Finite Group Databasebeta

← #72222733

Subgroups — #72222733

Order 2304.

4348 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10594669C211yesmaximal, characteristic
2#11899423C212yesmaximal, complemented
3#11899422C214yesmaximal, complemented
4#11899419C214yesmaximal, complemented
5#11899417C214yesmaximal, complemented
6C3×#82007C212yesmaximal, complemented
7#11899392C214yesmaximal, complemented
8#11899390C214yesmaximal, complemented
9C2×#10590625C211yesmaximal, characteristic, complemented
10D32×M32C214yesmaximal, complemented
11C2×C3⋊D3×M32C211yesmaximal, characteristic, complemented
12D3×#3407—32nomaximal
13C2×#64306C411yescharacteristic
14C22×C8×C3⋊D3C2211yescharacteristic
15C2×C3×#901C2212yes—
16C2×#63818C411yescharacteristic
17C2×#63815C412yes—
18C2×#63805C412yes—
19C2×#63803C2212yes—
20#10594669C412yes—
21#10594669C412yes—
22#10594669C412yes—
23#10594669C412yes—
24#10594669C2212yes—
25#10594669C2212yes—
26#10594669C2212yes—
27#10594669C2212yes—
28C2×#63791C412yes—
29C2×D32×C8C2212yes—
30C2×C32×M32C2211yescharacteristic, complemented
31C2×#63639C2211yescharacteristic, complemented
32C3⋊D3×M32C2212yes—
33C3⋊D3×M32C2212yescomplemented
34C3⋊D3×M32C2212yescomplemented
35C3⋊D3×M32C2212yescomplemented
36C2×#63625C2212yescomplemented
37C2×C16×C3⋊D3C2212yescomplemented
38C2×C3×#812C2212yescomplemented
39C3×#4907C2218yescomplemented
40C3×D3×M32C2218yescomplemented
41C3×#4901C2218yescomplemented
42C2×#63544C2212yescomplemented
43#10590625C2212yes—
44#10590625C2212yescomplemented
45#10590625C2212yescomplemented
46#10590625C2212yescomplemented
47C2×#63542C2212yescomplemented
48#10590622C2218yescomplemented
49#10590621C2218yescomplemented
50D3×#812C2218yescomplemented
51#10590229C2218yescomplemented
52#10590228C22116yescomplemented
53#10590227C2218yescomplemented
54#10590226C2218yescomplemented
55D3×#798C22116yescomplemented
56D32×C16C2218yescomplemented
57C2×D3×#131—32no—
58C3×#3407—32no—
59#83780—32no—
60#82012—38no—
61#82012—38no—
62D3×#504—38no—
63D3×#504—38no—
64#82007—32no—
65#82007—38no—
66#82007D312yescomplemented
67C2×D3×M32—32no—
68C2×D3×M32—38no—
69C2×D3×M32—32no—
70C2×D3×M32—61no—
71C22×C4×C3⋊D3C2×C411yescharacteristic
72C2×C3×#235C2×C412yes—
73C2×#3811C812yes—
74C2×#3805C812yes—
75#64306C812yes—
76#64306C812yes—
77#64306C812yes—
78#64306C812yes—
79#64306C2×C412yes—
80#64306C2×C412yes—
81#64306C2×C412yes—
82#64306C2×C412yes—
83C2×#3802C811yescharacteristic
84C2×C4×D32C2×C412yes—
85C2×#3798C2×C412yes—
86C2×#3797C811yescharacteristic
87C2×#3796C812yes—
88C22×C32×C8C2311yescharacteristic
89C22×C3⋊(C3⋊C8)C2×C411yescharacteristic
90C2×C8×C3⋊D3C2×C411yescharacteristic
91C2×C8×C3⋊D3C2×C411yescharacteristic
92C2×C8×C3⋊D3C2×C411yescharacteristic
93C2×C8×C3⋊D3C2×C411yescharacteristic
94C2×C8×C3⋊D3C2×C411yescharacteristic
95C2×C8×C3⋊D3C2×C411yescharacteristic
96C2×C8×C3⋊D3C2311yescharacteristic
97C2×C8×C3⋊D3C2311yescharacteristic
98C2×C8×C3⋊D3C2311yescharacteristic
99C2×C8×C3⋊D3C2311yescharacteristic
100C2×C8×C3⋊D3C2311yescharacteristic
101C2×C8×C3⋊D3C2311yescharacteristic
102C2×C3×#208C2×C412yes—
103C3×#901C2×C414yes—
104C3×#901C2×C414yes—
105C3×#901C2314yes—
106C3×#901C2314yes—
107C2×C3×ΓL(1,𝔽25)C2×C414yes—
108C2×C3×D3×C8C2314yes—
109C2×#3712C2×C412yes—
110C2×#3711C2×C414yes—
111#63818C2×C412yes—
112#63818C2×C412yes—
113#63818C2×C412yes—
114#63818C2×C412yes—
115C2×#3710C2×C412yes—
116#63815C2×C414yes—
117#63815C2×C414yes—
118#63815C2×C414yes—
119#63815C2×C414yes—
120C2×D3×C3⋊C8C2×C414yes—
121#63805C2×C414yes—
122#63805C2×C414yes—
123#63805C2×C414yes—
124#63805C2×C414yes—
125#63803C2×C414yes—
126#63803C2×C414yes—
127#63803C2314yes—
