Finite Group Databasebeta

← #11860603

Subgroups — #11860603

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596017C211yesmaximal, characteristic
2C2×#63931C211yesmaximal, characteristic
3#10593848C211yesmaximal, characteristic, complemented
4C3×#5018C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic, complemented
6#10591446C211yesmaximal, characteristic, complemented
7#10591445C211yesmaximal, characteristic, complemented
8#10591424C211yesmaximal, characteristic
9#10590601C211yesmaximal, characteristic, complemented
10#10590583C211yesmaximal, characteristic, complemented
11#10590485C211yesmaximal, characteristic, complemented
12#10590482C211yesmaximal, characteristic, complemented
13#10590383C211yesmaximal, characteristic, complemented
14C4×#3719C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79776—31nomaximal
17#79648—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C4×#638—21no—
23C2×#3750—21no—
24C4⋊C4×C3⋊D3C2211yescharacteristic
25#64096C2211yescharacteristic
26#64090—21no—
27#64086—21no—
28#64081C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63931C418yescomplemented
35#63849C2211yescharacteristic
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38#63837—21no—
39#63837—21no—
40#63836—21no—
41#63836—21no—
42C2×#3719C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#803C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63555C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×#915—31no—
63C2×#915—31no—
64#5572—31no—
65#5572—31no—
66#5546—31no—
67#5546—31no—
68#5546—61no—
69C3×#440—31no—
70C3×C4×SD16—31no—
71#5164—31no—
72Dic3×SD16—31no—
73#5030—31no—
74C4×#216—31no—
75#5018D311yescharacteristic, complemented
76C4×#214D311yescharacteristic, complemented
77#4881—31no—
78#4873—31no—
79#4861—31no—
80#4853—31no—
81D3×#103—31no—
82D3×#103—31no—
83#4790—31no—
84#4789—31no—
85#4772—31no—
86#4772—31no—
87#4758—31no—
88#4757—31no—
89#4716—31no—
90#4708—31no—
91C4×Dic12—31no—
92#4689—31no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97C22×C3⋊Dic3—21no—
98#3830—22no—
99#3830C2×C414yes—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#624—21no—
107#3797—22no—
108#3797C2×C414yescomplemented
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C42C2311yescharacteristic
112#3757—21no—
113#3752D411yescharacteristic
114#3752D411yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750D411yescharacteristic
120#3750D411yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C3×#214C2×C414yescomplemented
125C3×#214C2×C414yescomplemented
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32—21no—
142#3719C2×C414yescomplemented
143#3719C2×C414yescomplemented
144#3712C2×C414yescomplemented
145#3710—22no—
146#2947—91noSylow
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×#237—31no—
150C2×#237—31no—
151C2×#237—61no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—21no—
157C3×C4×D4C2×D311yescharacteristic
158C3×C4×D4C2×D311yescharacteristic
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161C2×#216—31no—
162C2×#216—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—61no—
166C2×#214C2×D311yescharacteristic
167C2×#214C2×D311yescharacteristic
168C4×#67—61no—
169C4×#67—61no—
170C4×#67—62no—
171C2×Dic3⋊C4—61no—
172C2×Dic3⋊C4—61no—
173C2×Dic3⋊C4—62no—
174#915—38no—
175#915—38no—
176C2×Dic12—31no—
177C2×Dic12—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182#892—31no—
183#892—31no—
184#892—61no—
185#892—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—61no—
189#887—31no—
190#887—31no—
191#887—31no—
192#887—31no—
193#887—61no—
194#887—61no—
195#887—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#67⋊C4—62no—
199#877—61no—
200#877—61no—
201#877—62no—
202#872—31no—
203#872—31no—
204#872—61no—
205#872—61no—
206#872—61no—
207C4×Dic6—31no—
208C4×Dic6—31no—
209C4×Dic6—61no—
210C4×Dic6—61no—
211C4×Dic6—61no—
212C4×Dic6C2×D311yescharacteristic
213C4×Dic6C2×D311yescharacteristic
214C3×#107—31no—
215C3×#106—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#835—31no—
223#835—31no—
224#832C2×D311yescharacteristic
225#832C2×D311yescharacteristic
226#818—31no—
227#817—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810—31no—
237#810—31no—
238#810C2×D311yescharacteristic
239#810C2×D311yescharacteristic
240#808—31no—
