Finite Group Databasebeta

← #13167769

Subgroups — #13167769

Order 1728.

1244 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11724387C211yesmaximal, characteristic
2#11723645C211yesmaximal, characteristic, complemented
3#11723333C211yesmaximal, characteristic, complemented
4#11723332C211yesmaximal, characteristic, complemented
5D3×#3743C211yesmaximal, characteristic, complemented
6C3×#63804C211yesmaximal, characteristic, complemented
7C3×#63803C211yesmaximal, characteristic, complemented
8C3×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
9#11722825C211yesmaximal, characteristic, complemented
10#11722824C211yesmaximal, characteristic, complemented
11#11722823C211yesmaximal, characteristic, complemented
12#11722822C211yesmaximal, characteristic, complemented
13#11722820C211yesmaximal, characteristic, complemented
14#11722819C211yesmaximal, characteristic, complemented
15D3×#3711C211yesmaximal, characteristic, complemented
16#10594706—31nomaximal
17#10594670—31nomaximal
18#10594668—31nomaximal
19C4×#1113C2211yescharacteristic
20C4×D3×C3⋊D3C2211yescharacteristic
21#89020C2211yescharacteristic
22#89020C2211yescharacteristic
23C3×C4×D32C2211yescharacteristic
24C3×#3798C2211yescharacteristic
25C3×#3798C2211yescharacteristic
26#88962C411yescharacteristic
27#88962C411yescharacteristic
28#88961C411yescharacteristic
29#88961C411yescharacteristic
30#88957C411yescharacteristic
31#88955C411yescharacteristic
32#88953C411yescharacteristic
33#88952C411yescharacteristic
34#88850C2211yescharacteristic, complemented
35C3×#3743C2211yescharacteristic
36C3×#3743C2211yescharacteristic, complemented
37C3×C8×C3⋊D3C2211yescharacteristic, complemented
38C32×ΓL(1,𝔽25)C2211yescharacteristic, complemented
39C32×D3×C8C2211yescharacteristic, complemented
40C32×D3×C8C2211yescharacteristic, complemented
41#88809C2211yescharacteristic
42#88809C2211yescharacteristic, complemented
43#88808C2211yescharacteristic, complemented
44#88788C2211yescharacteristic, complemented
45#88787C2211yescharacteristic
46#88787C2211yescharacteristic, complemented
47#88786C2211yescharacteristic, complemented
48#88785C2211yescharacteristic, complemented
49#88785C2211yescharacteristic, complemented
50C3⋊D3×C3⋊C8C2211yescharacteristic, complemented
51D3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
52D3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
53C3×#3712C2211yescharacteristic
54C3×#3712C2211yescharacteristic, complemented
55C3×#3711C2211yescharacteristic, complemented
56C3×#3711C2211yescharacteristic, complemented
57C3×#3711C2211yescharacteristic, complemented
58C3×#3711C2211yescharacteristic, complemented
59C3×#3710C2211yescharacteristic, complemented
60C3×D3×C3⋊C8C2211yescharacteristic, complemented
61C3×D3×C3⋊C8C2211yescharacteristic, complemented
62#64306—31no—
63D3×#235—31no—
64D3×#235—31no—
65#64116—31no—
66#64110—31no—
67C2×#3743—31no—
68C3×#907—31no—
69C3×D3×M16—31no—
70C3×#901—31no—
71C3×#901—31no—
72C3×#901—31no—
73C2×C3×ΓL(1,𝔽25)—31no—
74C2×#3711—31no—
75#63818—31no—
76#63817—31no—
77#63817—31no—
78#63815—31no—
79#63815—31no—
80#63815—31no—
81#63814—31no—
82D3×#208—31no—
83#63805—31no—
84#63805—31no—
85#63804—31no—
86#63804—31no—
87#63804—31no—
88#63804—31no—
89#63804—31no—
90#63804—31no—
91#63804—31no—
92#63804—61no—
93#63804—61no—
94#63804D311yescharacteristic, complemented
95#63803—31no—
96#63803D311yescharacteristic, complemented
97#63791—31no—
98#63791—31no—
99#63791—31no—
100#63791—31no—
101D3×ΓL(1,𝔽25)—31no—
102D3×ΓL(1,𝔽25)—31no—
