Finite Group Databasebeta

← #11867797

Subgroups — #11867797

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5629C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic, complemented
3#10594884C211yesmaximal, characteristic, complemented
4C2×#63815C211yesmaximal, characteristic, complemented
5#10592750C211yesmaximal, characteristic, complemented
6C3×#5052C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591598C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591179C211yesmaximal, characteristic, complemented
11#10591176C211yesmaximal, characteristic, complemented
12D3×#810C211yesmaximal, characteristic, complemented
13#10590581C211yesmaximal, characteristic, complemented
14#10590578C211yesmaximal, characteristic, complemented
15#10590515C211yesmaximal, characteristic, complemented
16#83423—31nomaximal
17#80907—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23#64133C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#896—21no—
31C3×#895—21no—
32C3×#895C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#884—21no—
35C3×#884—21no—
36#63969—21no—
37#63959—21no—
38#63943—24no—
39#63884—21no—
40#63857C2211yescharacteristic
41#63856C2211yescharacteristic
42#63841C2211yescharacteristic
43#63839—21no—
44C2×#3716C2211yescharacteristic
45C2×#3715C2211yescharacteristic
46C2×#3711C2211yescharacteristic
47C2×#3711C2211yescharacteristic
48#63815—24no—
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic
52#63637C2211yescharacteristic
53#63634C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#808C2211yescharacteristic
57#63575C2211yescharacteristic
58#63574C2211yescharacteristic
59#63567C2211yescharacteristic
60#63565C2211yescharacteristic
61#63563C2211yescharacteristic
62#63562C2211yescharacteristic
63C3×#537—31no—
64#5825—31no—
65C2×#951—31no—
66C2×#948—31no—
67C2×#918—31no—
68C2×#907—31no—
69#5629D311yescharacteristic
70#5628—31no—
71C3×#470—31no—
72#5233—31no—
73#5188—31no—
74#5134—31no—
75#5052—31no—
76#5052D311yescharacteristic, complemented
77#5051—31no—
78#5051—31no—
79#5051—31no—
80#5051—61no—
81#5048—31no—
82#5042—31no—
83#5042—31no—
84#5041—31no—
85#5041—31no—
86C2×#810—31no—
87#4964—31no—
88#4864—31no—
89#4861—31no—
90#4816—31no—
91#4812—31no—
92#4804—31no—
93D3×#103—31no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C2×C3×#67D411yescharacteristic
100C3×#239—22no—
101C3×#239—22no—
102C3×#235—22no—
103C3×#235—22no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12D411yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6D411yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#627—21no—
115C2×D3×Dic3—21no—
116D3×Dic6—22no—
117D3×Dic6—22no—
118C32×C4⋊C4—21no—
119C32×C4⋊C4C2311yescharacteristic
120C32×C22⋊C4—21no—
121#3757—21no—
122#3756—22no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125C2×C3⋊(C3⋊C8)—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#216—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×#208—22no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3724—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32—21no—
147#3716—22no—
148#3715—22no—
149#3711—22no—
150#3711D414yescomplemented
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153#3063—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C2×#239C2×D311yescharacteristic
157C2×D3×Q8—31no—
158C2×#235C2×D311yescharacteristic
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×M16—31no—
162C3×C22⋊Q8—21no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—61no—
166C3×C22⋊Q8C2×D311yescharacteristic
167C3×C22⋊Q8C2×D311yescharacteristic
