Finite Group Databasebeta

← #10827568

Subgroups — #10827568

Order 768.

1262 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5541C211yesmaximal, characteristic, complemented
2C2×#5133C211yesmaximal, characteristic, complemented
3#82402C211yesmaximal, characteristic
4C2×#4733C211yesmaximal, characteristic, complemented
5C3×#1870C211yesmaximal, characteristic, complemented
6#71989C211yesmaximal, characteristic, complemented
7#69964C211yesmaximal, characteristic, complemented
8#69962C211yesmaximal, characteristic, complemented
9#69933C211yesmaximal, characteristic, complemented
10#69931C211yesmaximal, characteristic, complemented
11#69925C211yesmaximal, characteristic, complemented
12#68690C211yesmaximal, characteristic, complemented
13#68686C211yesmaximal, characteristic, complemented
14#68685C211yesmaximal, characteristic, complemented
15#68679C211yesmaximal, characteristic, complemented
16#23978—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#935—21no—
21C2×#930C2211yescharacteristic
22C2×#926C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C2×#924C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×Dic12C2211yescharacteristic
28C22×#204C2211yescharacteristic
29#5541—24no—
30#5541—24no—
31C2×#889—21no—
32C2×#879—21no—
33C2×#877—21no—
34C2×#870C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39#5223—21no—
40#5212C2211yescharacteristic
41#5133—24no—
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#816C2211yescharacteristic
50#4989—21no—
51#4959—21no—
52#4956—21no—
53#4939C2211yescharacteristic
54#4929C2211yescharacteristic
55#4733—24no—
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64C2×#552—31no—
65C2×#452—31no—
66C2×#417—31no—
67#2407—31no—
68#2026—31no—
69#2025—31no—
70#2001—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1878—31no—
75#1875—31no—
76#1873—31no—
77#1870D311yescharacteristic, complemented
78#1824—31no—
79C22×C3×D4D411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C23×Dic3—21no—
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—41no—
90C2×#235—41no—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×Dic6C2311yescharacteristic
94C22×Dic6C2311yescharacteristic
95C2×C3×M16—22no—
96C2×C3×M16—41no—
97C2×C3×M16—41no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C2×C3×C4⋊C4D411yescharacteristic
105C2×C3×C22⋊C4D411yescharacteristic
106C2×C3×C22⋊C4D411yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113#935—28no—
114#930—22no—
115#930—41no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119#926—22no—
120#926—22no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—22no—
123C2×C4⋊Dic3D414yescomplemented
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129#924—22no—
130#924—22no—
131#924—22no—
132#924—22no—
133#924—41no—
134#924D414yescomplemented
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×C4×Dic3—21no—
142C2×C4×Dic3—21no—
143C2×Dic12—22no—
144C2×Dic12—22no—
145C2×Dic12—41no—
146C2×#204—22no—
147C2×#204—22no—
148C2×#204—41no—
149#889—28no—
150#879—28no—
151#877—28no—
152#870—22no—
153#870—22no—
154C4×Dic6—22no—
155C4×Dic6—22no—
156C3×C22⋊C8—22no—
157C3×C22⋊C8—41no—
158C3×C22⋊C8—41no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#821—22no—
163#821—22no—
164#821—22no—
165#816—22no—
166#816—22no—
167#816—22no—
168#816—41no—
169#816—41no—
170C22×#41—31no—
171C22×Q16—31no—
172C22×SD16—31no—
173C22×M16C2×D311yescharacteristic
174#552—64no—
175#552—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#125—61no—
179C2×#123—61no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184C2×C4×Q8—31no—
185C2×C4×D4C2×D311yescharacteristic
186C2×#117—31no—
187C2×#117—61no—
188C22×C4⋊C4—31no—
189#452—64no—
190#417—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8C2×D311yescharacteristic
200C2×C22⋊C8C2×D311yescharacteristic
201C2×C22⋊C8C2×D311yescharacteristic
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336C2×D311yescharacteristic
216#336C2×D311yescharacteristic
217C24×C3C2×D411yescharacteristic