128#63803C2314yes—
129#63791C2×C414yes—
130#63791C2×C414yes—
131#63791C2×C414yes—
132#63791C2×C414yes—
133D32×C8C2×C414yes—
134D32×C8C2×C414yes—
135D32×C8C2314yes—
136D32×C8C2314yes—
137C32×M32C2312yes—
138C32×M32C2312yescomplemented
139C2×C32×C16C2312yescomplemented
140#63639C2312yes—
141#63639C2312yescomplemented
142C2×C3⋊(C3⋊C16)C2312yescomplemented
143#63625C2314yes—
144#63625C2314yescomplemented
145C16×C3⋊D3C2314yes—
146C16×C3⋊D3C2314yescomplemented
147C3×#812C2314yes—
148C3×#812C2314yescomplemented
149C2×C3×C3⋊C16C2314yescomplemented
150C3×#798C23116yescomplemented
151C3×D3×C16C23116yescomplemented
152#63544C2314yes—
153#63544C2314yescomplemented
154#63543C23116yescomplemented
155#63542C2314yes—
156#63542C2314yescomplemented
157D3×C3⋊C16C23116yescomplemented
158C2×#3407—91noSylow
159C2×D3×#41—32no—
160C2×C3×#131—32no—
161C2×#948—32no—
162D3×#131—34no—
163D3×#131—34no—
164D3×#131—34no—
165D3×#131—34no—
166D3×#131—34no—
167D3×#131—34no—
168D3×#131—34no—
169D3×#131—34no—
170C2×#907—32no—
171C2×#907—34no—
172C2×D3×M16—32no—
173C2×D3×M16—34no—
174C2×#901—34no—
175C2×#901C2×D312yes—
176C22×D3×C8—32no—
177C22×D3×C8—34no—
178C22×D3×C8—61no—
179C3×#504—38no—
180C3×#504—38no—
181C2×C3×M32—21no—
182C2×C3×M32—32no—
183C2×C3×M32—38no—
184C2×C3×M32C2×D312yescomplemented
185#5140—38no—
186#5140—38no—
187C2×#812—32no—
188C2×#812—38no—
189C2×#812—61no—
190C2×#812C2×D312yescomplemented
191#4907—38no—
192#4907—316no—
193#4907—316no—
194#4907C2×D318yescomplemented
195D3×M32—38no—
196D3×M32—34no—
197D3×M32—34no—
198D3×M32—34no—
199D3×M32—34no—
200D3×M32—34no—
201D3×M32—34no—
202D3×M32—34no—
203D3×M32—34no—
204D3×M32—316no—
205D3×M32—316no—
206D3×M32—62no—
207D3×M32—62no—
208D3×M32—62no—
209D3×M32—62no—
210D3×M32C2×D318yescomplemented
211#4901—38no—
212#4901—316no—
213#4901—316no—
214#4901C2×D318yescomplemented
215C2×#798—34no—
216C2×#798—34no—
217C2×#798—316no—
218C2×#798—62no—
219C2×D3×C16—34no—
220C2×D3×C16—34no—
221C2×D3×C16—316no—
222C2×D3×C16—62no—
223C23×C3⋊D3C2×C811yescharacteristic
224C22×D32C2×C812yes—
225C22×C32×C4C22×C411yescharacteristic
226C22×C3⋊Dic3C2×C811yescharacteristic
227C2×C4×C3⋊D3C2×C811yescharacteristic
228C2×C4×C3⋊D3C2×C811yescharacteristic
229C2×C4×C3⋊D3C2×C811yescharacteristic
230C2×C4×C3⋊D3C2×C811yescharacteristic
231C2×C4×C3⋊D3C2×C811yescharacteristic
232C2×C4×C3⋊D3C2×C811yescharacteristic
233C2×C4×C3⋊D3C22×C411yescharacteristic
234C2×C4×C3⋊D3C22×C411yescharacteristic
235C2×C4×C3⋊D3C22×C411yescharacteristic
236C2×C4×C3⋊D3C22×C411yescharacteristic
237C2×C4×C3⋊D3C22×C411yescharacteristic
238C2×C4×C3⋊D3C22×C411yescharacteristic
239C2×C3×#67C2×C814yes—
240C3×#235C2×C814yes—
241C3×#235C2×C814yes—
242C3×#235C22×C414yes—
243C3×#235C22×C414yes—
244C2×C3×D12C2×C812yes—
245C2×C3×C4×D3C22×C414yes—
246C2×C3×Dic6C2×C812yes—
247#3811C2×C814yes—
248#3811C2×C814yes—
249#3811C2×C814yes—
250#3811C2×C814yes—
251C2×#627C2×C812yes—
252C2×#626C2×C814yes—
253C2×#625C2×C812yes—
254C2×#624C2×C812yes—
255#3805C2×C814yes—
256#3805C2×C814yes—
257#3805C2×C814yes—
258#3805C2×C814yes—
259C2×D3×Dic3C2×C814yes—
260#3802C2×C812yes—
261#3802C2×C812yes—
262#3802C2×C812yes—
263#3802C2×C812yes—
264C4×D32C2×C814yes—
265C4×D32C2×C814yes—
266C4×D32C22×C414yes—
267C4×D32C22×C414yes—
268#3798C2×C814yes—
269#3798C2×C814yes—
270#3798C22×C414yes—
271#3798C22×C414yes—
272#3797C2×C812yes—
273#3797C2×C812yes—
274#3797C2×C812yes—
275#3797C2×C812yes—
276#3796C2×C814yes—
277#3796C2×C814yes—
278#3796C2×C814yes—
279#3796C2×C814yes—
280C2×C32×C8C22×C411yescharacteristic
281C2×C32×C8C22×C411yescharacteristic
282C2×C32×C8C22×C411yescharacteristic
283C2×C32×C8C2411yescharacteristic