168C3×#121—31no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#121—61no—
172C3×#121—61no—
173C2×C3×C4⋊C4—31no—
174#951—64no—
175#948—64no—
176#946—31no—
177#946C2×D311yescharacteristic
178#944—61no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—61no—
182C2×#216C2×D311yescharacteristic
183C2×#215—31no—
184#936—61no—
185#935—61no—
186#935—61no—
187C2×#214—31no—
188C2×#214—31no—
189#930C2×D311yescharacteristic
190#926—31no—
191#924—31no—
192#924—31no—
193#924—31no—
194#924—31no—
195#924—61no—
196#924C2×D311yescharacteristic
197C2×#208—31no—
198C2×#208—31no—
199C2×#208C2×D311yescharacteristic
200C22×C3⋊C8—31no—
201C22×C3⋊C8—31no—
202C22×C3⋊C8—31no—
203C22×C3⋊C8—31no—
204C22×C3⋊C8—61no—
205#918—64no—
206#907—64no—
207C2×#204—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211C2×D3×C8—31no—
212#897—31no—
213#896—21no—
214#895—21no—
215#895C2×D311yescharacteristic
216#894—61no—
217#892—31no—
218D3×C4⋊C4C2×D311yescharacteristic
219#888—61no—
220#885—61no—
221#884—21no—
222#884—21no—
223#883—61no—
224C3×#106—31no—
225C3×#103—31no—
226C3×#103—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#835—61no—
231#835C2×D311yescharacteristic
232#832—31no—
233#832—31no—
234#821—31no—
235#818—31no—
236#816—31no—
237#810—31no—
238#810—31no—
239#810—31no—
240#810—31no—
241#810—61no—
242#810C2×D311yescharacteristic
243#809—31no—
244#808—31no—
245#808—31no—
246#808C2×D311yescharacteristic
247#807—31no—
248#807—31no—
249#807—31no—
250#807—61no—
251C23×C32C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3C2×D411yescharacteristic
254C22×C3×D3C2×D411yescharacteristic
255C32×Q8—21no—
256C32×Q8—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265#634—21no—
266#634—21no—
267C3×#67—22no—
268C3×#67—22no—
269C3×#67—81no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—22no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—42no—
279C3×D12—81no—
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282C3×C4×D3—42no—
283C3×C4×D3—81no—
284C3×C4×D3C2×D412yes—
285C3×C4×D3#4112yes—
286C3×Dic6—22no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289#627—42no—
290D3×Dic3—42no—
291C3⋊(C3⋊C8)—21no—
292C3⋊(C3⋊C8)C2×D412yes—
293C3×C3⋊C8—21no—
294C3×C3⋊C8C2×D412yes—
295C2×#137—91no—
296C2×#131—91no—
297#537—31no—
298#536—91no—
299#470—31no—
300#470—91no—
301#468—91no—
302#468—91no—
303#467—91no—
304#467—91no—
305#465—91no—
306#465—91no—
307#428—91no—
308#416—91no—
309C2×#103—91no—
310C3×#41—62no—
311C3×#41—62no—
312C3×#41—62no—
313C3×#41—62no—
314C2×C3×Q8—21no—
315C2×C3×Q8—31no—
316C2×C3×Q8—31no—
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—21no—
334C2×#67#6711yescharacteristic
335C2×#67#6711yescharacteristic
336C22×Dic3—61no—
337#239—22no—
338#239—22no—
339D3×Q8—62no—
340D3×Q8—62no—
341#235—22no—
342#235—22no—
343C2×D12—21no—
344C2×D12—21no—
345C2×D12#6711yescharacteristic
346C2×D12C22×D311yescharacteristic
347C2×C4×D3—21no—
348C2×C4×D3—21no—
349C2×C4×D3—61no—
350C2×C4×D3C22×D311yescharacteristic
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6—62no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6#6711yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×Q16—62no—
362C3×M16—62no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—41no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—41no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383#217—21no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#217—121no—
390#216—22no—
391#216—62no—
392#216—62no—
393#216—122no—
394#215—62no—
395#214—62no—
