Finite Group Databasebeta

← #11887635

Subgroups — #11887635

Order 1152.

916 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#638C211yesmaximal, characteristic
2#10594991C211yesmaximal, characteristic
3C3×#5228C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591631C211yesmaximal, characteristic, complemented
6#10591603C211yesmaximal, characteristic, complemented
7#10591601C211yesmaximal, characteristic, complemented
8#10591581C211yesmaximal, characteristic, complemented
9#10591580C211yesmaximal, characteristic, complemented
10#10591555C211yesmaximal, characteristic, complemented
11#10591552C211yesmaximal, characteristic, complemented
12#10591538C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14#10591148C211yesmaximal, characteristic
15#10591135C211yesmaximal, characteristic, complemented
16#80193—31nomaximal
17#78806—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20#64155—21no—
21#64155C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23#64153—21no—
24#64153C2211yescharacteristic
25C4×#638—21no—
26C4×#638C2211yescharacteristic
27#64133—21no—
28#64133C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34#63964—21no—
35#63952—21no—
36#63919C2211yescharacteristic
37#63900C2211yescharacteristic
38#63895—21no—
39#63871C2211yescharacteristic
40#63847—21no—
41#63843C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63575C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63557C2211yescharacteristic
60#63553C2211yescharacteristic
61Q8×#67—31no—
62Q8×#67—31no—
63Q8×#67—61no—
64#5635—31no—
65#5511—31no—
66C3×#451—31no—
67C2×C3×#103—31no—
68#5228D311yescharacteristic, complemented
69C2×#835D311yescharacteristic, complemented
70#5188—31no—
71#5186—31no—
72#5182—31no—
73Dic3×Q16—31no—
74#5116—31no—
75C8×#67—31no—
76#5051—31no—
77#4970—31no—
78#4813—31no—
79#4811—31no—
80#4811—31no—
81#4809—31no—
82D3×#103—31no—
83D3×#103—31no—
84#4795—31no—
85#4793—31no—
86#4793—31no—
87#4792—31no—
88#4792—31no—
89#4790—31no—
90#67⋊C8—31no—
91#4722—31no—
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638D411yescharacteristic
100Q8×C3⋊D3—22no—
101Q8×C3⋊D3—41no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634—21no—
105C2×#634C2311yescharacteristic
106C22×C3×Dic3—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#624—21no—
110#3757—21no—
111#3757D411yescharacteristic
112#3752—21no—
113#3752D411yescharacteristic
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750D411yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C3×#217—21no—
124C3×#216—22no—
125C3×#216—41no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141Dic32—21no—
142#3719—41no—
143#3710—41no—
144#3299—91noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8C2×D311yescharacteristic
147C22×C3×Q8C2×D311yescharacteristic
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×D3×Q8—61no—
151C2×C3×Q16—31no—
152C2×C3×Q16—31no—
153C22×C3×C8—31no—
154C3×C22⋊Q8—31no—
155C2×C3×C4⋊C4—31no—
156#946—31no—
157#946—31no—
158#946—31no—
159#946—61no—
160#946—61no—
161#946—61no—
162#946—62no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—31no—
166Q8×Dic3—61no—
167#944—31no—
168#944—31no—
169#944—61no—
170#944—61no—
171#944—61no—
172#944—62no—
173C2×#216—31no—
174C2×#216C2×D311yescharacteristic
175C2×#216C2×D311yescharacteristic
176C4×#67—31no—
177C4×#67—31no—
178C4×#67—61no—
179C4×#67—61no—
180C4×#67—61no—
181C4×#67—61no—
182C4×#67—62no—
183C2×C4⋊Dic3C2×D311yescharacteristic
184#924—31no—
185#924—31no—
186#924—61no—
187#924—61no—
188#924—61no—
189#924—61no—
190#924—62no—
191#924C2×D311yescharacteristic
192C22×C3⋊C8C2×D311yescharacteristic
193C2×Dic12—31no—
194C2×D3×C8—31no—
195C2×D3×C8—31no—
196#897—31no—
197#897—61no—
198#896—61no—
199D3×C4⋊C4—31no—
200D3×C4⋊C4—31no—
201#889—61no—
202#889—61no—
203#888—31no—
204#888—31no—
205#887—31no—
206#67⋊C4—61no—
207#878—61no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×C22⋊C8—31no—
215#835—31no—
216#835C2×D311yescharacteristic
217#835C2×D311yescharacteristic
218#835C2×D311yescharacteristic
219#835C2×D311yescharacteristic
220#835C2×D311yescharacteristic
221#835C2×D311yescharacteristic
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#818—31no—