241#808C2×D311yescharacteristic
242#807—31no—
243#807C2×D311yescharacteristic
244#803C2×D311yescharacteristic
245C4×C3⋊C8C2×D311yescharacteristic
246C23×C32—21no—
247C22×C3⋊D3C2×D411yescharacteristic
248C32×D4—21no—
249C32×D4C22×C412yes—
250C2×C32×C4—21no—
251C2×C32×C4—81no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255#638—24no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—24no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—81no—
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4×C3⋊D3—81no—
264C4×C3⋊D3C22×C412yes—
265C4×C3⋊D3#4112yes—
266#634—21no—
267#634C22×C412yes—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6C22×C412yes—
275C3×Dic6C22×C412yes—
276#627—24no—
277#624—24no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C3×C3⋊C8C22×C412yes—
282C2×#137—91no—
283#520—91no—
284#519—91no—
285#441—91no—
286#441—91no—
287#440—31no—
288#440—91no—
289C4×Q16—91no—
290C4×Q16—91no—
291C4×SD16—31no—
292C4×SD16—91no—
293#428—91no—
294#416—91no—
295C2×#103—91no—
296#405—91no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×D4—21no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C22×C3×C4—22no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—62no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—62no—
313C22×Dic3—62no—
314D3×Q8—34no—
315D3×Q8—34no—
316D3×Q8—62no—
317D3×Q8—62no—
318#237—34no—
319#237—34no—
320#237—64no—
321#237—62no—
322#237—62no—
323#237—64no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—62no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C3×SD16—34no—
340C3×SD16—34no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C22⋊C4—22no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C42—21no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#217—61no—
361#217—61no—
362#217—62no—
363#216—34no—
364#216—34no—
365#214C4×D314yescomplemented
366#214C4×D314yescomplemented
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
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—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—62no—
397Dic3⋊C4—62no—
398Dic3⋊C4—62no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—62no—
415C4×Dic3—62no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422Dic12—34no—
423Dic12—34no—
424ΓL(1,𝔽25)—34no—
425ΓL(1,𝔽25)—34no—
426D3×C8—62no—
427D3×C8—62no—
428C22×C32—22no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3C4×D412yes—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—41no—
438C32×C4C23×C411yescharacteristic
439C32×C4C2×#4111yescharacteristic
440C3⋊Dic3—22no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—41no—
444C3⋊Dic3C4×D412yes—
445C3×Dic3—22no—
446C3×Dic3—22no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C2×#41—91no—
450C22×Q8—91no—
451#137—98no—
452C2×Q16—91no—
453C2×Q16—91no—
454C2×SD16—31no—
455C2×SD16—31no—
456C2×M16—91no—
457C22×C8—91no—
458C4×Q8—31no—
459C4×Q8—31no—
460C4×Q8—91no—
461C4×Q8—91no—
462C4×Q8—91no—
463C4×Q8—91no—
464C4×Q8—181no—
465C4×Q8—181no—
466C4×D4—91no—
467C4×D4—181no—
468C4×D4—181no—
469C4×D4D3211yescharacteristic
470#117—91no—
471#117—91no—
472#117—181no—
473#117—181no—
474#117—181no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—181no—
477#107—31no—
478#107—91no—
479#106—31no—
480#106—91no—
481#103—31no—
482#103—31no—
483#103—91no—
484#103—91no—
485#103—91no—
486#103—91no—
487#102—31no—
488#102—31no—
489#97—31no—
490#97—91no—
491C4×C8—31no—
492C4×C8—91no—
493C23×C3—22no—
494C23×C3—21no—
495C23×C3—21no—
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—61no—
499C3×Q8—32no—
500C3×Q8—32no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×D4—22no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4C2×C4×D312yes—
508C3×D4C2×C4×D312yes—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—81no—
520C2×C3×C4—81no—
521C2×C3×C4—82no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—64no—
529#67—64no—
530#67—68no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—64no—
545C2×Dic3—64no—
546C2×Dic3—62no—
547C2×Dic3—68no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—62no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—241no—
554C2×Dic3—241no—
555C2×Dic3—242no—
556C4×D3—32no—
557C4×D3—32no—
558C4×D3—32no—
559C4×D3—32no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—64no—
