Finite Group Databasebeta

← #11860389

Subgroups — #11860389

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64124C211yesmaximal, characteristic
2Q8×#624C211yesmaximal, characteristic, complemented
3#10595190C211yesmaximal, characteristic
4C3×#5164C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591562C211yesmaximal, characteristic, complemented
7#10591541C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10591418C211yesmaximal, characteristic
10#10591405C211yesmaximal, characteristic, complemented
11#10591401C211yesmaximal, characteristic, complemented
12#10590810C211yesmaximal, characteristic, complemented
13#10590807C211yesmaximal, characteristic, complemented
14#10590688C211yesmaximal, characteristic, complemented
15#10590664C211yesmaximal, characteristic, complemented
16#79774—31nomaximal
17C4×#915—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3830C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23#64124C418yescomplemented
24C2×#3746C2211yescharacteristic
25C2×#3743C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30#63957—21no—
31C2×Dic32—21no—
32#63952—21no—
33#63952—21no—
34#63900—21no—
35#63900C2211yescharacteristic
36C4×#624—21no—
37C4×#624C2211yescharacteristic
38#63849C2211yescharacteristic
39#63844—21no—
40#63844—21no—
41#63844C2211yescharacteristic
42#63844C2211yescharacteristic
43#63844C2211yescharacteristic
44#63844C2211yescharacteristic
45C2×#3712C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54#63576C2211yescharacteristic
55#63574C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63567C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×#915—31no—
63C2×#915—31no—
64C2×#915—61no—
65C4×D3×Q8—31no—
66C4×D3×Q8—31no—
67C4×#237—31no—
68C4×#237—31no—
69C3×#440—31no—
70C3×C4×SD16—31no—
71#5164D311yescharacteristic, complemented
72Dic3×SD16D311yescharacteristic, complemented
73#5030—31no—
74C4×#216—31no—
75#5018—31no—
76C4×#214—31no—
77#4881—31no—
78#4873—31no—
79#4861—31no—
80#4853—31no—
81#4802—31no—
82#4802—31no—
83#4790—31no—
84#4789—31no—
85#4771—31no—
86#4771—31no—
87#4758—31no—
88#4757—31no—
89#4716—31no—
90#4707—31no—
91C4×Dic12—31no—
92C4×ΓL(1,𝔽25)—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97Q8×C3⋊D3—22no—
98Q8×C3⋊D3C2×C414yescomplemented
99#3830—22no—
100#3830C2×C414yes—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634—21no—
104C2×#634C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C2×#624—21no—
109C2×#624D411yescharacteristic
110C2×#624D411yescharacteristic
111C32×SD16C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113#3756C2×C414yescomplemented
114#3754C2×C414yescomplemented
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3746C2×C414yescomplemented
117#3743C2×C414yescomplemented
118C3×#217—21no—
119C3×#217—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133#3724—21no—
134#3724—21no—
135#3724—21no—
136#3724—21no—
137#3722—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32D411yescharacteristic
144Dic32D411yescharacteristic
145#3712—22no—
146C4×#137—91noSylow
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—61no—
150C2×#237—31no—
151C2×#237—31no—
152C2×#237—61no—
153C2×C3×SD16—21no—
154C2×C3×SD16C2×D311yescharacteristic
155C2×C3×SD16C2×D311yescharacteristic
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160Q8×Dic3C2×D311yescharacteristic
161Q8×Dic3C2×D311yescharacteristic
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—61no—
165D4×Dic3C2×D311yescharacteristic
166D4×Dic3C2×D311yescharacteristic
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—61no—
170C4×#67—61no—
171C4×#67—61no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3—61no—
174#915—38no—
175#915—38no—
176#915—68no—
177C2×Dic12—31no—
178C2×Dic12—31no—
179C2×Dic12—61no—
180C2×ΓL(1,𝔽25)—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—61no—
185#892—31no—
186#892—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4—61no—
191#887—31no—
192#887—31no—
193#887—31no—
194#887—31no—
195#887—61no—
196#887—61no—
197#67⋊C4—61no—
198#67⋊C4—61no—
199#877—61no—
200#877—61no—
201C42×D3—31no—
202C42×D3—31no—
203C42×D3—61no—
204C42×D3—61no—
205C4×Dic6—31no—
206C4×Dic6—31no—
207C4×Dic6—31no—
208C4×Dic6—31no—
209C4×Dic6—61no—
210C4×Dic6—61no—
211C3×#107—31no—
212C3×#106—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#97—31no—
218C3×C4×C8—31no—
219#835C2×D311yescharacteristic
220#835C2×D311yescharacteristic
221#832C2×D311yescharacteristic
