Finite Group Databasebeta

← #25303265

Subgroups — #25303265

Order 11008.

1484 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142862C211yesmaximal, characteristic, complemented
2#19142843C211yesmaximal, characteristic, complemented
3#19142839C211yesmaximal, characteristic, complemented
4#19142828C211yesmaximal, characteristic, complemented
5#19142824C211yesmaximal, characteristic, complemented
6#19142813C211yesmaximal, characteristic
7#19142809C211yesmaximal, characteristic
8#19142798C211yesmaximal, characteristic, complemented
9#19142794C211yesmaximal, characteristic, complemented
10#19142774C211yesmaximal, characteristic, complemented
11#19142765C211yesmaximal, characteristic
12#19142755C211yesmaximal, characteristic, complemented
13#19142751C211yesmaximal, characteristic, complemented
14#19142667C211yesmaximal, characteristic
15#19142654C211yesmaximal, characteristic, complemented
16#19137901C211yesmaximal, characteristic, complemented
17#19137899C211yesmaximal, characteristic, complemented
18#19137894C211yesmaximal, characteristic, complemented
19#19137892C211yesmaximal, characteristic, complemented
20#19137885C211yesmaximal, characteristic, complemented
21#19137877C211yesmaximal, characteristic
22#19137872C211yesmaximal, characteristic, complemented
23#19137866C211yesmaximal, characteristic, complemented
24#19137864C211yesmaximal, characteristic, complemented
25#19137862C211yesmaximal, characteristic, complemented
26#19137860C211yesmaximal, characteristic
27#19137853C211yesmaximal, characteristic
28C4⋊Q8×Dic43C211yesmaximal, characteristic, complemented
29#126×Dic43C211yesmaximal, characteristic, complemented
30#19137143C211yesmaximal, characteristic, complemented
31C43×#2821C211yesmaximal, characteristic, complemented
32C2×#13063319C2211yescharacteristic
33C2×Q8×Dic43C2211yescharacteristic
34C2×Q8×Dic43C2211yescharacteristic
35C2×#13063290C2211yescharacteristic
36C2×(C22⋊D43)⋊C4C2211yescharacteristic
37C2×#13063283C2211yescharacteristic
38C2×#13063281C2211yescharacteristic
39C43⋊#401C2211yescharacteristic
40C43⋊#401C2211yescharacteristic
41#14582841C2211yescharacteristic
42#14582841C2211yescharacteristic
43#14582841C2211yescharacteristic
44#14582841C2211yescharacteristic
45#14582841C2211yescharacteristic
46#14582841C2211yescharacteristic
47#14582841C2211yescharacteristic
48#14582840C2211yescharacteristic
49#14582840C2211yescharacteristic
50#14582840C2211yescharacteristic
51#14582840C2211yescharacteristic
52#14582839C2211yescharacteristic
53#14582839C2211yescharacteristic
54#14582839C2211yescharacteristic
55#14582838C2211yescharacteristic
56#14582838C2211yescharacteristic
57#14582837C2211yescharacteristic
58#14582837C2211yescharacteristic
59#14582837C2211yescharacteristic
60#14582837C2211yescharacteristic
61#14582836C2211yescharacteristic
62#14582835C2211yescharacteristic
63#14582834C2211yescharacteristic
64#14582834C2211yescharacteristic
65#14582833C2211yescharacteristic
66#14582833C2211yescharacteristic
67#14582833C2211yescharacteristic
68#14582833C2211yescharacteristic
69#14582833C2211yescharacteristic
70#14582832C2211yescharacteristic
71#14582832C2211yescharacteristic
72#14582832C2211yescharacteristic
73#14582832C2211yescharacteristic
