Finite Group Databasebeta

← #11675108

Subgroups — #11675108

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×#5732C211yesmaximal, characteristic, complemented
2#41×Dic6C211yesmaximal, characteristic, complemented
3C3×#3039C211yesmaximal, characteristic, complemented
4#83968C212yesmaximal
5Dic3×#137C212yesmaximal, complemented
6#83198C211yesmaximal, characteristic, complemented
7C4×#949C211yesmaximal, characteristic
8#80467C214yesmaximal, complemented
9#80464C212yesmaximal, complemented
10#80463C212yesmaximal, complemented
11#80419C214yesmaximal, complemented
12#80416C212yesmaximal, complemented
13#80415C212yesmaximal, complemented
14#79059C211yesmaximal, characteristic, complemented
15#79046C211yesmaximal, characteristic, complemented
16#78954C212yesmaximal, complemented
17#78949C212yesmaximal, complemented
18#61323—31nomaximal, Sylow
19C2×C3×#137C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C3×C4×#41C2211yescharacteristic
22Dic3×#41C2212yes—
23C2×#949C2211yescharacteristic
24C2×#947C2212yes—
25C2×Q8×Dic3C2212yes—
26#5732—21no—
27#5732—21no—
28#5732—22no—
29#5732C2212yes—
30#5732C2212yes—
31#5732C2214yes—
32#5570C2211yescharacteristic, complemented
33#5569C2212yescomplemented
34Q8×Dic6C2211yescharacteristic, complemented
35#5543—21no—
36#5543C2211yescharacteristic, complemented
37#5539—22no—
38#5539C2212yescomplemented
39D4×Dic6—21no—
40D4×Dic6C2211yescharacteristic, complemented
41#5517—22no—
42#5517C2212yes—
43C2×#898—22no—
44C2×#897—21no—
45C2×#892—21no—
46C2×C4×D12C2211yescharacteristic
47#5470—21no—
48#5470C2211yescharacteristic
49C2×C4×Dic6—21no—
50C2×C4×Dic6C2211yescharacteristic
51C3×#462C2212yescomplemented
52C3×#462C2212yescomplemented
53C3×#461C2212yescomplemented
54C3×#461C2212yescomplemented
55C3×#423C2211yescharacteristic
56C3×#419C2212yes—
57#5232C2211yescharacteristic
58#5225C2212yes—
59#5225C2212yes—
60#5185C2214yes—
61#5185C2214yes—
62#5184C2214yescomplemented
63Dic3×Q16C2214yescomplemented
64#5165C2214yes—
65#5165C2214yes—
66#5164C2214yescomplemented
67Dic3×SD16C2214yescomplemented
68#5131C2212yes—
69#5121C2212yes—
70#5118C2212yes—
71Dic3×M16C2212yes—
72#5082C2214yescomplemented
73#5079C2212yescomplemented
74#5079C2212yescomplemented
75#5026C2212yes—
76C4×#215C2212yes—
77#5014C2212yes—
78C4×#213C2212yes—
79#5001C2211yescharacteristic
80#4995C2211yescharacteristic
81C4×#208C2211yescharacteristic
82#4847C2214yes—
83#4846C2212yes—
84#4842C2212yes—
85#4831C2212yescomplemented
86#4830C2212yescomplemented
87#4828C2214yescomplemented
88#4800C2214yes—
89#4800C2214yes—
90#4799C2214yescomplemented
91#4796C2214yescomplemented
92#4794C2214yes—
93#4794C2214yes—
94#4793C2214yescomplemented
95#4791C2214yescomplemented
96Q8×#41—31no—
97C2×#556—31no—
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#3039D311yescharacteristic, complemented
110Q8×M16—31no—
111C4×#137—32no—
112C4×AGL(1,ℤ/8)—31no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8C2312yes—
