Finite Group Databasebeta

← #11675096

Subgroups — #11675096

Order 768.

1814 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#556C211yesmaximal, characteristic, complemented
2Q8×#235C211yesmaximal, characteristic, complemented
3#83678C214yesmaximal, complemented
4#83677C212yesmaximal, complemented
5#83676C212yesmaximal, complemented
6#83669C214yesmaximal, complemented
7#83668C212yesmaximal, complemented
8#83667C212yesmaximal, complemented
9#83209C211yesmaximal, characteristic, complemented
10#83198C211yesmaximal, characteristic, complemented
11#82945C212yesmaximal
12#82939C212yesmaximal, complemented
13Q8×#208C211yesmaximal, characteristic, complemented
14#82431C212yesmaximal, complemented
15C4×#942C212yesmaximal, complemented
16#82296C211yesmaximal, characteristic, complemented
17C4×#932C211yesmaximal, characteristic
18#61323—31nomaximal, Sylow
19C3×#556—21no—
20C3×#556—21no—
21C3×#556—22no—
22C3×#556C2212yes—
23C3×#556C2212yes—
24C3×#556C2214yes—
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×#126—22no—
27C2×C3×#124C2212yes—
28C2×C3×C22⋊Q8—21no—
29C2×C3×C4×Q8C2212yes—
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×#117—21no—
33Q8×#67—21no—
34C2×#942C2212yes—
35C2×#932C2211yescharacteristic
36#5579C2211yescharacteristic, complemented
37#5579C2212yescomplemented
38#5578—21no—
39#5578—22no—
40Q8×D12C2211yescharacteristic, complemented
41C4×D3×Q8—21no—
42#5567C2211yescharacteristic, complemented
43#5567C2212yescomplemented
44Q8×Dic6C2211yescharacteristic, complemented
45#5511—21no—
46#5511—22no—
47C4×#235C2212yes—
48C4×#235C2211yescharacteristic
49#5470C2211yescharacteristic
50#5470C2212yes—
51#5225C2212yes—
52#5225C2212yes—
53#5225C2212yes—
54#5215C2212yes—
55#5215C2211yescharacteristic
56#5090C2212yescomplemented
57#5090C2212yescomplemented
58#5083C2212yescomplemented
59#5083C2212yescomplemented
60#5082C2214yescomplemented
61#5079C2212yescomplemented
62#5079C2212yescomplemented
63#5057C2214yes—
64#5057C2214yes—
65#5056C2214yes—
66#5056C2214yes—
67#5055C2214yes—
68#5055C2214yes—
69#5054C2214yes—
70#5054C2214yes—
71#5030C2214yescomplemented
72C4×#216C2214yescomplemented
73#5026C2214yescomplemented
74C4×#215C2214yescomplemented
75#5024C2212yescomplemented
76#5024C2214yescomplemented
77Q8×C3⋊C8C2212yescomplemented
78#5022C2214yescomplemented
79#5022C2214yescomplemented
80#5021C2214yescomplemented
81#5020C2214yescomplemented
82#5018C2212yes—
83C4×#214C2212yes—
84#5014C2212yes—
85C4×#213C2212yes—
86#5009C2214yes—
87#5008C2212yes—
88#5007C2212yes—
89#4966C2211yescharacteristic
90#4964C2211yescharacteristic
91#4964C2212yes—
92#4924C2212yes—
93#4924C2211yescharacteristic
94C4×#208C2211yescharacteristic
95C4×#208C2212yes—
96Q8×#41—31no—
97C2×#556D311yescharacteristic, complemented
98#3377—34no—
99#3376—34no—
100#3369—32no—
101#3367—32no—
102#3364—32no—
103#3360—32no—
104#3140—32no—
105#3139—31no—
106#3078—32no—
107#3077—31no—
108#3040—32no—
109#3039—31no—
110Q8×M16—31no—
