Finite Group Databasebeta

← #11860392

Subgroups — #11860392

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 767 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#624C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic
3#10594360C211yesmaximal, characteristic
4#10592501C211yesmaximal, characteristic, complemented
5C3×#4817C211yesmaximal, characteristic, complemented
6C3×#4790C211yesmaximal, characteristic, complemented
7#10591576C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10590957C211yesmaximal, characteristic
10#10590794C211yesmaximal, characteristic, complemented
11#10590744C211yesmaximal, characteristic, complemented
12#10590664C211yesmaximal, characteristic, complemented
13#10590590C211yesmaximal, characteristic, complemented
14#10590582C211yesmaximal, characteristic, complemented
15#10590481C211yesmaximal, characteristic, complemented
16#79774—31nomaximal
17C4×#918—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63951C418yescomplemented
29#63904—21no—
30#63900—21no—
31#63900C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33C4×#624—21no—
34C4×#624C2211yescharacteristic
35#63880—21no—
36#63878—21no—
37C4×D3×Dic3—21no—
38#63844—21no—
39#63844—21no—
40#63844C2211yescharacteristic
41#63844C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C2×#3716C2211yescharacteristic
45C2×#3712C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63662C2211yescharacteristic
48#63643C2211yescharacteristic
49#63637C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#807C2211yescharacteristic
55C3×#807C2211yescharacteristic
56#63573C2211yescharacteristic
57#63573C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×#918—31no—
63C2×#915—31no—
64C4×#239—31no—
65C4×D3×Q8—31no—
66C4×D3×Q8—31no—
67C4×#237—31no—
68C3×#440—31no—
69C3×C4×Q16—31no—
70#5184—31no—
71Dic3×SD16—31no—
72#5030—31no—
73C4×#216—31no—
74C4×#215—31no—
75#5018—31no—
76#4889—31no—
77#4881—31no—
78#4881—31no—
79#4873—31no—
80#4817D311yescharacteristic, complemented
81#4803—31no—
82#4802—31no—
83#4802—31no—
84#4802—61no—
85#4790D311yescharacteristic, complemented
86#4789—31no—
87#4771—31no—
88#4758—31no—
89#4716—31no—
90#4707—31no—
91C4×#204—31no—
92C4×ΓL(1,𝔽25)—31no—
93C2×C32×Q8C2311yescharacteristic
94Q8×C3⋊D3—22no—
95Q8×C3⋊D3C2×C414yescomplemented
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#624—21no—
105C2×#624D411yescharacteristic
106C2×#624D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3796—22no—
110#3796C2×C414yes—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3743—22no—
118C3×#216C2×C414yescomplemented
119C3×#215C2×C414yescomplemented
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143#3719C2×C414yescomplemented
144#3716C2×C414yescomplemented
145#3712C2×C414yescomplemented
146C4×#137—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×D3×Q8—61no—
151C2×#237—31no—
152C2×C3×Q16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158Q8×Dic3—31no—
159Q8×Dic3C2×D311yescharacteristic
160Q8×Dic3C2×D311yescharacteristic
161C2×#216—31no—
162C2×#216C2×D311yescharacteristic
163C2×#215C2×D311yescharacteristic
164D4×Dic3—31no—
165C2×#214—31no—
166C4×#67—61no—
167C2×C4×Dic3—61no—
168#918—38no—
169#915—38no—
170C2×Dic12—31no—
171C2×#204—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—61no—
177#893—61no—
178#893C2×D311yescharacteristic
179#892—31no—
180#892—31no—
181#892—61no—
182#892—61no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4—61no—
187#887—31no—
188#887—31no—
189#887—61no—
190#887—61no—
191#887C2×D311yescharacteristic
192#67⋊C4—61no—
193#877—61no—
194C4×D12—31no—
195C4×D12—61no—
196C42×D3—31no—
197C42×D3—31no—
198C42×D3—61no—
199C42×D3—61no—
200C42×D3—61no—
201C4×Dic6—31no—
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—61no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#107—31no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#102—31no—
213C3×#97—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835—31no—
217#835—31no—
218#835—61no—
219#832—31no—
220#821C2×D311yescharacteristic
221#817—31no—
222#817—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816C2×D311yescharacteristic
227#815—31no—