115C22×D12C2311yescharacteristic
116C22×C4×D3—21no—
117C22×Dic6—21no—
118C22×Dic6D411yescharacteristic
119C3×#137—28no—
120C2×C3×Q16C2314yes—
121C2×C3×SD16C2314yes—
122C2×C3×M16C2312yes—
123C3×C4⋊Q8—21no—
124C3×C4⋊Q8—21no—
125C3×C4⋊Q8C2312yes—
126C3×C4⋊Q8C2312yes—
127C3×C4×Q8C2311yescharacteristic
128C3×C4×Q8C2311yescharacteristic
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C3×C4×D4C2311yescharacteristic
132C3×C4×D4C2311yescharacteristic
133C3×#117—21no—
134C3×#117C2311yescharacteristic
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C42—21no—
138C2×C3×C42C2311yescharacteristic
139#949—24no—
140#947—22no—
141#947—22no—
142#947C2314yes—
143#947C2314yes—
144Q8×Dic3—22no—
145Q8×Dic3—22no—
146Q8×Dic3C2314yes—
147Q8×Dic3C2314yes—
148Q8×Dic3C2312yes—
149Q8×Dic3C2312yes—
150C2×#215C2312yes—
151D4×Dic3—22no—
152D4×Dic3—22no—
153D4×Dic3C2312yes—
154D4×Dic3C2312yes—
155C2×#213C2312yes—
156C2×(C2×D3)⋊C4—21no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159#926—22no—
160#926C2312yes—
161C2×C4⋊Dic3—22no—
162C2×C4⋊Dic3—21no—
163C2×C4⋊Dic3D411yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165#924—21no—
166#924—21no—
167#924—21no—
168#924—21no—
169#924—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4D412yes—
172C2×C4×Dic3—22no—
173C2×C4×Dic3—22no—
174C2×C4×Dic3C2312yes—
175C2×#208C2311yescharacteristic
176C2×#208C2311yescharacteristic
177#898—24no—
178#898—24no—
179#898—24no—
180#898—24no—
181#897—22no—
182#897—22no—
183#897—24no—
184#892—22no—
185#892—22no—
186#892—24no—
187#890—22no—
188#890—22no—
189#890C2312yes—
190#890C2312yes—
191#888—22no—
192#888—22no—
193#888C2312yes—
194#888C2312yes—
195#878—22no—
196#878—22no—
197#878—22no—
198#878—22no—
199#878—22no—
200#878—22no—
201C4×D12—21no—
202C4×D12—21no—
203C4×D12C2312yes—
204C4×D12C2312yes—
205#870—22no—
206#870C2312yes—
207#869—21no—
208#869—21no—
209#869C2311yescharacteristic
210#869C2311yescharacteristic
211C4×Dic6—21no—
212C4×Dic6—21no—
213C4×Dic6—21no—
214C4×Dic6—21no—
215C4×Dic6—22no—
216C4×Dic6—22no—
217C4×Dic6—22no—
218C4×Dic6D411yescharacteristic
219C4×Dic6D411yescharacteristic
220C4×Dic6D412yes—
221C4×Dic6C2311yescharacteristic
222C4×Dic6C2312yes—
223C4×Dic6C2311yescharacteristic
224C3×C4⋊C8C2312yes—
225C3×C4⋊C8C2312yes—
226C3×#103C2314yes—
227C3×#103C2314yes—
228#835C2314yes—
229#835C2314yes—
230#835C2314yes—
231#835C2314yes—
232#835C2312yes—
233#832C2312yes—
234#821C2314yes—
235#821C2314yes—
236#818C2314yes—
237#817C2314yes—
238#815C2314yes—
239Dic3⋊C8C2314yes—
240Dic3⋊C8C2314yes—
241C8×Dic3C2314yes—
242#809C2312yes—
243#809C2312yes—
244#808C2312yes—
245#807C2312yes—
246#803C2312yes—
247C4×C3⋊C8C2312yes—
248C2×#137C2×D312yes—
249C2×AGL(1,ℤ/8)—31no—
250Q82—31no—
251#557—31no—
252#557—32no—
253#556—32no—
254#556—32no—
255#556—34no—
256#556—61no—
257#556—62no—
258#556—61no—
259#554—31no—
260#554—32no—
261#554—62no—
262#554—61no—
263D4×Q8—31no—
264D4×Q8—61no—
265#533—32no—
266#533—31no—
