Finite Group Databasebeta

← #11675775

Subgroups — #11675775

Order 768.

1826 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5730C211yesmaximal, characteristic, complemented
2#41×Dic6C211yesmaximal, characteristic, complemented
3C3×#3079C211yesmaximal, characteristic, complemented
4#83207C211yesmaximal, characteristic, complemented
5C4×#949C211yesmaximal, characteristic
6#81137C212yesmaximal, complemented
7#81136C212yesmaximal, complemented
8#81089C212yesmaximal, complemented
9#81054C212yesmaximal, complemented
10#81008C214yesmaximal, complemented
11#80962C214yesmaximal, complemented
12#79239C212yesmaximal, complemented
13#79204C212yesmaximal, complemented
14#79059C211yesmaximal, characteristic, complemented
15#79046C211yesmaximal, characteristic, complemented
16#78871C212yesmaximal, complemented
17#78866C212yesmaximal
18#61367—31nomaximal, Sylow
19C2×C3×C4⋊Q8C2211yescharacteristic
20C3×C4×#41C2211yescharacteristic
21Dic3×#41C2212yes—
22C2×#949C2211yescharacteristic
23C2×#946—22no—
24#5730—21no—
25#5730—21no—
26#5730—22no—
27#5730C2214yes—
28#5730C2212yes—
29#5730C2212yes—
30#5570C2211yescharacteristic, complemented
31#5569C2212yescomplemented
32Q8×Dic6C2211yescharacteristic, complemented
33#5543—21no—
34#5543C2211yescharacteristic, complemented
35#5539—22no—
36#5539C2212yescomplemented
37D4×Dic6—21no—
38D4×Dic6C2211yescharacteristic, complemented
39#5517—22no—
40#5517C2212yes—
41C2×#897—21no—
42C2×#893C2212yes—
43C2×D3×C4⋊C4—21no—
44C2×#890C2212yes—
45C2×C4×D12C2211yescharacteristic
46#5470—21no—
47#5470C2211yescharacteristic
48C2×C4×Dic6—21no—
49C2×C4×Dic6C2211yescharacteristic
50C3×#477C2212yescomplemented
51C3×#476C2212yescomplemented
52C3×#475C2212yescomplemented
53C3×#474C2212yescomplemented
54C3×#428C2212yes—
55C3×#423C2211yescharacteristic
56C3×#417C2212yes—
57#5232C2211yescharacteristic
58#5131C2212yes—
59#5121C2212yes—
60#5118C2212yes—
61Dic3×M16C2212yes—
62#5081C2214yescomplemented
63#5080C2212yescomplemented
64#5078C2212yescomplemented
65#5026C2212yes—
66C4×#215C2212yes—
67#5014C2212yes—
68C4×#213C2212yes—
69#5001C2211yescharacteristic
70#4995C2211yescharacteristic
71#4964C2212yes—
72#4964C2212yes—
73C4×#208C2211yescharacteristic
74#4891C2214yes—
75#4890C2214yes—
76#4878C2214yescomplemented
77#4876C2214yescomplemented
78#4871C2214yes—
79#4870C2214yes—
80#4858C2214yescomplemented
81#4856C2214yescomplemented
82#4847C2214yes—
83#4846C2212yes—
84#4842C2212yes—
85#4831C2212yescomplemented
86#4830C2212yescomplemented
87#4828C2214yescomplemented
88#4817C2214yes—
89#4799C2214yescomplemented
90#4796C2214yescomplemented
91#4788C2214yes—
92#4785C2214yes—
93#4766C2214yescomplemented
94#4763C2214yescomplemented
95#4756C2214yes—
96Q8×#41—31no—
97C2×#554—31no—
98#3389—34no—
99#3388—34no—
100#3385—32no—
101#3384—32no—
102#3381—32no—
103#3380—32no—
104#3166—32no—
105#3165—31no—
106#3080—32no—
107#3079D311yescharacteristic, complemented
108#3077—32no—
109#3077—31no—
110Q8×M16—31no—
111C4×AGL(1,ℤ/8)—32no—
112C4×AGL(1,ℤ/8)—31no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8—21no—