74#14582832C2211yescharacteristic
75#14582831C2211yescharacteristic
76#14582831C2211yescharacteristic
77#14582831C2211yescharacteristic
78#14582831C2211yescharacteristic
79#14582831C2211yescharacteristic
80#14582830C2211yescharacteristic
81#14582830C2211yescharacteristic
82#14582830C2211yescharacteristic
83#14582829C2211yescharacteristic
84#14582829C2211yescharacteristic
85#14582828C2211yescharacteristic
86#14582828C2211yescharacteristic
87#14582827C2211yescharacteristic
88#14582827C2211yescharacteristic
89#14582827C2211yescharacteristic
90#14582826C2211yescharacteristic
91#14582826C2211yescharacteristic
92#14582825C2211yescharacteristic
93#14582825C2211yescharacteristic
94#14582825C2211yescharacteristic
95#14582824C2211yescharacteristic
96#14582824C2211yescharacteristic
97#14582822C2211yescharacteristic
98#14582822C2211yescharacteristic
99#14582822C2211yescharacteristic
100#14582822C2211yescharacteristic
101#14582822C2211yescharacteristic
102#14582821C2211yescharacteristic
103#14582821C2211yescharacteristic
104#14582821C2211yescharacteristic
105#14582821C2211yescharacteristic
106#14582821C2211yescharacteristic
107#14582820C2211yescharacteristic
108#14582820C2211yescharacteristic
109#14582820C2211yescharacteristic
110#14582820C2211yescharacteristic
111#14582818C2211yescharacteristic
112#14582818C2211yescharacteristic
113#14582815C2211yescharacteristic
114#14582815C2211yescharacteristic
115#14582815C2211yescharacteristic
116#14582815C2211yescharacteristic
117#14582815C2211yescharacteristic
118#14582814C2211yescharacteristic
119#14582812C2211yescharacteristic
120#14582811C2211yescharacteristic
121#14582810C2211yescharacteristic
122#14582810C2211yescharacteristic
123#14582806C2211yescharacteristic
124#14582806C2211yescharacteristic
125#14582798C2211yescharacteristic
126#14582798C2211yescharacteristic
127#14582798C2211yescharacteristic
128#14582798C2211yescharacteristic
129#14582792C2211yescharacteristic
130#14582792C2211yescharacteristic
131#14582792C2211yescharacteristic
132#14582788C2211yescharacteristic
133#14582788C2211yescharacteristic
134#14582788C2211yescharacteristic
135#14582785C2211yescharacteristic
136#14582785C2211yescharacteristic
137#14582785C2211yescharacteristic
138#14582781C2211yescharacteristic
139#14582781C2211yescharacteristic
140#14582781C2211yescharacteristic
141#14582769C2211yescharacteristic
142#14582767C2211yescharacteristic
143C4⋊C4×Dic43C2211yescharacteristic
144C4⋊C4×Dic43C2211yescharacteristic
145C4⋊C4×Dic43C2211yescharacteristic
146C4⋊C4×Dic43C2211yescharacteristic
147C4⋊C4×Dic43C2211yescharacteristic
148C4⋊C4×Dic43C2211yescharacteristic
149C4⋊C4×Dic43C2211yescharacteristic
150C4⋊C4×Dic43C2211yescharacteristic
151C4⋊C4×Dic43C2211yescharacteristic
152#14582750C2211yescharacteristic
153#14582750C2211yescharacteristic
154#14582750C2211yescharacteristic
155#14582750C2211yescharacteristic
156#14582750C2211yescharacteristic
157#14582750C2211yescharacteristic
158#14582750C2211yescharacteristic
159C22⋊C4×Dic43C2211yescharacteristic
160C22⋊C4×Dic43C2211yescharacteristic
161C22⋊C4×Dic43C2211yescharacteristic
162C22⋊C4×Dic43C2211yescharacteristic
163C22⋊C4×Dic43C2211yescharacteristic
164#14582746C2211yescharacteristic
165#14582746C2211yescharacteristic