267#533—61no—
268#533—62no—
269C2×C4⋊Q8C2×D311yescharacteristic
270C2×#126—62no—
271C2×#124—32no—
272C2×C22⋊Q8—61no—
273C4×#41—32no—
274C4×#41C2×D311yescharacteristic
275C2×C4×Q8—31no—
276C2×C4×Q8—32no—
277C2×C4×Q8—61no—
278C2×C4×D4—31no—
279C2×#117—61no—
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#462C2×D312yescomplemented
299#462C2×D312yescomplemented
300#461C2×D312yescomplemented
301#461C2×D312yescomplemented
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—32no—
316#423C2×D311yescharacteristic
317#419—32no—
318#419—32no—
319#419C2×D312yes—
320#418—32no—
321#418—31no—
322#417—31no—
323C4×M16—32no—
324C4×M16—31no—
325C23×D3—21no—
326C3×#41—22no—
327C3×#41#4114yes—
328C2×C3×Q8—22no—
329C2×C3×Q8—24no—
330C2×C3×Q8—24no—
331C2×C3×Q8C2414yes—
332C2×C3×Q8C2411yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4C2411yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—22no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4C2×D411yescharacteristic
340C22×C3×C4C2×D411yescharacteristic
341C22×C3×C4C2411yescharacteristic
342C22×Dic3—21no—
343C22×Dic3—22no—
344C22×Dic3—22no—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C2×D12—22no—
348C2×D12—22no—
349C2×D12—21no—
350C2×D12C2412yes—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—44no—
354C2×Dic6—21no—
355C2×Dic6—22no—
356C2×Dic6—21no—
357C2×Dic6—22no—
358C2×Dic6—42no—
359C2×Dic6—44no—
360C2×Dic6C2×D411yescharacteristic
361C2×Dic6C2×D411yescharacteristic
362C2×Dic6C2×D412yes—
363C3×Q16—28no—
364C3×SD16—28no—
365C3×M16—24no—
366C2×C3×C8C2414yes—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—22no—
370C3×C4⋊C4—22no—
371C3×C4⋊C4—22no—
372C3×C4⋊C4—22no—
373C3×C4⋊C4C2411yescharacteristic
374C3×C4⋊C4C2411yescharacteristic
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42C2×D411yescharacteristic
382C3×C42C2×D411yescharacteristic
383C3×C42C2411yescharacteristic
384C3×C42C2411yescharacteristic
385#217—22no—
386#217—22no—
387#217—22no—
388#215—24no—
389#213—24no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—22no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394(C2×D3)⋊C4—24no—
395(C2×D3)⋊C4—24no—
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3—22no—
400C4⋊Dic3—22no—
401C4⋊Dic3—22no—
402C4⋊Dic3—22no—
403C4⋊Dic3—24no—
404C4⋊Dic3—24no—
405C4⋊Dic3C2×D411yescharacteristic
406C4⋊Dic3C2×D411yescharacteristic
407C4⋊Dic3C2×D412yes—
408C4⋊Dic3C2412yes—
409C4⋊Dic3C2412yes—
410C4⋊Dic3C2412yes—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4C2×D412yes—
418Dic3⋊C4C2×D412yes—
419Dic3⋊C4C2×D412yes—
420Dic3⋊C4C2×D412yes—
421C4×Dic3—22no—
422C4×Dic3—22no—
423C4×Dic3—22no—
424C4×Dic3—24no—
425C4×Dic3—24no—
426C4×Dic3C2×D412yes—
427C4×Dic3C2×D412yes—
428C4×Dic3C2412yes—
429C4×Dic3C2412yes—
430#208—22no—
431#208—22no—
432C2×C3⋊C8C2412yes—
433C2×C3⋊C8C2412yes—
434C2×#41C22×D311yescharacteristic
435C22×Q8—31no—
436C22×Q8—61no—
437C22×Q8C22×D312yes—
438C22×D4—31no—
439C23×C4—61no—
440#137—28no—