115C22×D12C2311yescharacteristic
116C22×C4×D3—21no—
117C22×C4×D3—22no—
118C22×Dic6—21no—
119C22×Dic6D411yescharacteristic
120C2×C3×M16C2312yes—
121C3×C4⋊Q8—21no—
122C3×C4⋊Q8—21no—
123C3×C4⋊Q8C2312yes—
124C3×C4⋊Q8C2312yes—
125C3×C4×Q8C2311yescharacteristic
126C3×C4×Q8C2311yescharacteristic
127C3×C4×D4—21no—
128C3×C4×D4—21no—
129C3×C4×D4C2311yescharacteristic
130C3×C4×D4C2311yescharacteristic
131C3×#117—21no—
132C3×#117C2311yescharacteristic
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C42—21no—
136C2×C3×C42C2311yescharacteristic
137#949Q818yescomplemented
138#946—24no—
139#946—24no—
140#946—24no—
141#946—24no—
142Q8×Dic3C2312yes—
143Q8×Dic3C2312yes—
144C2×#215C2312yes—
145D4×Dic3—22no—
146D4×Dic3—22no—
147D4×Dic3C2312yes—
148D4×Dic3C2312yes—
149C2×#213C2312yes—
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4—22no—
152#926—22no—
153#926C2312yes—
154C2×C4⋊Dic3—22no—
155C2×C4⋊Dic3—21no—
156C2×C4⋊Dic3D411yescharacteristic
157C2×C4⋊Dic3C2311yescharacteristic
158#924—21no—
159#924—21no—
160#924—21no—
161#924—21no—
162#924—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4D412yes—
166C2×C4×Dic3—22no—
167C2×C4×Dic3C2312yes—
168C2×#208C2311yescharacteristic
169C2×#208C2311yescharacteristic
170#897—22no—
171#897—22no—
172#897—24no—
173#893—22no—
174#893—22no—
175#893C2314yes—
176#893C2314yes—
177D3×C4⋊C4—22no—
178D3×C4⋊C4—22no—
179D3×C4⋊C4—24no—
180#890—22no—
181#890—22no—
182#890—22no—
183#890—22no—
184#890C2312yes—
185#890C2314yes—
186#890C2312yes—
187#890C2314yes—
188#888—22no—
189#888—22no—
190#888C2312yes—
191#888C2312yes—
192#878—22no—
193#878—22no—
194#878—22no—
195#878—22no—
196#878—22no—
197#878—22no—
198C4×D12—21no—
199C4×D12—21no—
200C4×D12C2312yes—
201C4×D12C2312yes—
202#870—22no—
203#870C2312yes—
204#869—21no—
205#869—21no—
206#869C2311yescharacteristic
207#869C2311yescharacteristic
208C4×Dic6—21no—
209C4×Dic6—21no—
210C4×Dic6—21no—
211C4×Dic6—21no—
212C4×Dic6—22no—
213C4×Dic6—22no—
214C4×Dic6—22no—
215C4×Dic6D411yescharacteristic
216C4×Dic6D411yescharacteristic
217C4×Dic6D412yes—
218C4×Dic6C2311yescharacteristic
219C4×Dic6C2312yes—
220C4×Dic6C2311yescharacteristic
221C3×#107C2314yes—
222C3×#106C2314yes—
223C3×C4⋊C8C2312yes—
224C3×C4⋊C8C2312yes—
225C3×#103C2314yes—
226C3×#102C2314yes—
227#835C2312yes—
228#832C2312yes—
229#821C2314yes—
230#821C2314yes—
231#818C2314yes—
232#817C2314yes—
233#815C2314yes—
234Dic3⋊C8C2314yes—
235Dic3⋊C8C2314yes—
236C8×Dic3C2314yes—
237#809C2312yes—
238#809C2312yes—
239#808C2314yes—
240#808C2312yes—
241#808C2314yes—
242#807C2314yes—
243#807C2314yes—
244#807C2312yes—
245#803C2312yes—
246C4×C3⋊C8C2312yes—
247C2×AGL(1,ℤ/8)—31no—
248Q82—31no—
249#557—31no—
250#557—32no—
251#554—32no—
252#554—32no—
253#554—34no—
254#554—31no—
255#554—32no—
256#554—62no—
257#554—61no—
258#554—61no—
259#554—62no—
260#554—61no—
261D4×Q8—31no—
262D4×Q8—61no—
263#533—32no—
264#533—31no—
265#533—61no—
266#533—62no—
267C2×C4⋊Q8C2×D311yescharacteristic
268C2×#125—32no—
269C2×C22⋊Q8—61no—
270C2×C22⋊Q8—62no—
271C4×#41—32no—