103D3×ΓL(1,𝔽25)—31no—
104D3×ΓL(1,𝔽25)—31no—
105D3×ΓL(1,𝔽25)—31no—
106D3×ΓL(1,𝔽25)—31no—
107D3×ΓL(1,𝔽25)—31no—
108D3×ΓL(1,𝔽25)—61no—
109D3×ΓL(1,𝔽25)D311yescharacteristic, complemented
110C2×#1113C2×C411yescharacteristic
111C2×D3×C3⋊D3C2×C411yescharacteristic
112C2×C3×D32C2×C411yescharacteristic
113C4×C3⋊(C3⋊D3)C2311yescharacteristic
114C3×C4×C3⋊D3C2311yescharacteristic
115C3×C4×C3⋊D3C2311yescharacteristic
116C3×C4×C3⋊D3C2311yescharacteristic
117C32×C4×D3C2311yescharacteristic
118C32×C4×D3C2311yescharacteristic
119C32×C4×D3C2311yescharacteristic
120#6294C2×C411yescharacteristic
121#6294C2×C411yescharacteristic
122#6294C2×C411yescharacteristic
123#6293C2×C411yescharacteristic
124#6293C2×C411yescharacteristic
125#6292C2×C411yescharacteristic
126#6292C2×C411yescharacteristic
127#6291C2×C411yescharacteristic
128#6291C2×C411yescharacteristic
129#6290C2×C411yescharacteristic
130#6290C2×C411yescharacteristic
131#6289C2×C411yescharacteristic
132Dic3×C3⋊D3C2×C411yescharacteristic
133D3×C3⋊Dic3C2×C411yescharacteristic
134C3×#627C2×C411yescharacteristic
135C3×#627C2×C411yescharacteristic
136C3×#626C2×C411yescharacteristic
137C3×#626C2×C411yescharacteristic
138C3×#626C2×C411yescharacteristic
139C3×#626C2×C411yescharacteristic
140C3×#625C2×C411yescharacteristic
141C3×#625C2×C411yescharacteristic
142C3×#624C2×C411yescharacteristic
143C3×D3×Dic3C2×C411yescharacteristic
144C3×D3×Dic3C2×C411yescharacteristic
145C33×C8C2311yescharacteristic
146C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
147C3×C3⋊(C3⋊C8)C2311yescharacteristic
148C3×C3⋊(C3⋊C8)C2311yescharacteristic
149C3×C3⋊(C3⋊C8)C2311yescharacteristic
150C32×C3⋊C8C2311yescharacteristic
151C32×C3⋊C8C2311yescharacteristic
152C32×C3⋊C8C2311yescharacteristic
153#5750—91no—
154#5750—91no—
155#5745—91no—
156#3828—31no—
157#3828—31no—
158C2×C4×C3⋊D3—31no—
159C3×#235—31no—
160C3×#235—31no—
161C3×#235—31no—
162C3×#235—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165#3811—31no—
166#3811—31no—
167D3×#67—31no—
168D3×#67—31no—
169D3×#67—31no—
170D3×#67—31no—
171#3805—31no—
172#3805—31no—
173#3804—31no—
174#3804—31no—
175#3804—31no—
176#3804—31no—
177#3802—31no—
178D3×D12—31no—
179D3×D12—31no—
180C4×D32—31no—
181C4×D32—31no—
182C4×D32—31no—
183C4×D32—31no—
184C4×D32—31no—
185C4×D32—61no—
186C4×D32C2×D311yescharacteristic
187#3799—31no—
188#3799—31no—
189#3798—31no—
190#3798—31no—
191#3798—31no—
192#3798—31no—
193#3798—61no—
194#3798—61no—
195#3798C2×D311yescharacteristic
196#3798C2×D311yescharacteristic
197#3797—31no—
198#3796—31no—
199#3796—31no—
200#3795—31no—
201#3795—31no—
202D3×Dic6—31no—
203D3×Dic6—31no—
204C32×M16—31no—
205C2×C32×C8—31no—
206C2×C32×C8—31no—
207#3748—31no—
208C2×C3⋊(C3⋊C8)—31no—
209C2×C3⋊(C3⋊C8)—31no—
210#3743—31no—
211#3743—31no—
212#3743—31no—
213#3743—31no—
214#3743—31no—
215#3743—31no—
216#3743—61no—
217#3743—61no—
218#3743—61no—
219#3743—121no—
220#3743C2×D311yescharacteristic
221#3743C2×D311yescharacteristic, complemented
222C8×C3⋊D3—31no—
223C8×C3⋊D3—31no—
224C8×C3⋊D3—31no—
225C8×C3⋊D3C2×D311yescharacteristic, complemented
226C3×#208—31no—
227C3×#208—31no—
228C3×#208—31no—
229C3×#208—31no—
230C2×C3×C3⋊C8—31no—
231C2×C3×C3⋊C8—31no—
232C3×ΓL(1,𝔽25)—21no—
233C3×ΓL(1,𝔽25)—31no—
234C3×ΓL(1,𝔽25)—31no—
235C3×ΓL(1,𝔽25)—31no—
236C3×ΓL(1,𝔽25)—31no—
237C3×ΓL(1,𝔽25)—31no—
238C3×ΓL(1,𝔽25)—31no—
239C3×ΓL(1,𝔽25)—31no—
240C3×ΓL(1,𝔽25)—31no—
241C3×ΓL(1,𝔽25)—31no—
242C3×ΓL(1,𝔽25)—31no—
243C3×ΓL(1,𝔽25)—31no—
244C3×ΓL(1,𝔽25)—31no—
245C3×ΓL(1,𝔽25)—61no—