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C2×C3×D4—22no—
221C2×C3×D4—41no—
222C2×C3×D4—41no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2411yescharacteristic
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—81no—
246C22×Dic3—24no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—42no—
255C22×Dic3—42no—
256#235—28no—
257#235—44no—
258#235—44no—
259#235—44no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12#4112yes—
266C2×C4×D3—42no—
267C2×C4×D3—42no—
268C2×C4×D3—42no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6C2×D412yes—
280C2×Dic6#4112yes—
281C3×M16—44no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C3×C4⋊C4—22no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—22no—
297C3×C42—21no—
298C3×C42—21no—
299#217—24no—
300#217—24no—
301#217—24no—
302#217—42no—
303#217—81no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—81no—
307C4⋊Dic3—24no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3C2×D412yes—
316C4⋊Dic3C2×D412yes—
317C4⋊Dic3C2×D412yes—
318Dic3⋊C4—24no—
319Dic3⋊C4—24no—
320Dic3⋊C4—24no—
321Dic3⋊C4—24no—
322Dic3⋊C4—24no—
323Dic3⋊C4—42no—
324C4×Dic3—24no—
325C4×Dic3—24no—
326Dic12—44no—
327#204—44no—
328C2×#41—62no—
329C2×#41—62no—
330C2×#41—62no—
331C2×#41—62no—
332C2×#41—121no—
333C2×#41—121no—
334C22×Q8—31no—
335C22×Q8—31no—
336C22×D4—31no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4D1211yescharacteristic
340C23×C4—61no—
341C23×C4—61no—
342C23×C4C22×D311yescharacteristic
343C23×C4C22×D311yescharacteristic
344C2×Q16—62no—
345C2×Q16—62no—
346C2×Q16—121no—
347C2×SD16—62no—
348C2×SD16—62no—
349C2×SD16—121no—
350C2×M16—22no—
351C2×M16—41no—
352C2×M16—41no—
353C22×C8C22×D311yescharacteristic
354C22×C8C22×D311yescharacteristic
355C22×C8C22×D311yescharacteristic
356C22×C8C22×D311yescharacteristic
357#126—68no—
358#125—62no—
359#125—62no—
360#125—68no—
361#123—68no—
362C22⋊Q8—34no—
363C22⋊Q8—62no—
364C22⋊Q8—62no—
365C22⋊Q8—62no—
366C22⋊Q8—62no—
367C22⋊Q8—121no—
368#121—62no—
369#121—121no—
370C4×Q8—62no—
371C4×Q8—62no—
372C4×D4—22no—
373C4×D4—22no—
374#117—68no—
375#117—62no—
376#117—62no—
377C2×C4⋊C4—34no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4D1211yescharacteristic
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4D1211yescharacteristic
401C2×C22⋊C4D1211yescharacteristic
402C2×C42—61no—
403C2×C42—61no—
404C2×C42C22×D311yescharacteristic
405#103—62no—
406#103—62no—
407#103—62no—
408#103—121no—
409#103—121no—
410#102—62no—
411#102—62no—
412#102—62no—
413C22⋊C8—22no—
414C22⋊C8—41no—
415C22⋊C8—41no—
416#95—61no—
417#95—61no—
418#95—61no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3#12012yes—
433C23×C3C22×D411yescharacteristic
434C22×D3—22no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C3×D4—44no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4#12012yes—
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468#67—48no—
469#67—84no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—48no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492D12—22no—
493D12—22no—
494D12—41no—
495D12—41no—
496C4×D3—48no—
497Dic6—22no—
498Dic6—22no—
499Dic6—22no—
500Dic6—22no—
501Dic6—41no—
502Dic6—41no—
503Dic6—41no—
504Dic6—41no—
505C3×C8—41no—
506C3×C8—41no—
507C3×C8—41no—
508C3×C8—41no—
509C24—61no—
510C24C2×D1211yescharacteristic
511C24C2×D1211yescharacteristic
512#41—68no—
513#41—124no—
514#41—124no—
515#41—124no—
516C2×Q8—32no—
517C2×Q8—32no—
518C2×Q8—61no—
519C2×Q8—61no—
520C2×Q8—61no—
521C2×Q8—61no—
522C2×Q8—61no—
523C2×Q8—61no—
524C2×Q8—61no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×D4—22no—
529C2×D4—32no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—241no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—64no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—122no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—122no—
565C22×C4—122no—
566C22×C4C2×D1211yescharacteristic
567C22×C4C2×D1211yescharacteristic
568C22×C4C2×D1211yescharacteristic
569C22×C4C2×D1211yescharacteristic
