Finite Group Databasebeta

← #10828147

Subgroups — #10828147

Order 768.

1380 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×#5834C211yesmaximal, characteristic
2C2×#4804C211yesmaximal, characteristic, complemented
3C2×#4784C211yesmaximal, characteristic, complemented
4#74024C211yesmaximal, characteristic, complemented
5C3×#1788C211yesmaximal, characteristic, complemented
6#72135C211yesmaximal, characteristic, complemented
7#70267C211yesmaximal, characteristic, complemented
8#70237C211yesmaximal, characteristic, complemented
9#70236C211yesmaximal, characteristic, complemented
10#70211C211yesmaximal, characteristic, complemented
11#70202C211yesmaximal, characteristic, complemented
12#70177C211yesmaximal, characteristic, complemented
13#69957C211yesmaximal, characteristic, complemented
14#69934C211yesmaximal, characteristic, complemented
15#69524C211yesmaximal, characteristic, complemented
16#24034—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×#239C2211yescharacteristic
19#5834—24no—
20#5834—24no—
21C2×Q8×Dic3C2211yescharacteristic
22C2×#940—21no—
23C2×#940C2211yescharacteristic
24C2×#938—21no—
25C2×#938C2211yescharacteristic
26C2×#930—21no—
27C2×#930C2211yescharacteristic
28C2×C4×#67—21no—
29C2×C4×#67C2211yescharacteristic
30C22×D3×C8C2211yescharacteristic
31C2×#892C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5212C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#818C2211yescharacteristic
48#4987C2211yescharacteristic
49#4984C2211yescharacteristic
50#4972C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54#4959—21no—
55#4951—21no—
56#4804—24no—
57#4784—24no—
58#4674—21no—
59#4652—21no—
60#4551C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#550—31no—
65C2×#482—31no—
66C2×#416—31no—
67#2485—31no—
68#2041—31no—
69#2041—31no—
70#2034—31no—
71#2033—31no—
72#1893—31no—
73#1869—31no—
74#1865—31no—
75#1863—31no—
76#1788—31no—
77#1788—31no—
78#1788D311yescharacteristic, complemented
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4C2311yescharacteristic
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C22×#67—21no—
91C22×#67—21no—
92C22×#67—21no—
93C22×#67—21no—
94C22×#67D411yescharacteristic
95C2×#239—22no—
96C2×#239—22no—
97C2×#239—22no—
98C2×#239—41no—
99C2×#239—41no—
100C2×#239D414yes—
101C22×D12—21no—
102C22×D12C2311yescharacteristic
103C22×C4×D3—21no—
104C22×C4×D3C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217D411yescharacteristic
113Q8×Dic3—22no—
114Q8×Dic3—22no—
115#940—28no—
116#940—22no—
117#940—22no—
118#938—28no—
119#938—22no—
120#938D414yes—
121#930—28no—
122#930—22no—
123#930—22no—
124C4×#67—28no—
125C4×#67—22no—
126C4×#67—22no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4D411yescharacteristic
138C2×C4×Dic3—21no—
139C2×C4×Dic3—21no—
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×D3×C8—22no—
144C2×D3×C8—41no—
145C2×D3×C8—41no—
146#892—22no—
147#892—22no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#102—22no—
151C3×#102—41no—
152C3×C22⋊C8—41no—
153C3×#95—21no—
154#835—22no—
155#835—22no—
156#832—22no—
157#832—41no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#830—41no—
163#821—22no—
164#821—41no—
165(C2×D3)⋊C8—22no—
166#818—22no—
167#809—22no—
168#809—41no—
169#808—22no—
170C22×#41—31no—
171C22×#41C2×D311yescharacteristic
172C23×C8—31no—
173#550—64no—
174#550—64no—
175C2×#127—31no—
176C2×#127—61no—
177C2×#121—31no—
178C2×#121—31no—
179C2×#121—61no—
180C2×#121—61no—
181C2×C4×Q8—31no—
182C2×C4×D4—31no—
183C2×C4×D4—61no—
184C2×#117—31no—
185#482—64no—
186C2×#107—31no—
187C2×#106—31no—
188#416—64no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103C2×D311yescharacteristic
192C2×#103C2×D311yescharacteristic
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102C2×D311yescharacteristic
200C2×#102C2×D311yescharacteristic
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8C2×D311yescharacteristic
204#397—61no—
205#394—61no—
206#389—31no—
207#389—31no—
208#388—61no—
209#387—61no—
210#380—31no—
211#380—31no—
212#380C2×D311yescharacteristic
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C23×D3C2×D411yescharacteristic
221C3×#41—44no—
222C3×#41—44no—
223C3×#41—44no—
224C3×#41—44no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8C2×D412yes—
229C2×C3×Q8#4112yes—
230C2×C3×Q8#4112yes—
231C2×C3×D4—24no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4C2×D412yes—
240C22×C3×C4—21no—
241C22×C3×C4—24no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—42no—
251C22×C3×C4—42no—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2411yescharacteristic
