Finite Group Databasebeta

← #11889725

Subgroups — #11889725

Order 1152.

914 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595018C211yesmaximal, characteristic
2#10594988C211yesmaximal, characteristic, complemented
3#10592430C211yesmaximal, characteristic, complemented
4C3×#4730C211yesmaximal, characteristic, complemented
5C3×#4722C211yesmaximal, characteristic, complemented
6#10591187C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590970C211yesmaximal, characteristic, complemented
9#10590893C211yesmaximal, characteristic, complemented
10#10590838C211yesmaximal, characteristic, complemented
11#10590813C211yesmaximal, characteristic, complemented
12#10590773C211yesmaximal, characteristic, complemented
13#10590764C211yesmaximal, characteristic, complemented
14#10590679C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#81486—31nomaximal
17#79503—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20#64133C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28#63981—21no—
29#63974—21no—
30Dic3×#67—21no—
31#63964—21no—
32#63918C2211yescharacteristic, complemented
33#63910—21no—
34#63909C2211yescharacteristic
35#63899—21no—
36#63897—21no—
37#63894C2211yescharacteristic
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63864C2211yescharacteristic
40#63857C2211yescharacteristic, complemented
41#63846—21no—
42#63844C2211yescharacteristic, complemented
43C2×#3719C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
48C3×#818C2211yescharacteristic, complemented
49C3×#818C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5630—31no—
62#5550—31no—
63#5543—31no—
64#5511—31no—
65C3×#484—31no—
66C3×#435—31no—
67#5134—31no—
68#5133—31no—
69#5116—31no—
70C2×#821—31no—
71#5051—31no—
72C2×#809—31no—
73#4890—31no—
74#4889—31no—
75#4886—31no—
76#4882—31no—
77#4846—31no—
78#4845—31no—
79#4808—31no—
80#4803—31no—
81#4798—31no—
82#4794—31no—
83#4736—31no—
84#4733—31no—
85#4731—31no—
86#4731—31no—
87#4731—61no—
88#4730D311yescharacteristic, complemented
89#4722D311yescharacteristic, complemented
90#4714—31no—
91#4710—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110#3799—22no—
111#3799—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3744—22no—
118#3744—41no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8—41no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3719—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C2×C3×M16—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#947—31no—
156C2×#216—31no—
157#937—61no—
158D4×Dic3—61no—
159#930—31no—
160C4×#67—61no—
161C4×#67C2×D311yescharacteristic
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3C2×D311yescharacteristic
164#924—31no—
165#924—31no—
166#924—31no—
167#924—61no—
168#924—61no—
169#924C2×D311yescharacteristic
170C22×C3⋊C8C2×D311yescharacteristic
171C2×Dic12—31no—
172C2×#204—31no—
173C2×#204—31no—
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—61no—
177C2×#204—61no—
178C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
179#897—31no—
180#896—61no—
181#895—31no—
182#895—61no—
183#894—61no—
184#894—61no—
185#893—31no—
186D3×C4⋊C4—31no—
187#890—61no—
188#889—61no—
189#888—31no—
190#887—31no—
191#884—61no—
192#882—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#878—61no—
196#878—61no—
197#875—31no—
198C4×D12—31no—
199#869—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8C2×D311yescharacteristic
209C3×C22⋊C8C2×D311yescharacteristic
210C3×#97—31no—
211#835—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#821—61no—
222(C2×D3)⋊C8C2×D311yescharacteristic, complemented
223#818—31no—
224#818C2×D311yescharacteristic, complemented
225#818C2×D311yescharacteristic, complemented
226#816—31no—
227#816—31no—
228#816C2×D311yescharacteristic, complemented
229#816C2×D311yescharacteristic, complemented
230#815C2×D311yescharacteristic, complemented
231Dic3⋊C8C2×D311yescharacteristic, complemented
232#810—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—42no—
255C4⋊(C3⋊D3)#4112yes—
256#634—21no—
257#634—21no—
258C3×#67—22no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#627—81no—
272#626—42no—
273#626—81no—
