Finite Group Databasebeta

← #11889402

Subgroups — #11889402

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic
3C3×#5011C211yesmaximal, characteristic
4#10591190C211yesmaximal, characteristic, complemented
5#10591190C211yesmaximal, characteristic, complemented
6#10591187C211yesmaximal, characteristic, complemented
7#10591134C211yesmaximal, characteristic, complemented
8#10591124C211yesmaximal, characteristic, complemented
9#10591121C211yesmaximal, characteristic, complemented
10#10591107C211yesmaximal, characteristic, complemented
11C2×#63567C211yesmaximal, characteristic, complemented
12#10590385C211yesmaximal, characteristic, complemented
13#10590383C211yesmaximal, characteristic, complemented
14#10590295C211yesmaximal, characteristic, complemented
15#10590292C211yesmaximal, characteristic, complemented
16#83603—31nomaximal
17#79511—31nomaximal
18C22×#634C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21D4×C3⋊Dic3—21no—
22#64133C2211yescharacteristic
23#64133C2211yescharacteristic
24#64097—21no—
25#64087—21no—
26#64087—21no—
27#64078C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C3×#935—21no—
30C3×#926C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic
36C3×#889—21no—
37C3×#879—21no—
38C3×#877—21no—
39C3×#870C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×C4⋊(C3⋊C8)C2211yescharacteristic
47C3×#803C2211yescharacteristic
48#63575C2211yescharacteristic
49#63573C2211yescharacteristic
50#63573C2211yescharacteristic
51#63567C2211yescharacteristic
52#63567C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61C3×#552—31no—
62#5541D311yescharacteristic
63D4×Dic6—31no—
64D4×Dic6—31no—
65D4×Dic6—61no—
66C3×#435—31no—
67#5137—31no—
68#5120—31no—
69#5116—31no—
70C2×#816—31no—
71#5069—31no—
72#5063—31no—
73#5052—31no—
74#5051—31no—
75#5050—31no—
76#5050—31no—
77#5031—31no—
78#5030—31no—
79#5011D311yescharacteristic
80#5004—31no—
81#4996—31no—
82#4971—31no—
83C2×#810—31no—
84#4849—31no—
85#4829—31no—
86#4739—31no—
87#4739—31no—
88#4723—31no—
89#4721—31no—
90#4716—31no—
91#4703—31no—
92C2×C32×D4D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C22×C3⋊Dic3—21no—
97C2×#634—22no—
98C2×#634—22no—
99C2×#634—21no—
100C2×#634—21no—
101C2×#634—41no—
102C2×#634—41no—
103C2×#634C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C22×C3×Dic3—21no—
107C2×C3×Dic6C2311yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C22⋊C4D411yescharacteristic
110C32×C22⋊C4D411yescharacteristic
111C32×C42C2311yescharacteristic
112#3757—21no—
113#3757—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×#208—41no—
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3719—22no—
142#3719—41no—
143#3719—41no—
144#3312—91noSylow
145C22×Dic6—31no—
146C22×Dic6—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—61no—
150C22×Dic6—61no—
151C2×C3×M16—31no—
152C22×C3×C8—31no—
153C3×#126—61no—
154C3×#125—31no—
155C3×#125—61no—
156C3×#123—61no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—21no—
161C3×C4×D4C2×D311yescharacteristic
162C3×C4×D4C2×D311yescharacteristic
163C3×#117—31no—
164C3×#117—61no—
165C2×C3×C4⋊C4—31no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169#935—21no—
170D4×Dic3—62no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173#926C2×D311yescharacteristic
174C2×C4⋊Dic3C2×D311yescharacteristic
175#924—31no—
176#924—31no—
177#924—31no—
178#924—31no—
179#924—61no—
180#924—61no—
181#924C2×D311yescharacteristic
182#924C2×D311yescharacteristic
183C2×#208C2×D311yescharacteristic
184C22×C3⋊C8C2×D311yescharacteristic
185C2×Dic12—31no—
186C2×Dic12—31no—
187C2×Dic12—31no—
188#889—21no—
189#888—62no—
190#888—61no—
191#888—61no—
192#879—21no—
193#878—62no—
194#878—62no—
195#878—61no—
196#878—61no—
197#878—61no—
198#878—61no—
199#877—21no—
200#870C2×D311yescharacteristic
201#869—31no—
202#869—31no—
203#869—61no—
204C4×Dic6—31no—
205C4×Dic6—31no—
206C4×Dic6—61no—
207C4×Dic6C2×D311yescharacteristic
208C3×C4⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211C3×#97—31no—
212#835—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic
215#818—31no—
216#817—31no—
217#817—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—31no—