111C4×#137—32no—
112C4×AGL(1,ℤ/8)—31no—
113C22×C3×Q8D411yescharacteristic
114C22×C3×Q8C2312yes—
115C22×C3×D4C2311yescharacteristic
116C23×C3×C4—21no—
117C2×D3×Q8—21no—
118C2×#235C2311yescharacteristic
119C3×C4⋊Q8—21no—
120C3×C4⋊Q8—21no—
121C3×C4⋊Q8C2312yes—
122C3×C4⋊Q8C2312yes—
123C3×#126—24no—
124C3×#126—24no—
125C3×#126—24no—
126C3×#126—24no—
127C3×#124—22no—
128C3×#124—22no—
129C3×#124C2314yes—
130C3×#124C2314yes—
131C3×C22⋊Q8—22no—
132C3×C22⋊Q8—22no—
133C3×C22⋊Q8—24no—
134C3×C4×Q8—22no—
135C3×C4×Q8—22no—
136C3×C4×Q8D411yescharacteristic
137C3×C4×Q8D411yescharacteristic
138C3×C4×Q8D412yes—
139C3×C4×Q8C2314yes—
140C3×C4×Q8C2314yes—
141C3×C4×Q8C2311yescharacteristic
142C3×C4×Q8C2311yescharacteristic
143C3×C4×Q8C2312yes—
144C3×C4×D4—21no—
145C3×C4×D4—21no—
146C3×C4×D4C2312yes—
147C3×C4×D4C2312yes—
148C3×#117—22no—
149C3×#117—22no—
150C3×#117—24no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—22no—
153C2×C3×C4⋊C4—21no—
154C2×C3×C4⋊C4D411yescharacteristic
155C2×C3×C4⋊C4D412yes—
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C42—22no—
161C2×C3×C42C2311yescharacteristic
162C2×C3×C42C2312yes—
163#946—21no—
164#946—22no—
165Q8×Dic3—21no—
166#944—21no—
167#944—22no—
168C2×#216C2314yes—
169#942—28no—
170C2×#215C2314yes—
171C2×#214C2312yes—
172#932—24no—
173C2×#213C2312yes—
174C4×#67—22no—
175C4×#67—21no—
176C4×#67—21no—
177C4×#67—22no—
178#926C2312yes—
179#926C2311yescharacteristic
180#924—22no—
181#924—21no—
182#924—21no—
183#924—22no—
184C2×#208C2311yescharacteristic
185C2×#208C2312yes—
186C2×#208C2311yescharacteristic
187#897—21no—
188#897—22no—
189#896—22no—
190#896—22no—
191#896—22no—
192D3×C4⋊C4—21no—
193D3×C4⋊C4—22no—
194#889—22no—
195#889—22no—
196#889—22no—
197#888—21no—
198#888—22no—
199#887—21no—
200#887—22no—
201C4×D12C2311yescharacteristic
202C4×D12C2311yescharacteristic
203C4×D12C2312yes—
204C4×D12C2312yes—
205#872—21no—
206#872—22no—
207C42×D3—21no—
208C42×D3—22no—
209#870C2312yes—
210#870C2312yes—
211#870C2312yes—
212#869C2311yescharacteristic
213#869C2311yescharacteristic
214#869C2312yes—
215#869C2312yes—
216C4×Dic6—21no—
217C4×Dic6—22no—
218C4×Dic6—21no—
219C4×Dic6—22no—
220C4×Dic6C2311yescharacteristic
221C4×Dic6C2311yescharacteristic
222C4×Dic6C2312yes—
223C4×Dic6C2312yes—
224#835C2314yes—
225#835C2314yes—
226#835C2314yes—
227#835C2314yes—
228#835C2314yes—
229#835C2314yes—
230#832C2314yes—
231#832C2314yes—
232#832C2312yes—
233#832C2312yes—
234#810C2312yes—
235#809C2312yes—
236#808C2314yes—
237#808C2312yes—
238#807C2314yes—
239#807C2312yes—
240C4⋊(C3⋊C8)C2312yes—
241C4⋊(C3⋊C8)C2312yes—
242C4⋊(C3⋊C8)C2314yes—
243C4⋊(C3⋊C8)C2314yes—
244#803C2312yes—
245#803C2314yes—
246C4×C3⋊C8C2312yes—
247C4×C3⋊C8C2314yes—
248C2×#137—32no—
249C2×AGL(1,ℤ/8)—31no—
250Q82—31no—
251#557—31no—
252#557—32no—
253#556—21no—
254#556—22no—
255#556—21no—
256#556C2×D312yes—
257#556C2×D312yes—
258#556C2×D314yes—
259#554—31no—
260#554—32no—
261#554—61no—
262#554—62no—
263D4×Q8—31no—
264D4×Q8—61no—
265#533—31no—