274#624—42no—
275#624—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C32×C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—31no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—31no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C23×D3—121no—
299C2×C3×Q8—31no—
300C2×C3×D4—31no—
301C22×C3×C4—21no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—61no—
307C2×#67—61no—
308C2×#67D1211yescharacteristic
309C22×Dic3—21no—
310C22×Dic3—61no—
311#239—62no—
312#239—121no—
313#235—62no—
314#235—121no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—62no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—122no—
328C2×D12—121no—
329C2×D12—121no—
330C2×D12—121no—
331C2×D12—122no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—61no—
343C2×Dic6C22×D311yescharacteristic
344C3×M16—121no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8—121no—
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364#217—21no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—121no—
369#217D1211yescharacteristic
370#216—121no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4D1211yescharacteristic
381C4⋊Dic3—21no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400Dic3⋊C4D1211yescharacteristic
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—41no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—121no—
408#204—62no—
409#204—62no—
410#204—122no—
411#204—121no—
412#204—121no—
413#204—122no—
414ΓL(1,𝔽25)—41no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32#13712yes—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—84no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C32×C4—21no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—91no—
442C22×D4—91no—
443C2×Q16—91no—
444C2×SD16—91no—
445C2×SD16—91no—
446C2×M16—31no—
447C22×C8—31no—
448C4⋊Q8—91no—
449#125—181no—
450#124—91no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457#121—91no—
458#121—181no—
459#120—181no—
460C4×Q8—91no—
461C4×D4—31no—
462C4×D4—91no—
463C4×D4—181no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—91no—
466C2×C22⋊C4—181no—
467#107—31no—
468#107—31no—
469#107—91no—
470C4⋊C8—31no—
471#103—31no—
472#103—31no—
473#103—91no—
474#103—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—31no—
482C22⋊C8D3211yescharacteristic
483#97—31no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3C2×D1211yescharacteristic
487C23×C3D3×D411yescharacteristic
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—121no—
493C22×D3—121no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—124no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—242no—
500C22×D3—241no—
501C22×D3—241no—
502C22×D3—242no—
503C22×D3C2×D1211yescharacteristic
504C3×Q8—61no—
505C3×Q8—61no—
506C3×D4—62no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—241no—
525C2×C3×C4C2×D1211yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—22no—
530#67—122no—
531#67—241no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—81no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—241no—
544C2×Dic3C2×D1211yescharacteristic
545C2×Dic3C2×D1211yescharacteristic
546C2×Dic3C2×D1211yescharacteristic
547D12—32no—
548D12—32no—
549D12—62no—
550D12—62no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—121no—
558D12—121no—
559D12—122no—
560D12—122no—
561D12—124no—
562D12—122no—
563D12—241no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—122no—
567C4×D3—122no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571Dic6—21no—
572Dic6—21no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—61no—
577Dic6—121no—
578Dic6—121no—
579Dic6—241no—
580Dic6—241no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—41no—
586C3×C8—41no—
587C3×C8—61no—
588C3×C8—61no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C2×C32—22no—
592C2×C32#54611yescharacteristic
593C2×C32C2×#13711yescharacteristic
594C2×C32#57611yescharacteristic
595C3⋊D3—42no—
596C3⋊D3—81no—
597C3×D3—41no—
598C24—181no—
599#41—182no—
600#41—361no—
601C2×Q8—31no—
602C2×Q8—91no—
603C2×Q8—181no—
604C2×D4—31no—
605C2×D4—91no—
606C2×D4—91no—