246C3×ΓL(1,𝔽25)—61no—
247C3×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
248C3×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
249C3×D3×C8—21no—
250C3×D3×C8—21no—
251C3×D3×C8—31no—
252C3×D3×C8—31no—
253C3×D3×C8—31no—
254C3×D3×C8—31no—
255C3×D3×C8—31no—
256C3×D3×C8—31no—
257C3×D3×C8—61no—
258C3×D3×C8C2×D311yescharacteristic, complemented
259C3×D3×C8C2×D311yescharacteristic, complemented
260C3×D3×C8C2×D311yescharacteristic, complemented
261C3×D3×C8C2×D311yescharacteristic, complemented
262#3712—31no—
263#3712—31no—
264#3712—31no—
265#3712—31no—
266#3712—61no—
267#3712C2×D311yescharacteristic
268#3712C2×D311yescharacteristic, complemented
269#3711—31no—
270#3711—31no—
271#3711—31no—
272#3711—31no—
273#3711—31no—
274#3711—31no—
275#3711—31no—
276#3711—31no—
277#3711—31no—
278#3711—31no—
279#3711—61no—
280#3711—61no—
281#3711—61no—
282#3711C2×D311yescharacteristic, complemented
283#3711C2×D311yescharacteristic, complemented
284#3711C2×D311yescharacteristic, complemented
285#3711C2×D311yescharacteristic, complemented
286#3710—31no—
287#3710—31no—
288#3710—31no—
289#3710—31no—
290#3710—31no—
291#3710—61no—
292#3710—61no—
293#3710C2×D311yescharacteristic, complemented
294D3×C3⋊C8—31no—
295D3×C3⋊C8—31no—
296D3×C3⋊C8—31no—
297D3×C3⋊C8—31no—
298D3×C3⋊C8—31no—
299D3×C3⋊C8—31no—
300D3×C3⋊C8—31no—
301D3×C3⋊C8—31no—
302D3×C3⋊C8—61no—
303D3×C3⋊C8—61no—
304D3×C3⋊C8—61no—
305D3×C3⋊C8C2×D311yescharacteristic, complemented
306D3×C3⋊C8C2×D311yescharacteristic, complemented
307C2×C3⋊(C3⋊D3)C22×C411yescharacteristic
308C2×C3×C3⋊D3C22×C411yescharacteristic
309C2×C3×C3⋊D3C22×C411yescharacteristic
310C2×C3×C3⋊D3C22×C411yescharacteristic
311C2×C32×D3C22×C411yescharacteristic
312C2×C32×D3C22×C411yescharacteristic
313C2×C32×D3C22×C411yescharacteristic
314#1113—41no—
315D3×C3⋊D3—41no—
316C3×D32—41no—
317C33×C4C2411yescharacteristic
318C3⋊(C3⋊Dic3)C22×C411yescharacteristic
319C3×C3⋊Dic3C22×C411yescharacteristic
320C3×C3⋊Dic3C22×C411yescharacteristic
321C3×C3⋊Dic3C22×C411yescharacteristic
322C32×Dic3C22×C411yescharacteristic
323C32×Dic3C22×C411yescharacteristic
324C32×Dic3C22×C411yescharacteristic
325D3×#41—91no—
326D3×#41—91no—
327C2×#235—91no—
328C3×#131—91no—
329C3×#131—91no—
330C2×C3×M16—91no—
331#948—91no—
332#948—91no—
333C2×#208—91no—
334#907—31no—
335#907—91no—
336#907—91no—
337#907—91no—
338#907—91no—
339#907—91no—
340#907—91no—
341#907—91no—
342#907—91no—
343#907—91no—
344#907—181no—
345D3×M16—31no—
346D3×M16—91no—
347D3×M16—91no—
348D3×M16—91no—
349D3×M16—91no—
350D3×M16—91no—
351D3×M16—91no—
352D3×M16—91no—
353D3×M16—91no—
354D3×M16—91no—
355#901—31no—
356#901—31no—
357#901—31no—
358#901—91no—
359#901—91no—
360#901—91no—
361#901—91no—
362#901—91no—
363#901—91no—
364#901—91no—
365#901—181no—
366C2×ΓL(1,𝔽25)—31no—
367C2×ΓL(1,𝔽25)—91no—
368C2×ΓL(1,𝔽25)—91no—
369C2×ΓL(1,𝔽25)—91no—
370C2×ΓL(1,𝔽25)—91no—
371C2×ΓL(1,𝔽25)—91no—
372C2×ΓL(1,𝔽25)—181no—
373C22×C3⋊D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—31no—
376C2×D32—31no—
377C2×D32—31no—
378C2×D32—31no—
379C2×D32—31no—
380C2×D32—31no—
381C2×D32—61no—
382C2×D32C4×D311yescharacteristic
383C2×C32×C4—31no—
384C2×C32×C4—31no—
385C2×C32×C4—31no—
386#638—31no—
387#638—31no—
388#638—31no—
389#638—31no—
390C2×C3⋊Dic3—31no—
391C4⋊(C3⋊D3)—31no—
392C4⋊(C3⋊D3)—31no—
393C4×C3⋊D3—31no—
394C4×C3⋊D3—31no—
395C4×C3⋊D3—31no—
396C4×C3⋊D3—31no—
397C4×C3⋊D3—31no—
398C4×C3⋊D3—61no—
399C4×C3⋊D3—61no—
400C4×C3⋊D3—61no—
401C4×C3⋊D3—121no—
402C4×C3⋊D3C22×D311yescharacteristic