228#815C2×D311yescharacteristic
229C8×Dic3—31no—
230C8×Dic3C2×D311yescharacteristic
231#810—31no—
232#810—31no—
233#810—31no—
234#810—61no—
235#809—31no—
236#808—31no—
237#808—31no—
238#807C2×D311yescharacteristic
239#807C2×D311yescharacteristic
240#803—31no—
241C4×C3⋊C8—31no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C32×Q8—21no—
245C32×Q8C22×C412yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4×C3⋊D3—24no—
253C4×C3⋊D3C22×C412yes—
254C4×C3⋊D3#4112yes—
255#634—21no—
256#634—24no—
257#634C22×C412yes—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12C22×C412yes—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6C22×C412yes—
270#626—24no—
271#624—22no—
272#624—41no—
273#624—42no—
274D3×Dic3—24no—
275D3×Dic3—42no—
276C32×C8—21no—
277C3⋊(C3⋊C8)—21no—
278C3×C3⋊C8C22×C412yes—
279C3×C3⋊C8C22×C412yes—
280C2×#137—91no—
281C4×#41—91no—
282C2×C4×Q8—91no—
283#441—91no—
284#441—91no—
285#440—31no—
286#440—91no—
287C4×Q16—31no—
288C4×Q16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#428—91no—
292#419—91no—
293#417—91no—
294C4×M16—91no—
295C2×C3×Q8—21no—
296C2×C3×Q8—31no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—31no—
300C22×C3×C4—61no—
301C2×#67—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304#239—34no—
305#239—62no—
306D3×Q8—34no—
307D3×Q8—34no—
308D3×Q8—64no—
309D3×Q8—62no—
310D3×Q8—62no—
311D3×Q8—122no—
312#237—34no—
313#237—62no—
314C2×D12—61no—
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—121no—
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—121no—
337C2×Dic6C22×D311yescharacteristic
338C3×Q16—34no—
339C3×SD16—34no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C42—31no—
355C3×C42—31no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42—61no—
359#217—61no—
360#216—34no—
361#216C4×D314yescomplemented
362#215C4×D314yescomplemented
363#214—34no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—121no—
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C4×Dic3C22×D311yescharacteristic
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408Dic12—34no—
409#204—34no—
410ΓL(1,𝔽25)—34no—
411ΓL(1,𝔽25)—34no—
412ΓL(1,𝔽25)—62no—
413ΓL(1,𝔽25)—62no—
414ΓL(1,𝔽25)—122no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3C4×D412yes—
419C2×C3×D3—22no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—22no—
423C32×C4—41no—
424C32×C4C23×C411yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3⋊Dic3—22no—
427C3⋊Dic3—41no—
428C3⋊Dic3C4×D412yes—
429C3×Dic3—22no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3#13712yescomplemented
436C2×#41—91no—
437C22×Q8—91no—
438#137—98no—
439C2×Q16—31no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×M16—91no—
444C2×M16—91no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×Q8—181no—
452C4×Q8—181no—
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—181no—
456C4×D4—181no—
457#117—91no—
458#117—181no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—181no—
461C2×C42—91no—
462C2×C42—181no—
463C2×C42—181no—
464#107—31no—
465#107—31no—
466#106—91no—
467#106—91no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103D3211yescharacteristic
474#102—31no—
475#102—91no—
476#97—31no—
477#97—91no—
478C4×C8—31no—
479C4×C8—91no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—22no—
488C3×Q8—32no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8C2×C4×D312yes—
492C3×Q8C2×C4×D312yes—
493C3×D4—32no—
494C3×D4—61no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—64no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—61no—
519C2×Dic3—64no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—122no—
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531D12—21no—
532D12—64no—
533D12C2×C4×D312yes—
534C4×D3—32no—
535C4×D3—32no—
536C4×D3—32no—
537C4×D3—32no—
538C4×D3—42no—
539C4×D3—62no—
540C4×D3—62no—
541C4×D3—62no—
542C4×D3—64no—
543C4×D3—64no—
544C4×D3—64no—
545C4×D3—62no—
546C4×D3—124no—
547C4×D3—121no—
548C4×D3—121no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552Dic6—21no—
553Dic6—32no—
554Dic6—32no—
555Dic6—62no—
556Dic6—64no—
557Dic6—64no—
558Dic6—61no—
559Dic6—61no—
560Dic6—124no—
561Dic6—121no—
562Dic6C2×C4×D312yes—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—32no—
