×C43#349311yescharacteristic
686C2×C43#350511yescharacteristic
687C2×C43#353511yescharacteristic
688C2×C43#354111yescharacteristic
689C2×C43#355311yescharacteristic
690C2×C43#356411yescharacteristic
691D43—81no—
692C2×#126—431no—
693C2×#125—431no—
694C2×#125—431no—
695C2×C22⋊Q8—431no—
696C2×C22⋊Q8C2×D4311yescharacteristic
697C2×C4×D4—431no—
698C22×C4⋊C4—431no—
699C22×C4⋊C4C2×D4311yescharacteristic
700C22×C42—431no—
701#401—431no—
702#401—431no—
703#401—431no—
704#400—431no—
705#400—431no—
706#400—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#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#398C2×D4311yescharacteristic
734#398C2×D4311yescharacteristic
735#397—431no—
736#397—431no—
737#397—431no—
738#397—431no—
739#397—431no—
740#397—431no—
741#397—431no—
742#396—431no—
743#396—431no—
744#396—431no—
745#396—431no—
746#396—431no—
747#395C2×D4311yescharacteristic
748#395C2×D4311yescharacteristic
749#391—431no—
750#391—431no—
751#391—431no—
752#389—431no—
753#389—431no—
754#389—431no—
755#389—431no—
756#389—431no—
757#389—431no—
758#389—431no—
759#389—431no—
760#389—431no—
761#389C2×D4311yescharacteristic
762#389C2×D4311yescharacteristic
763#389C2×D4311yescharacteristic
764#389C2×D4311yescharacteristic
765#388—431no—
766#388—431no—
767#388—431no—
768#388—431no—
769#388—431no—
770#388—431no—
771#388—431no—
772#388—431no—
773#388—431no—
774#387—431no—
775#387—431no—
776#387—431no—
777#387—431no—
778#387—431no—
779#387—431no—
780#387—431no—
781#387—431no—
782#387—431no—
783#387—431no—
784#387—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#386—431no—
804#386—431no—
805#386—431no—
806#386—431no—
807#386—431no—
808#386—431no—
809#385—431no—
810#385—431no—
811#385—431no—
812#385—431no—
813#385—431no—
814#385—431no—
815#385—431no—
816#385—431no—
817#385—431no—
818#385—431no—
819#385C2×D4311yescharacteristic
820#385C2×D4311yescharacteristic
821#385C2×D4311yescharacteristic
822#385C2×D4311yescharacteristic
823#383—431no—
824#383—431no—
825#383—431no—
826#383—431no—
827#382—431no—
828#382—431no—
829#382—431no—
830#382—431no—
831#382—431no—
832#381—431no—
833#380—431no—
834#380—431no—
835#380—431no—
836#380—431no—
837#380—431no—
838#380—431no—
839#380—431no—
840C4×C22⋊C4—431no—
841C4×C22⋊C4—431no—
842C4×C22⋊C4C2×D4311yescharacteristic
843C2×#95—431no—
844C2×#95—431no—
845C2×#95—431no—
846C2×#95—431no—
847C43#3678211yescharacteristic, complemented, Sylow
848C22×Q8C22×D4311yescharacteristic
849C22×D4—431no—
850C23×C4—431no—
851C23×C4—431no—
852C23×C4—431no—
853C23×C4—431no—
854C23×C4—431no—
855C23×C4C22×D4311yescharacteristic
856C23×C4C22×D4311yescharacteristic
857C23×C4C22×D4311yescharacteristic
858#126—1722no—
859#125—1722no—
860#125—1722no—
861C22⋊Q8—24no—
862C22⋊Q8—1722no—
863C4×D4—864no—
864C2×C4⋊C4—24no—
865C2×C4⋊C4—431no—
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—1722no—
897C2×C4⋊C4C22×D4311yescharacteristic
898C2×C4⋊C4C22×D4311yescharacteristic
899C2×C4⋊C4C22×D4311yescharacteristic
900C2×C4⋊C4C22×D4311yescharacteristic
901C2×C4⋊C4C22×D4311yescharacteristic
902C2×C4⋊C4C22×D4311yescharacteristic
903C2×C4⋊C4C22×D4311yescharacteristic
904C2×C4⋊C4C22×D4311yescharacteristic
905C2×C4⋊C4C22×D4311yescharacteristic
906C2×C4⋊C4C22×D4311yescharacteristic
907C2×C4⋊C4C22×D4311yescharacteristic
908C2×C4⋊C4C22×D4311yescharacteristic
909C2×C4⋊C4C22×D4311yescharacteristic
910C2×C4⋊C4C22×D4311yescharacteristic
911C2×C4⋊C4C22×D4311yescharacteristic
912C2×C22⋊C4—431no—
913C2×C22⋊C4—431no—
914C2×C22⋊C4—431no—
915C2×C22⋊C4—431no—
916C2×C22⋊C4—431no—
917C2×C22⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
929C2×C22⋊C4C22×D4311yescharacteristic
930C2×C22⋊C4C22×D4311yescharacteristic
931C2×C22⋊C4C22×D4311yescharacteristic
932C2×C42—431no—
933C2×C42—431no—
934C2×C42—431no—
935C2×C42—431no—
936C2×C42—431no—
937C2×C42—431no—
938C2×C42—431no—
939C2×C42—431no—
940C2×C42—431no—
941C2×C42—1722no—
942C2×C42C22×D4311yescharacteristic
943C2×C42C22×D4311yescharacteristic
944#95—431no—
945#95—431no—
946#95—431no—
947#95—431no—
948#95—431no—
949#95—431no—
950#95—431no—
951#95—431no—
952#95—431no—
953#95—431no—
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#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
1012C24—431no—
1013C24C23×D4311yescharacteristic
1014C2×Q8—22no—
1015C2×Q8—41no—
1016C2×Q8—41no—
1017C2×D4—862no—
1018C2×D4—862no—
1019C2×D4—862no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—431no—
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—431no—
1041C22×C4—431no—
1042C22×C4—431no—
1043C22×C4—862no—
1044C22×C4—862no—
1045C22×C4—862no—
1046C22×C4—862no—
1047C22×C4—862no—
1048C22×C4—862no—
1049C22×C4—1721no—
1050C22×C4—1721no—
1051C22×C4—1721no—
1052C22×C4—1721no—
1053C22×C4—1721no—
1054C22×C4—1721no—
1055C22×C4—1721no—
1056C22×C4—1721no—
1057C22×C4—1721no—
1058C22×C4#1062190014yes—
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
1069C22×C4C23×D4311yescharacteristic
1070C22×C4C23×D4311yescharacteristic
1071C22×C4C23×D4311yescharacteristic
1072C22×C4C23×D4311yescharacteristic
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—862no—
1089C4⋊C4—862no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—862no—
1093C4⋊C4—862no—
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—
1119C22⋊C4—22no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—862no—
1124C22⋊C4—862no—
1125C22⋊C4—862no—
1126C22⋊C4—862no—
1127C22⋊C4—862no—
1128C22⋊C4—1721no—
1129C22⋊C4—1721no—
1130C22⋊C4—1721no—
1131C22⋊C4—1721no—
1132C22⋊C4—1721no—
1133C22⋊C4—1721no—
1134C22⋊C4—1721no—
1135C22⋊C4—1721no—
1136C22⋊C4—1721no—
1137C22⋊C4—1721no—
1138C22⋊C4—1721no—
1139C42—41no—
1140C42—41no—
1141C42—862no—
1142C42—862no—
1143C42—862no—
1144C42—1721no—
1145C42—1721no—
1146C42—1721no—
1147C42—1721no—
1148C42—1721no—
1149C42—1721no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—861no—
1155C23—861no—
1156C23—861no—
1157C23—861no—
1158C23—861no—
1159C23—861no—
1160C23—861no—
1161C23C2×#1062190012yes—
1162C23#1306337312yes—
1163C23#1306337312yes—
1164C23C24×D4311yescharacteristic
1165Q8—82no—
1166D4—1724no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
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—44no—
1208C2×C4—44no—
1209C2×C4—44no—
1210C2×C4—432no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—861no—
1214C2×C4—861no—
1215C2×C4—861no—
1216C2×C4—861no—
1217C2×C4—861no—
1218C2×C4—861no—
1219C2×C4—861no—
1220C2×C4—861no—
1221C2×C4—861no—
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—3442no—
1256C2×C4—3442no—
1257C2×C4—3442no—
1258C2×C4—1724no—
1259C2×C4—1724no—
1260C2×C4C2×#1062190012yes—
1261C2×C4C2×#1062190012yes—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—1721no—
1269C22—1721no—
1270C22—1721no—
1271C22—1721no—
1272C22—1721no—
1273C22—1721no—
1274C22—1721no—
1275C22#1458351014yes—
1276C22C22×#1062190011yescharacteristic
1277C22H(5,𝔽2)×D4311yescharacteristic
1278C22C2×#1306337311yescharacteristic
1279C22C2×#1306337311yescharacteristic
1280C22#1458373411yescharacteristic
1281C22#1458373511yescharacteristic
1282C22#1458373511yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—862no—
1298C4—1721no—
1299C4—1721no—
1300C4—1721no—
1301C4—1721no—
1302C4—1721no—
1303C4—1721no—
1304C4—1721no—
1305C4—1721no—
1306C4—1721no—
1307C4—1721no—
1308C4—1721no—
1309C4—1721no—
1310C4—1721no—
1311C4—1721no—
1312C2—24no—
1313C2—3441no—
1314C2C2×#1458351011yescharacteristic
1315C2#1914831211yescharacteristic
1316C2#1914843211yescharacteristic
1317C2#1914879911yescharacteristic
1318C2#1914888111yescharacteristic
1319C2#1914904711yescharacteristic
1320C2#1914921811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2583C2
prime radicalC22×C22⋊D43C23
hypercenter#2583D43
hypocenterC43#36782
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2583