272C4×#41C2×D311yescharacteristic
273C2×C4×Q8—31no—
274C2×C4×Q8—61no—
275C2×C4×D4—32no—
276C2×C4×D4—31no—
277C22×C4⋊C4—61no—
278#501—34no—
279#501—34no—
280#501—34no—
281#500—32no—
282#499—34no—
283#499—34no—
284#498—32no—
285#479—34no—
286#479—34no—
287#478—34no—
288#478—34no—
289#478—34no—
290#478—34no—
291#478—34no—
292#477C2×D312yescomplemented
293#476—34no—
294#476—32no—
295#476C2×D312yescomplemented
296#475C2×D312yescomplemented
297#474—34no—
298#474—32no—
299#474C2×D312yescomplemented
300#446—32no—
301#446—34no—
302C8×Q8—32no—
303#442—32no—
304#442—34no—
305#440—32no—
306#440—34no—
307C4×SD16—32no—
308C4×SD16—34no—
309C4×D8—32no—
310C4×D8—34no—
311#428—32no—
312#428—31no—
313#428—32no—
314#428—32no—
315#428C2×D312yes—
316#423—32no—
317#423C2×D311yescharacteristic
318#418—32no—
319#418—31no—
320#417—31no—
321#417C2×D312yes—
322C4×M16—32no—
323C4×M16—31no—
324C23×D3—21no—
325C3×#41—22no—
326C3×#41C2×Q814yes—
327C2×C3×Q8—22no—
328C2×C3×Q8—22no—
329C2×C3×Q8—82no—
330C2×C3×Q8C2411yescharacteristic
331C2×C3×D4—21no—
332C2×C3×D4C2411yescharacteristic
333C22×C3×C4—21no—
334C22×C3×C4—22no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4C2×D411yescharacteristic
338C22×C3×C4C2×D411yescharacteristic
339C22×C3×C4C2411yescharacteristic
340C22×Dic3—21no—
341C22×Dic3—22no—
342C22×Dic3—22no—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C2×D12—21no—
346C2×D12—22no—
347C2×D12C2×Q814yescomplemented
348C2×D12C2412yes—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—24no—
352C2×C4×D3—24no—
353C2×C4×D3—44no—
354C2×C4×D3—84no—
355C2×Dic6—21no—
356C2×Dic6—22no—
357C2×Dic6—21no—
358C2×Dic6—22no—
359C2×Dic6—42no—
360C2×Dic6—44no—
361C2×Dic6C2×D411yescharacteristic
362C2×Dic6C2×D411yescharacteristic
363C2×Dic6C2×D412yes—
364C3×M16—24no—
365C2×C3×C8C2414yes—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—22no—
370C3×C4⋊C4—22no—
371C3×C4⋊C4C2414yes—
372C3×C4⋊C4C2411yescharacteristic
373C3×C4⋊C4C2411yescharacteristic
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42C2×D411yescharacteristic
381C3×C42C2×D411yescharacteristic
382C3×C42C2411yescharacteristic
383C3×C42C2411yescharacteristic
384#217—22no—
385#217—22no—
386#217—22no—
387#215C2×Q818yescomplemented
388#213C2×Q818yescomplemented
389(C2×D3)⋊C4—22no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4—24no—
393C4⋊Dic3—21no—
394C4⋊Dic3—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3—22no—
397C4⋊Dic3—22no—
398C4⋊Dic3—22no—
399C4⋊Dic3—22no—
400C4⋊Dic3—24no—
401C4⋊Dic3—24no—
402C4⋊Dic3C2×D411yescharacteristic
403C4⋊Dic3C2×D411yescharacteristic
404C4⋊Dic3C2×D412yes—
405C4⋊Dic3C2412yes—
406C4⋊Dic3C2412yes—
407C4⋊Dic3C2412yes—
408Dic3⋊C4—22no—
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—24no—
415Dic3⋊C4—24no—
416Dic3⋊C4C2×D412yes—
417Dic3⋊C4C2×D412yes—
418Dic3⋊C4C2×D412yes—
419Dic3⋊C4C2×D412yes—
420C4×Dic3—22no—
421C4×Dic3—22no—
422C4×Dic3—22no—
423C4×Dic3C2×D412yes—
424C4×Dic3C2×D412yes—
425C4×Dic3C2412yes—
426C4×Dic3C2412yes—
427#208—22no—
428#208C2×Q814yescomplemented
429C2×C3⋊C8C2412yes—