166#14582746C2211yescharacteristic
167#14582746C2211yescharacteristic
168#14582746C2211yescharacteristic
169#14582744C2211yescharacteristic
170#14582744C2211yescharacteristic
171C42×Dic43C2211yescharacteristic
172C2×C4⋊Q8×C43C2211yescharacteristic
173C2×#126×C43C2211yescharacteristic
174C43×#400C2211yescharacteristic
175C43×#400C2211yescharacteristic
176C43×#399C2211yescharacteristic
177C43×#399C2211yescharacteristic
178C43×#398C2211yescharacteristic
179C43×#398C2211yescharacteristic
180C43×#397C2211yescharacteristic
181C43×#397C2211yescharacteristic
182C43×#395C2211yescharacteristic
183C43×#395C2211yescharacteristic
184C43×#393C2211yescharacteristic
185C43×#393C2211yescharacteristic
186C43×#383C2211yescharacteristic
187C22×Dic86C2311yescharacteristic
188C22×C22⋊D43C2311yescharacteristic
189C23×Dic43C2311yescharacteristic
190C22×C4×D43C2311yescharacteristic
191#13063319—24no—
192Q8×Dic43—42no—
193Q8×Dic43—42no—
194#13063290—42no—
195(C22⋊D43)⋊C4—42no—
196#13063283—42no—
197#13063281—42no—
198C2×C4⋊Dic43C2311yescharacteristic
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×C4⋊Dic43C2311yescharacteristic
210C2×C4⋊Dic43C2311yescharacteristic
211C2×C4⋊Dic43C2311yescharacteristic
212C2×C4⋊Dic43C2311yescharacteristic
213C2×C4⋊Dic43C2311yescharacteristic
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×C22⋊Dic43C2311yescharacteristic
234C2×C22⋊Dic43C2311yescharacteristic
235C2×C22⋊Dic43C2311yescharacteristic
236C2×C22⋊Dic43C2311yescharacteristic
237C2×C22⋊Dic43C2311yescharacteristic
238C2×C22⋊Dic43C2311yescharacteristic
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×(C2×D43)⋊C4C2311yescharacteristic
247C2×(C2×D43)⋊C4C2311yescharacteristic
248C2×(C2×D43)⋊C4C2311yescharacteristic
249C2×(C2×D43)⋊C4C2311yescharacteristic
250C2×(C2×D43)⋊C4C2311yescharacteristic
251C2×(C2×D43)⋊C4C2311yescharacteristic
252C2×C4×Dic43C2311yescharacteristic
253C2×C4×Dic43C2311yescharacteristic
254C2×C4×Dic43C2311yescharacteristic
255C2×C4×Dic43C2311yescharacteristic
256C2×C4×Dic43C2311yescharacteristic
257C2×C4×Dic43C2311yescharacteristic
258C2×C4×Dic43C2311yescharacteristic
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
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
315C22×Q8×C43C2311yescharacteristic
316C4⋊Q8×C43—24no—
317#126×C43—24no—
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×C22⋊C4×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
349#95×C43C2311yescharacteristic
350#95×C43C2311yescharacteristic
351C24×C43C2411yescharacteristic
352C23×D43C2411yescharacteristic
353C2×Q8×C43—22no—
354C2×Q8×C43—22no—
355C2×Q8×C43—41no—
356C2×Q8×C43—41no—
357C2×Q8×C43—41no—
358C2×Q8×C43—41no—
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
368C22×C4×C43C2411yescharacteristic
369C22×C4×C43C2411yescharacteristic
370C22×C4×C43C2411yescharacteristic
371C22×C4×C43C2411yescharacteristic
372C22×C4×C43C2411yescharacteristic
373C2×C22⋊D43—41no—
374C2×C22⋊D43—41no—
375C2×C22⋊D43—41no—
376C22×Dic43—22no—
377C22×Dic43—22no—
378C22×Dic43—22no—
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
392C22×Dic43C2411yescharacteristic
393C22×Dic43C2411yescharacteristic
394C2×C4×D43—22no—
395C2×C4×D43—22no—
396C2×C4×D43—22no—
397C2×Dic86—41no—
398C2×Dic86—41no—