266#533—32no—
267#533—61no—
268#533—62no—
269C2×C4⋊Q8C2×D311yescharacteristic
270C2×#126—22no—
271C2×#124C2×D312yes—
272C2×C22⋊Q8—21no—
273C4×#41—31no—
274C4×#41—32no—
275C2×C4×Q8—61no—
276C2×C4×Q8C2×D312yes—
277C2×C4×Q8C2×D311yescharacteristic
278C2×C4×D4C2×D311yescharacteristic
279C2×#117—21no—
280#491—34no—
281#489—34no—
282#489—34no—
283#488—34no—
284#488—34no—
285#487—32no—
286#487—32no—
287#479—34no—
288#479—34no—
289#478—34no—
290#477—34no—
291#476—32no—
292#475—34no—
293#474—32no—
294#464—34no—
295#464—34no—
296#463—34no—
297#463—34no—
298#462—32no—
299#462—32no—
300#461—32no—
301#461—32no—
302#446—32no—
303#446—34no—
304C8×Q8—32no—
305#442—32no—
306#441—34no—
307#440—34no—
308#440—32no—
309C4×Q16—34no—
310C4×SD16—34no—
311C4×SD16—32no—
312C4×D8—32no—
313#428—32no—
314#428—31no—
315#423—31no—
316#423—32no—
317#419—32no—
318#419—32no—
319#419—32no—
320#418—32no—
321#418—31no—
322#417—31no—
323C4×M16—31no—
324C4×M16—32no—
325C24×C3—21no—
326C2×C3×Q8—22no—
327C2×C3×Q8—24no—
328C2×C3×Q8—24no—
329C2×C3×Q8—42no—
330C2×C3×Q8C2×D411yescharacteristic
331C2×C3×Q8C2×D411yescharacteristic
332C2×C3×Q8C2×D412yes—
333C2×C3×Q8C2414yes—
334C2×C3×D4—21no—
335C2×C3×D4—22no—
336C2×C3×D4—22no—
337C2×C3×D4C2412yes—
338C22×C3×C4—21no—
339C22×C3×C4—22no—
340C22×C3×C4—22no—
341C22×C3×C4—22no—
342C22×C3×C4—44no—
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2×D412yes—
345C22×C3×C4C2×D411yescharacteristic
346C22×C3×C4C2×D412yes—
347C22×C3×C4C2411yescharacteristic
348C2×#67—21no—
349D3×Q8—44no—
350#235—22no—
351#235#4114yes—
352C2×D12C2411yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—22no—
355C2×C4×D3—21no—
356C2×C4×D3—22no—
357C2×C4×D3—21no—
358C2×Dic6—22no—
359C2×Dic6—21no—
360C2×Dic6—22no—
361C2×Dic6—21no—
362C2×Dic6C2411yescharacteristic
363C3×C4⋊C4—22no—
364C3×C4⋊C4—22no—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—24no—
367C3×C4⋊C4—22no—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4C2×D411yescharacteristic
371C3×C4⋊C4C2×D412yes—
372C3×C4⋊C4C2×D411yescharacteristic
373C3×C4⋊C4C2×D412yes—
374C3×C4⋊C4C2×D412yes—
375C3×C4⋊C4C2×D412yes—
376C3×C4⋊C4C2×D412yes—
377C3×C4⋊C4C2412yes—
378C3×C22⋊C4—24no—
379C3×C22⋊C4—24no—
380C3×C22⋊C4—22no—
381C3×C22⋊C4—22no—
382C3×C22⋊C4—24no—
383C3×C22⋊C4—24no—
384C3×C42—24no—
385C3×C42—24no—
386C3×C42C2×D411yescharacteristic
387C3×C42C2×D412yes—
388C3×C42C2×D411yescharacteristic
389C3×C42C2×D412yes—
390C3×C42C2411yescharacteristic
391C3×C42C2412yes—
392C3×C42C2412yes—
393C3×C42C2411yescharacteristic
394#217—21no—
395#217—22no—
396#216—28no—
397#215—28no—
398#214—24no—
399#213—24no—
400(C2×D3)⋊C4—22no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—21no—
404C4⋊Dic3—22no—
405C4⋊Dic3—21no—
406C4⋊Dic3—22no—
407C4⋊Dic3—21no—
408C4⋊Dic3C2412yes—
409C4⋊Dic3C2411yescharacteristic
410C4⋊Dic3C2412yes—
411C4⋊Dic3C2411yescharacteristic
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—21no—
420Dic3⋊C4—22no—
421Dic3⋊C4—21no—
422C4×Dic3—22no—