430C2×C3⋊C8C2412yes—
431C2×#41C22×D311yescharacteristic
432C22×Q8—21no—
433C22×Q8—31no—
434C22×Q8—61no—
435C22×D4—31no—
436C23×C4—62no—
437C23×C4—61no—
438AGL(1,ℤ/8)—38no—
439C2×SD16—32no—
440C2×D8—32no—
441C2×M16—31no—
442C2×M16—31no—
443C2×M16C22×D312yes—
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446C4⋊Q8—32no—
447C4⋊Q8—32no—
448C4⋊Q8—31no—
449C4⋊Q8—31no—
450C4⋊Q8—61no—
451C4⋊Q8—61no—
452C4⋊Q8—62no—
453C4⋊Q8—62no—
454C4⋊Q8C22×D312yes—
455C4⋊Q8C22×D312yes—
456#125—34no—
457#125—34no—
458#125—32no—
459#125—32no—
460#125—32no—
461#125—62no—
462#125—62no—
463#125—62no—
464#125—62no—
465#125—62no—
466C22⋊Q8—62no—
467C22⋊Q8—62no—
468C22⋊Q8—62no—
469C22⋊Q8—62no—
470C22⋊Q8—62no—
471C22⋊Q8—62no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474C22⋊Q8—64no—
475C22⋊Q8—61no—
476C22⋊Q8—62no—
477C22⋊Q8—64no—
478C22⋊Q8—64no—
479C22⋊Q8—64no—
480C22⋊Q8—64no—
481C22⋊Q8—61no—
482C22⋊Q8—61no—
483C22⋊Q8—61no—
484C4×Q8—31no—
485C4×Q8—32no—
486C4×Q8—31no—
487C4×Q8—31no—
488C4×Q8—31no—
489C4×Q8—32no—
490C4×Q8—32no—
491C4×Q8—32no—
492C4×Q8—62no—
493C4×Q8—62no—
494C4×Q8—62no—
495C4×Q8—61no—
496C4×Q8—61no—
497C4×Q8—61no—
498C4×Q8—61no—
499C4×Q8C22×D311yescharacteristic
500C4×Q8C22×D311yescharacteristic
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—32no—
504C4×D4—32no—
505C4×D4—34no—
506C4×D4—34no—
507C4×D4—32no—
508C4×D4—32no—
509C4×D4—62no—
510C4×D4—62no—
511C4×D4—62no—
512C4×D4—62no—
513C4×D4—61no—
514C4×D4—61no—
515C4×D4C22×D311yescharacteristic
516C4×D4C22×D311yescharacteristic
517#117—21no—
518#117—32no—
519#117—62no—
520#117C22×D311yescharacteristic
521C2×C4⋊C4—21no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—62no—
526C2×C4⋊C4—64no—
527C2×C4⋊C4—62no—
528C2×C4⋊C4—62no—
529C2×C4⋊C4—61no—
530C2×C4⋊C4—62no—
531C2×C4⋊C4—62no—
532C2×C4⋊C4C22×D312yes—
533C2×C22⋊C4—62no—
534C2×C22⋊C4—61no—
535C2×C42—21no—
536C2×C42—32no—
537C2×C42—62no—
538C2×C42C22×D311yescharacteristic
539#107—34no—
540#107—32no—
541#107—34no—
542#107—34no—
543#107C22×D314yes—
544#106—34no—
545#106—34no—
546#106—32no—
547#106—34no—
548#106C22×D314yes—
549C4⋊C8—34no—
550C4⋊C8—34no—
551C4⋊C8C22×D312yes—
552C4⋊C8C22×D312yes—
553#103—32no—
554#103C22×D314yes—
555#102—32no—
556#102—34no—
557#102—34no—
558#102—32no—
559#102—32no—
560#102C22×D314yes—
561#97—34no—
562#97—32no—
563C4×C8—34no—
564C4×C8—32no—
565C23×C3—21no—
566C23×C3C22×D411yescharacteristic
567C22×D3—24no—
568C22×D3—22no—
569C22×D3—42no—
570C22×D3—42no—
571C3×Q8—21no—
572C3×Q8—82no—
573C3×Q8—82no—
574C3×Q8C22×Q812yes—
575C3×D4—24no—
576C3×D4—21no—
577C3×D4C22×Q812yes—
578C2×C3×C4—21no—
579C2×C3×C4—24no—
580C2×C3×C4—22no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—24no—
584C2×C3×C4—41no—
585C2×C3×C4—44no—
586C2×C3×C4—42no—
587C2×C3×C4—81no—
588C2×C3×C4C22×D411yescharacteristic
589C2×C3×C4C22×D411yescharacteristic
590C2×C3×C4C22×D411yescharacteristic
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×D411yescharacteristic
593C2×C3×C4C22×Q812yes—
594C2×C3×C42−1+412yes—
595C2×C3×C4C2511yescharacteristic