399C2×Dic86—41no—
400C4⋊C4×C43—22no—
401C4⋊C4×C43—22no—
402C4⋊C4×C43—22no—
403C4⋊C4×C43—22no—
404C4⋊C4×C43—22no—
405C4⋊C4×C43—22no—
406C4⋊C4×C43—22no—
407C4⋊C4×C43—41no—
408C4⋊C4×C43—41no—
409C4⋊C4×C43—41no—
410C4⋊C4×C43—41no—
411C22⋊C4×C43—22no—
412C22⋊C4×C43—22no—
413C22⋊C4×C43—22no—
414C22⋊C4×C43—41no—
415C22⋊C4×C43—41no—
416C22⋊C4×C43—41no—
417C22⋊C4×C43—41no—
418C42×C43#4114yes—
419C22⋊Dic43—41no—
420C22⋊Dic43—41no—
421C22⋊Dic43—41no—
422C22⋊Dic43—41no—
423C22⋊Dic43—41no—
424C22⋊Dic43—41no—
425(C2×D43)⋊C4—22no—
426(C2×D43)⋊C4—22no—
427(C2×D43)⋊C4—22no—
428(C2×D43)⋊C4—41no—
429(C2×D43)⋊C4—41no—
430(C2×D43)⋊C4—41no—
431(C2×D43)⋊C4—41no—
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—
438C4⋊Dic43—41no—
439C4⋊Dic43—41no—
440C4⋊Dic43—41no—
441C4⋊Dic43—41no—
442C4⋊Dic43—41no—
443C4⋊Dic43—41no—
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—
454Dic43⋊C4—22no—
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—
473C4×Dic43—22no—
474C4×Dic43—22no—
475C4×Dic43—22no—
476C4×Dic43—22no—
477C4×Dic43—22no—
478C4×Dic43—22no—
479C4×Dic43—22no—
480C4×Dic43—22no—
481C4×Dic43—22no—
482C4×Dic43—22no—
483C4×Dic43—22no—
484C4×Dic43—22no—
485C4×Dic43—22no—
486C4×Dic43—41no—
487C4×Dic43—41no—
488C4×Dic43—41no—
489C23×C43—21no—
490C23×C43—21no—
491C23×C43—21no—
492C23×C43—21no—
493C23×C43—21no—
494C23×C43—21no—
495C23×C43—21no—
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—44no—
505Q8×C43—44no—
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×C43C2×#4112yes—
546C2×C4×C43C2×#4112yes—
547C2×C4×C43C2×#4112yes—
548C22⋊D43—44no—
549C2×Dic43—21no—
550C2×Dic43—21no—
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—44no—
592C2×Dic43H(5,𝔽2)12yes—
593C2×Dic432−1+412yes—
594C2×Dic432−1+412yes—
595C4×D43—44no—
596Dic86—44no—
597#36697—431nomaximal, Sylow
598C22×C43—41no—
599C22×C43—41no—
600C22×C43—41no—
601C22×C43—41no—
602C22×C43—41no—
603C22×C43—41no—
604C22×C43—41no—
605C22×C43C22×#4111yescharacteristic
606C22×C43C2×H(5,𝔽2)11yescharacteristic
607C22×C43C2×2−1+411yescharacteristic
608C22×C43C2×2−1+411yescharacteristic
609C22×C43#58511yescharacteristic
610C22×C43#58511yescharacteristic
611C22×C43#58511yescharacteristic
612C2×D43—41no—
613C2×D43—41no—
614C2×D43—41no—
615C2×D43—41no—
616C2×D43—41no—
617C2×D43—41no—
618C2×D43—41no—
619C4×C43—22no—
620C4×C43—22no—
621C4×C43—22no—
622C4×C43—41no—
623C4×C43—41no—
624C4×C43—41no—
625C4×C43—41no—
626C4×C43—41no—
627C4×C43—41no—
628C4×C43—41no—
629C4×C43—41no—
630C4×C43—41no—
631C4×C43—41no—
632C4×C43—41no—
633Dic43—41no—
634Dic43—41no—
635Dic43—41no—
636Dic43—41no—
637Dic43—41no—
638Dic43—41no—
639Dic43—41no—
640Dic43—41no—
641Dic43—41no—
642Dic43—41no—
643Dic43—41no—
644Dic43—41no—
645Dic43—41no—
646Dic43—41no—
647Dic43#56314yes—
648#2843—431no—
649#2839—431no—
650#2839—431no—
651#2838—431no—
652#2838—431no—
653#2837—431no—
654#2837—431no—
655#2836—431no—
656#2836—431no—
657#2833—431no—
658#2832—431no—
659#2831—431no—
660#2831—431no—
661#2823—431no—
662#2821—431no—
663#2821D4311yescharacteristic, complemented
664#2402—431no—
665#2402—431no—
666#2401—431no—
667#2401—431no—
668#2399—431no—
669#2398—431no—
670#2396—431no—
671#2396—431no—
672#2396—431no—
673#2396—431no—
674#2395—431no—
675#2395—431no—
676C4×C4⋊Q8—431no—