403C4×C3⋊D3C22×D311yescharacteristic
404C4×C3⋊D3C22×D311yescharacteristic
405#634—31no—
406#634—31no—
407C3×#67—31no—
408C3×#67—31no—
409C3×#67—31no—
410C3×#67—31no—
411C3×#67—31no—
412C3×#67—31no—
413C3×#67—31no—
414C3×#67—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C3×D12—31no—
418C3×D12—31no—
419C3×D12—31no—
420C3×D12—31no—
421C3×C4×D3—21no—
422C3×C4×D3—21no—
423C3×C4×D3—21no—
424C3×C4×D3—31no—
425C3×C4×D3—31no—
426C3×C4×D3—31no—
427C3×C4×D3—31no—
428C3×C4×D3—31no—
429C3×C4×D3—31no—
430C3×C4×D3—31no—
431C3×C4×D3—31no—
432C3×C4×D3—31no—
433C3×C4×D3—31no—
434C3×C4×D3—61no—
435C3×C4×D3—61no—
436C3×C4×D3—61no—
437C3×C4×D3C22×D311yescharacteristic
438C3×C4×D3C22×D311yescharacteristic
439C3×C4×D3C22×D311yescharacteristic
440C3×C4×D3C22×D311yescharacteristic
441C3×C4×D3C22×D311yescharacteristic
442C3×C4×D3C22×D311yescharacteristic
443C3×Dic6—31no—
444C3×Dic6—31no—
445C3×Dic6—31no—
446C3×Dic6—31no—
447#627—31no—
448#627—31no—
449#627—31no—
450#627—31no—
451#627—61no—
452#627—61no—
453#627C4×D311yescharacteristic
454#627C4×D311yescharacteristic
455#626—31no—
456#626—31no—
457#626—31no—
458#626—31no—
459#626—31no—
460#626—31no—
461#626—31no—
462#626—31no—
463#626—61no—
464#626—61no—
465#626—61no—
466#626—61no—
467#626C4×D311yescharacteristic
468#626C4×D311yescharacteristic
469#626C4×D311yescharacteristic
470#626C4×D311yescharacteristic
471#625—31no—
472#625—31no—
473#625—31no—
474#625—31no—
475#625—61no—
476#625—61no—
477#625C4×D311yescharacteristic
478#625C4×D311yescharacteristic
479#624—31no—
480#624—31no—
481#624—31no—
482#624—31no—
483#624—31no—
484#624—61no—
485#624C4×D311yescharacteristic
486D3×Dic3—31no—
487D3×Dic3—31no—
488D3×Dic3—31no—
489D3×Dic3—31no—
490D3×Dic3—31no—
491D3×Dic3—31no—
492D3×Dic3—31no—
493D3×Dic3—31no—
494D3×Dic3—31no—
495D3×Dic3—31no—
496D3×Dic3—61no—
497D3×Dic3—61no—
498D3×Dic3C4×D311yescharacteristic
499D3×Dic3C4×D311yescharacteristic
500C32×C8—21no—
501C32×C8—21no—
502C32×C8—21no—
503C32×C8—31no—
504C32×C8—31no—
505C32×C8—31no—
506C32×C8—41no—
507C32×C8C22×D311yescharacteristic
508C32×C8C22×D311yescharacteristic
509C32×C8C22×D311yescharacteristic
510C3⋊(C3⋊C8)—31no—
511C3⋊(C3⋊C8)—31no—
512C3⋊(C3⋊C8)—31no—
513C3⋊(C3⋊C8)—61no—
514C3⋊(C3⋊C8)—61no—
515C3⋊(C3⋊C8)—61no—
516C3⋊(C3⋊C8)—121no—
517C3⋊(C3⋊C8)C22×D311yescharacteristic
518C3⋊(C3⋊C8)C22×D311yescharacteristic
519C3⋊(C3⋊C8)C22×D311yescharacteristic
520C3×C3⋊C8—21no—
521C3×C3⋊C8—21no—
522C3×C3⋊C8—21no—
523C3×C3⋊C8—31no—
524C3×C3⋊C8—31no—
525C3×C3⋊C8—31no—
526C3×C3⋊C8—31no—
527C3×C3⋊C8—31no—
528C3×C3⋊C8—31no—
529C3×C3⋊C8—61no—
530C3×C3⋊C8—61no—
531C3×C3⋊C8—61no—
532C3×C3⋊C8C22×D311yescharacteristic
533C3×C3⋊C8C22×D311yescharacteristic
534C3×C3⋊C8C22×D311yescharacteristic
535C3×C3⋊C8C22×D311yescharacteristic
536C3×C3⋊C8C22×D311yescharacteristic
537C3×C3⋊C8C22×D311yescharacteristic
538#568—271noSylow
539C2×C33C23×C411yescharacteristic
540C3⋊(C3⋊D3)—21no—
541C3×C3⋊D3—21no—
542C3×C3⋊D3—21no—
543C3×C3⋊D3—21no—
544C32×D3—21no—
545C32×D3—21no—
546C32×D3—21no—
547C3×#41—91no—
548C3×#41—91no—
549C22×C3×C4—91no—
550C2×#67—91no—
551C2×#67—91no—
552#239—91no—
553#239—91no—
554D3×Q8—91no—
555D3×Q8—91no—
556#237—91no—
557#237—91no—
558#237—91no—
559#237—91no—
560#237—91no—
561#237—91no—
562D3×D4—91no—
563D3×D4—91no—
564D3×D4—91no—
565D3×D4—91no—
566D3×D4—91no—
567D3×D4—91no—
568#235—31no—
569#235—31no—
570#235—31no—
571#235—31no—
572#235—91no—
573#235—91no—
574#235—91no—
575#235—91no—
576#235—91no—
577#235—91no—
578#235—91no—
579#235—91no—
580#235—91no—