222#832C2×D311yescharacteristic
223#818C2×D311yescharacteristic
224#817C2×D311yescharacteristic
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#815—31no—
230#815C2×D311yescharacteristic
231C8×Dic3—31no—
232C8×Dic3C2×D311yescharacteristic
233#810—31no—
234#810—31no—
235#810—31no—
236#810—31no—
237#808—31no—
238#808—31no—
239#807—31no—
240#807—31no—
241#803—31no—
242C4×C3⋊C8—31no—
243C23×C32—21no—
244C22×C3⋊D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C32×D4—21no—
248C32×D4C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251#638—24no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—24no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4×C3⋊D3—24no—
257C4×C3⋊D3C22×C412yes—
258C4×C3⋊D3#4112yes—
259#634—21no—
260#634—21no—
261#634—24no—
262#634C22×C412yes—
263#634C22×C412yes—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—42no—
269C2×C3×Dic3—42no—
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274#624—22no—
275#624—41no—
276#624—42no—
277C32×C8C22×C412yes—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C2×#137—91no—
282C4×#41—91no—
283C2×C4×Q8—91no—
284#441—91no—
285#441—91no—
286#440—31no—
287#440—91no—
288C4×Q16—91no—
289C4×Q16—91no—
290C4×SD16—31no—
291C4×SD16—91no—
292#428—91no—
293#419—91no—
294#417—91no—
295C4×M16—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—121no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—121no—
312D3×Q8—34no—
313D3×Q8—34no—
314D3×Q8—64no—
315D3×Q8—62no—
316D3×Q8—62no—
317D3×Q8—122no—
318#237—34no—
319#237—34no—
320#237—64no—
321#237—62no—
322#237—62no—
323#237—122no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—121no—
336C2×Dic6—31no—
337C2×Dic6—31no—
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—61no—
343C2×Dic6—61no—
344C2×Dic6—121no—
345C3×SD16—24no—
346C3×SD16C4×D314yescomplemented
347C3×SD16C4×D314yescomplemented
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—31no—
362C3×C42—31no—
363C3×C42—61no—
364C3×C42—61no—
365#217—21no—
366#217—21no—
367#216—34no—
368#216—34no—
369#216—64no—
370#214—34no—
371#214—34no—
372#214—64no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3C22×D311yescharacteristic
408C4×Dic3C22×D311yescharacteristic
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414Dic12—34no—
415Dic12—34no—
416Dic12—64no—
417ΓL(1,𝔽25)—34no—
418ΓL(1,𝔽25)—34no—
419ΓL(1,𝔽25)—64no—
420ΓL(1,𝔽25)—62no—
421ΓL(1,𝔽25)—62no—
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32C22×D411yescharacteristic
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3C4×D412yes—
429C32×C4—22no—
430C32×C4C23×C411yescharacteristic
431C32×C4C2×#4111yescharacteristic
432C3⋊Dic3—22no—
433C3⋊Dic3—22no—
434C3⋊Dic3C4×D412yes—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3#13712yescomplemented
443C2×#41—91no—
444C22×Q8—91no—
445#137—98no—
446C2×Q16—91no—
447C2×Q16—91no—
448C2×SD16—91no—
449C2×SD16D3211yescharacteristic
450C2×M16—91no—
451C2×M16—91no—
452C4×Q8—31no—
453C4×Q8—31no—
454C4×Q8—91no—
455C4×Q8—91no—
456C4×Q8—91no—
457C4×Q8—91no—
458C4×Q8—181no—
459C4×Q8—181no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—181no—
463C4×D4—181no—
464#117—91no—
465#117—181no—
466C2×C4⋊C4—91no—
467C2×C4⋊C4—181no—
468C2×C42—91no—
469C2×C42—181no—
470C2×C42—181no—
471#107—31no—
472#107—91no—
473#106—31no—
474#106—91no—
475#103—31no—
476#103—31no—
477#103—91no—
478#103—91no—
479#103—91no—
480#103—91no—
481#102—31no—
482#102—31no—
483#97—31no—
484#97—91no—
485C4×C8—31no—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—41no—
490C22×D3—31no—
491C22×D3—31no—
492C22×D3—61no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—22no—
496C3×Q8—41no—
497C3×Q8C2×C4×D312yes—
498C3×Q8C2×C4×D312yes—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—22no—
502C3×D4—41no—
503C3×D4C2×C4×D312yes—
504C3×D4C2×C4×D312yes—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—122no—
518C2×C3×C4—122no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—64no—
522#67—64no—
523#67—124no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—42no—
531C2×Dic3—42no—
532C2×Dic3—61no—
533C2×Dic3—64no—
534C2×Dic3—64no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—124no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546C4×D3—32no—
547C4×D3—32no—
548C4×D3—32no—
549C4×D3—32no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—64no—
554C4×D3—64no—
555C4×D3—62no—
556C4×D3—124no—
557C4×D3—121no—
558C4×D3—121no—
559C4×D3—122no—
560C4×D3—122no—