284C2×C32×C8C2411yescharacteristic
285C2×C32×C8C2411yescharacteristic
286C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
287C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
288C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
289C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
290C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
291C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
292C8×C3⋊D3C22×C411yescharacteristic
293C8×C3⋊D3C22×C411yescharacteristic
294C8×C3⋊D3C22×C411yescharacteristic
295C8×C3⋊D3C22×C411yescharacteristic
296C8×C3⋊D3C22×C411yescharacteristic
297C8×C3⋊D3C22×C411yescharacteristic
298C8×C3⋊D3C22×C411yescharacteristic
299C8×C3⋊D3C22×C411yescharacteristic
300C8×C3⋊D3C22×C411yescharacteristic
301C8×C3⋊D3C22×C411yescharacteristic
302C8×C3⋊D3C22×C411yescharacteristic
303C8×C3⋊D3C22×C411yescharacteristic
304C8×C3⋊D3C2411yescharacteristic
305C8×C3⋊D3C2411yescharacteristic
306C8×C3⋊D3C2411yescharacteristic
307C8×C3⋊D3C2411yescharacteristic
308C3×#208C22×C414yes—
309C3×#208C22×C414yes—
310C2×C3×C3⋊C8C22×C414yes—
311C3×ΓL(1,𝔽25)C22×C418yes—
312C3×ΓL(1,𝔽25)C22×C418yes—
313C3×D3×C8C22×C418yes—
314C3×D3×C8C2418yes—
315#3712C22×C414yes—
316#3712C22×C414yes—
317#3711C22×C418yes—
318#3711C22×C418yes—
319#3710C22×C414yes—
320#3710C22×C414yes—
321D3×C3⋊C8C22×C418yes—
322D3×C3⋊C8C22×C418yes—
323C32×C16C2414yes—
324C3⋊(C3⋊C16)C2414yes—
325C3×C3⋊C16C2418yes—
326C22×#131—91no—
327#3407—32no—
328#3407—92no—
329#3407—94no—
330#3407—94no—
331#3407—94no—
332C2×#504—94no—
333C2×#504—94no—
334C22×M32—94no—
335C22×M32—91no—
336C22×M32—91no—
337C2×C3×#41—32no—
338D3×#41—34no—
339D3×#41—34no—
340D3×#41—34no—
341D3×#41—34no—
342D3×#41—34no—
343D3×#41—34no—
344D3×#41—34no—
345D3×#41—34no—
346C2×#239—32no—
347C2×D3×Q8—32no—
348C2×#237—34no—
349C2×#237—32no—
350C2×D3×D4—34no—
351C2×D3×D4—32no—
352C2×#235—34no—
353C2×#235C4×D312yes—
354C22×C4×D3—32no—
355C22×C4×D3—34no—
356C22×C4×D3—61no—
357C3×#131—34no—
358C3×#131—34no—
359C3×#131—34no—
360C3×#131—34no—
361C2×C3×M16—32no—
362C2×C3×M16—34no—
363C22×C3×C8—21no—
364C22×C3×C8—34no—
365C22×C3×C8C22×D312yes—
366#948—34no—
367#948—34no—
368#948—34no—
369#948—34no—
370C2×#208—34no—
371C2×#208C4×D312yes—
372C22×C3⋊C8—32no—
373C22×C3⋊C8—34no—
374C22×C3⋊C8—61no—
375#907—34no—
376#907—34no—
377#907—34no—
378#907—34no—
379#907—38no—
380#907—38no—
381#907—38no—
382#907—38no—
383D3×M16—34no—
384D3×M16—34no—
385D3×M16—34no—
386D3×M16—34no—
387D3×M16—38no—
388D3×M16—38no—
389D3×M16—38no—
390D3×M16—38no—
391#901—38no—
392#901—38no—
393#901—38no—
394#901—38no—
395#901C4×D314yes—
396#901C4×D314yes—
397#901C22×D314yes—
398#901C22×D314yes—
399C2×ΓL(1,𝔽25)—34no—
400C2×ΓL(1,𝔽25)—34no—
401C2×ΓL(1,𝔽25)C4×D314yes—
402C2×D3×C8—34no—
403C2×D3×C8—32no—
404C2×D3×C8—32no—
405C2×D3×C8—32no—
406C2×D3×C8—32no—
407C2×D3×C8—32no—
408C2×D3×C8—32no—
409C2×D3×C8—32no—
410C2×D3×C8—32no—
411C2×D3×C8—32no—
412C2×D3×C8—32no—
413C2×D3×C8—32no—
414C2×D3×C8—32no—
415C2×D3×C8—34no—
416C2×D3×C8—38no—
417C2×D3×C8—38no—
418C2×D3×C8—38no—
419C2×D3×C8—38no—
420C2×D3×C8—61no—
421C2×D3×C8—61no—
422C2×D3×C8—61no—
423C2×D3×C8—61no—
424C2×D3×C8—61no—
425C2×D3×C8—61no—
426C2×D3×C8—61no—
427C2×D3×C8—61no—
428C2×D3×C8—61no—
429C2×D3×C8—61no—
430C2×D3×C8—61no—
431C2×D3×C8—61no—
432C2×D3×C8C22×D314yes—
433C3×M32—22no—
434C3×M32—22no—
435C3×M32—34no—
436C3×M32—34no—
437C3×M32—316no—
438C3×M32C22×D314yes—
439C3×M32C22×D314yescomplemented
440C2×C3×C16—22no—
441C2×C3×C16—34no—
442C2×C3×C16—316no—
443C2×C3×C16C22×D314yescomplemented
444#812—34no—
445#812—34no—
446#812—316no—
447#812—62no—
448#812—62no—
449#812C22×D314yes—