423C4×Dic3—21no—
424C4×Dic3—22no—
425C4×Dic3—21no—
426C4×Dic3—22no—
427C4×Dic3—21no—
428#208—22no—
429#208—24no—
430#208—22no—
431C2×C3⋊C8C2412yes—
432C2×C3⋊C8C2414yes—
433C2×C3⋊C8C2412yes—
434C2×#41—31no—
435C22×Q8—61no—
436C22×Q8#6711yescharacteristic
437C22×Q8C22×D312yes—
438C22×D4C22×D311yescharacteristic
439C23×C4—21no—
440#137—68no—
441AGL(1,ℤ/8)—64no—
442C2×Q16—34no—
443C2×SD16—34no—
444C2×SD16—32no—
445C2×D8—32no—
446C2×M16—31no—
447C2×M16—32no—
448C2×M16—31no—
449C4⋊Q8—21no—
450C4⋊Q8—21no—
451C4⋊Q8—31no—
452C4⋊Q8—32no—
453C4⋊Q8—32no—
454C4⋊Q8—31no—
455C4⋊Q8—61no—
456C4⋊Q8—62no—
457C4⋊Q8—61no—
458C4⋊Q8—62no—
459C4⋊Q8C22×D312yes—
460C4⋊Q8C22×D312yes—
461#126—24no—
462#126—24no—
463#126—24no—
464#126—24no—
465#125—32no—
466#125—32no—
467#125—32no—
468#125—62no—
469#125—62no—
470#125—62no—
471#124—22no—
472#124—22no—
473#124C22×D314yes—
474#124C22×D314yes—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—24no—
478C22⋊Q8—61no—
479C22⋊Q8—62no—
480C22⋊Q8—61no—
481C22⋊Q8—62no—
482C22⋊Q8—62no—
483C22⋊Q8—61no—
484C22⋊Q8—61no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C22⋊Q8—62no—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—32no—
492C4×Q8—31no—
493C4×Q8—31no—
494C4×Q8—32no—
495C4×Q8—61no—
496C4×Q8—61no—
497C4×Q8—62no—
498C4×Q8—61no—
499C4×Q8—62no—
500C4×Q8—61no—
501C4×Q8—62no—
502C4×Q8#6711yescharacteristic
503C4×Q8#6711yescharacteristic
504C4×Q8#6712yes—
505C4×Q8C22×D314yes—
506C4×Q8C22×D314yes—
507C4×Q8C22×D311yescharacteristic
508C4×Q8C22×D311yescharacteristic
509C4×Q8C22×D312yes—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—31no—
513C4×D4—32no—
514C4×D4—32no—
515C4×D4—31no—
516C4×D4—61no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4—61no—
520C4×D4C22×D312yes—
521C4×D4C22×D312yes—
522#117—22no—
523#117—24no—
524#117—22no—
525#117—31no—
526#117—32no—
527#117—61no—
528#117—62no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—61no—
533C2×C4⋊C4—62no—
534C2×C4⋊C4#6711yescharacteristic
535C2×C4⋊C4#6712yes—
536C2×C4⋊C4C22×D311yescharacteristic
537C2×C22⋊C4—22no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—22no—
540C2×C42—22no—
541C2×C42—61no—
542C2×C42—62no—
543C2×C42C22×D311yescharacteristic
544C2×C42C22×D312yes—
545#107—32no—
546#107—34no—
547#106—34no—
548#106—32no—
549C4⋊C8—32no—
550C4⋊C8—34no—
551C4⋊C8—32no—
552C4⋊C8—34no—
553#103—34no—
554#103—34no—
555#103—34no—
556#103—34no—
557#103—34no—
558#103—34no—
559#103—32no—
560#102—32no—
561#102—32no—
562#102—34no—
563#102—34no—
564#102—32no—
565#97—34no—
566#97—32no—
567C4×C8—32no—
568C4×C8—34no—
569C23×C3—22no—
570C23×C3—42no—
571C23×C3—42no—
572C23×C3—42no—
573C23×C3C22×D411yescharacteristic
574C22×D3—21no—
575C3×Q8—22no—
576C3×Q8—22no—
577C3×Q8—24no—
578C3×Q8—24no—
579C3×Q8—42no—
580C3×Q8—44no—
581C3×D4—22no—
582C3×D4—22no—
583C3×D4—42no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—24no—
587C2×C3×C4—42no—
588C2×C3×C4—41no—
589C2×C3×C4—42no—
590C2×C3×C4—44no—
591C2×C3×C4—42no—
592C2×C3×C4—44no—