227#818—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232Dic3⋊C8—31no—
233Dic3⋊C8—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810—31no—
237#810—31no—
238#810—31no—
239#807—31no—
240#807—31no—
241#807—31no—
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—42no—
248C32×Q8#4112yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638Q1614yescomplemented
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C4×C3⋊D3—42no—
265#634—21no—
266#634—21no—
267#634—42no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#627—81no—
276#624—81no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282D4×Q8—91no—
283#487—91no—
284#484—91no—
285#484—91no—
286#477—91no—
287#467—91no—
288#467—91no—
289#462—91no—
290#451—31no—
291#451—91no—
292C4×Q16—91no—
293C8×D4—91no—
294C2×#103—31no—
295C2×#103—91no—
296C2×C3×Q8—22no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—22no—
300C2×C3×Q8—22no—
301C2×C3×Q8—21no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8—42no—
305C2×C3×Q8—41no—
306C2×C3×Q8—41no—
307C2×C3×Q8—42no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×Q8C22×D311yescharacteristic
312C22×C3×C4—22no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—31no—
320C2×#67—31no—
321C2×#67—61no—
322C22×Dic3—21no—
323D3×Q8—62no—
324D3×Q8—62no—
325D3×Q8—122no—
326D3×Q8—121no—
327D3×Q8—121no—
328D3×Q8—122no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—62no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×Dic6—31no—
338C2×Dic6—31no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—62no—
343C2×Dic6—61no—
344C2×Dic6—61no—
345C2×Dic6C22×D311yescharacteristic
346C3×Q16—62no—
347C3×Q16—121no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C22⋊C4—61no—
359#217—21no—
360#217—31no—
361#217—31no—
362#217—61no—
363#217—62no—
364#217—61no—
365#217—61no—
366#216—22no—
367#216—41no—
368#216—121no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
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—62no—
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—62no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—62no—
406Dic3⋊C4—62no—
407Dic3⋊C4—62no—
408Dic3⋊C4—62no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—62no—
419C2×C3⋊C8—41no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424Dic12—121no—
425D3×C8—121no—
426D3×C8—121no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32C2×Q1612yes—
430C22×C32C22×D411yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3C2×Q1612yes—
434C32×C4—22no—
435C32×C4—21no—
436C32×C4—41no—
437C32×C4C2×#4111yescharacteristic
438C32×C4H(5,𝔽2)11yescharacteristic
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3⋊Dic3C2×Q1612yes—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×Q8—91no—
449C22×Q8D3211yescharacteristic
450C2×Q16—31no—
451C2×Q16—31no—
452C2×Q16—91no—
453C22×C8—31no—
454C22×C8—91no—
455C4⋊Q8—91no—
456C4⋊Q8—91no—
457C4⋊Q8—181no—
458#125—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—181no—
464C22⋊Q8—181no—
465C22⋊Q8—181no—
466C22⋊Q8—181no—
467C4×Q8—91no—
468C4×Q8—91no—
469C4×D4—91no—
470C4×D4—181no—
471C4×D4—181no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—91no—
474#107—91no—
475#107—91no—
476#107—91no—
477C4⋊C8—91no—
478#103—31no—
479#103—31no—
480#103—31no—
481#103—31no—
482#103—31no—
483#103—31no—
484#103—91no—
485#103—91no—
486#103—91no—
487#103—91no—
488C22⋊C8—31no—
489C22⋊C8—91no—
490C4×C8—91no—
491C23×C3—21no—
492C23×C3D3×D411yescharacteristic
493C23×C3D3×D411yescharacteristic
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—61no—
497C3×Q8—22no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—22no—
505C3×Q8—41no—
506C3×Q8—41no—
507C3×Q8—42no—
508C3×Q8—42no—
509C3×Q8—44no—
510C3×Q8—61no—
511C3×Q8—61no—
512C3×Q8#23512yes—
513C3×Q8#23712yes—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—22no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×C3×C4—44no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—241no—
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—34no—
541#67—34no—
542#67—64no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—81no—
563C4×D3—61no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—61no—
567C4×D3—121no—
568C4×D3—121no—
569C4×D3—122no—
570C4×D3—122no—
571C4×D3—124no—
572C4×D3—241no—