561Dic6—32no—
562Dic6—32no—
563Dic6—32no—
564Dic6—32no—
565Dic6—62no—
566Dic6—62no—
567Dic6—64no—
568Dic6—64no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—61no—
573Dic6—124no—
574Dic6—121no—
575Dic6—121no—
576C3×C8—22no—
577C3×C8—61no—
578C3×C8—61no—
579C3×C8C2×C4×D312yes—
580C3×C8C2×C4×D312yes—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—32no—
584C3⋊C8—32no—
585C3⋊C8—62no—
586C2×C32—42no—
587C2×C32C2×C4×D411yescharacteristic
588C2×C32C2×#13711yescharacteristic
589C2×C32#57511yescharacteristic
590C3⋊D3—22no—
591#41—94no—
592#41—182no—
593C2×Q8—94no—
594C2×Q8—91no—
595C2×Q8—91no—
596C2×Q8—181no—
597C2×Q8—182no—
598C2×Q8C2×D3211yescharacteristic
599C2×D4—181no—
600C2×D4C2×D3211yescharacteristic
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4—91no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609Q16—94no—
610Q16—94no—
611SD16—94no—
612SD16#62414yescomplemented
613M16—94no—
614M16—182no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—181no—
633C42—31no—
634C42—31no—
635C42—61no—
636C42—61no—
637C42—91no—
638C42—91no—
639C42—181no—
640C42—181no—
641C42—181no—
642C42—181no—
643C42—181no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—21no—
647C22×C3—42no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—32no—
657C2×D3—32no—
658C2×D3—62no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—121no—
664C2×D3—121no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—32no—
670C3×C4—42no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C22×C4×D311yescharacteristic
679C3×C4C22×C4×D311yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—32no—
686Dic3—32no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—62no—
692Dic3—62no—
693Dic3—62no—
694Dic3—62no—
695Dic3—62no—
696Dic3—122no—
697Dic3—122no—
698Dic3#91512yescomplemented
699C32C4×#13711yescharacteristic, complemented, Sylow
700C23—21no—
701C23—91no—
702Q8—21no—
703Q8—92no—
704Q8—92no—
705Q8—184no—
706Q8—181no—
707Q8—181no—
708Q8C2×#62412yes—
709D4—21no—
710D4—184no—
711D4C2×#62412yes—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—91no—
722C2×C4—92no—
723C2×C4—92no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4—184no—
727C2×C4—182no—
728C2×C4—184no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—361no—
732C2×C4—362no—
733C2×C4C22×D3211yescharacteristic
734C8—61no—
735C8—61no—
736C8—92no—
737C8C2×#62412yes—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—42no—
743C2×C3—82no—
744C2×C3C4×D3×D411yescharacteristic
745C2×C3C4×D3×D411yescharacteristic
746C2×C3C2×#91511yescharacteristic
747C2×C3#576811yescharacteristic
748C2×C3#577311yescharacteristic
749C2×C3D3×#13711yescharacteristic
750D3—62no—
751D3—62no—
752D3—122no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—92no—
757C22—181no—
758C22—181no—
759C22D32×D411yescharacteristic
760C4—22no—
761C4—32no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—92no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—182no—
771C4—182no—
772C4#6431211yescharacteristic
773C4C22×#62411yescharacteristic
774C3—21no—
775C3C4×#91511yescharacteristic, complemented
776C3#7977411yescharacteristic, complemented
777C2—42no—
778C2—182no—
779C2D3×#91511yescharacteristic
780C2#1059474511yescharacteristic
781C2D4×#62411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×#3830C22
cosocleC2×C32×C4C24
hypercenterC2×SD16D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. Q8×#624C2semidirect
4. C3×#5164C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591562C2semidirect
7. #10591541C2semidirect
8. #10591537C2semidirect
10. #10591405C2semidirect
11. #10591401C2semidirect
12. #10590810C2semidirect
13. #10590807C2semidirect
14. #10590688C2semidirect
15. #10590664C2semidirect
23. #64124C4semidirect
71. #5164D3semidirect
72. Dic3×SD16D3semidirect
98. Q8×C3⋊D3C2×C4semidirect
111. C32×SD16C2×C4semidirect
113. #3756C2×C4semidirect
114. #3754C2×C4semidirect
116. #3746C2×C4semidirect
117. #3743C2×C4semidirect
346. C3×SD16C4×D3semidirect
347. C3×SD16C4×D3semidirect
442. C3×Dic3#137semidirect
612. SD16#624semidirect
698. Dic3#915semidirect
699. C32C4×#137semidirect
775. C3C4×#915semidirect
776. C3#79774semidirect

Maximal subgroups

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

subgroupindex
C2×#641242
Q8×#6242
#105951902
C3×#51642
C3×Dic3×SD162
#105915622
#105915412
#105915372
#105914182
#105914052
#105914012
#105908102
#105908072
#105906882
#105906642
#797743
C4×#9153