581#235—91no—
582#235—181no—
583#235—181no—
584C2×D12—91no—
585C2×C4×D3—31no—
586C2×C4×D3—31no—
587C2×C4×D3—91no—
588C2×C4×D3—91no—
589C2×C4×D3—91no—
590C2×C4×D3—91no—
591C2×C4×D3—91no—
592C2×C4×D3—91no—
593C2×C4×D3—181no—
594C2×Dic6—91no—
595C3×M16—31no—
596C3×M16—31no—
597C3×M16—61no—
598C3×M16—91no—
599C3×M16—91no—
600C3×M16—91no—
601C3×M16—91no—
602C3×M16—91no—
603C3×M16—91no—
604C3×M16—91no—
605C3×M16—91no—
606C2×C3×C8—31no—
607C2×C3×C8—31no—
608C2×C3×C8—31no—
609C2×C3×C8—31no—
610C2×C3×C8—61no—
611C2×C3×C8—61no—
612C2×C3×C8—91no—
613C2×C3×C8—91no—
614C2×C3×C8—91no—
615C2×C3×C8—91no—
616#208—31no—
617#208—31no—
618#208—31no—
619#208—31no—
620#208—91no—
621#208—91no—
622#208—91no—
623#208—91no—
624#208—91no—
625#208—91no—
626#208—181no—
627C2×C3⋊C8—31no—
628C2×C3⋊C8—31no—
629C2×C3⋊C8—91no—
630C2×C3⋊C8—91no—
631C2×C3⋊C8—91no—
632C2×C3⋊C8—91no—
633C2×C3⋊C8—91no—
634C2×C3⋊C8—91no—
635C2×C3⋊C8—181no—
636C2×C3⋊C8—181no—
637ΓL(1,𝔽25)—31no—
638ΓL(1,𝔽25)—31no—
639ΓL(1,𝔽25)—31no—
640ΓL(1,𝔽25)—31no—
641ΓL(1,𝔽25)—31no—
642ΓL(1,𝔽25)—31no—
643ΓL(1,𝔽25)—31no—
644ΓL(1,𝔽25)—31no—
645ΓL(1,𝔽25)—31no—
646ΓL(1,𝔽25)—31no—
647ΓL(1,𝔽25)—31no—
648ΓL(1,𝔽25)—31no—
649ΓL(1,𝔽25)—61no—
650ΓL(1,𝔽25)—61no—
651ΓL(1,𝔽25)—91no—
652ΓL(1,𝔽25)—91no—
653ΓL(1,𝔽25)—91no—
654ΓL(1,𝔽25)—91no—
655ΓL(1,𝔽25)—91no—
656ΓL(1,𝔽25)—91no—
657ΓL(1,𝔽25)—91no—
658ΓL(1,𝔽25)—91no—
659ΓL(1,𝔽25)—91no—
660ΓL(1,𝔽25)—91no—
661ΓL(1,𝔽25)—91no—
662ΓL(1,𝔽25)—91no—
663ΓL(1,𝔽25)—91no—
664ΓL(1,𝔽25)—91no—
665ΓL(1,𝔽25)—91no—
666ΓL(1,𝔽25)—181no—
667ΓL(1,𝔽25)—181no—
668ΓL(1,𝔽25)—181no—
669ΓL(1,𝔽25)—181no—
670ΓL(1,𝔽25)—181no—
671ΓL(1,𝔽25)—181no—
672ΓL(1,𝔽25)—361no—
673ΓL(1,𝔽25)D3211yescharacteristic, complemented
674D3×C8—31no—
675D3×C8—31no—
676D3×C8—31no—
677D3×C8—31no—
678D3×C8—31no—
679D3×C8—31no—
680D3×C8—61no—
681D3×C8—91no—
682D3×C8—91no—
683D3×C8—91no—
684D3×C8—91no—
685D3×C8—91no—
686D3×C8—91no—
687D3×C8—91no—
688D3×C8—91no—
689D3×C8—91no—
690D3×C8—91no—
691D3×C8—91no—
692D3×C8—91no—
693D3×C8—181no—
694D3×C8—181no—
695D3×C8—181no—
696D3×C8D3211yescharacteristic, complemented
697D3×C8D3211yescharacteristic, complemented
698C22×C32—31no—
699C22×C32—31no—
700C22×C32—31no—
701C2×C3⋊D3—31no—
702C2×C3⋊D3—31no—
703C2×C3⋊D3—31no—
704C2×C3⋊D3—61no—
705C2×C3⋊D3—61no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3C2×C4×D311yescharacteristic
710C2×C3⋊D3C2×C4×D311yescharacteristic
711C2×C3⋊D3C2×C4×D311yescharacteristic
712C2×C3×D3—21no—
713C2×C3×D3—21no—
714C2×C3×D3—21no—
715C2×C3×D3—31no—
716C2×C3×D3—31no—
717C2×C3×D3—31no—
718C2×C3×D3—31no—
719C2×C3×D3—31no—
720C2×C3×D3—31no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—61no—
724C2×C3×D3—121no—
725C2×C3×D3—121no—
726C2×C3×D3C2×C4×D311yescharacteristic
727C2×C3×D3C2×C4×D311yescharacteristic
728C2×C3×D3C2×C4×D311yescharacteristic
729C2×C3×D3C2×C4×D311yescharacteristic
730C2×C3×D3C2×C4×D311yescharacteristic
731C2×C3×D3C2×C4×D311yescharacteristic
732D32—41no—
733D32—121no—
734D32—121no—
735D32—122no—
736D32—121no—
737D32—121no—
738D32—121no—
739C32×C4—21no—
740C32×C4—21no—
741C32×C4—21no—
742C32×C4—31no—
743C32×C4—31no—
744C32×C4—31no—
745C32×C4—41no—
746C32×C4C23×D311yescharacteristic
747C32×C4C23×D311yescharacteristic
748C32×C4C23×D311yescharacteristic
749C3⋊Dic3—31no—
750C3⋊Dic3—31no—
751C3⋊Dic3—31no—
752C3⋊Dic3—61no—
753C3⋊Dic3—61no—
754C3⋊Dic3—61no—
755C3⋊Dic3—121no—
756C3⋊Dic3C2×C4×D311yescharacteristic
757C3⋊Dic3C2×C4×D311yescharacteristic
758C3⋊Dic3C2×C4×D311yescharacteristic
759C3×Dic3—21no—
760C3×Dic3—21no—
761C3×Dic3—21no—