441AGL(1,ℤ/8)—64no—
442C2×Q16C22×D314yes—
443C2×SD16—32no—
444C2×SD16C22×D314yes—
445C2×D8—32no—
446C2×M16—31no—
447C2×M16—31no—
448C2×M16C22×D312yes—
449C4⋊Q8—21no—
450C4⋊Q8—21no—
451C4⋊Q8—32no—
452C4⋊Q8—32no—
453C4⋊Q8—31no—
454C4⋊Q8—31no—
455C4⋊Q8—61no—
456C4⋊Q8—61no—
457C4⋊Q8—62no—
458C4⋊Q8—62no—
459C4⋊Q8C22×D312yes—
460C4⋊Q8C22×D312yes—
461#126—64no—
462#126—64no—
463#126—64no—
464#126—64no—
465#125—32no—
466#125—32no—
467#125—32no—
468#125—62no—
469#125—62no—
470#125—62no—
471#124—34no—
472#124—34no—
473#124—62no—
474#124—62no—
475C22⋊Q8—62no—
476C22⋊Q8—62no—
477C22⋊Q8—62no—
478C22⋊Q8—62no—
479C22⋊Q8—62no—
480C22⋊Q8—62no—
481C22⋊Q8—62no—
482C22⋊Q8—62no—
483C22⋊Q8—64no—
484C22⋊Q8—61no—
485C22⋊Q8—62no—
486C22⋊Q8—61no—
487C22⋊Q8—61no—
488C22⋊Q8—61no—
489C4×Q8—31no—
490C4×Q8—32no—
491C4×Q8—31no—
492C4×Q8—31no—
493C4×Q8—31no—
494C4×Q8—32no—
495C4×Q8—34no—
496C4×Q8—34no—
497C4×Q8—32no—
498C4×Q8—32no—
499C4×Q8—62no—
500C4×Q8—62no—
501C4×Q8—62no—
502C4×Q8—61no—
503C4×Q8—61no—
504C4×Q8—62no—
505C4×Q8—62no—
506C4×Q8—61no—
507C4×Q8—61no—
508C4×Q8C22×D311yescharacteristic
509C4×Q8C22×D311yescharacteristic
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—32no—
513C4×D4—32no—
514C4×D4—32no—
515C4×D4—32no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—61no—
519C4×D4—61no—
520C4×D4C22×D311yescharacteristic
521C4×D4C22×D311yescharacteristic
522#117—21no—
523#117—32no—
524#117—62no—
525#117—62no—
526#117—64no—
527#117—62no—
528#117C22×D311yescharacteristic
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—32no—
533C2×C4⋊C4—31no—
534C2×C4⋊C4—62no—
535C2×C4⋊C4—61no—
536C2×C4⋊C4—62no—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—62no—
539C2×C22⋊C4—61no—
540C2×C42—21no—
541C2×C42—32no—
542C2×C42—62no—
543C2×C42—62no—
544C2×C42C22×D311yescharacteristic
545#107—34no—
546#107—32no—
547#106—34no—
548#106—32no—
549C4⋊C8—34no—
550C4⋊C8—34no—
551C4⋊C8C22×D312yes—
552C4⋊C8C22×D312yes—
553#103—32no—
554#103—34no—
555#103—34no—
556#103—34no—
557#103—34no—
558#103C22×D314yes—
559#103C22×D314yes—
560#102—32no—
561#102—34no—
562#102—34no—
563#102—32no—
564#102—32no—
565#97—34no—
566#97—32no—
567C4×C8—34no—
568C4×C8—32no—
569C23×C3—21no—
570C23×C3C22×D411yescharacteristic
571C22×D3—22no—
572C22×D3—42no—
573C22×D3—42no—
574C22×D3—42no—
575C3×Q8—21no—
576C3×Q8—24no—
577C3×Q8—24no—
578C3×Q8—44no—
579C3×Q8C2×#4112yes—
580C3×D4—24no—
581C3×D4—21no—
582C3×D4C2×#4112yes—
583C2×C3×C4—21no—
584C2×C3×C4—24no—
585C2×C3×C4—22no—
586C2×C3×C4—24no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—41no—
590C2×C3×C4—44no—
591C2×C3×C4—42no—
592C2×C3×C4—81no—
593C2×C3×C4C22×D411yescharacteristic
594C2×C3×C4C22×D411yescharacteristic
595C2×C3×C4C22×D411yescharacteristic
596C2×C3×C4C22×D411yescharacteristic
597C2×C3×C4C22×D411yescharacteristic
598C2×C3×C4C2×#4112yes—
599C2×C3×C42−1+412yes—
600C2×C3×C4C2511yescharacteristic
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—42no—
605C2×Dic3—42no—