607C2×D4—182no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—361no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4C2×D3211yescharacteristic
618Q16—361no—
619SD16—182no—
620SD16—361no—
621M16—121no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—121no—
625C2×C8C2×D3211yescharacteristic
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—181no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—22no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3#90912yes—
662C22×C3#91812yes—
663C22×C3C22×D1211yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—122no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—122no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3—244no—
687C2×D3—244no—
688C2×D3—248no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—41no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4#100411yescharacteristic
702C3×C4D3×#4111yescharacteristic
703C3×C4D3×#4111yescharacteristic
704C3×C4#100911yescharacteristic
705Dic3—21no—
706Dic3—21no—
707Dic3—21no—
708Dic3—41no—
709Dic3—41no—
710Dic3—41no—
711Dic3—41no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—241no—
717Dic3—241no—
718C32#331411yescharacteristic, complemented, Sylow
719C23—31no—
720C23—181no—
721C23—181no—
722C23—362no—
723C23—362no—
724C23—721no—
725C23D3×D1211yescharacteristic
726Q8—61no—
727Q8—61no—
728Q8—181no—
729Q8—181no—
730Q8—721no—
731D4—62no—
732D4—92no—
733D4—181no—
734D4—181no—
735D4—181no—
736D4—362no—
737D4—362no—
738D4—721no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—241no—
753C2×C4—362no—
754C2×C4—721no—
755C2×C4—721no—
756C2×C4D3×D1211yescharacteristic
757C2×C4C22×D3211yescharacteristic
758C8—21no—
759C8—21no—
760C8—61no—
761C8—61no—
762C2×C3—22no—
763C2×C3—22no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—42no—
768C2×C3—121no—
769C2×C3#555411yescharacteristic
770C2×C3#565411yescharacteristic
771C2×C3C2×#90911yescharacteristic
772C2×C3#575211yescharacteristic
773C2×C3C2×#91811yescharacteristic
774C2×C3#577411yescharacteristic
775D3—41no—
776D3—122no—
777D3—122no—
778D3—242no—
779D3—242no—
780D3—241no—
781D3—241no—
782C22—21no—
783C22—21no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—182no—
788C22—361no—
789C22—361no—
790C22—361no—
791C22—361no—
792C22—361no—
793C22—724no—
794C22#6380112yes—
795C22C2×D3×D1211yescharacteristic
796C4—21no—
797C4—61no—
798C4—61no—
799C4—61no—
800C4—121no—
801C4—121no—
802C4—121no—
803C4—121no—
804C4—361no—
805C4—361no—
806C4#6431211yescharacteristic
807C4#6431411yescharacteristic
808C3—21no—
809C3#7950311yescharacteristic, complemented
810C3#8148611yescharacteristic, complemented
811C2—22no—
812C2—121no—
813C2—362no—
814C2—721no—
815C2#1059429311yescharacteristic
816C2C2×#6380111yescharacteristic
817C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC22⋊C8D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594988C2semidirect
3. #10592430C2semidirect
4. C3×#4730C2semidirect
5. C3×#4722C2semidirect
6. #10591187C2semidirect
7. C2×#63564C2semidirect
8. #10590970C2semidirect
9. #10590893C2semidirect
10. #10590838C2semidirect
11. #10590813C2semidirect
12. #10590773C2semidirect
13. #10590764C2semidirect
14. #10590679C2semidirect
15. #10590671C2semidirect
27. C2×C3×ΓL(1,𝔽25)C22semidirect
32. #63918C22semidirect
38. D3×C4⋊Dic3C22semidirect
40. #63857C22semidirect
42. #63844C22semidirect
43. C2×#3719C22semidirect
47. C3×(C2×D3)⋊C8C22semidirect
48. C3×#818C22semidirect
49. C3×#818C22semidirect
50. C3×#816C22semidirect
51. C3×#816C22semidirect
52. C3×#815C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
88. #4730D3semidirect
89. #4722D3semidirect
178. C2×ΓL(1,𝔽25)C2×D3semidirect
222. (C2×D3)⋊C8C2×D3semidirect
224. #818C2×D3semidirect
225. #818C2×D3semidirect
228. #816C2×D3semidirect
229. #816C2×D3semidirect
230. #815C2×D3semidirect
231. Dic3⋊C8C2×D3semidirect
718. C32#3314semidirect
809. C3#79503semidirect
810. C3#81486semidirect

Maximal subgroups

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

subgroupindex
#105950182
#105949882
#105924302
C3×#47302
C3×#47222
#105911872
C2×#635642
#105909702
#105908932
#105908382
#105908132
#105907732
#105907642
#105906792
#105906712
#814863
#795033