762C3×Dic3—31no—
763C3×Dic3—31no—
764C3×Dic3—31no—
765C3×Dic3—31no—
766C3×Dic3—31no—
767C3×Dic3—31no—
768C3×Dic3—61no—
769C3×Dic3—61no—
770C3×Dic3—61no—
771C3×Dic3C2×C4×D311yescharacteristic
772C3×Dic3C2×C4×D311yescharacteristic
773C3×Dic3C2×C4×D311yescharacteristic
774C3×Dic3C2×C4×D311yescharacteristic
775C3×Dic3C2×C4×D311yescharacteristic
776C3×Dic3C2×C4×D311yescharacteristic
777C2×#41—271no—
778#131—91no—
779#131—91no—
780#131—271no—
781#131—271no—
782#131—271no—
783#131—271no—
784#131—271no—
785#131—271no—
786C2×M16—91no—
787C2×M16—271no—
788C2×M16—271no—
789C2×M16—271no—
790C2×M16—271no—
791C2×M16—271no—
792C33#56811yescharacteristic, complemented, Sylow
793C23×C3—91no—
794C22×D3—31no—
795C22×D3—31no—
796C22×D3—91no—
797C22×D3—91no—
798C22×D3—91no—
799C22×D3—91no—
800C22×D3—91no—
801C22×D3—91no—
802C22×D3—181no—
803C3×Q8—91no—
804C3×Q8—91no—
805C3×D4—91no—
806C3×D4—91no—
807C3×D4—91no—
808C3×D4—91no—
809C3×D4—91no—
810C3×D4—91no—
811C2×C3×C4—31no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—61no—
818C2×C3×C4—61no—
819C2×C3×C4—61no—
820C2×C3×C4—91no—
821C2×C3×C4—91no—
822C2×C3×C4—91no—
823C2×C3×C4—91no—
824C2×C3×C4—91no—
825C2×C3×C4—91no—
826#67—31no—
827#67—31no—
828#67—31no—
829#67—31no—
830#67—31no—
831#67—31no—
832#67—31no—
833#67—31no—
834#67—91no—
835#67—91no—
836#67—91no—
837#67—91no—
838#67—91no—
839#67—91no—
840#67—91no—
841#67—91no—
842#67—91no—
843#67—91no—
844#67—91no—
845#67—91no—
846#67—181no—
847#67—181no—
848#67—181no—
849#67—181no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—91no—
853C2×Dic3—91no—
854C2×Dic3—91no—
855C2×Dic3—91no—
856C2×Dic3—91no—
857C2×Dic3—91no—
858C2×Dic3—181no—
859D12—31no—
860D12—31no—
861D12—31no—
862D12—31no—
863D12—91no—
864D12—91no—
865D12—91no—
866D12—91no—
867D12—91no—
868D12—91no—
869D12—181no—
870D12—181no—
871C4×D3—31no—
872C4×D3—31no—
873C4×D3—31no—
874C4×D3—31no—
875C4×D3—31no—
876C4×D3—31no—
877C4×D3—31no—
878C4×D3—31no—
879C4×D3—31no—
880C4×D3—31no—
881C4×D3—61no—
882C4×D3—61no—
883C4×D3—61no—
884C4×D3—91no—
885C4×D3—91no—
886C4×D3—91no—
887C4×D3—91no—
888C4×D3—91no—
889C4×D3—91no—
890C4×D3—91no—
891C4×D3—91no—
892C4×D3—91no—
893C4×D3—91no—
894C4×D3—91no—
895C4×D3—91no—
896C4×D3—91no—
897C4×D3—91no—
898C4×D3—91no—
899C4×D3—181no—
900C4×D3—181no—
901C4×D3—181no—
902C4×D3—181no—
903C4×D3—181no—
904C4×D3—361no—
905C4×D3C2×D3211yescharacteristic
906C4×D3C2×D3211yescharacteristic
907C4×D3C2×D3211yescharacteristic
908Dic6—31no—
909Dic6—31no—
910Dic6—31no—
911Dic6—31no—
912Dic6—91no—
913Dic6—91no—
914Dic6—91no—
915Dic6—91no—
916Dic6—91no—
917Dic6—91no—
918Dic6—181no—
919Dic6—181no—
920C3×C8—21no—
921C3×C8—21no—
922C3×C8—21no—
923C3×C8—31no—
924C3×C8—31no—
925C3×C8—31no—
926C3×C8—31no—
927C3×C8—31no—
928C3×C8—31no—
929C3×C8—41no—
930C3×C8—61no—
931C3×C8—61no—
932C3×C8—61no—
933C3×C8—91no—
934C3×C8—91no—
935C3×C8—91no—
936C3×C8C2×D3211yescharacteristic
937C3×C8C2×D3211yescharacteristic
938C3×C8C2×D3211yescharacteristic
939C3⋊C8—31no—
940C3⋊C8—31no—
941C3⋊C8—31no—
942C3⋊C8—31no—
943C3⋊C8—31no—
944C3⋊C8—31no—
945C3⋊C8—61no—
946C3⋊C8—61no—
947C3⋊C8—61no—
948C3⋊C8—91no—
949C3⋊C8—91no—
950C3⋊C8—91no—
951C3⋊C8—181no—
952C3⋊C8—181no—
953C3⋊C8—181no—
954C3⋊C8—361no—
955C3⋊C8C2×D3211yescharacteristic
956C3⋊C8C2×D3211yescharacteristic
957C3⋊C8C2×D3211yescharacteristic
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—21no—
961C2×C32—41no—
962C2×C32—61no—
963C2×C32—61no—
964C2×C32—61no—
965C2×C32C22×C4×D311yescharacteristic
966C2×C32C22×C4×D311yescharacteristic