396#214—62no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—121no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420#208—22no—
421#208—34no—
422#208—62no—
423C2×C3⋊C8—31no—
424C2×C3⋊C8—31no—
425C2×C3⋊C8—31no—
426C2×C3⋊C8—31no—
427C2×C3⋊C8—61no—
428C2×C3⋊C8—61no—
429C2×C3⋊C8—62no—
430C2×C3⋊C8—62no—
431C2×C3⋊C8—62no—
432C2×C3⋊C8—62no—
433C2×C3⋊C8—122no—
434C2×C3⋊C8C22×D311yescharacteristic
435C2×C3⋊C8C22×D311yescharacteristic
436#204—62no—
437ΓL(1,𝔽25)—34no—
438ΓL(1,𝔽25)—62no—
439D3×C8—62no—
440D3×C8—62no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32C22×D411yescharacteristic
445C2×C3×D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3#12112yes—
454C32×C4—21no—
455C32×C4—41no—
456C32×C4—41no—
457C32×C4C22×D411yescharacteristic
458C32×C4C2×#4111yescharacteristic
459C3⋊Dic3—41no—
460C3⋊Dic3—41no—
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C2×#41—31no—
467C2×#41—31no—
468C22×Q8—91no—
469#137—184no—
470C2×Q16—31no—
471C2×Q16—91no—
472C2×SD16—91no—
473C2×SD16—91no—
474#131—184no—
475C2×M16—31no—
476C2×M16—91no—
477C2×M16—91no—
478C22×C8—91no—
479C22×C8—91no—
480C22×C8—91no—
481C4⋊Q8—181no—
482#124—181no—
483#123—181no—
484#123—181no—
485C22⋊Q8—31no—
486C22⋊Q8—31no—
487C22⋊Q8—61no—
488C22⋊Q8—91no—
489C22⋊Q8—91no—
490C22⋊Q8—91no—
491C22⋊Q8D3211yescharacteristic
492#121—31no—
493#121—31no—
494#121—61no—
495#121—61no—
496#121—61no—
497#117—91no—
498C2×C4⋊C4—31no—
499#107—91no—
500#107—91no—
501#106—31no—
502#106—91no—
503#103—31no—
504#103—31no—
505#103—91no—
506#103—91no—
507#103—91no—
508#103—91no—
509#102—91no—
510#102—91no—
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3D3×D411yescharacteristic
516C23×C3C2×#6711yescharacteristic
517C22×D3—21no—
518C22×D3C2×#6711yescharacteristic
519C22×D3C2×#6711yescharacteristic
520C3×Q8—21no—
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—41no—
525C3×Q8—41no—
526C3×Q8—62no—
527C3×Q8—61no—
528C3×Q8—61no—
529C3×D4—62no—
530C3×D4—62no—
531C3×D4—62no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—122no—
535C3×D4—241no—
536C3×D4—241no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—31no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—31no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—122no—
561C2×C3×C4—241no—
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4C2×#6711yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—22no—
567#67—22no—
568#67—81no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—121no—
577C2×Dic3—121no—
578C2×Dic3—122no—
579C2×Dic3C2×#6711yescharacteristic
580C2×Dic3C2×#6711yescharacteristic
581D12—22no—
582D12—21no—
583D12—21no—
584D12—42no—
585D12—81no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—42no—
589C4×D3—81no—
590C4×D3—122no—
591C4×D3D3×D412yes—
592C4×D3#23712yes—
593Dic6—22no—
594Dic6—21no—
595Dic6—21no—
596Dic6—61no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—121no—
601Dic6—121no—
602Dic6—122no—
603Dic6—122no—
604C3×C8—32no—
605C3×C8—61no—
606C3⋊C8—21no—
607C3⋊C8—32no—
608C3⋊C8—32no—
609C3⋊C8—62no—
610C3⋊C8—61no—
611C3⋊C8—61no—
612C3⋊C8—121no—
613C3⋊C8D3×D412yes—
614C2×C32—41no—
615C2×C32C2×#12111yescharacteristic
616C2×C32#57711yescharacteristic
617C2×C32#57811yescharacteristic
618C3×D3—22no—
619C3×D3—41no—
620C3×D3—81no—
621#41—62no—
622#41—62no—
623#41—62no—
624#41—62no—
625C2×Q8—31no—
626C2×Q8—31no—
627C2×Q8—91no—
628C2×Q8—181no—
629C2×Q8—182no—
630C2×Q8—182no—
631C2×Q8C2×D3211yescharacteristic
632C2×D4—31no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—61no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—181no—
644C22×C4C2×D3211yescharacteristic