254C2×#67—24no—
255C2×#67—22no—
256C2×#67—24no—
257C2×#67—24no—
258C2×#67—24no—
259C2×#67—22no—
260C2×#67—41no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—81no—
264C2×#67—81no—
265C2×#67—81no—
266C2×#67—81no—
267C2×#67—81no—
268C2×#67—81no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3C2×D411yescharacteristic
273C22×Dic3C2×D411yescharacteristic
274C22×Dic3C2×D411yescharacteristic
275#239—28no—
276#239—44no—
277#239—44no—
278#239—44no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—24no—
284C2×D12—21no—
285C2×D12—42no—
286C2×D12—42no—
287C2×D12C2×D412yes—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—24no—
293C2×C4×D3—42no—
294C2×C4×D3—42no—
295C2×C4×D3C2×D412yes—
296C2×C4×D3C2×D412yes—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C22⋊C4—42no—
308#217—22no—
309#217—24no—
310#217—81no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—81no—
315C4⋊Dic3—24no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—81no—
322C4⋊Dic3C2×D412yes—
323Dic3⋊C4—22no—
324Dic3⋊C4—42no—
325C4×Dic3—24no—
326C4×Dic3—21no—
327C4×Dic3—21no—
328C4×Dic3—42no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335D3×C8—44no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—34no—
341C2×#41—41no—
342C2×#41—41no—
343C2×#41—62no—
344C2×#41—62no—
345C2×#41—62no—
346C2×#41—121no—
347C2×#41—121no—
348C22×Q8C22×D311yescharacteristic
349C22×D4—21no—
350C22×D4—31no—
351C22×D4—31no—
352C22×D4—61no—
353C22×D4—61no—
354C22×D4—61no—
355C22×D4—61no—
356C22×D4—61no—
357C22×D4C22×D311yescharacteristic
358C23×C4—21no—
359C23×C4—31no—
360C23×C4—61no—
361C23×C4C22×D311yescharacteristic
362C22×C8—31no—
363C22×C8—31no—
364C22×C8—62no—
365C22×C8—121no—
366C22×C8—121no—
367C22×C8C22×D311yescharacteristic
368C22×C8C22×D311yescharacteristic
369#127—62no—
370#127—68no—
371#127—62no—
372#121—34no—
373#121—62no—
374#121—62no—
375#121—68no—
376#121—62no—
377#121—68no—
378C4×Q8—62no—
379C4×Q8—62no—
380C4×D4—62no—
381C4×D4—62no—
382C4×D4—68no—
383#117—62no—
384#117—62no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4C22×D311yescharacteristic
393C2×C4⋊C4C22×D311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—31no—
396C2×C22⋊C4—31no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C22⋊C4—61no—
402C2×C42—31no—
403C2×C42—61no—
404C2×C42—61no—
405#107—62no—
406#106—62no—
407#103—22no—
408#103—22no—
409#103—62no—
410#103—62no—
411#102—22no—
412#102—41no—
413#102—62no—
414#102—62no—
415#102—62no—
416#102—121no—
417#102—121no—
418#102—121no—
419C22⋊C8—41no—
420C22⋊C8—62no—
421C22⋊C8—121no—
422#95—21no—
423#95—61no—
424#95—61no—
425#95—61no—
426#95—61no—
427C23×C3—21no—
428C23×C3—22no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3C22×D411yescharacteristic
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—22no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3#12012yes—
456C3×Q8—22no—
457C3×Q8—22no—
458C3×Q8—22no—
459C3×Q8#12314yes—
460C3×D4—22no—
461C3×D4—22no—
462C3×D4—48no—
463C3×D4—41no—
464C3×D4—41no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—48no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C2×#4111yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486C2×C3×C4H(5,𝔽2)11yescharacteristic
487C2×C3×C4H(5,𝔽2)11yescharacteristic
488#67—44no—
489#67—48no—
490#67—84no—
491#67—84no—
492#67—84no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—22no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3#12012yes—
510C2×Dic3#13512yes—
511D12—22no—
512D12—22no—
513D12—48no—
514D12—41no—
515D12—41no—
516C4×D3—22no—
517C4×D3—22no—
518C4×D3—22no—
519C4×D3—22no—
520C4×D3—48no—
521C3×C8—41no—
522C3×C8—41no—
523C3⋊C8—41no—
524C3⋊C8—41no—
525C24—21no—
526C24—31no—
527C24—61no—
528C24D3×D411yescharacteristic
529#41—44no—
530#41—44no—
531#41—44no—
532#41—44no—
533#41—68no—
534#41—124no—
535#41—124no—
536#41—124no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8#23512yes—
541C2×Q8D3×D412yes—
542C2×Q8#23712yes—
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—32no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—64no—
553C2×D4—62no—
554C2×D4—62no—
555C2×D4—64no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4—61no—
562C2×D4—61no—
563C2×D4—61no—
564C2×D4—122no—
565C2×D4—122no—
566C2×D4—122no—
567C2×D4—121no—
568C2×D4—122no—
569C2×D4—241no—
570C2×D4—241no—
571C2×D4—241no—
572C2×D4—241no—
573C2×D4—241no—
574C2×D4—241no—
575C2×D4D3×D412yes—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—31no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—64no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—122no—