566C3×C8—32no—
567C3×C8—41no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C3⋊C8C2×C4×D312yes—
572C3⋊C8C2×C4×D312yes—
573C2×C32C2×C4×D411yescharacteristic
574C2×C32C2×#13711yescharacteristic
575C2×C32#57511yescharacteristic
576C3⋊D3—22no—
577C3×D3—42no—
578#41—94no—
579#41—182no—
580C2×Q8—31no—
581C2×Q8—94no—
582C2×Q8—91no—
583C2×Q8—181no—
584C2×Q8—182no—
585C2×Q8C2×D3211yescharacteristic
586C2×D4—31no—
587C2×D4—181no—
588C22×C4—61no—
589C22×C4—91no—
590C22×C4—91no—
591C22×C4—91no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596Q16—34no—
597Q16—94no—
598SD16—34no—
599SD16—94no—
600M16—94no—
601M16—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8C2×D3211yescharacteristic
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—61no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—31no—
621C42—31no—
622C42—61no—
623C42—61no—
624C42—61no—
625C42—91no—
626C42—91no—
627C42—181no—
628C42—181no—
629C42—181no—
630C42—181no—
631C22×C3—21no—
632C22×C3—62no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C2×D3—22no—
638C2×D3—32no—
639C2×D3—32no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—62no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—121no—
648C2×D3—121no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—32no—
654C3×C4—42no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—62no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4C22×C4×D311yescharacteristic
665C3×C4C22×C4×D311yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—22no—
672Dic3—32no—
673Dic3—32no—
674Dic3—41no—
675Dic3—41no—
676Dic3—62no—
677Dic3—62no—
678Dic3—62no—
679Dic3—122no—
680Dic3—121no—
681Dic3—121no—
682Dic3—241no—
683Dic3#91812yescomplemented
684C32C4×#13711yescharacteristic, complemented, Sylow
685C23—61no—
686C23—91no—
687Q8—21no—
688Q8—32no—
689Q8—61no—
690Q8—92no—
691Q8—184no—
692Q8—181no—
693Q8C4×D3212yes—
694D4—32no—
695D4—61no—
696D4—184no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—91no—
707C2×C4—92no—
708C2×C4—92no—
709C2×C4—122no—
710C2×C4—184no—
711C2×C4—182no—
712C2×C4—184no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—362no—
716C2×C4—361no—
717C2×C4—362no—
718C2×C4C22×D3211yescharacteristic
719C8—21no—
720C8—32no—
721C8—32no—
722C8—181no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—122no—
727C2×C3C4×D3×D411yescharacteristic
728C2×C3C4×D3×D411yescharacteristic
729C2×C3C2×#91811yescharacteristic
730C2×C3#576811yescharacteristic
731C2×C3#577311yescharacteristic
732C2×C3D3×#13711yescharacteristic
733D3—42no—
734D3—62no—
735D3—62no—
736D3—122no—
737C22—62no—
738C22—92no—
739C22—121no—
740C22—121no—
741C22—181no—
742C22—181no—
743C22D32×D411yescharacteristic
744C4—22no—
745C4—32no—
746C4—41no—
747C4—61no—
748C4—61no—
749C4—61no—
750C4—62no—
751C4—92no—
752C4—121no—
753C4—121no—
754C4—182no—
755C4—361no—
756C4C2×C4×D3211yescharacteristic
757C4#6431211yescharacteristic
758C3—21no—
759C3C4×#91811yescharacteristic, complemented
760C3#7977411yescharacteristic, complemented
761C2—122no—
762C2—182no—
763C2#1059425511yescharacteristic
764C2#1059474511yescharacteristic
765C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. Q8×#624C2semidirect
4. #10592501C2semidirect
5. C3×#4817C2semidirect
6. C3×#4790C2semidirect
7. #10591576C2semidirect
8. Dic3×#215C2semidirect
10. #10590794C2semidirect
11. #10590744C2semidirect
12. #10590664C2semidirect
13. #10590590C2semidirect
14. #10590582C2semidirect
15. #10590481C2semidirect
28. #63951C4semidirect
80. #4817D3semidirect
85. #4790D3semidirect
95. Q8×C3⋊D3C2×C4semidirect
118. C3×#216C2×C4semidirect
119. C3×#215C2×C4semidirect
143. #3719C2×C4semidirect
144. #3716C2×C4semidirect
145. #3712C2×C4semidirect
361. #216C4×D3semidirect
362. #215C4×D3semidirect
435. C3×Dic3#137semidirect
683. Dic3#918semidirect
684. C32C4×#137semidirect
759. C3C4×#918semidirect
760. C3#79774semidirect

Maximal subgroups

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

subgroupindex
Q8×#6242
C2×#639512
#105943602
#105925012
C3×#48172
C3×#47902
#105915762
Dic3×#2152
#105909572
#105907942
#105907442
#105906642
#105905902
#105905822
#105904812
#797743
C4×#9183