Finite Group Databasebeta

← #10830653

Subgroups — #10830653

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5817C211yesmaximal, characteristic
2C2×#5228C211yesmaximal, characteristic, complemented
3C2×#4798C211yesmaximal, characteristic, complemented
4C2×#4808C211yesmaximal, characteristic, complemented
5C2×#4790C211yesmaximal, characteristic, complemented
6#73934C211yesmaximal, characteristic, complemented
7C3×#1787C211yesmaximal, characteristic, complemented
8#70275C211yesmaximal, characteristic, complemented
9#70273C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70226C211yesmaximal, characteristic, complemented
12#70222C211yesmaximal, characteristic, complemented
13#69962C211yesmaximal, characteristic, complemented
14#69916C211yesmaximal, characteristic, complemented
15#69523C211yesmaximal, characteristic, complemented
16#24246—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×#239C2211yescharacteristic
19#5817—24no—
20#5817—24no—
21C2×#947—21no—
22C2×#947C2211yescharacteristic
23C2×#946—21no—
24C2×#946C2211yescharacteristic
25C2×Q8×Dic3C2211yescharacteristic
26C22×#216C2211yescharacteristic
27C22×#216C2211yescharacteristic
28C2×#930—21no—
29C2×#930C2211yescharacteristic
30C2×C4×#67—21no—
31C2×C4×#67C2211yescharacteristic
32C2×#924C2211yescharacteristic
33C22×#204C2211yescharacteristic
34C2×#897C2211yescharacteristic
35C2×#887C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C3×#380C2211yescharacteristic
42#5228—24no—
43C2×#835C2211yescharacteristic
44C2×#835C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×#816C2211yescharacteristic
50C2×Dic3⋊C8C2211yescharacteristic
51C2×C8×Dic3C2211yescharacteristic
52#4987C2211yescharacteristic
53#4977C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×#807C2211yescharacteristic
57#4959—21no—
58#4951—21no—
59#4808—24no—
60#4798—24no—
61#4790—24no—
62#4669—21no—
63#4657—21no—
64#4551C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#548—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#451—31no—
70C2×C4×Q16—31no—
71#2536—31no—
72#2036—31no—
73#2033—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1805—31no—
79#1788—31no—
80#1787D311yescharacteristic, complemented
81C22×C3×Q8—22no—
82C22×C3×Q8—22no—
83C22×C3×Q8—21no—
84C22×C3×Q8—22no—
85C22×C3×Q8—22no—
86C22×C3×Q8—41no—
87C22×C3×Q8—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C22×#67—21no—
93C22×#67D411yescharacteristic
94C2×#239—22no—
95C2×#239—22no—
96C2×#239—22no—
97C2×#239—22no—
98C2×#239—41no—
99C2×#239—41no—
100C22×D12—21no—
101C22×D12C2311yescharacteristic
102C22×C4×D3—21no—
103C22×C4×D3C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111C2×#217D411yescharacteristic
112#947—28no—
113#947—22no—
114#947D414yes—
115#946—28no—
116#946—22no—
117#946—22no—
118Q8×Dic3—22no—
119Q8×Dic3D414yes—
120C2×#216—22no—
121C2×#216—22no—
122C2×#216—22no—
123C2×#216—22no—
124C2×#216—41no—
125C2×#216D414yescomplemented
126#930—28no—
127#930—22no—
128#930—22no—
129C4×#67—28no—
130C4×#67—22no—
131C4×#67—22no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4D411yescharacteristic
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3C2311yescharacteristic
142C2×C4⋊Dic3C2311yescharacteristic
143#924—22no—
144#924—41no—
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4D411yescharacteristic
149C2×C4×Dic3—21no—
150C2×C4×Dic3—21no—
151C2×C4×Dic3C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C2×#204—22no—
155C2×#204—22no—
156C2×#204—41no—
157#897—22no—
158#897—41no—
159#887—22no—
160#887—22no—
161C3×#103—22no—
162C3×#103—22no—
163C3×#103—22no—
164C3×#103—41no—