602C22×C4—122no—
603C22×C4D3×D411yescharacteristic
604C22×C4C23×D311yescharacteristic
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—61no—
612C2×C8—61no—
613C2×C8—61no—
614C2×C8—61no—
615C2×C8—61no—
616C2×C8—61no—
617C2×C8—124no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—32no—
623C4⋊C4—62no—
624C4⋊C4—64no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—122no—
631C4⋊C4—241no—
632C22⋊C4—42no—
633C22⋊C4—62no—
634C22⋊C4—64no—
635C22⋊C4—62no—
636C22⋊C4—64no—
637C22⋊C4—122no—
638C22⋊C4—241no—
639C22⋊C4—241no—
640C42—64no—
641C42—61no—
642C42—61no—
643C42—122no—
644C22×C3—42no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—42no—
648C22×C3—41no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3C2×#12011yescharacteristic
659C22×C3#54611yescharacteristic
660C22×C3#54611yescharacteristic
661C22×C3C2×#13511yescharacteristic
662C22×C3#57511yescharacteristic
663C22×C3#57611yescharacteristic
664C22×C3#57711yescharacteristic
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—22no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—81no—
676C2×D3—81no—
677C2×D3—81no—
678C2×D3—81no—
679C3×C4—24no—
680C3×C4—41no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4C2×#12311yescharacteristic
684C3×C4#53411yescharacteristic
685C3×C4#54611yescharacteristic
686C3×C4#54611yescharacteristic
687Dic3—22no—
688Dic3—22no—
689Dic3—41no—
690Dic3—42no—
691Dic3—81no—
692Dic3—81no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—21no—
701C23—32no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—61no—
709C23—61no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—62no—
715C23—121no—
716C23—121no—
717C23—121no—
718C23—121no—
719C23—121no—
720C23—121no—
721C23C2×D3×D411yescharacteristic
722Q8—22no—
723Q8—22no—
724Q8—22no—
725Q8#88314yes—
726D4—22no—
727D4—22no—
728D4—48no—
729D4—41no—
730D4—41no—
731D4—62no—
732D4—62no—
733D4—128no—
734D4—124no—
735D4—128no—
736D4—121no—
737D4—121no—
738D4—244no—
739D4—244no—
740D4—244no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—32no—
748C2×C4—32no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—62no—
771C2×C4—61no—
772C2×C4—128no—
773C2×C4—121no—
774C2×C4—121no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4C2×#23511yescharacteristic
782C2×C4C2×D3×D411yescharacteristic
783C2×C4C2×D3×D411yescharacteristic
784C2×C4C2×#23711yescharacteristic
785C2×C4#100411yescharacteristic
786C2×C4#100411yescharacteristic
787C8—41no—
788C8—41no—
789C8—121no—
790C8—121no—
791C2×C3—81no—
792C2×C3—82no—
793C2×C3#240511yescharacteristic
794C2×C3#300211yescharacteristic
795C2×C3#301211yescharacteristic
796C2×C3#330411yescharacteristic
797C2×C3#330511yescharacteristic
798C2×C3#330911yescharacteristic
799C2×C3#331711yescharacteristic
800D3—42no—
801D3—82no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—62no—
813C22—62no—
814C22—62no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—122no—
824C22—122no—
825C22—122no—
826C22—241no—
827C22—241no—
828C22—241no—
829C22—241no—
830C22#549011yescharacteristic
831C22D3×#12011yescharacteristic
832C22#559111yescharacteristic
833C22D3×#13511yescharacteristic
834C22#576911yescharacteristic
835C22#577311yescharacteristic
836C22#577811yescharacteristic
837C4—24no—
838C4—41no—
839C4—62no—
840C4—62no—
841C4—81no—
842C4—81no—
843C4—121no—
844C4—122no—
845C4—241no—
846C4—241no—
847C4C2×#88311yescharacteristic
848C4#549011yescharacteristic
849C4#558911yescharacteristic
850C4#559111yescharacteristic
851C3#2403411yescharacteristic, complemented, Sylow
852C2—81no—
853C2—82no—
854C2—122no—
855C2—242no—
856C2#7385311yescharacteristic
857C2#7885211yescharacteristic
858C2#7890111yescharacteristic
859C2#8008211yescharacteristic
860C2#8011111yescharacteristic
861C2#8023111yescharacteristic
862C2#8024911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1788C2
socleC23×C3C22×D4
prime radicalC2×#5834C2
hypercenter#1788D3
hypocenterC3#24034
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#4804C2semidirect
3. C2×#4784C2semidirect
4. #74024C2semidirect
5. C3×#1788C2semidirect
6. #72135C2semidirect
7. #70267C2semidirect
8. #70237C2semidirect
9. #70236C2semidirect
10. #70211C2semidirect
11. #70202C2semidirect
12. #70177C2semidirect
13. #69957C2semidirect
14. #69934C2semidirect
15. #69524C2semidirect
78. #1788D3semidirect
851. C3#24034semidirect

Maximal subgroups

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

subgroupindex
C2×#58342
C2×#48042
C2×#47842
#740242
C3×#17882
#721352
#702672
#702372
#702362
#702112
#702022
#701772
#699572
#699342
#695242
#240343