593C2×C3×C4—44no—
594C2×C3×C4C22×D412yes—
595C2×C3×C4C22×D411yescharacteristic
596C2×C3×C4C22×D412yes—
597C2×C3×C4C22×D412yes—
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D412yes—
600C2×C3×C4C22×D411yescharacteristic
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C2×#4112yes—
604C2×C3×C42−1+412yes—
605C2×C3×C4C2511yescharacteristic
606#67—24no—
607C2×Dic3—21no—
608C2×Dic3—22no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—22no—
612D12—21no—
613D12C2×#4112yes—
614C4×D3—24no—
615C4×D3—44no—
616C4×D3—42no—
617C4×D3—82no—
618C4×D3—81no—
619Dic6—21no—
620Dic6—44no—
621Dic6—42no—
622Dic6—82no—
623Dic6—81no—
624Dic6C2×#4112yes—
625C3⋊C8—22no—
626C3⋊C8—24no—
627C3⋊C8—22no—
628C24—21no—
629#41—34no—
630#41—62no—
631C2×Q8—22no—
632C2×Q8—24no—
633C2×Q8—24no—
634C2×Q8—31no—
635C2×Q8—42no—
636C2×Q8—62no—
637C2×Q8—61no—
638C2×Q8—62no—
639C2×Q8—61no—
640C2×Q8—124no—
641C2×Q8C2×#6711yescharacteristic
642C2×Q8C2×#6711yescharacteristic
643C2×Q8C2×#6712yes—
644C2×Q8C23×D314yes—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—31no—
649C2×D4—61no—
650C2×D4C23×D312yes—
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—44no—
656C22×C4—61no—
657C22×C4—62no—
658C22×C4—61no—
659C22×C4—62no—
660C22×C4—61no—
661C22×C4C2×#6711yescharacteristic
662C22×C4C2×#6712yes—
663C22×C4C2×#6711yescharacteristic
664C22×C4C2×#6712yes—
665C22×C4C23×D311yescharacteristic
666Q16—68no—
667SD16—64no—
668SD16—68no—
669D8—64no—
670M16—62no—
671M16—64no—
672M16—62no—
673C2×C8—32no—
674C2×C8—34no—
675C2×C8—32no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—31no—
684C4⋊C4—32no—
685C4⋊C4—31no—
686C4⋊C4—32no—
687C4⋊C4—62no—
688C4⋊C4—62no—
689C4⋊C4—62no—
690C4⋊C4—62no—
691C4⋊C4—61no—
692C4⋊C4—62no—
693C4⋊C4—62no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—61no—
701C4⋊C4C2×#6711yescharacteristic
702C4⋊C4C2×#6712yes—
703C4⋊C4C2×#6712yes—
704C4⋊C4C2×#6711yescharacteristic
705C4⋊C4C2×#6712yes—
706C4⋊C4C2×#6712yes—
707C4⋊C4C2×#6712yes—
708C4⋊C4C23×D312yes—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—61no—
716C22⋊C4—62no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C42—24no—
722C42—24no—
723C42—61no—
724C42—62no—
725C42—62no—
726C42—61no—
727C42—62no—
728C42—61no—
729C42C2×#6711yescharacteristic
730C42C2×#6712yes—
731C42C2×#6711yescharacteristic
732C42C2×#6712yes—
733C42C23×D311yescharacteristic
734C42C23×D312yes—
735C42C23×D311yescharacteristic
736C42C23×D312yes—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—84no—
743C22×C3#54812yes—
744C22×C3C23×D411yescharacteristic
745C2×D3—22no—
746C2×D3—41no—
747C2×D3—41no—
748C3×C4—22no—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—22no—
753C3×C4—21no—
754C3×C4—22no—
755C3×C4—44no—
756C3×C4—42no—
757C3×C4#54812yes—
758C3×C4#57512yes—
759C3×C4C22×#4111yescharacteristic
760C3×C4C2×2−1+411yescharacteristic
761Dic3—22no—
762Dic3—41no—
763Dic3—42no—
764Dic3—41no—
765Dic3—42no—
766C23—22no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—61no—