165C3×C22⋊C8—41no—
166C3×#95—21no—
167#835—22no—
168#835—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172#830—22no—
173#821—41no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—41no—
176#816—22no—
177Dic3⋊C8—22no—
178C8×Dic3—22no—
179#809—22no—
180#809—22no—
181#807—22no—
182C22×#41—31no—
183C23×Q8C2×D311yescharacteristic
184C22×Q16—31no—
185C22×Q16—31no—
186C22×SD16—31no—
187#548—64no—
188#548—64no—
189C2×#124—31no—
190C2×#124—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—31no—
194C2×C22⋊Q8—61no—
195C2×#121—31no—
196C2×#121—61no—
197C2×C4×Q8—31no—
198C2×C4×Q8—31no—
199C2×C4×D4—31no—
200C2×C4×D4—61no—
201#464—64no—
202#452—64no—
203#451—64no—
204C4×Q16—64no—
205C2×#107—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103C2×D311yescharacteristic
211C2×#103C2×D311yescharacteristic
212C2×#103C2×D311yescharacteristic
213C2×#103C2×D311yescharacteristic
214C2×#102—31no—
215C2×#102—31no—
216C2×#102—31no—
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic
221C2×C4×C8—31no—
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382—31no—
227#380—31no—
228#380C2×D311yescharacteristic
229#340—31no—
230#340—31no—
231C24×C3C2×D411yescharacteristic
232C23×D3—21no—
233C23×D3C2×D411yescharacteristic
234C2×C3×Q8—24no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—42no—
244C2×C3×Q8—42no—
245C2×C3×Q8—44no—
246C2×C3×Q8—44no—
247C2×C3×Q8—44no—
248C2×C3×Q8—44no—
249C2×C3×Q8C2×D412yes—
250C2×C3×Q8C2×D412yes—
251C2×C3×Q8C2×D412yes—
252C2×C3×Q8#4112yes—
253C22×C3×C4—21no—
254C22×C3×C4—24no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—42no—
265C22×C3×C4—42no—
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C2×#67—24no—
269C2×#67—22no—
270C2×#67—22no—
271C2×#67—41no—
272C2×#67—42no—
273C2×#67—42no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3C2×D411yescharacteristic
278C22×Dic3C2×D411yescharacteristic
279C22×Dic3C2×D411yescharacteristic
280#239—44no—
281#239—44no—
282#239—44no—
283#239—44no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—24no—
289C2×D12—21no—
290C2×D12—42no—
291C2×D12—42no—
292C2×D12C2×D412yes—
293C2×C4×D3—24no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×Dic6—21no—
303C2×Dic6—21no—
304C2×Dic6—21no—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6C2×D412yes—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C22⋊C4—42no—
319#217—22no—
320#217—42no—
321#216—28no—
322#216—44no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—42no—
329(C2×D3)⋊C4—42no—
330C4⋊Dic3—21no—
331C4⋊Dic3—24no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—42no—
335C4⋊Dic3C2×D412yes—
336Dic3⋊C4—24no—
337Dic3⋊C4—22no—
338Dic3⋊C4—42no—
339Dic3⋊C4—42no—
340C4×Dic3—24no—
341C4×Dic3—42no—
342C4×Dic3C2×D412yes—
343C4×Dic3C2×D412yes—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8C2×D412yes—
350#204—44no—
351C2×#41—62no—
352C2×#41—62no—
353C2×#41—62no—
354C2×#41—62no—
355C2×#41—121no—
356C2×#41—121no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—21no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—31no—
363C22×Q8—41no—
364C22×Q8—41no—
365C22×Q8C22×D311yescharacteristic
366C22×Q8C22×D311yescharacteristic
367C22×D4—31no—
368C22×D4—31no—
369C22×D4—61no—
370C22×D4—61no—
371C23×C4—21no—
372C23×C4—31no—
373C23×C4—61no—
374C23×C4C22×D311yescharacteristic
375C2×Q16—34no—
376C2×Q16—62no—
377C2×Q16—62no—
378C2×Q16—62no—
379C2×Q16—62no—
380C2×Q16—121no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×SD16—121no—
384C22×C8—31no—
385C22×C8—31no—
386C22×C8C22×D311yescharacteristic
387C22×C8C22×D311yescharacteristic
388#124—34no—
389#124—62no—