677C4×#126—431no—
678C4×#126—431no—
679C2×C43—81no—
680C2×C43#346011yescharacteristic
681C2×C43#346111yescharacteristic
682C2×C43#346111yescharacteristic
683C2×C43C2×#56311yescharacteristic
684C2×C43#352911yescharacteristic
685C2×C43#353111yescharacteristic
686C2×C43#353111yescharacteristic
687D43—81no—
688C2×C4⋊Q8C2×D4311yescharacteristic
689C2×#126—431no—
690C2×#126C2×D4311yescharacteristic
691C2×C4×Q8—431no—
692C2×C4×Q8—431no—
693C2×C4×Q8—431no—
694C2×C4×D4—431no—
695C2×#117—431no—
696C2×#117—431no—
697#401—431no—
698#401—431no—
699#400—431no—
700#400—431no—
701#400—431no—
702#400—431no—
703#400—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#400C2×D4311yescharacteristic
720#400C2×D4311yescharacteristic
721#399—431no—
722#399—431no—
723#399—431no—
724#399—431no—
725#399C2×D4311yescharacteristic
726#399C2×D4311yescharacteristic
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#398—431no—
736#398—431no—
737#398—431no—
738#398—431no—
739#398—431no—
740#398—431no—
741#398—431no—
742#398—431no—
743#398—431no—
744#398—431no—
745#398—431no—
746#398—431no—
747#398C2×D4311yescharacteristic
748#398C2×D4311yescharacteristic
749#397—431no—
750#397—431no—
751#397—431no—
752#397—431no—
753#397—431no—
754#397—431no—
755#397—431no—
756#397—431no—
757#397—431no—
758#397—431no—
759#397—431no—
760#397—431no—
761#397C2×D4311yescharacteristic
762#397C2×D4311yescharacteristic
763#396—431no—
764#396—431no—
765#396—431no—
766#396—431no—
767#396—431no—
768#396—431no—
769#396—431no—
770#396—431no—
771#396—431no—
772#396—431no—
773#395—431no—
774#395—431no—
775#395—431no—
776#395—431no—
777#395—431no—
778#395—431no—
779#395C2×D4311yescharacteristic
780#395C2×D4311yescharacteristic
781#394—431no—
782#394—431no—
783#394—431no—
784#394—431no—
785#394—431no—
786#394—431no—
787#393—431no—
788#393—431no—
789#393—431no—
790#393—431no—
791#393C2×D4311yescharacteristic
792#393C2×D4311yescharacteristic
793#391—431no—
794#391—431no—
795#389—431no—
796#389—431no—
797#389—431no—
798#389—431no—
799#388—431no—
800#388—431no—
801#388—431no—
802#388—431no—
803#388—431no—
804#388—431no—
805#387—431no—
806#387—431no—
807#387—431no—
808#387—431no—
809#387—431no—
810#387—431no—
811#384—431no—
812#383—431no—
813#383C2×D4311yescharacteristic
814C4×C4⋊C4—431no—
815C4×C4⋊C4—431no—
816C4×C4⋊C4—431no—
817C4×C4⋊C4—431no—
818C4×C4⋊C4—431no—
819C4×C4⋊C4—431no—
820C4×C4⋊C4—431no—
821C4×C4⋊C4—431no—
822C4×C4⋊C4—431no—
823C4×C4⋊C4—431no—
824C4×C4⋊C4—431no—
825C4×C4⋊C4—431no—
826C4×C4⋊C4—431no—
827C4×C4⋊C4—431no—
828C4×C4⋊C4—431no—
829C4×C4⋊C4—431no—
830C4×C22⋊C4—431no—
831C4×C22⋊C4—431no—
832C4×C22⋊C4—431no—
833C4×C22⋊C4—431no—
834C4×C22⋊C4—431no—
835C4×C22⋊C4—431no—
836C4×C22⋊C4—431no—
837C4×C22⋊C4—431no—
838C4×C22⋊C4—431no—
839C4×C22⋊C4—431no—
840#376—431no—
841#376—431no—
842C43—431no—
843C43#3669711yescharacteristic, complemented, Sylow
844C22×Q8—431no—
845C22×Q8C22×D4311yescharacteristic
846C22×Q8C22×D4311yescharacteristic
847C22×D4—431no—
848C23×C4—431no—
849C23×C4—431no—
850C4⋊Q8—24no—
851#126—24no—
852#126—864no—
853C4×Q8—1722no—
854C4×Q8—1722no—
855C4×Q8—1722no—
856C4×D4—1722no—
857#117—1722no—
858#117—1722no—
859C2×C4⋊C4—431no—
860C2×C4⋊C4—431no—
861C2×C4⋊C4—431no—
862C2×C4⋊C4—431no—