450#812C22×D314yescomplemented
451C2×C3⋊C16—34no—
452C2×C3⋊C16—316no—
453C2×C3⋊C16—62no—
454C2×C3⋊C16C22×D314yescomplemented
455#798—316no—
456#798—38no—
457#798—38no—
458#798—38no—
459#798—38no—
460#798—64no—
461#798—64no—
462#798C22×D3116yescomplemented
463D3×C16—316no—
464D3×C16—38no—
465D3×C16—38no—
466D3×C16—38no—
467D3×C16—38no—
468D3×C16—64no—
469D3×C16—64no—
470D3×C16C22×D3116yescomplemented
471C23×C32C22×C811yescharacteristic
472C22×C3⋊D3—42no—
473C22×C3⋊D3C22×C811yescharacteristic
474C22×C3⋊D3C22×C811yescharacteristic
475C22×C3⋊D3C22×C811yescharacteristic
476C22×C3⋊D3C22×C811yescharacteristic
477C22×C3⋊D3C22×C811yescharacteristic
478C22×C3⋊D3C22×C811yescharacteristic
479C22×C3×D3C22×C814yes—
480C2×D32—44no—
481C2×D32C22×C814yes—
482C2×D32C22×C814yes—
483C2×C32×C4C22×C811yescharacteristic
484C2×C32×C4C22×C811yescharacteristic
485C2×C32×C4C22×C811yescharacteristic
486C2×C32×C4C23×C411yescharacteristic
487C2×C32×C4C23×C411yescharacteristic
488C2×C32×C4C23×C411yescharacteristic
489C2×C3⋊Dic3C22×C811yescharacteristic
490C2×C3⋊Dic3C22×C811yescharacteristic
491C2×C3⋊Dic3C22×C811yescharacteristic
492C2×C3⋊Dic3C22×C811yescharacteristic
493C2×C3⋊Dic3C22×C811yescharacteristic
494C2×C3⋊Dic3C22×C811yescharacteristic
495C4×C3⋊D3C22×C811yescharacteristic
496C4×C3⋊D3C22×C811yescharacteristic
497C4×C3⋊D3C22×C811yescharacteristic
498C4×C3⋊D3C22×C811yescharacteristic
499C4×C3⋊D3C22×C811yescharacteristic
500C4×C3⋊D3C22×C811yescharacteristic
501C4×C3⋊D3C22×C811yescharacteristic
502C4×C3⋊D3C22×C811yescharacteristic
503C4×C3⋊D3C22×C811yescharacteristic
504C4×C3⋊D3C22×C811yescharacteristic
505C4×C3⋊D3C22×C811yescharacteristic
506C4×C3⋊D3C22×C811yescharacteristic
507C4×C3⋊D3C23×C411yescharacteristic
508C4×C3⋊D3C23×C411yescharacteristic
509C4×C3⋊D3C23×C411yescharacteristic
510C4×C3⋊D3C23×C411yescharacteristic
511C3×#67C22×C818yes—
512C3×#67C22×C818yes—
513C2×C3×Dic3C22×C814yes—
514C3×D12C22×C814yes—
515C3×D12C22×C814yes—
516C3×C4×D3C22×C818yes—
517C3×C4×D3C23×C418yes—
518C3×Dic6C22×C814yes—
519C3×Dic6C22×C814yes—
520#627C22×C814yes—
521#627C22×C814yes—
522#626C22×C818yes—
523#626C22×C818yes—
524#625C22×C814yes—
525#625C22×C814yes—
526#624C22×C814yes—
527#624C22×C814yes—
528D3×Dic3C22×C818yes—
529D3×Dic3C22×C818yes—
530C32×C8C23×C411yescharacteristic
531C32×C8C23×C411yescharacteristic
532C32×C8C23×C411yescharacteristic
533C32×C8C2511yescharacteristic
534C3⋊(C3⋊C8)C23×C411yescharacteristic
535C3⋊(C3⋊C8)C23×C411yescharacteristic
536C3⋊(C3⋊C8)C23×C411yescharacteristic
537C3⋊(C3⋊C8)C23×C411yescharacteristic
538C3×C3⋊C8C23×C418yes—
539C22×#41—91no—
540C2×#131—32no—
541C2×#131—92no—
542C2×#131—92no—
543C2×#131—92no—
544C2×#131—92no—
545C2×#131—92no—
546C2×#131—92no—
547C2×#131—92no—
548C2×#131—92no—
549C2×#131—92no—
550C2×#131—92no—
551C2×#131—92no—
552C22×M16—91no—
553C22×M16—92no—
554C23×C8—92no—
555C23×C8—91no—
556#504—38no—
557#504—38no—
558#504—98no—
559#504—916no—
560#504—98no—
561#504—98no—
562#504—98no—
563C2×M32—32no—
564C2×M32—38no—
565C2×M32—92no—
566C2×M32—916no—
567C2×M32—92no—
568C2×M32—92no—
569C2×M32—98no—
570C2×M32—92no—
571C2×M32—92no—
572C2×M32—98no—
573C2×M32—91no—
574C2×M32—92no—
575C2×M32—92no—
576C2×M32—92no—
577C2×M32—92no—
578C2×M32—92no—
579C2×M32D3211yescharacteristic, complemented
580C22×C16—92no—
581C22×C16—98no—
582C22×C16—92no—
583C23×D3—32no—
584C23×D3—34no—
585C23×D3—61no—
586C3×#41—34no—
587C3×#41—34no—
588C3×#41—34no—
589C3×#41—34no—
590C2×C3×Q8—32no—
591C2×C3×D4—34no—
592C2×C3×D4—32no—
593C22×C3×C4—21no—
594C22×C3×C4—34no—
595C22×C3×C4C2×C4×D312yes—
596C2×#67—34no—
597C2×#67—34no—
598C2×#67D3×C814yes—
599C22×Dic3—32no—