570C22×C4D3×D412yes—
571C22×C4D3×D412yes—
572C22×C4C23×D311yescharacteristic
573Q16—124no—
574SD16—124no—
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C4⋊C4—22no—
589C4⋊C4—32no—
590C4⋊C4—32no—
591C4⋊C4—32no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—64no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—122no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C22⋊C4—64no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C22⋊C4—241no—
615C22⋊C4—241no—
616C42—21no—
617C42—21no—
618C42—64no—
619C42—64no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3C2×#12011yescharacteristic
635C22×C3#54611yescharacteristic
636C22×C3#54611yescharacteristic
637C22×C3#57511yescharacteristic
638C22×C3#57511yescharacteristic
639C22×C3#57711yescharacteristic
640C22×C3#57811yescharacteristic
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—81no—
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
648C3×C4—22no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4#52511yescharacteristic
653C3×C4#53511yescharacteristic
654C3×C4#54611yescharacteristic
655C3×C4#54611yescharacteristic
656Dic3—42no—
657Dic3—42no—
658Dic3—42no—
659Dic3—42no—
660Dic3—42no—
661Dic3—81no—
662Dic3—81no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—62no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23#88212yes—
684C23C22×D1211yescharacteristic
685Q8—62no—
686Q8—62no—
687Q8—62no—
688Q8—62no—
689Q8—121no—
690Q8—121no—
691Q8—121no—
692Q8—121no—
693D4—44no—
694D4—62no—
695D4—62no—
696D4—128no—
697D4—121no—
698D4—121no—
699D4—244no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—128no—
725C2×C4—128no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4#88212yes—
743C2×C4C2×D3×D411yescharacteristic
744C2×C4C2×D3×D411yescharacteristic
745C2×C4#100411yescharacteristic
746C2×C4#100411yescharacteristic
747C2×C4D3×#4111yescharacteristic
748C2×C4D3×#4111yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C2×C3—42no—
754C2×C3—81no—
755C2×C3#240411yescharacteristic
756C2×C3#300511yescharacteristic
757C2×C3#301311yescharacteristic
758C2×C3#331511yescharacteristic
759C2×C3#331711yescharacteristic
760C2×C3#332311yescharacteristic
761C2×C3#332711yescharacteristic
762D3—82no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—122no—
778C22—122no—
779C22—122no—
780C22—241no—
781C22—241no—
782C22—241no—
783C22—241no—
784C22C2×#88211yescharacteristic
785C22#555411yescharacteristic
786C22#555411yescharacteristic
787C22#574811yescharacteristic
788C22#574811yescharacteristic
789C22#575111yescharacteristic
790C22#575311yescharacteristic
791C4—22no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—122no—
796C4—122no—
797C4—122no—
798C4—122no—
799C4—122no—
800C4—241no—
801C4—241no—
802C4#559211yescharacteristic
803C4#561011yescharacteristic
804C4#561011yescharacteristic
805C4#565611yescharacteristic
806C3#2397811yescharacteristic, complemented, Sylow
807C2—42no—
808C2—81no—
809C2—242no—
810C2#7488511yescharacteristic
811C2#7863811yescharacteristic
812C2#7868011yescharacteristic
813C2#7950411yescharacteristic
814C2#7951411yescharacteristic
815C2#7955411yescharacteristic
816C2#7956211yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1870C2
socleC23×C3C22×D4
prime radical#82402C2
hypercenter#1870D3
hypocenterC3#23978
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#5541C2semidirect
2. C2×#5133C2semidirect
4. C2×#4733C2semidirect
5. C3×#1870C2semidirect
6. #71989C2semidirect
7. #69964C2semidirect
8. #69962C2semidirect
9. #69933C2semidirect
10. #69931C2semidirect
11. #69925C2semidirect
12. #68690C2semidirect
13. #68686C2semidirect
14. #68685C2semidirect
15. #68679C2semidirect
77. #1870D3semidirect
123. C2×C4⋊Dic3D4semidirect
134. #924D4semidirect
806. C3#23978semidirect

Maximal subgroups

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

subgroupindex
C2×#55412
C2×#51332
#824022
C2×#47332
C3×#18702
#719892
#699642
#699622
#699332
#699312
#699252
#686902
#686862
#686852
#686792
#239783