234#810—31no—
235#810—31no—
236#810—31no—
237#808—31no—
238#808—31no—
239#807—31no—
240C4⋊(C3⋊C8)C2×D311yescharacteristic
241#803C2×D311yescharacteristic
242C23×C32C2×D411yescharacteristic
243C23×C32C2×D411yescharacteristic
244C32×D4—22no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—42no—
259C2×C3⋊Dic3—42no—
260#634—21no—
261#634—21no—
262#634—21no—
263#634—21no—
264#634—21no—
265#634—42no—
266#634—42no—
267#634#4112yes—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—42no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280D4×Q8—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#479—91no—
285#470—91no—
286#467—91no—
287#462—91no—
288#451—91no—
289#451—91no—
290#441—91no—
291#435—31no—
292#419—91no—
293C2×#103—91no—
294C2×C3×Q8—31no—
295C2×C3×D4—21no—
296C2×C3×D4D1211yescharacteristic
297C2×C3×D4#6711yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—61no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×Dic3—21no—
306C22×Dic3—62no—
307C22×Dic3—62no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C2×Dic6—31no—
313C2×Dic6—31no—
314C2×Dic6—31no—
315C2×Dic6—31no—
316C2×Dic6—31no—
317C2×Dic6—31no—
318C2×Dic6—61no—
319C2×Dic6—61no—
320C2×Dic6—61no—
321C2×Dic6—62no—
322C2×Dic6—62no—
323C2×Dic6—62no—
324C2×Dic6—62no—
325C2×Dic6—62no—
326C2×Dic6—62no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—122no—
332C2×Dic6—122no—
333C2×Dic6—121no—
334C2×Dic6—121no—
335C2×Dic6—121no—
336C2×Dic6—121no—
337C2×Dic6—122no—
338C2×Dic6—122no—
339C2×Dic6C22×D311yescharacteristic
340C3×M16—121no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4D1211yescharacteristic
357C3×C4⋊C4#6711yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4D1211yescharacteristic
364C3×C22⋊C4D1211yescharacteristic
365C3×C22⋊C4#6711yescharacteristic
366C3×C22⋊C4#6711yescharacteristic
367C3×C42—21no—
368C3×C42—61no—
369C3×C42—61no—
370C3×C42C22×D311yescharacteristic
371C3×C42C22×D311yescharacteristic
372#217—21no—
373#217—21no—
374#217—21no—
375#217—62no—
376#217—62no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—61no—
381#216—62no—
382#216—121no—
383#216—121no—
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—62no—
389C4⋊Dic3—62no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—62no—
403Dic3⋊C4—62no—
404Dic3⋊C4—62no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411C4×Dic3—21no—
412C4×Dic3—21no—
413C4×Dic3—62no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416#208—41no—
417C2×C3⋊C8—41no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422Dic12—62no—
423Dic12—121no—
424Dic12—121no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32#13712yes—
431C22×C32C22×D411yescharacteristic
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4C2×#4111yescharacteristic
437C32×C4H(5,𝔽2)11yescharacteristic
438C3⋊Dic3—22no—
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3⋊Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×Q8—91no—
447C22×Q8—91no—
448C2×Q16—91no—
449C2×Q16—91no—
450C2×Q16—91no—
451C2×M16—31no—
452C22×C8—31no—
453C4⋊Q8—91no—
454C4⋊Q8—181no—
455#126—61no—
456#125—31no—
457#125—61no—
458#123—61no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—181no—
464C22⋊Q8—181no—
465C4×Q8—31no—
466C4×Q8—91no—
467C4×D4—181no—
468C4×D4D3211yescharacteristic
469#117—31no—
470#117—61no—
471C2×C4⋊C4—31no—
472#107—91no—
473#106—91no—
474#106—91no—
475C4⋊C8—31no—
476#103—91no—
477#103—91no—
478#103—91no—
479#103—91no—
480#103—91no—
481#103—91no—
482#103—91no—
483#103—91no—
484#103—91no—
485#103—91no—
486C22⋊C8—31no—
487C22⋊C8—31no—
488#97—31no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3C2×D1211yescharacteristic
492C23×C3C2×D1211yescharacteristic
493C23×C3C2×#6711yescharacteristic
494C23×C3C2×#6711yescharacteristic
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—24no—
498C3×D4—22no—
499C3×D4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
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—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—122no—
522C2×C3×C4C2×D1211yescharacteristic
523C2×C3×C4C2×D1211yescharacteristic
524C2×C3×C4C2×D1211yescharacteristic