606C2×Dic3—44no—
607C2×Dic3—42no—
608C2×Dic3—82no—
609C2×Dic3C22×D412yes—
610C2×Dic3C22×D412yes—
611C2×Dic3C22×D412yes—
612C2×Dic3C22×D412yes—
613D12—22no—
614D12—22no—
615D12—42no—
616C4×D3—44no—
617C4×D3—44no—
618Dic6—22no—
619Dic6—22no—
620Dic6—42no—
621Dic6—44no—
622Dic6—42no—
623Dic6—82no—
624Dic6—81no—
625C3×C8—24no—
626C3⋊C8—22no—
627C3⋊C8—22no—
628C24—61no—
629#41—22no—
630#41#23714yes—
631C2×Q8—22no—
632C2×Q8—24no—
633C2×Q8—24no—
634C2×Q8—31no—
635C2×Q8—31no—
636C2×Q8—32no—
637C2×Q8—62no—
638C2×Q8—62no—
639C2×Q8—61no—
640C2×Q8—61no—
641C2×Q8—122no—
642C2×Q8—124no—
643C2×Q8C23×D314yes—
644C2×Q8C23×D311yescharacteristic
645C2×D4—21no—
646C2×D4—32no—
647C2×D4—61no—
648C2×D4—62no—
649C2×D4—62no—
650C2×D4C23×D311yescharacteristic
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—32no—
656C22×C4—32no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—61no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—124no—
663C22×C4D3×D411yescharacteristic
664C22×C4D3×D411yescharacteristic
665C22×C4C23×D311yescharacteristic
666Q16—28no—
667SD16—28no—
668SD16—64no—
669D8—64no—
670M16—24no—
671M16—62no—
672M16—62no—
673C2×C8—32no—
674C2×C8—32no—
675C2×C8C23×D314yes—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—31no—
683C4⋊C4—32no—
684C4⋊C4—32no—
685C4⋊C4—31no—
686C4⋊C4—32no—
687C4⋊C4—32no—
688C4⋊C4—32no—
689C4⋊C4—32no—
690C4⋊C4—32no—
691C4⋊C4—32no—
692C4⋊C4—64no—
693C4⋊C4—64no—
694C4⋊C4—62no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—62no—
701C4⋊C4—62no—
702C4⋊C4—61no—
703C4⋊C4—62no—
704C4⋊C4—61no—
705C4⋊C4—62no—
706C4⋊C4—61no—
707C4⋊C4C23×D311yescharacteristic
708C4⋊C4C23×D311yescharacteristic
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—64no—
713C22⋊C4—64no—
714C22⋊C4—64no—
715C22⋊C4—64no—
716C22⋊C4—62no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—32no—
725C42—32no—
726C42—32no—
727C42—32no—
728C42—64no—
729C42—64no—
730C42—62no—
731C42—62no—
732C42—62no—
733C42D3×D411yescharacteristic
734C42D3×D411yescharacteristic
735C42C23×D311yescharacteristic
736C42C23×D311yescharacteristic
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—22no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3#54812yes—
743C22×C3C23×D411yescharacteristic
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—84no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—41no—
753C3×C4—44no—
754C3×C4—41no—
755C3×C4#54812yes—
756C3×C4#57512yes—
757C3×C4C22×#4111yescharacteristic
758C3×C4C2×2−1+411yescharacteristic
759Dic3—22no—
760Dic3—22no—
761Dic3—22no—
762Dic3—22no—
763Dic3—42no—
764Dic3—42no—
765Dic3—42no—
766C23—21no—
767C23—62no—
768C23—122no—
769C23—122no—
770C23—122no—
771C23C2×D3×D411yescharacteristic
772Q8—21no—
773Q8—24no—
774Q8—24no—
775Q8—44no—
776Q8—62no—
777Q8—62no—
778Q8—122no—
779Q8—124no—
780Q8—122no—
781Q8—241no—
782Q8—242no—
783Q8C2×#23712yes—
784D4—24no—
785D4—21no—
786D4—62no—
787D4—62no—
788D4—122no—