390#124—68no—
391C22⋊Q8—62no—
392C22⋊Q8—68no—
393C22⋊Q8—62no—
394C22⋊Q8—62no—
395C22⋊Q8—62no—
396C22⋊Q8—121no—
397C22⋊Q8—121no—
398#121—62no—
399#121—62no—
400#121—68no—
401C4×Q8—34no—
402C4×Q8—62no—
403C4×Q8—62no—
404C4×Q8—62no—
405C4×D4—62no—
406C4×D4—62no—
407C4×D4—68no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—31no—
420C2×C22⋊C4—31no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C42—31no—
429C2×C42—61no—
430C2×C42—61no—
431#107—62no—
432C4⋊C8—62no—
433#103—22no—
434#103—22no—
435#103—22no—
436#103—41no—
437#103—62no—
438#103—62no—
439#103—62no—
440#102—62no—
441#102—62no—
442#102—121no—
443C22⋊C8—41no—
444C22⋊C8—62no—
445C22⋊C8—62no—
446C22⋊C8—121no—
447C4×C8—62no—
448#95—21no—
449#95—61no—
450#95—61no—
451#95—61no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3#13512yes—
459C23×C3C22×D411yescharacteristic
460C22×D3—21no—
461C22×D3—22no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C3×Q8—22no—
475C3×Q8—22no—
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—22no—
479C3×Q8—48no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8#12114yes—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—48no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4C22×D411yescharacteristic
504C2×C3×C4C22×D411yescharacteristic
505C2×C3×C4C22×D411yescharacteristic
506C2×C3×C4C2×#4111yescharacteristic
507C2×C3×C4H(5,𝔽2)11yescharacteristic
508C2×C3×C4H(5,𝔽2)11yescharacteristic
509#67—44no—
510#67—48no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—22no—
516C2×Dic3—21no—
517C2×Dic3—22no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3#12012yes—
528C2×Dic3#12012yes—
529D12—22no—
530D12—22no—
531D12—48no—
532D12—41no—
533D12—41no—
534C4×D3—48no—
535C4×D3—41no—
536C4×D3—41no—
537C4×D3—41no—
538C4×D3—41no—
539Dic6—22no—
540Dic6—22no—
541Dic6—41no—
542Dic6—41no—
543C3×C8—41no—
544C3×C8—41no—
545C3⋊C8—22no—
546C3⋊C8—41no—
547C24—31no—
548C24—61no—
549C24D3×D411yescharacteristic
550#41—124no—
551#41—124no—
552#41—124no—
553#41—124no—
554C2×Q8—24no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—32no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8—44no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—61no—
571C2×Q8—61no—
572C2×Q8—61no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8#23512yes—
576C2×Q8D3×D412yes—
577C2×Q8D3×D412yes—
578C2×Q8D3×D412yes—
579C2×D4—32no—
580C2×D4—64no—
581C2×D4—62no—
582C2×D4—64no—
583C2×D4—62no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—122no—
590C2×D4—122no—
591C2×D4—121no—
592C2×D4—122no—
593C2×D4—122no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—64no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—122no—
621C22×C4—122no—
622C22×C4D3×D411yescharacteristic
623C22×C4C23×D311yescharacteristic
624Q16—68no—
625Q16—124no—
626SD16—124no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—32no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—61no—
638C2×C8—61no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—32no—
644C4⋊C4—62no—
645C4⋊C4—64no—
646C4⋊C4—64no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—122no—
651C4⋊C4—122no—
652C4⋊C4—122no—
653C22⋊C4—42no—
654C22⋊C4—62no—
655C22⋊C4—64no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—62no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C42—32no—
664C42—32no—
665C42—64no—
666C42—122no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3C2×#12011yescharacteristic
675C22×C3D4211yescharacteristic
676C22×C3#54611yescharacteristic
677C22×C3C2×#13511yescharacteristic
678C22×C3#57511yescharacteristic
679C22×C3#57811yescharacteristic