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—42no—
600C2×Dic3—42no—
601C2×Dic3—44no—
602C2×Dic3—42no—
603C2×Dic3—82no—
604C2×Dic3C22×D412yes—
605C2×Dic3C22×D412yes—
606C2×Dic3C22×D412yes—
607C2×Dic3C22×D412yes—
608D12—24no—
609D12—22no—
610D12C22×Q814yes—
611C4×D3—44no—
612C4×D3—44no—
613C4×D3—84no—
614C4×D3—84no—
615Dic6—22no—
616Dic6—22no—
617Dic6—42no—
618Dic6—44no—
619Dic6—42no—
620Dic6—82no—
621Dic6—81no—
622C3×C8—24no—
623C3⋊C8—22no—
624C3⋊C8C22×Q814yes—
625C24—61no—
626#41—22no—
627#41D3×Q814yes—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—31no—
631C2×Q8—31no—
632C2×Q8—32no—
633C2×Q8—62no—
634C2×Q8—62no—
635C2×Q8—61no—
636C2×Q8—61no—
637C2×Q8—82no—
638C2×Q8—122no—
639C2×Q8—124no—
640C2×Q8C23×D311yescharacteristic
641C2×D4—21no—
642C2×D4—34no—
643C2×D4—32no—
644C2×D4—61no—
645C2×D4—62no—
646C2×D4C23×D311yescharacteristic
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—32no—
652C22×C4—32no—
653C22×C4—64no—
654C22×C4—64no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—61no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—124no—
661C22×C4—244no—
662C22×C4D3×D411yescharacteristic
663C22×C4D3×D411yescharacteristic
664C22×C4C23×D311yescharacteristic
665SD16—38no—
666D8—38no—
667M16—24no—
668M16—34no—
669M16—62no—
670C2×C8—32no—
671C2×C8—32no—
672C2×C8C23×D314yes—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—31no—
679C4⋊C4—32no—
680C4⋊C4—31no—
681C4⋊C4—32no—
682C4⋊C4—32no—
683C4⋊C4—32no—
684C4⋊C4—32no—
685C4⋊C4—32no—
686C4⋊C4—32no—
687C4⋊C4—32no—
688C4⋊C4—64no—
689C4⋊C4—64no—
690C4⋊C4—62no—
691C4⋊C4—62no—
692C4⋊C4—62no—
693C4⋊C4—64no—
694C4⋊C4—64no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—61no—
701C4⋊C4—62no—
702C4⋊C4—61no—
703C4⋊C4—62no—
704C4⋊C4—61no—
705C4⋊C4C23×D311yescharacteristic
706C4⋊C4C23×D311yescharacteristic
707C4⋊C4C23×D314yes—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—64no—
712C22⋊C4—64no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—62no—
717C22⋊C4—62no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—32no—
722C42—32no—
723C42—32no—
724C42—32no—
725C42—62no—
726C42—62no—
727C42—62no—
728C42D3×D411yescharacteristic
729C42D3×D411yescharacteristic
730C42C23×D311yescharacteristic
731C42C23×D311yescharacteristic
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—22no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3D4×Q812yes—
738C22×C3C23×D411yescharacteristic
739C2×D3—24no—
740C2×D3—48no—
741C2×D3—42no—
742C2×D3—42no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—22no—
746C3×C4—21no—
747C3×C4—41no—
748C3×C4—44no—
749C3×C4—41no—
750C3×C4D4×Q812yes—
751C3×C4#57512yes—
752C3×C4C23×Q811yescharacteristic
753C3×C4C2×2−1+411yescharacteristic
754Dic3—22no—
755Dic3—22no—
756Dic3—22no—
757Dic3—22no—
758Dic3—42no—
759Dic3—42no—
760Dic3—42no—
761C23—21no—
762C23—64no—
763C23—62no—
764C23—122no—
765C23—122no—
766C23C2×D3×D411yescharacteristic
767Q8—21no—
768Q8—62no—
769Q8—62no—
770Q8—82no—
771Q8—82no—
772Q8—122no—
773Q8—124no—
774Q8—122no—
775Q8—241no—
776Q8—242no—
777Q8C2×D3×Q812yes—
778D4—24no—
779D4—21no—