Complements

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

NH ≅ G/Ntype
2. #19142901C2semidirect
3. #19142283C2semidirect
4. #19142283C2semidirect
5. #19142178C2semidirect
6. #19142178C2semidirect
7. #19142123C2semidirect
8. #19142088C2semidirect
9. #19142047C2semidirect
10. #19142045C2semidirect
11. #19141999C2semidirect
12. #19141999C2semidirect
13. #19141796C2semidirect
14. #19141756C2semidirect
15. #19141535C2semidirect
16. #19141460C2semidirect
17. #19141060C2semidirect
18. #19141045C2semidirect
19. #19140567C2semidirect
24. #19139094C2semidirect
25. #19139094C2semidirect
26. #19138319C2semidirect
28. #19137330C2semidirect
30. C2×#14582785C2semidirect
31. C43×#2583C2semidirect
672. #2583D43semidirect
847. C43#36782semidirect

Maximal subgroups

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

subgroupindex
#191429122
#191429012
#191422832
#191421782
#191421232
#191420882
#191420472
#191420452
#191419992
#191417962
#191417562
#191415352
#191414602
#191410602
#191410452
#191405672
#191405512
#191399422
#191391612
#191390942
#191383192
#191380472
#191373302
#191372222
C2×#145827852
C43×#25832
#3678243