680C22×C3#57811yescharacteristic
681C2×D3—42no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—42no—
685C2×D3—41no—
686C2×D3—42no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—81no—
692C2×D3—81no—
693C2×D3—81no—
694C2×D3—81no—
695C3×C4—24no—
696C3×C4—41no—
697C3×C4—42no—
698C3×C4—81no—
699C3×C4—81no—
700C3×C4C2×#12111yescharacteristic
701C3×C4#53511yescharacteristic
702C3×C4D4211yescharacteristic
703C3×C4#54611yescharacteristic
704Dic3—22no—
705Dic3—22no—
706Dic3—42no—
707Dic3—41no—
708Dic3—42no—
709Dic3—81no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—62no—
722C23—61no—
723C23—61no—
724C23—121no—
725C23—121no—
726C23—121no—
727C23—121no—
728C23—121no—
729C23—121no—
730C23#91612yes—
731C23C2×D3×D411yescharacteristic
732Q8—22no—
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—48no—
738Q8—41no—
739Q8—41no—
740Q8—62no—
741Q8—62no—
742Q8—121no—
743Q8—121no—
744Q8#88414yes—
745D4—62no—
746D4—62no—
747D4—128no—
748D4—124no—
749D4—128no—
750D4—121no—
751D4—121no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—48no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—62no—
780C2×C4—61no—
781C2×C4—62no—
782C2×C4—61no—
783C2×C4—128no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4C2×#23511yescharacteristic
796C2×C4C2×D3×D411yescharacteristic
797C2×C4C2×D3×D411yescharacteristic
798C2×C4C2×D3×D411yescharacteristic
799C2×C4#100411yescharacteristic
800C2×C4#100411yescharacteristic
801C8—41no—
802C8—41no—
803C8—62no—
804C8—121no—
805C2×C3—42no—
806C2×C3#240811yescharacteristic
807C2×C3#300211yescharacteristic
808C2×C3#301111yescharacteristic
809C2×C3#327711yescharacteristic
810C2×C3#328511yescharacteristic
811C2×C3#330011yescharacteristic
812C2×C3#332711yescharacteristic
813D3—81no—
814D3—82no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—121no—
823C22—122no—
824C22—121no—
825C22—122no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—122no—
830C22—121no—
831C22—121no—
832C22—241no—
833C22—241no—
834C22—241no—
835C22—241no—
836C22#549011yescharacteristic
837C22D3×#12011yescharacteristic
838C22#559011yescharacteristic
839C22C2×#91611yescharacteristic
840C22#576611yescharacteristic
841C22#577711yescharacteristic
842C22#577911yescharacteristic
843C4—24no—
844C4—41no—
845C4—42no—
846C4—62no—
847C4—62no—
848C4—81no—
849C4—81no—
850C4—121no—
851C4—122no—
852C4—122no—
853C4—241no—
854C4C2×#88411yescharacteristic
855C4#549011yescharacteristic
856C4#559011yescharacteristic
857C4#559211yescharacteristic
858C3#2424611yescharacteristic, complemented, Sylow
859C2—42no—
860C2—241no—
861C2—242no—
862C2#7382411yescharacteristic
863C2#7880711yescharacteristic
864C2#7897111yescharacteristic
865C2#8003811yescharacteristic
866C2#8006711yescharacteristic
867C2#8018511yescharacteristic
868C2#8021011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1787C2
socleC23×C3C22×D4
prime radicalC2×#5817C2
hypercenter#1787D3
hypocenterC3#24246
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#5228C2semidirect
3. C2×#4798C2semidirect
4. C2×#4808C2semidirect
5. C2×#4790C2semidirect
6. #73934C2semidirect
7. C3×#1787C2semidirect
8. #70275C2semidirect
9. #70273C2semidirect
10. #70267C2semidirect
11. #70226C2semidirect
12. #70222C2semidirect
13. #69962C2semidirect
14. #69916C2semidirect
15. #69523C2semidirect
80. #1787D3semidirect
125. C2×#216D4semidirect
858. C3#24246semidirect

Maximal subgroups

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

subgroupindex
C2×#58172
C2×#52282
C2×#47982
C2×#48082
C2×#47902
#739342
C3×#17872
#702752
#702732
#702672
#702262
#702222
#699622
#699162
#695232
#242463