780D4—34no—
781D4—64no—
782D4—62no—
783D4C2×D3×Q812yes—
784C2×C4—21no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—24no—
790C2×C4—32no—
791C2×C4—32no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—81no—
801C2×C4—124no—
802C2×C4—122no—
803C2×C4—122no—
804C2×C4—124no—
805C2×C4—122no—
806C2×C4—124no—
807C2×C4—244no—
808C2×C4—244no—
809C2×C4—242no—
810C2×C4C2×D3×D411yescharacteristic
811C2×C4C2×D3×D411yescharacteristic
812C2×C4C2×D3×D411yescharacteristic
813C2×C4C2×D3×D411yescharacteristic
814C2×C4C2×D3×D411yescharacteristic
815C2×C4C2×D3×Q812yes—
816C2×C4#101012yes—
817C2×C4C24×D311yescharacteristic
818C8—24no—
819C8—34no—
820C8—62no—
821C2×C3—22no—
822C2×C3—42no—
823C2×C3C2×D4×Q811yescharacteristic
824C2×C3C2×#57511yescharacteristic
825C2×C3#358511yescharacteristic
826D3—44no—
827C22—21no—
828C22—21no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—64no—
833C22—128no—
834C22—122no—
835C22—122no—
836C22#563212yes—
837C22C22×D3×D411yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—22no—
842C4—44no—
843C4—41no—
844C4—41no—
845C4—62no—
846C4—62no—
847C4—62no—
848C4—62no—
849C4—122no—
850C4—122no—
851C4—122no—
852C4#563212yes—
853C4#577712yes—
854C4C22×D3×Q811yescharacteristic
855C4C2×#101011yescharacteristic
856C3#6136711yescharacteristic, complemented, Sylow
857C2—22no—
858C2—42no—
859C2—124no—
860C2C2×#563211yescharacteristic
861C2#8719211yescharacteristic
862C2C2×#577711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3079C2
socleC22×C3C23×D4
prime radicalC2×#949C22
hypercenter#3079D3
hypocenterC3#61367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. C2×#5730C2semidirect
2. #41×Dic6C2semidirect
3. C3×#3079C2semidirect
4. #83207C2semidirect
6. #81137C2semidirect
7. #81136C2semidirect
8. #81089C2semidirect
9. #81054C2semidirect
10. #81008C2semidirect
11. #80962C2semidirect
12. #79239C2semidirect
13. #79204C2semidirect
14. #79059C2semidirect
15. #79046C2semidirect
16. #78871C2semidirect
30. #5570C22semidirect
31. #5569C22semidirect
32. Q8×Dic6C22semidirect
34. #5543C22semidirect
36. #5539C22semidirect
38. D4×Dic6C22semidirect
50. C3×#477C22semidirect
51. C3×#476C22semidirect
52. C3×#475C22semidirect
53. C3×#474C22semidirect
62. #5081C22semidirect
63. #5080C22semidirect
64. #5078C22semidirect
76. #4878C22semidirect
77. #4876C22semidirect
80. #4858C22semidirect
81. #4856C22semidirect
85. #4831C22semidirect
86. #4830C22semidirect
87. #4828C22semidirect
89. #4799C22semidirect
90. #4796C22semidirect
93. #4766C22semidirect
94. #4763C22semidirect
107. #3079D3semidirect
137. #949Q8semidirect
292. #477C2×D3semidirect
295. #476C2×D3semidirect
296. #475C2×D3semidirect
299. #474C2×D3semidirect
347. C2×D12C2×Q8semidirect
387. #215C2×Q8semidirect
388. #213C2×Q8semidirect
428. #208C2×Q8semidirect
856. C3#61367semidirect

Maximal subgroups

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

subgroupindex
C2×#57302
#41×Dic62
C3×#30792
#832072
C4×#9492
#811372
#811362
#810892
#810542
#810082
#809622
#792392
#792042
#790592
#790462
#788712
#788662
#613673