600C22×Dic3—34no—
601C22×Dic3—61no—
602#239—34no—
603#239—34no—
604#239—34no—
605#239—34no—
606D3×Q8—34no—
607D3×Q8—34no—
608D3×Q8—34no—
609D3×Q8—34no—
610#237—38no—
611#237—38no—
612#237—38no—
613#237—38no—
614#237—34no—
615#237—34no—
616#237—34no—
617#237—34no—
618D3×D4—38no—
619D3×D4—38no—
620D3×D4—38no—
621D3×D4—38no—
622D3×D4—34no—
623D3×D4—34no—
624D3×D4—34no—
625D3×D4—34no—
626#235—38no—
627#235—38no—
628#235—38no—
629#235—38no—
630#235D3×C814yes—
631#235D3×C814yes—
632#235C2×C4×D314yes—
633#235C2×C4×D314yes—
634C2×D12—34no—
635C2×D12D3×C812yes—
636C2×C4×D3—34no—
637C2×C4×D3—32no—
638C2×C4×D3—32no—
639C2×C4×D3—32no—
640C2×C4×D3—32no—
641C2×C4×D3—32no—
642C2×C4×D3—32no—
643C2×C4×D3—32no—
644C2×C4×D3—32no—
645C2×C4×D3—32no—
646C2×C4×D3—32no—
647C2×C4×D3—32no—
648C2×C4×D3—32no—
649C2×C4×D3—34no—
650C2×C4×D3—38no—
651C2×C4×D3—38no—
652C2×C4×D3—38no—
653C2×C4×D3—38no—
654C2×C4×D3—61no—
655C2×C4×D3—61no—
656C2×C4×D3—61no—
657C2×C4×D3—61no—
658C2×C4×D3—61no—
659C2×C4×D3—61no—
660C2×C4×D3—61no—
661C2×C4×D3—61no—
662C2×C4×D3—61no—
663C2×C4×D3—61no—
664C2×C4×D3—61no—
665C2×C4×D3—61no—
666C2×C4×D3C2×C4×D314yes—
667C2×Dic6—34no—
668C2×Dic6D3×C812yes—
669C3×M16—34no—
670C3×M16—34no—
671C3×M16—38no—
672C3×M16—38no—
673C2×C3×C8—21no—
674C2×C3×C8—21no—
675C2×C3×C8—21no—
676C2×C3×C8—21no—
677C2×C3×C8—21no—
678C2×C3×C8—21no—
679C2×C3×C8—34no—
680C2×C3×C8—38no—
681C2×C3×C8—38no—
682C2×C3×C8C2×C4×D312yes—
683C2×C3×C8C2×C4×D312yes—
684C2×C3×C8C2×C4×D312yes—
685C2×C3×C8C23×D312yes—
686C2×C3×C8C23×D312yes—
687C2×C3×C8C23×D312yes—
688#208—38no—
689#208—38no—
690#208C2×C4×D314yes—
691#208C2×C4×D314yes—
692C2×C3⋊C8—32no—
693C2×C3⋊C8—32no—
694C2×C3⋊C8—32no—
695C2×C3⋊C8—32no—
696C2×C3⋊C8—32no—
697C2×C3⋊C8—32no—
698C2×C3⋊C8—38no—
699C2×C3⋊C8—38no—
700C2×C3⋊C8—61no—
701C2×C3⋊C8—61no—
702C2×C3⋊C8—61no—
703C2×C3⋊C8—61no—
704C2×C3⋊C8—61no—
705C2×C3⋊C8—61no—
706C2×C3⋊C8C2×C4×D314yes—
707ΓL(1,𝔽25)—38no—
708ΓL(1,𝔽25)—38no—
709ΓL(1,𝔽25)—38no—
710ΓL(1,𝔽25)—38no—
711ΓL(1,𝔽25)C2×C4×D318yes—
712ΓL(1,𝔽25)C2×C4×D318yes—
713D3×C8—38no—
714D3×C8—38no—
715D3×C8—32no—
716D3×C8—32no—
717D3×C8—32no—
718D3×C8—32no—
719D3×C8—32no—
720D3×C8—32no—
721D3×C8—32no—
722D3×C8—32no—
723D3×C8—32no—
724D3×C8—32no—
725D3×C8—32no—
726D3×C8—32no—
727D3×C8—32no—
728D3×C8—32no—
729D3×C8—32no—
730D3×C8—32no—
731D3×C8—38no—
732D3×C8—38no—
733D3×C8—61no—
734D3×C8—61no—
735D3×C8—61no—
736D3×C8—61no—
737D3×C8—61no—
738D3×C8—61no—
739D3×C8—61no—
740D3×C8—61no—
741D3×C8—61no—
742D3×C8—61no—
743D3×C8—61no—
744D3×C8—61no—
745D3×C8—61no—
746D3×C8—61no—
747D3×C8—61no—
748D3×C8—61no—
749D3×C8C2×C4×D318yes—
750D3×C8C23×D318yes—
751C3×C16—24no—
752C3×C16—38no—
753C3×C16C23×D318yes—
754C3⋊C16—38no—
755C3⋊C16—64no—
756C3⋊C16C23×D318yes—
757C22×C32—41no—
758C22×C32C23×C811yescharacteristic
759C22×C32C23×C811yescharacteristic
760C22×C32C23×C811yescharacteristic
761C2×C3⋊D3—22no—
762C2×C3⋊D3—22no—
763C2×C3⋊D3—22no—
764C2×C3⋊D3—41no—
765C2×C3⋊D3—41no—
766C2×C3⋊D3—41no—
767C2×C3⋊D3C23×C811yescharacteristic
768C2×C3⋊D3C23×C811yescharacteristic
769C2×C3⋊D3C23×C811yescharacteristic
770C2×C3⋊D3C23×C811yescharacteristic
771C2×C3×D3—44no—
772C2×C3×D3C23×C818yes—
773D32—28no—
774D32—44no—
775C32×C4C23×C811yescharacteristic
776C32×C4C23×C811yescharacteristic
777C32×C4C23×C811yescharacteristic
778C32×C4C24×C411yescharacteristic
779C3⋊Dic3C23×C811yescharacteristic
780C3⋊Dic3C23×C811yescharacteristic
781C3⋊Dic3C23×C811yescharacteristic
782C3⋊Dic3C23×C811yescharacteristic
783C3×Dic3C23×C818yes—
784C2×#41—32no—
785C2×#41—92no—
786C2×#41—92no—
787C2×#41—92no—
788C2×#41—92no—
789C2×#41—92no—
790C2×#41—92no—
791C2×#41—92no—