789D4C2×#23712yes—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—24no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—32no—
799C2×C4—32no—
800C2×C4—41no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—81no—
807C2×C4—124no—
808C2×C4—122no—
809C2×C4—122no—
810C2×C4—124no—
811C2×C4—122no—
812C2×C4—124no—
813C2×C4—242no—
814C2×C4C2×D3×D411yescharacteristic
815C2×C4C2×D3×D411yescharacteristic
816C2×C4C2×D3×D411yescharacteristic
817C2×C4C2×D3×D411yescharacteristic
818C2×C4C2×D3×D411yescharacteristic
819C2×C4C2×#23712yes—
820C2×C4#101012yes—
821C2×C4C24×D311yescharacteristic
822C8—24no—
823C8—62no—
824C8—62no—
825C2×C3—22no—
826C2×C3—42no—
827C2×C3C2×#54811yescharacteristic
828C2×C3C2×#57511yescharacteristic
829C2×C3#358611yescharacteristic
830D3—82no—
831C22—21no—
832C22—21no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—122no—
837C22—122no—
838C22—122no—
839C22—244no—
840C22#559812yes—
841C22C22×D3×D411yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—22no—
846C4—41no—
847C4—41no—
848C4—44no—
849C4—62no—
850C4—62no—
851C4—62no—
852C4—62no—
853C4—122no—
854C4—122no—
855C4—122no—
856C4#559812yes—
857C4#577712yes—
858C4C22×#23711yescharacteristic
859C4C2×#101011yescharacteristic
860C3#6132311yescharacteristic, complemented, Sylow
861C2—22no—
862C2—42no—
863C2—242no—
864C2C2×#559811yescharacteristic
865C2C2×#577711yescharacteristic
866C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3039C2
socleC22×C3C23×D4
prime radicalC2×#949C22
hypercenter#3039D3
hypocenterC3#61323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3039

Complements

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

NH ≅ G/Ntype
1. C2×#5732C2semidirect
2. #41×Dic6C2semidirect
3. C3×#3039C2semidirect
5. Dic3×#137C2semidirect
6. #83198C2semidirect
8. #80467C2semidirect
9. #80464C2semidirect
10. #80463C2semidirect
11. #80419C2semidirect
12. #80416C2semidirect
13. #80415C2semidirect
14. #79059C2semidirect
15. #79046C2semidirect
16. #78954C2semidirect
17. #78949C2semidirect
32. #5570C22semidirect
33. #5569C22semidirect
34. Q8×Dic6C22semidirect
36. #5543C22semidirect
38. #5539C22semidirect
40. D4×Dic6C22semidirect
51. C3×#462C22semidirect
52. C3×#462C22semidirect
53. C3×#461C22semidirect
54. C3×#461C22semidirect
62. #5184C22semidirect
63. Dic3×Q16C22semidirect
66. #5164C22semidirect
67. Dic3×SD16C22semidirect
72. #5082C22semidirect
73. #5079C22semidirect
74. #5079C22semidirect
85. #4831C22semidirect
86. #4830C22semidirect
87. #4828C22semidirect
90. #4799C22semidirect
91. #4796C22semidirect
94. #4793C22semidirect
95. #4791C22semidirect
109. #3039D3semidirect
298. #462C2×D3semidirect
299. #462C2×D3semidirect
300. #461C2×D3semidirect
301. #461C2×D3semidirect
860. C3#61323semidirect

Maximal subgroups

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

subgroupindex
C2×#57322
#41×Dic62
C3×#30392
#839682
Dic3×#1372
#831982
C4×#9492
#804672
#804642
#804632
#804192
#804162
#804152
#790592
#790462
#789542
#789492
#613233