771C23C22×#6711yescharacteristic
772Q8—22no—
773Q8—22no—
774Q8—24no—
775Q8—24no—
776Q8—32no—
777Q8—42no—
778Q8—44no—
779Q8—61no—
780Q8—124no—
781Q8—122no—
782Q8—242no—
783Q8—241no—
784D4—22no—
785D4—22no—
786D4—32no—
787D4—42no—
788D4—64no—
789D4—61no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—61no—
801C2×C4—64no—
802C2×C4—62no—
803C2×C4—61no—
804C2×C4—62no—
805C2×C4—61no—
806C2×C4—124no—
807C2×C4—122no—
808C2×C4—242no—
809C2×C4—241no—
810C2×C4D3×#4112yes—
811C2×C4#101012yes—
812C2×C4C22×#6712yes—
813C2×C4C22×#6712yes—
814C2×C4C22×#6711yescharacteristic
815C2×C4C22×#6712yes—
816C2×C4C22×#6712yes—
817C2×C4C22×#6711yescharacteristic
818C2×C4C22×#6711yescharacteristic
819C2×C4C22×#6711yescharacteristic
820C2×C4C22×#6711yescharacteristic
821C2×C4C24×D311yescharacteristic
822C8—62no—
823C8—64no—
824C8—62no—
825C2×C3—22no—
826C2×C3—82no—
827C2×C3C2×#54811yescharacteristic
828C2×C3C2×#57511yescharacteristic
829C2×C3#358611yescharacteristic
830D3—42no—
831C22—21no—
832C22—21no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—62no—
837C22—84no—
838C22—121no—
839C22—121no—
840C22#583112yes—
841C22C23×#6711yescharacteristic
842C4—21no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—21no—
847C4—22no—
848C4—21no—
849C4—42no—
850C4—44no—
851C4—62no—
852C4—122no—
853C4—121no—
854C4—122no—
855C4—121no—
856C4#582212yes—
857C4#583112yes—
858C4C2×D3×#4111yescharacteristic
859C4C2×#101011yescharacteristic
860C3#6132311yescharacteristic, complemented, Sylow
861C2—22no—
862C2—82no—
863C2—122no—
864C2C2×#582211yescharacteristic
865C2C2×#583111yescharacteristic
866C2#8728711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#556C2
socleC22×C3C23×D4
prime radicalC2×#932C22
hypercenterC2×#556D3
hypocenterC3#61323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×C3×#556C2semidirect
2. Q8×#235C2semidirect
3. #83678C2semidirect
4. #83677C2semidirect
5. #83676C2semidirect
6. #83669C2semidirect
7. #83668C2semidirect
8. #83667C2semidirect
9. #83209C2semidirect
10. #83198C2semidirect
12. #82939C2semidirect
13. Q8×#208C2semidirect
14. #82431C2semidirect
15. C4×#942C2semidirect
16. #82296C2semidirect
36. #5579C22semidirect
37. #5579C22semidirect
40. Q8×D12C22semidirect
42. #5567C22semidirect
43. #5567C22semidirect
44. Q8×Dic6C22semidirect
56. #5090C22semidirect
57. #5090C22semidirect
58. #5083C22semidirect
59. #5083C22semidirect
60. #5082C22semidirect
61. #5079C22semidirect
62. #5079C22semidirect
71. #5030C22semidirect
72. C4×#216C22semidirect
73. #5026C22semidirect
74. C4×#215C22semidirect
75. #5024C22semidirect
76. #5024C22semidirect
77. Q8×C3⋊C8C22semidirect
78. #5022C22semidirect
79. #5022C22semidirect
80. #5021C22semidirect
81. #5020C22semidirect
97. C2×#556D3semidirect
860. C3#61323semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5562
Q8×#2352
#836782
#836772
#836762
#836692
#836682
#836672
#832092
#831982
#829452
#829392
Q8×#2082
#824312
C4×#9422
#822962
C4×#9322
#613233