792C2×#41—92no—
793C2×#41—92no—
794C2×#41—92no—
795C2×#41—92no—
796C22×Q8—91no—
797C22×D4—92no—
798C22×D4—91no—
799C23×C4—92no—
800C23×C4—91no—
801#131—34no—
802#131—34no—
803#131—34no—
804#131—34no—
805#131—94no—
806#131—94no—
807#131—94no—
808#131—94no—
809#131—94no—
810#131—94no—
811#131—94no—
812#131—94no—
813#131—94no—
814#131—94no—
815#131—94no—
816#131—94no—
817C2×M16—32no—
818C2×M16—34no—
819C2×M16—92no—
820C2×M16—94no—
821C2×M16—92no—
822C2×M16—92no—
823C2×M16—92no—
824C2×M16—92no—
825C2×M16—94no—
826C2×M16—94no—
827C2×M16—94no—
828C2×M16—94no—
829C22×C8—34no—
830C22×C8—92no—
831C22×C8—94no—
832C22×C8—94no—
833C22×C8—94no—
834C22×C8—94no—
835C22×C8—94no—
836C22×C8—91no—
837C22×C8—91no—
838C22×C8—91no—
839C22×C8—91no—
840C22×C8—91no—
841C22×C8—91no—
842C22×C8—91no—
843C22×C8—91no—
844C22×C8—91no—
845C22×C8—91no—
846C22×C8—91no—
847C22×C8—91no—
848C22×C8—91no—
849C22×C8C2×D3211yescharacteristic
850M32—34no—
851M32—34no—
852M32—316no—
853M32—94no—
854M32—94no—
855M32—916no—
856M32—92no—
857M32—92no—
858M32—94no—
859M32—94no—
860M32C2×D3212yes—
861M32C2×D3212yescomplemented
862C2×C16—34no—
863C2×C16—316no—
864C2×C16—94no—
865C2×C16—94no—
866C2×C16—916no—
867C2×C16—92no—
868C2×C16—94no—
869C2×C16—94no—
870C2×C16C2×D3212yescomplemented
871C23×C3—21no—
872C23×C3—34no—
873C23×C3C2×D3×C812yes—
874C22×D3—32no—
875C22×D3—32no—
876C22×D3—32no—
877C22×D3—32no—
878C22×D3—32no—
879C22×D3—32no—
880C22×D3—38no—
881C22×D3—38no—
882C22×D3—61no—
883C22×D3—61no—
884C22×D3—61no—
885C22×D3—61no—
886C22×D3—61no—
887C22×D3—61no—
888C22×D3—128no—
889C22×D3—124no—
890C22×D3—124no—
891C22×D3C2×D3×C814yes—
892C3×Q8—34no—
893C3×Q8—34no—
894C3×D4—38no—
895C3×D4—38no—
896C3×D4—34no—
897C3×D4—34no—
898C2×C3×C4—21no—
899C2×C3×C4—21no—
900C2×C3×C4—21no—
901C2×C3×C4—21no—
902C2×C3×C4—21no—
903C2×C3×C4—21no—
904C2×C3×C4—34no—
905C2×C3×C4—38no—
906C2×C3×C4—38no—
907C2×C3×C4C2×D3×C812yes—
908C2×C3×C4C2×D3×C812yes—
909C2×C3×C4C2×D3×C812yes—
910C2×C3×C4C22×C4×D312yes—
911C2×C3×C4C22×C4×D312yes—
912C2×C3×C4C22×C4×D312yes—
913#67—38no—
914#67—38no—
915#67—38no—
916#67—38no—
917#67C2×D3×C818yes—
918#67C2×D3×C818yes—
919C2×Dic3—32no—
920C2×Dic3—32no—
921C2×Dic3—32no—
922C2×Dic3—32no—
923C2×Dic3—32no—
924C2×Dic3—32no—
925C2×Dic3—38no—
926C2×Dic3—38no—
927C2×Dic3—61no—
928C2×Dic3—61no—
929C2×Dic3—61no—
930C2×Dic3—61no—
931C2×Dic3—61no—
932C2×Dic3—61no—
933C2×Dic3C2×D3×C814yes—
934D12—38no—
935D12—38no—
936D12C2×D3×C814yes—
937D12C2×D3×C814yes—
938C4×D3—38no—
939C4×D3—38no—
940C4×D3—32no—
941C4×D3—32no—
942C4×D3—32no—
943C4×D3—32no—
944C4×D3—32no—
945C4×D3—32no—
946C4×D3—32no—
947C4×D3—32no—
948C4×D3—32no—
949C4×D3—32no—
950C4×D3—32no—
951C4×D3—32no—
952C4×D3—32no—
953C4×D3—32no—
954C4×D3—32no—
955C4×D3—32no—
956C4×D3—38no—
957C4×D3—38no—
958C4×D3—61no—
959C4×D3—61no—
960C4×D3—61no—
961C4×D3—61no—
962C4×D3—61no—
963C4×D3—61no—
964C4×D3—61no—
965C4×D3—61no—
966C4×D3—61no—
967C4×D3—61no—
968C4×D3—61no—
969C4×D3—61no—
970C4×D3—61no—
971C4×D3—61no—
972C4×D3—61no—
973C4×D3—61no—
974C4×D3C2×D3×C818yes—
975C4×D3C22×C4×D318yes—
976Dic6—38no—
977Dic6—38no—
978Dic6C2×D3×C814yes—
979Dic6C2×D3×C814yes—
980C3×C8—21no—
981C3×C8—21no—
982C3×C8—21no—
983C3×C8—21no—
984C3×C8—38no—
985C3×C8C22×C4×D312yes—
986C3×C8C22×C4×D312yes—
987C3×C8C22×C4×D312yes—
988C3×C8C24×D312yes—
989C3⋊C8—32no—
990C3⋊C8—32no—
991C3⋊C8—32no—
992C3⋊C8—32no—
993C3⋊C8—61no—
994C3⋊C8—61no—
995C3⋊C8—61no—
996C3⋊C8—61no—
997C3⋊C8C22×C4×D318yes—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32C24×C811yescharacteristic
1002C3⋊D3—21no—
1003C3⋊D3—21no—
1004C3⋊D3—21no—
1005C3⋊D3#340712yescomplemented
1006C3×D3—28no—