863C2×C4⋊C4—431no—
864C2×C4⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
895C2×C4⋊C4C22×D4311yescharacteristic
896C2×C4⋊C4C22×D4311yescharacteristic
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×C22⋊C4—431no—
906C2×C22⋊C4—431no—
907C2×C22⋊C4—431no—
908C2×C22⋊C4—431no—
909C2×C22⋊C4—431no—
910C2×C22⋊C4—431no—
911C2×C22⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
925C2×C22⋊C4C22×D4311yescharacteristic
926C2×C22⋊C4C22×D4311yescharacteristic
927C2×C22⋊C4C22×D4311yescharacteristic
928C2×C22⋊C4C22×D4311yescharacteristic
929C2×C22⋊C4C22×D4311yescharacteristic
930C2×C22⋊C4C22×D4311yescharacteristic
931C2×C42—431no—
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—431no—
942C2×C42—431no—
943C2×C42—431no—
944C2×C42—431no—
945C2×C42—431no—
946C2×C42—431no—
947C2×C42C22×D4311yescharacteristic
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#95C22×D4311yescharacteristic
995#95C22×D4311yescharacteristic
996#95C22×D4311yescharacteristic
997#95C22×D4311yescharacteristic
998#95C22×D4311yescharacteristic
999#95C22×D4311yescharacteristic
1000#95C22×D4311yescharacteristic
1001#95C22×D4311yescharacteristic
1002#95C22×D4311yescharacteristic
1003#95C22×D4311yescharacteristic
1004#95C22×D4311yescharacteristic
1005#95C22×D4311yescharacteristic
1006#95C22×D4311yescharacteristic
1007#95C22×D4311yescharacteristic
1008C24—431no—
1009C24C23×D4311yescharacteristic
1010C2×Q8—22no—
1011C2×Q8—22no—
1012C2×Q8—41no—
1013C2×Q8—41no—
1014C2×Q8—41no—
1015C2×Q8—41no—
1016C2×Q8—1721no—
1017C2×Q8—1721no—
1018C2×Q8—1721no—
1019C2×D4—1721no—
1020C2×D4—1721no—
1021C2×D4—1721no—
1022C22×C4—431no—
1023C22×C4—431no—
1024C22×C4—431no—
1025C22×C4—431no—
1026C22×C4—431no—
1027C22×C4—431no—
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—862no—
1038C22×C4—862no—
1039C22×C4—862no—
1040C22×C4—862no—
1041C22×C4—862no—
1042C22×C4—862no—
1043C22×C4C23×D4311yescharacteristic
1044C22×C4C23×D4311yescharacteristic
1045C22×C4C23×D4311yescharacteristic
1046C22×C4C23×D4311yescharacteristic
1047C22×C4C23×D4311yescharacteristic
1048C22×C4C23×D4311yescharacteristic
1049C22×C4C23×D4311yescharacteristic
1050C22×C4C23×D4311yescharacteristic
1051C22×C4C23×D4311yescharacteristic
1052C22×C4C23×D4311yescharacteristic
1053C22×C4C23×D4311yescharacteristic
1054C22×C4C23×D4311yescharacteristic
1055C22×C4C23×D4311yescharacteristic
1056C22×C4C23×D4311yescharacteristic
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—862no—
1069C4⋊C4—862no—
1070C4⋊C4—862no—
1071C4⋊C4—1721no—
1072C4⋊C4—1721no—
1073C4⋊C4—1721no—
1074C4⋊C4—1721no—
1075C4⋊C4—1721no—
1076C4⋊C4—1721no—
1077C4⋊C4—1721no—
1078C4⋊C4—1721no—
1079C4⋊C4—1721no—
1080C4⋊C4—1721no—
1081C4⋊C4—1721no—
1082C4⋊C4—1721no—
1083C4⋊C4—1721no—
1084C4⋊C4—1721no—
1085C4⋊C4—1721no—
1086C4⋊C4—1721no—
1087C4⋊C4—1721no—
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—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—41no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—862no—
1113C22⋊C4—1721no—
1114C22⋊C4—1721no—
1115C22⋊C4—1721no—
1116C22⋊C4—1721no—
1117C22⋊C4—1721no—
1118C22⋊C4—1721no—
1119C22⋊C4—1721no—
1120C22⋊C4—1721no—
1121C22⋊C4—1721no—
1122C22⋊C4—1721no—
1123C22⋊C4—1721no—
1124C22⋊C4—1721no—
1125C22⋊C4—1721no—
1126C22⋊C4—1721no—