525C2×C3×C4C2×D1211yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C2×#6711yescharacteristic
528C2×C3×C4C2×#6711yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—42no—
537C2×Dic3—62no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—122no—
550C2×Dic3—122no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C2×Dic3—124no—
554C2×Dic3—124no—
555Dic6—21no—
556Dic6—21no—
557Dic6—32no—
558Dic6—32no—
559Dic6—62no—
560Dic6—62no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—121no—
572Dic6—121no—
573Dic6—121no—
574Dic6—121no—
575Dic6—122no—
576Dic6—122no—
577Dic6—122no—
578Dic6—122no—
579Dic6—124no—
580Dic6—124no—
581C3×C8—61no—
582C3×C8—61no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C2×C32—22no—
590C2×C32—41no—
591C2×C32#54611yescharacteristic
592C2×C32C2×#13711yescharacteristic
593C2×C32#57811yescharacteristic
594C2×Q8—31no—
595C2×Q8—91no—
596C2×Q8—91no—
597C2×Q8—91no—
598C2×Q8—182no—
599C2×Q8—182no—
600C2×Q8—181no—
601C2×Q8—181no—
602C2×Q8—361no—
603C2×Q8—361no—
604C2×D4#62611yescharacteristic
605C22×C4—61no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4C2×D3211yescharacteristic
609C22×C4C2×D3211yescharacteristic
610Q16—182no—
611Q16—361no—
612Q16—361no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—121no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4#62611yescharacteristic
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4#62611yescharacteristic
641C22⋊C4#62611yescharacteristic
642C42—61no—
643C42—61no—
644C42—181no—
645C42C2×D3211yescharacteristic
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—22no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3#90912yes—
664C22×C3#95112yes—
665C22×C3C22×D1211yescharacteristic
666C22×C3C22×#6711yescharacteristic
667C3×C4—22no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4#100411yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—64no—
694Dic3—62no—
695Dic3—62no—
696Dic3—122no—
697Dic3—122no—
698Dic3—122no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705C32#331211yescharacteristic, complemented, Sylow
706C23C2×#62611yescharacteristic
707C23C2×#62611yescharacteristic
708Q8—61no—
709Q8—61no—
710Q8—92no—
711Q8—181no—
712Q8—181no—
713Q8—181no—
714Q8—181no—
715Q8—181no—
716Q8—362no—
717Q8—362no—
718D4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—122no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—362no—
733C2×C4—362no—
734C2×C4C2×#62611yescharacteristic
735C2×C4C2×#62611yescharacteristic
736C2×C4C2×#62611yescharacteristic
737C2×C4C2×#62611yescharacteristic
738C2×C4C22×D3211yescharacteristic
739C8—61no—
740C8—61no—
741C8—61no—
742C8—61no—
743C2×C3—22no—
744C2×C3—22no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—42no—
749C2×C3—42no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3#555411yescharacteristic
753C2×C3C2×#90911yescharacteristic
754C2×C3#575311yescharacteristic
755C2×C3C2×#95111yescharacteristic
756C2×C3#582911yescharacteristic
757C2×C3#583811yescharacteristic
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22#6383112yes—
764C22C22×#62611yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—121no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—182no—
774C4—361no—
775C4—361no—
776C4—361no—
777C4#6431211yescharacteristic
778C4#6431411yescharacteristic
779C3—21no—
780C3#7951111yescharacteristic, complemented
781C3#8360311yescharacteristic, complemented
782C2—22no—
783C2—41no—
784C2C2×#6383111yescharacteristic
785C2#1059525411yescharacteristic
786C2#1059545011yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #10591190C2semidirect
5. #10591190C2semidirect
6. #10591187C2semidirect
7. #10591134C2semidirect
8. #10591124C2semidirect
9. #10591121C2semidirect
10. #10591107C2semidirect
11. C2×#63567C2semidirect
12. #10590385C2semidirect
13. #10590383C2semidirect
14. #10590295C2semidirect
15. #10590292C2semidirect
705. C32#3312semidirect
780. C3#79511semidirect
781. C3#83603semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×#55412
C3×#50112
#105911902
#105911872
#105911342
#105911242
#105911212
#105911072
C2×#635672
#105903852
#105903832
#105902952
#105902922
#836033
#795113