1007C24—92no—
1008C24—91no—
1009#41—34no—
1010#41—34no—
1011#41—34no—
1012#41—34no—
1013#41—94no—
1014#41—94no—
1015#41—94no—
1016#41—94no—
1017#41—94no—
1018#41—94no—
1019#41—94no—
1020#41—94no—
1021#41—94no—
1022#41—94no—
1023#41—94no—
1024#41—94no—
1025C2×Q8—32no—
1026C2×Q8—92no—
1027C2×Q8—92no—
1028C2×Q8—92no—
1029C2×Q8—92no—
1030C2×Q8—92no—
1031C2×D4—34no—
1032C2×D4—32no—
1033C2×D4—94no—
1034C2×D4—94no—
1035C2×D4—94no—
1036C2×D4—94no—
1037C2×D4—94no—
1038C2×D4—92no—
1039C2×D4—92no—
1040C2×D4—92no—
1041C2×D4—92no—
1042C2×D4—92no—
1043C22×C4—34no—
1044C22×C4—94no—
1045C22×C4—94no—
1046C22×C4—92no—
1047C22×C4—94no—
1048C22×C4—94no—
1049C22×C4—94no—
1050C22×C4—91no—
1051C22×C4—91no—
1052C22×C4—91no—
1053C22×C4—91no—
1054C22×C4—91no—
1055C22×C4—91no—
1056C22×C4—91no—
1057C22×C4—91no—
1058C22×C4—91no—
1059C22×C4—91no—
1060C22×C4—91no—
1061C22×C4—91no—
1062C22×C4—91no—
1063C22×C4C4×D3211yescharacteristic
1064M16—34no—
1065M16—34no—
1066M16—38no—
1067M16—38no—
1068M16—94no—
1069M16—94no—
1070M16—98no—
1071M16—98no—
1072C2×C8—34no—
1073C2×C8—38no—
1074C2×C8—38no—
1075C2×C8—94no—
1076C2×C8—94no—
1077C2×C8—98no—
1078C2×C8—98no—
1079C2×C8—91no—
1080C2×C8—91no—
1081C2×C8—91no—
1082C2×C8—91no—
1083C2×C8—91no—
1084C2×C8—91no—
1085C2×C8—91no—
1086C2×C8—91no—
1087C2×C8—91no—
1088C2×C8—91no—
1089C2×C8—91no—
1090C2×C8—91no—
1091C2×C8—91no—
1092C2×C8—91no—
1093C2×C8—91no—
1094C2×C8—91no—
1095C2×C8—91no—
1096C2×C8—91no—
1097C2×C8—91no—
1098C2×C8—91no—
1099C2×C8—91no—
1100C2×C8—91no—
1101C2×C8C4×D3211yescharacteristic
1102C2×C8C4×D3211yescharacteristic
1103C2×C8C4×D3211yescharacteristic
1104C2×C8C22×D3211yescharacteristic
1105C2×C8C22×D3211yescharacteristic
1106C2×C8C22×D3211yescharacteristic
1107C16—38no—
1108C16—94no—
1109C16C22×D3214yes—
1110C22×C3—21no—
1111C22×C3—21no—
1112C22×C3—21no—
1113C22×C3—38no—
1114C22×C3—42no—
1115C22×C3—42no—
1116C22×C3—124no—
1117C22×C3C22×D3×C812yes—
1118C22×C3C22×D3×C812yes—
1119C22×C3C22×D3×C812yes—
1120C2×D3—32no—
1121C2×D3—32no—
1122C2×D3—32no—
1123C2×D3—32no—
1124C2×D3—44no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—616no—
1130C2×D3—64no—
1131C2×D3—64no—
1132C2×D3—64no—
1133C2×D3—64no—
1134C2×D3—122no—
1135C2×D3—122no—
1136C2×D3—128no—
1137C2×D3—122no—
1138C2×D3—122no—
1139C2×D3—122no—
1140C2×D3—122no—
1141C2×D3—122no—
1142C2×D3—122no—
1143C2×D3C22×D3×C818yes—
1144C3×C4—21no—
1145C3×C4—21no—
1146C3×C4—21no—
1147C3×C4—21no—
1148C3×C4—38no—
1149C3×C4C22×D3×C812yes—
1150C3×C4C22×D3×C812yes—
1151C3×C4C22×D3×C812yes—
1152C3×C4C23×C4×D312yes—
1153Dic3—32no—
1154Dic3—32no—
1155Dic3—32no—
1156Dic3—32no—
1157Dic3—61no—
1158Dic3—61no—
1159Dic3—61no—
1160Dic3—61no—
1161Dic3C22×D3×C818yes—
1162C32C2×#340711yescharacteristic, complemented, Sylow
1163C23—34no—
1164C23—94no—
1165C23—94no—
1166C23—91no—
1167C23—91no—
1168C23—91no—
1169C23—91no—
1170C23—91no—
1171C23—91no—
1172C23—362no—
1173C23—364no—
1174C23D32×C811yescharacteristic
1175Q8—34no—
1176Q8—34no—
1177Q8—94no—
1178Q8—94no—
1179D4—38no—
1180D4—38no—
1181D4—34no—
1182D4—34no—
1183D4—98no—
1184D4—98no—
1185D4—94no—
1186D4—94no—
1187C2×C4—34no—
1188C2×C4—38no—
1189C2×C4—38no—
1190C2×C4—94no—
1191C2×C4—94no—
1192C2×C4—98no—
1193C2×C4—98no—
1194C2×C4—91no—
1195C2×C4—91no—
1196C2×C4—91no—
1197C2×C4—91no—
1198C2×C4—91no—
1199C2×C4—91no—
1200C2×C4—91no—
1201C2×C4—91no—
1202C2×C4—91no—
1203C2×C4—91no—
1204C2×C4—91no—
1205C2×C4—91no—
1206C2×C4—91no—
1207C2×C4—91no—
1208C2×C4—91no—
1209C2×C4—91no—
1210C2×C4—91no—
1211C2×C4—91no—
1212C2×C4—91no—
1213C2×C4—91no—
1214C2×C4—91no—
1215C2×C4—91no—
1216C2×C4D32×C811yescharacteristic
1217C2×C4D32×C811yescharacteristic