967C2×C32C22×C4×D311yescharacteristic
968C3⋊D3—21no—
969C3⋊D3—21no—
970C3⋊D3—21no—
971C3⋊D3—61no—
972C3⋊D3—61no—
973C3⋊D3—61no—
974C3⋊D3—121no—
975C3⋊D3—121no—
976C3⋊D3—121no—
977C3⋊D3—241no—
978C3×D3—22no—
979C3×D3—21no—
980C3×D3—21no—
981C3×D3—21no—
982C3×D3—21no—
983C3×D3—21no—
984C3×D3—21no—
985C3×D3—41no—
986C3×D3—41no—
987C3×D3—61no—
988C3×D3—61no—
989C3×D3—61no—
990C3×D3—61no—
991C3×D3—61no—
992C3×D3—61no—
993C3×D3—121no—
994C3×D3—121no—
995C3×D3—121no—
996#41—91no—
997#41—91no—
998#41—271no—
999#41—271no—
1000#41—271no—
1001#41—271no—
1002#41—271no—
1003#41—271no—
1004C2×Q8—271no—
1005C2×D4—271no—
1006C2×D4—271no—
1007C2×D4—271no—
1008C22×C4—91no—
1009C22×C4—271no—
1010C22×C4—271no—
1011M16—31no—
1012M16—91no—
1013M16—91no—
1014M16—91no—
1015M16—91no—
1016M16—91no—
1017M16—91no—
1018M16—91no—
1019M16—91no—
1020M16—271no—
1021M16—271no—
1022M16—271no—
1023M16—271no—
1024M16—271no—
1025M16—271no—
1026M16—271no—
1027C2×C8—31no—
1028C2×C8—31no—
1029C2×C8—91no—
1030C2×C8—91no—
1031C2×C8—91no—
1032C2×C8—91no—
1033C2×C8—271no—
1034C2×C8—271no—
1035C2×C8—271no—
1036C2×C8—271no—
1037C2×C8—271no—
1038C2×C8—271no—
1039C22×C3—31no—
1040C22×C3—31no—
1041C22×C3—31no—
1042C22×C3—31no—
1043C22×C3—31no—
1044C22×C3—31no—
1045C22×C3—61no—
1046C22×C3—61no—
1047C22×C3—61no—
1048C22×C3—91no—
1049C22×C3—91no—
1050C22×C3—91no—
1051C22×C3—361no—
1052C2×D3—31no—
1053C2×D3—31no—
1054C2×D3—31no—
1055C2×D3—31no—
1056C2×D3—31no—
1057C2×D3—31no—
1058C2×D3—61no—
1059C2×D3—61no—
1060C2×D3—61no—
1061C2×D3—91no—
1062C2×D3—91no—
1063C2×D3—91no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—181no—
1067C2×D3—181no—
1068C2×D3—181no—
1069C2×D3—361no—
1070C2×D3—361no—
1071C2×D3—361no—
1072C2×D3—361no—
1073C2×D3—361no—
1074C2×D3—361no—
1075C2×D3—361no—
1076C2×D3—362no—
1077C2×D3C4×D3211yescharacteristic
1078C2×D3C4×D3211yescharacteristic
1079C2×D3C4×D3211yescharacteristic
1080C3×C4—21no—
1081C3×C4—21no—
1082C3×C4—21no—
1083C3×C4—31no—
1084C3×C4—31no—
1085C3×C4—31no—
1086C3×C4—31no—
1087C3×C4—31no—
1088C3×C4—31no—
1089C3×C4—41no—
1090C3×C4—61no—
1091C3×C4—61no—
1092C3×C4—61no—
1093C3×C4—91no—
1094C3×C4—91no—
1095C3×C4—91no—
1096C3×C4C22×D3211yescharacteristic
1097C3×C4C22×D3211yescharacteristic
1098C3×C4C22×D3211yescharacteristic
1099Dic3—31no—
1100Dic3—31no—
1101Dic3—31no—
1102Dic3—31no—
1103Dic3—31no—
1104Dic3—31no—
1105Dic3—61no—
1106Dic3—61no—
1107Dic3—61no—
1108Dic3—91no—
1109Dic3—91no—
1110Dic3—91no—
1111Dic3—181no—
1112Dic3—181no—
1113Dic3—181no—
1114Dic3—361no—
1115Dic3C4×D3211yescharacteristic
1116Dic3C4×D3211yescharacteristic
1117Dic3C4×D3211yescharacteristic
1118C32—21no—
1119C32—21no—
1120C32—21no—
1121C32—41no—
1122C32#574511yescharacteristic, complemented
1123C32#575011yescharacteristic, complemented
1124C32#575011yescharacteristic, complemented
1125C23—91no—
1126C23—271no—
1127C23—271no—
1128Q8—91no—
1129Q8—91no—
1130Q8—271no—
1131Q8—271no—
1132D4—91no—
1133D4—91no—
1134D4—91no—
1135D4—91no—
1136D4—91no—
1137D4—91no—
1138D4—271no—
1139D4—271no—
1140D4—271no—
1141D4—271no—
1142D4—271no—
1143D4—271no—
1144C2×C4—31no—
1145C2×C4—31no—
1146C2×C4—31no—
1147C2×C4—91no—
1148C2×C4—91no—
1149C2×C4—91no—
1150C2×C4—91no—
1151C2×C4—91no—
1152C2×C4—91no—
1153C2×C4—271no—
1154C2×C4—271no—
1155C2×C4—271no—
1156C2×C4—271no—
1157C2×C4—271no—
1158C2×C4—271no—
1159C2×C4—271no—
1160C8—31no—
1161C8—31no—
1162C8—31no—
1163C8—91no—
1164C8—91no—
1165C8—91no—
1166C8—271no—
1167C8D3311yescharacteristic
1168C2×C3—21no—
1169C2×C3—21no—