1127C22⋊C4—1721no—
1128C22⋊C4—1721no—
1129C42—862no—
1130C42—862no—
1131C42—862no—
1132C42—862no—
1133C42—862no—
1134C42—862no—
1135C42—862no—
1136C42—862no—
1137C42—862no—
1138C42—862no—
1139C42—862no—
1140C42—862no—
1141C42—862no—
1142C42—1721no—
1143C42—1721no—
1144C42—1721no—
1145C42#1062190014yes—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—861no—
1154C23—861no—
1155C23—861no—
1156C23—861no—
1157C23—861no—
1158C23—861no—
1159C23—861no—
1160C23C24×D4311yescharacteristic
1161Q8—44no—
1162Q8—44no—
1163Q8—1724no—
1164D4—1724no—
1165C2×C4—21no—
1166C2×C4—21no—
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—432no—
1205C2×C4—432no—
1206C2×C4—432no—
1207C2×C4—861no—
1208C2×C4—861no—
1209C2×C4—861no—
1210C2×C4—861no—
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—1724no—
1250C2×C4—1724no—
1251C2×C4C2×#1062190012yes—
1252C2×C4C2×#1062190012yes—
1253C2×C4C2×#1062190012yes—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—1721no—
1262C22—1721no—
1263C22—1721no—
1264C22—1721no—
1265C22—1721no—
1266C22—1721no—
1267C22—1721no—
1268C22C22×#1062190011yescharacteristic
1269C22H(5,𝔽2)×D4311yescharacteristic
1270C222−1+4×D4311yescharacteristic
1271C222−1+4×D4311yescharacteristic
1272C22#1458373411yescharacteristic
1273C22#1458373611yescharacteristic
1274C22#1458373611yescharacteristic
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—434no—
1290C4—1721no—
1291C4—1721no—
1292C4—1721no—
1293C4—1721no—
1294C4—1721no—
1295C4—1721no—
1296C4—1721no—
1297C4—1721no—
1298C4—1721no—
1299C4—1721no—
1300C4—1721no—
1301C4—1721no—
1302C4—1721no—
1303C4—1721no—
1304C2—81no—
1305C2—3441no—
1306C2#1914800811yescharacteristic
1307C2#1914801911yescharacteristic
1308C2#1914801911yescharacteristic
1309C2#563×D4311yescharacteristic
1310C2#1914873611yescharacteristic
1311C2#1914874111yescharacteristic
1312C2#1914874111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2821C2
prime radicalC22×C22⋊D43C23
hypercenter#2821D43
hypocenterC43#36697
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2821

Complements

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

NH ≅ G/Ntype
1. #19142862C2semidirect
2. #19142843C2semidirect
3. #19142839C2semidirect
4. #19142828C2semidirect
5. #19142824C2semidirect
8. #19142798C2semidirect
9. #19142794C2semidirect
10. #19142774C2semidirect
12. #19142755C2semidirect
13. #19142751C2semidirect
15. #19142654C2semidirect
16. #19137901C2semidirect
17. #19137899C2semidirect
18. #19137894C2semidirect
19. #19137892C2semidirect
20. #19137885C2semidirect
22. #19137872C2semidirect
23. #19137866C2semidirect
24. #19137864C2semidirect
25. #19137862C2semidirect
28. C4⋊Q8×Dic43C2semidirect
29. #126×Dic43C2semidirect
30. #19137143C2semidirect
31. C43×#2821C2semidirect
663. #2821D43semidirect
843. C43#36697semidirect

Maximal subgroups

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

subgroupindex
#191428622
#191428432
#191428392
#191428282
#191428242
#191428132
#191428092
#191427982
#191427942
#191427742
#191427652
#191427552
#191427512
#191426672
#191426542
#191379012
#191378992
#191378942
#191378922
#191378852
#191378772
#191378722
#191378662
#191378642
#191378622
#191378602
#191378532
C4⋊Q8×Dic432
#126×Dic432
#191371432
C43×#28212
#3669743