573C4×D3—241no—
574Dic6—21no—
575Dic6—21no—
576Dic6—61no—
577Dic6—61no—
578Dic6—61no—
579Dic6—61no—
580Dic6—121no—
581Dic6—121no—
582Dic6—122no—
583Dic6—122no—
584Dic6—124no—
585Dic6—241no—
586Dic6—241no—
587C3×C8—61no—
588C3×C8—61no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—21no—
595C2×C32—22no—
596C2×C32#54611yescharacteristic
597C2×C32C22×Q1611yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—22no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—31no—
603C2×Q8—41no—
604C2×Q8—91no—
605C2×Q8—181no—
606C2×Q8—181no—
607C2×Q8—182no—
608C2×Q8—361no—
609C2×Q8C2×D3211yescharacteristic
610C2×Q8C2×D3211yescharacteristic
611C2×D4—91no—
612C22×C4—21no—
613C22×C4—61no—
614C22×C4—91no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4C2×D3211yescharacteristic
618Q16—62no—
619Q16—121no—
620Q16—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—121no—
626C2×C8—361no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—91no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C22⋊C4—61no—
644C22⋊C4—91no—
645C22⋊C4—91no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C42—91no—
650C42—181no—
651C42—181no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—22no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3D3×Q1612yes—
661C22×C3D3×Q1612yes—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—32no—
665C2×D3—32no—
666C2×D3—62no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—121no—
672C2×D3—121no—
673C3×C4—24no—
674C3×C4—22no—
675C3×C4—21no—
676C3×C4—22no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—42no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4C2×#23511yescharacteristic
689C3×C4C2×#23711yescharacteristic
690C3×C4#100411yescharacteristic
691C3×C4#100411yescharacteristic
692Dic3—32no—
693Dic3—32no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—62no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—121no—
704Dic3—121no—
705Dic3—122no—
706Dic3—122no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—121no—
711C32#329911yescharacteristic, complemented, Sylow
712C23—91no—
713C23#381111yescharacteristic
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—42no—
718Q8—61no—
719Q8—61no—
720Q8—181no—
721Q8—181no—
722Q8—362no—
723Q8—721no—
724Q8#380412yes—
725D4—94no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—42no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—241no—
743C2×C4—362no—
744C2×C4—721no—
745C2×C4#381111yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—61no—
748C8—61no—
749C8—61no—
750C8—61no—
751C2×C3—22no—
752C2×C3—22no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—42no—
757C2×C3#549011yescharacteristic
758C2×C3#559111yescharacteristic
759C2×C3#576211yescharacteristic
760C2×C3C2×D3×Q1611yescharacteristic
761C2×C3C2×D3×Q1611yescharacteristic
762C2×C3#577811yescharacteristic
763D3—62no—
764D3—62no—
765D3—122no—
766C22—21no—
767C22—21no—
768C22—92no—
769C22—181no—
770C22—181no—
771C22#6394412yes—
772C22C2×#381111yescharacteristic
773C4—21no—
774C4—22no—
775C4—41no—
776C4—92no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—181no—
782C4—181no—
783C4—361no—
784C4—361no—
785C4C2×#380411yescharacteristic
786C4#6433011yescharacteristic
787C3—21no—
788C3#7880611yescharacteristic, complemented
789C3#8019311yescharacteristic, complemented
790C2—22no—
791C2—182no—
792C2#1059532411yescharacteristic
793C2C2×#6394411yescharacteristic
794C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#638D4
hypercenterC22×Q8D32
hypocenterC32#3299
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
3. C3×#5228C2semidirect
4. C2×C3×#835C2semidirect
5. #10591631C2semidirect
6. #10591603C2semidirect
7. #10591601C2semidirect
8. #10591581C2semidirect
9. #10591580C2semidirect
10. #10591555C2semidirect
11. #10591552C2semidirect
12. #10591538C2semidirect
13. #10591187C2semidirect
15. #10591135C2semidirect
68. #5228D3semidirect
69. C2×#835D3semidirect
256. #638Q16semidirect
711. C32#3299semidirect
788. C3#78806semidirect
789. C3#80193semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
#105949912
C3×#52282
C2×C3×#8352
#105916312
#105916032
#105916012
#105915812
#105915802
#105915552
#105915522
#105915382
#105911872
#105911482
#105911352
#801933
#788063