563C4×D3—64no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—242no—
567Dic6—21no—
568Dic6—21no—
569Dic6—32no—
570Dic6—32no—
571Dic6—62no—
572Dic6—64no—
573Dic6—64no—
574Dic6—62no—
575Dic6—61no—
576Dic6—61no—
577Dic6C2×C4×D312yes—
578Dic6C2×C4×D312yes—
579C3×C8—32no—
580C3×C8—32no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8C2×C4×D312yes—
586C3⋊C8C2×C4×D312yes—
587C2×C32—42no—
588C2×C32C2×C4×D411yescharacteristic
589C2×C32#57711yescharacteristic
590C2×C32#57811yescharacteristic
591C3⋊D3—22no—
592#41—94no—
593#41—182no—
594C2×Q8—31no—
595C2×Q8—31no—
596C2×Q8—94no—
597C2×Q8—91no—
598C2×Q8—181no—
599C2×Q8—182no—
600C2×D4—181no—
601C2×D4C2×D3211yescharacteristic
602C22×C4—21no—
603C22×C4—91no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—94no—
609Q16—94no—
610SD16—34no—
611SD16—34no—
612M16—94no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—182no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C42—61no—
637C42—61no—
638C42—91no—
639C42—181no—
640C42—181no—
641C42—181no—
642C42—181no—
643C42—181no—
644C42C2×D3211yescharacteristic
645C22×C3—24no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—32no—
658C2×D3—32no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—121no—
665C2×D3—121no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—62no—
678C3×C4—62no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4C22×C4×D311yescharacteristic
682C3×C4C22×C4×D311yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4D3×#4111yescharacteristic
685Dic3—22no—
686Dic3—22no—
687Dic3—32no—
688Dic3—32no—
689Dic3—41no—
690Dic3—41no—
691Dic3—62no—
692Dic3—64no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—62no—
698Dic3—62no—
699Dic3—121no—
700Dic3—121no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704C32#294711yescharacteristic, complemented, Sylow
705C23—21no—
706C23—91no—
707Q8—32no—
708Q8—32no—
709Q8—61no—
710Q8—61no—
711Q8—92no—
712Q8—184no—
713Q8—181no—
714D4—21no—
715D4—184no—
716D4C4×D3212yes—
717C2×C4—21no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—81no—
723C2×C4—91no—
724C2×C4—92no—
725C2×C4—92no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—184no—
729C2×C4—184no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—721no—
733C2×C4—721no—
734C2×C4#381111yescharacteristic
735C2×C4#381111yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—32no—
738C8—32no—
739C8—61no—
740C8—61no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—44no—
745C2×C3—42no—
746C2×C3—42no—
747C2×C3C4×D3×D411yescharacteristic
748C2×C3C4×D3×D411yescharacteristic
749C2×C3#576211yescharacteristic
750C2×C3#577111yescharacteristic
751C2×C3#577511yescharacteristic
752C2×C3#577911yescharacteristic
753D3—62no—
754D3—62no—
755D3—122no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—92no—
760C22—181no—
761C22—181no—
762C22C2×#381111yescharacteristic
763C4—21no—
764C4—21no—
765C4—41no—
766C4—62no—
767C4—62no—
768C4—92no—
769C4—121no—
770C4—121no—
771C4—181no—
772C4—181no—
773C4—182no—
774C4—361no—
775C4C2×C4×D3211yescharacteristic
776C4#6430611yescharacteristic
777C3—21no—
778C3#7964811yescharacteristic, complemented
779C3#7977611yescharacteristic, complemented
780C2—42no—
781C2—182no—
782C2C4×#381111yescharacteristic
783C2#1059511511yescharacteristic
784C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#3830C22
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593848C2semidirect
4. C3×#5018C2semidirect
5. C3×C4×#214C2semidirect
6. #10591446C2semidirect
7. #10591445C2semidirect
9. #10590601C2semidirect
10. #10590583C2semidirect
11. #10590485C2semidirect
12. #10590482C2semidirect
13. #10590383C2semidirect
14. C4×#3719C2semidirect
15. #10590321C2semidirect
34. #63931C4semidirect
75. #5018D3semidirect
76. C4×#214D3semidirect
108. #3797C2×C4semidirect
124. C3×#214C2×C4semidirect
125. C3×#214C2×C4semidirect
142. #3719C2×C4semidirect
143. #3719C2×C4semidirect
144. #3712C2×C4semidirect
365. #214C4×D3semidirect
366. #214C4×D3semidirect
704. C32#2947semidirect
778. C3#79648semidirect
779. C3#79776semidirect

Maximal subgroups

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

subgroupindex
#105960172
C2×#639312
#105938482
C3×#50182
C3×C4×#2142
#105914462
#105914452
#105914242
#105906012
#105905832
#105904852
#105904822
#105903832
C4×#37192
#105903212
#797763
#796483