1218C2×C4D32×C811yescharacteristic
1219C2×C4C2×C4×D3211yescharacteristic
1220C2×C4C2×C4×D3211yescharacteristic
1221C2×C4C2×C4×D3211yescharacteristic
1222C8—38no—
1223C8—91no—
1224C8—91no—
1225C8—91no—
1226C8—91no—
1227C8C2×C4×D3211yescharacteristic
1228C8C2×C4×D3211yescharacteristic
1229C8C2×C4×D3211yescharacteristic
1230C8C23×D3211yescharacteristic
1231C2×C3—22no—
1232C2×C3—22no—
1233C2×C3—22no—
1234C2×C3—22no—
1235C2×C3—21no—
1236C2×C3—41no—
1237C2×C3—41no—
1238C2×C3—68no—
1239C2×C3C23×D3×C812yes—
1240D3—28no—
1241D3—34no—
1242D3—62no—
1243D3—62no—
1244D3—62no—
1245D3—62no—
1246D3—62no—
1247D3—121no—
1248D3—121no—
1249C22—38no—
1250C22—41no—
1251C22—91no—
1252C22—91no—
1253C22—91no—
1254C22—91no—
1255C22—124no—
1256C22—182no—
1257C22—182no—
1258C22—182no—
1259C22—188no—
1260C22—361no—
1261C22—361no—
1262C22—361no—
1263C22—364no—
1264C22C2×D32×C811yescharacteristic
1265C22C2×D32×C811yescharacteristic
1266C22C2×D32×C811yescharacteristic
1267C4—38no—
1268C4—91no—
1269C4—91no—
1270C4—91no—
1271C4—91no—
1272C4C2×D32×C811yescharacteristic
1273C4C2×D32×C811yescharacteristic
1274C4C2×D32×C811yescharacteristic
1275C4C22×C4×D3211yescharacteristic
1276C3—21no—
1277C3D3×#340712yescomplemented
1278C2—21no—
1279C2—21no—
1280C2—21no—
1281C2—68no—
1282C2—92no—
1283C2—181no—
1284C2—181no—
1285C2—181no—
1286C2C22×D32×C811yescharacteristic
subgroupG/H
center, FrattiniC8C23×D32
commutator, socleC2×C32C24×C8
FittingC2×C32×M32C22
prime radicalC2×#64306C4
cosocleC32×C8C25
hypercenterC2×M32D32
hypocenterC32C2×#3407
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
2. #11899423C2semidirect
3. #11899422C2semidirect
4. #11899419C2semidirect
5. #11899417C2semidirect
6. C3×#82007C2semidirect
7. #11899392C2semidirect
8. #11899390C2semidirect
9. C2×#10590625C2semidirect
10. D32×M32C2semidirect
11. C2×C3⋊D3×M32C2semidirect
30. C2×C32×M32C22semidirect
31. C2×#63639C22semidirect
33. C3⋊D3×M32C22semidirect
34. C3⋊D3×M32C22semidirect
35. C3⋊D3×M32C22semidirect
36. C2×#63625C22semidirect
37. C2×C16×C3⋊D3C22semidirect
38. C2×C3×#812C22semidirect
39. C3×#4907C22semidirect
40. C3×D3×M32C22semidirect
41. C3×#4901C22semidirect
42. C2×#63544C22semidirect
44. #10590625C22semidirect
45. #10590625C22semidirect
46. #10590625C22semidirect
47. C2×#63542C22semidirect
48. #10590622C22semidirect
49. #10590621C22semidirect
50. D3×#812C22semidirect
51. #10590229C22semidirect
52. #10590228C22semidirect
53. #10590227C22semidirect
54. #10590226C22semidirect
55. D3×#798C22semidirect
56. D32×C16C22semidirect
66. #82007D3semidirect
138. C32×M32C23semidirect
139. C2×C32×C16C23semidirect
141. #63639C23semidirect
142. C2×C3⋊(C3⋊C16)C23semidirect
144. #63625C23semidirect
146. C16×C3⋊D3C23semidirect
148. C3×#812C23semidirect
149. C2×C3×C3⋊C16C23semidirect
150. C3×#798C23semidirect
151. C3×D3×C16C23semidirect
153. #63544C23semidirect
154. #63543C23semidirect
156. #63542C23semidirect
157. D3×C3⋊C16C23semidirect
184. C2×C3×M32C2×D3semidirect
190. C2×#812C2×D3semidirect
194. #4907C2×D3semidirect
210. D3×M32C2×D3semidirect
214. #4901C2×D3semidirect
439. C3×M32C22×D3semidirect
443. C2×C3×C16C22×D3semidirect
450. #812C22×D3semidirect
454. C2×C3⋊C16C22×D3semidirect
462. #798C22×D3semidirect
470. D3×C16C22×D3semidirect
579. C2×M32D32semidirect
861. M32C2×D32semidirect
870. C2×C16C2×D32semidirect
1005. C3⋊D3#3407semidirect
1162. C32C2×#3407semidirect
1277. C3D3×#3407semidirect

Maximal subgroups

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

subgroupindex
C2×#105946692
#118994232
#118994222
#118994192
#118994172
C3×#820072
#118993922
#118993902
C2×#105906252
D32×M322
C2×C3⋊D3×M322
D3×#34073