645Q16—62no—
646Q16—182no—
647SD16—182no—
648SD16—182no—
649M16—62no—
650M16—94no—
651M16—182no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—91no—
655C2×C8—91no—
656C2×C8—182no—
657C2×C8—182no—
658C2×C8—182no—
659C4⋊C4—21no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4C2×D3211yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—181no—
680C22×C3—22no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—32no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3C2×D3×D411yescharacteristic
700C22×C3C22×#6711yescharacteristic
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3#93912yes—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—32no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—61no—
721C3×C4—81no—
722C3×C4—81no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4C2×D3×D411yescharacteristic
727C3×C4C2×D3×D411yescharacteristic
728C3×C4C2×#23711yescharacteristic
729C3×C4D3×#4111yescharacteristic
730Dic3—21no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—241no—
739Dic3—241no—
740Dic3#93912yes—
741C32#306311yescharacteristic, complemented, Sylow
742C23—31no—
743C23—31no—
744C23—61no—
745C23D3×#6711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—62no—
749Q8—61no—
750Q8—61no—
751Q8—181no—
752Q8—181no—
753Q8—362no—
754D4—62no—
755D4—62no—
756D4—62no—
757D4—61no—
758D4—61no—
759D4—122no—
760D4—241no—
761D4—241no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—31no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—31no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—122no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—241no—
779C2×C4—362no—
780C2×C4D3×#6711yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—32no—
783C8—61no—
784C8—92no—
785C8—181no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—42no—
790C2×C3—41no—
791C2×C3—41no—
792C2×C3—62no—
793C2×C3—121no—
794C2×C3—241no—
795C2×C3D3×#12111yescharacteristic
796C2×C3#577811yescharacteristic
797C2×C3#577911yescharacteristic
798C2×C3C2×#93911yescharacteristic
799C2×C3#583611yescharacteristic
800C2×C3#583811yescharacteristic
801D3—22no—
802D3—41no—
803D3—81no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—32no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22C2×D3×#6711yescharacteristic
817C4—21no—
818C4—32no—
819C4—41no—
820C4—41no—
821C4—61no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—361no—
826C4—361no—
827C4D32×D411yescharacteristic
828C4D3×#23711yescharacteristic
829C3—21no—
830C3#8090711yescharacteristic, complemented
831C3#8342311yescharacteristic, complemented
832C2—41no—
833C2—62no—
834C2—121no—
835C2—241no—
836C2D3×#93911yescharacteristic
837C2#1059532811yescharacteristic
838C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC3×#5629C2
hypercenterC22⋊Q8D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63943C2semidirect
3. #10594884C2semidirect
4. C2×#63815C2semidirect
5. #10592750C2semidirect
6. C3×#5052C2semidirect
7. #10591635C2semidirect
8. #10591598C2semidirect
9. #10591556C2semidirect
10. #10591179C2semidirect
11. #10591176C2semidirect
12. D3×#810C2semidirect
13. #10590581C2semidirect
14. #10590578C2semidirect
15. #10590515C2semidirect
76. #5052D3semidirect
150. #3711D4semidirect
741. C32#3063semidirect
830. C3#80907semidirect
831. C3#83423semidirect

Maximal subgroups

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

subgroupindex
C3×#56292
C2×#639432
#105948842
C2×#638152
#105927502
C3×#50522
#105916352
#105915982
#105915562
#105911792
#105911762
D3×#8102
#105905812
#105905782
#105905152
#834233
#809073