1170C2×C3—21no—
1171C2×C3—41no—
1172C2×C3—62no—
1173C2×C3—61no—
1174C2×C3—61no—
1175C2×C3—61no—
1176C2×C3—61no—
1177C2×C3—61no—
1178C2×C3—61no—
1179C2×C3—121no—
1180C2×C3—121no—
1181C2×C3—181no—
1182C2×C3—181no—
1183C2×C3—181no—
1184C2×C3C2×C4×D3211yescharacteristic
1185C2×C3C2×C4×D3211yescharacteristic
1186C2×C3C2×C4×D3211yescharacteristic
1187D3—21no—
1188D3—21no—
1189D3—21no—
1190D3—61no—
1191D3—61no—
1192D3—61no—
1193D3—61no—
1194D3—61no—
1195D3—61no—
1196D3—121no—
1197D3—121no—
1198D3—121no—
1199D3—181no—
1200D3—181no—
1201D3—181no—
1202D3—361no—
1203D3—361no—
1204D3—361no—
1205D3—721no—
1206C22—31no—
1207C22—31no—
1208C22—31no—
1209C22—91no—
1210C22—91no—
1211C22—91no—
1212C22—271no—
1213C22—361no—
1214C22—1081no—
1215C22—1081no—
1216C4—31no—
1217C4—31no—
1218C4—31no—
1219C4—91no—
1220C4—91no—
1221C4—91no—
1222C4—271no—
1223C4C2×D3311yescharacteristic
1224C3—21no—
1225C3—21no—
1226C3—21no—
1227C3—41no—
1228C3#1059466811yescharacteristic, complemented
1229C3#1059467011yescharacteristic, complemented
1230C3#1059470611yescharacteristic, complemented
1231C2—61no—
1232C2—61no—
1233C2—61no—
1234C2—181no—
1235C2—181no—
1236C2—181no—
1237C2—541no—
1238C2C4×D3311yescharacteristic
subgroupG/H
center, FrattiniC4C2×D33
commutator, socleC2×C33C23×C4
FittingC33×C8C23
prime radical#11724387C2
cosocleC33×C4C24
hypercenterC8D33
hypocenterC33#568
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
2. #11723645C2semidirect
3. #11723333C2semidirect
4. #11723332C2semidirect
5. D3×#3743C2semidirect
6. C3×#63804C2semidirect
7. C3×#63803C2semidirect
8. C3×D3×ΓL(1,𝔽25)C2semidirect
9. #11722825C2semidirect
10. #11722824C2semidirect
11. #11722823C2semidirect
12. #11722822C2semidirect
13. #11722820C2semidirect
14. #11722819C2semidirect
15. D3×#3711C2semidirect
34. #88850C22semidirect
36. C3×#3743C22semidirect
37. C3×C8×C3⋊D3C22semidirect
38. C32×ΓL(1,𝔽25)C22semidirect
39. C32×D3×C8C22semidirect
40. C32×D3×C8C22semidirect
42. #88809C22semidirect
43. #88808C22semidirect
44. #88788C22semidirect
46. #88787C22semidirect
47. #88786C22semidirect
48. #88785C22semidirect
49. #88785C22semidirect
50. C3⋊D3×C3⋊C8C22semidirect
51. D3×C3⋊(C3⋊C8)C22semidirect
52. D3×C3⋊(C3⋊C8)C22semidirect
54. C3×#3712C22semidirect
55. C3×#3711C22semidirect
56. C3×#3711C22semidirect
57. C3×#3711C22semidirect
58. C3×#3711C22semidirect
59. C3×#3710C22semidirect
60. C3×D3×C3⋊C8C22semidirect
61. C3×D3×C3⋊C8C22semidirect
94. #63804D3semidirect
96. #63803D3semidirect
109. D3×ΓL(1,𝔽25)D3semidirect
221. #3743C2×D3semidirect
225. C8×C3⋊D3C2×D3semidirect
247. C3×ΓL(1,𝔽25)C2×D3semidirect
248. C3×ΓL(1,𝔽25)C2×D3semidirect
258. C3×D3×C8C2×D3semidirect
259. C3×D3×C8C2×D3semidirect
260. C3×D3×C8C2×D3semidirect
261. C3×D3×C8C2×D3semidirect
268. #3712C2×D3semidirect
282. #3711C2×D3semidirect
283. #3711C2×D3semidirect
284. #3711C2×D3semidirect
285. #3711C2×D3semidirect
293. #3710C2×D3semidirect
305. D3×C3⋊C8C2×D3semidirect
306. D3×C3⋊C8C2×D3semidirect
673. ΓL(1,𝔽25)D32semidirect
696. D3×C8D32semidirect
697. D3×C8D32semidirect
792. C33#568semidirect
1122. C32#5745semidirect
1123. C32#5750semidirect
1124. C32#5750semidirect
1228. C3#10594668semidirect
1229. C3#10594670semidirect
1230. C3#10594706semidirect

Maximal subgroups

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

subgroupindex
#117243872
#117236452
#117233332
#117233322
D3×#37432
C3×#638042
C3×#638032
C3×D3×ΓL(1,𝔽25)2
#117228252
#117228242
#117228232
#117228222
#117228202
#117228192
D3×#37112
#105947063
#105946703
#105946683