Finite Group Databasebeta

← #10848724

Subgroups — #10848724

Order 768.

1216 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5624C211yesmaximal, characteristic, complemented
2C2×#5168C211yesmaximal, characteristic, complemented
3#82698C211yesmaximal, characteristic, complemented
4C2×#4768C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6#72048C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic
9#70239C211yesmaximal, characteristic, complemented
10#70226C211yesmaximal, characteristic, complemented
11#70208C211yesmaximal, characteristic, complemented
12#69962C211yesmaximal, characteristic, complemented
13Dic3×C22⋊C8C211yesmaximal, characteristic, complemented
14#68896C211yesmaximal, characteristic, complemented
15#68804C211yesmaximal, characteristic, complemented
16#25601—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C2×#936C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C22×#204C2211yescharacteristic
29#5624—24no—
30#5624—24no—
31C2×#898—21no—
32C2×#893C2211yescharacteristic
33C2×#892—21no—
34C2×#890C2211yescharacteristic
35C2×#886—21no—
36C2×#67⋊C4—21no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×#835C2211yescharacteristic
41#5221C2211yescharacteristic
42#5220—21no—
43#5220—21no—
44C2×#832C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5168—24no—
47C2×#821C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×C8×Dic3C2211yescharacteristic
50C2×C8×Dic3C2211yescharacteristic
51#4977C2211yescharacteristic
52#4973C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4945—21no—
56#4945—21no—
57#4768—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#529—31no—
65C2×#495—31no—
66C2×#488—31no—
67#2850—31no—
68#2001—31no—
69#2000—31no—
70#2000D311yescharacteristic, complemented
71#1999—31no—
72#1991—31no—
73#1958—31no—
74#1880—31no—
75#1879—31no—
76#1878—31no—
77#1877—31no—
78C4×C22⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C23×Dic3D411yescharacteristic
85C23×Dic3D411yescharacteristic
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×Dic6C2311yescharacteristic
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—41no—
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8—22no—
96C3×#121—41no—
97C3×#121—41no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108#947—22no—
109#947D414yescomplemented
110Q8×Dic3—22no—
111Q8×Dic3—22no—
112C2×#216—22no—
113C2×#216—22no—
114C2×#216—41no—
115#936—22no—
116#936—22no—
117C2×#213—22no—
118C2×#213—22no—
119C2×#213—41no—
120#930—22no—
121#930—22no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130#924—41no—
131#924—41no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3—22no—
136C2×C4×Dic3—22no—
137C2×C4×Dic3D411yescharacteristic
138C2×C4×Dic3D411yescharacteristic
139C2×C4×Dic3C2311yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×#204—22no—
144C2×#204—22no—
145C2×#204—41no—
146#898—28no—
147#893—22no—
148#893—22no—
149#892—28no—
150#890—22no—
151#890D414yescomplemented
152#886—28no—
153#67⋊C4—28no—
154C3×#103—41no—
155C3×#102—22no—
156C3×C22⋊C8—22no—
157#835—41no—
158#832—22no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#830—22no—
164#821—41no—
165#816—22no—
166C8×Dic3—22no—
167C8×Dic3—22no—
168#810—22no—
169#809—41no—
170C22×Q16—31no—
171C22×SD16—31no—
172C22×SD16C2×D311yescharacteristic
173C22×D8—31no—
174#529—64no—
175#529—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#124—31no—
179C2×#124—31no—
180C2×#123—61no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8C2×D311yescharacteristic
183C2×#121—31no—
184C2×#121C2×D311yescharacteristic
185C2×C4×Q8—31no—
186C2×C4×D4—31no—
187C2×C4×D4—61no—
188C2×#117—61no—
189C22×C42—31no—
190#495—64no—
191#488—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103C2×D311yescharacteristic
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102C2×D311yescharacteristic
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202C2×C4×C8—31no—
203C2×C4×C8—31no—
204#391—31no—
205#390—31no—
206#388—61no—
207#388—61no—
208#386—61no—
209#386—61no—
210#382—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8C2×D412yes—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2411yescharacteristic
246C2×#67—24no—
247C2×#67—42no—
248C2×#67—42no—
249C22×Dic3—22no—
250C22×Dic3—21no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—41no—
257C22×Dic3—41no—
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12C2×D412yes—
268C2×C4×D3—24no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C3×SD16—44no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8#4112yes—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—24no—
290C3×C22⋊C4—42no—
291#217—42no—
292#217—42no—
293#217—42no—
294#217—42no—
295#217—42no—
296#216—44no—
297#213—44no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—24no—
302C4⋊Dic3—24no—
303C4⋊Dic3—21no—
304C4⋊Dic3—24no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3C2×D412yes—
308Dic3⋊C4—24no—
309Dic3⋊C4—42no—
310C4×Dic3—24no—
311C4×Dic3—21no—
312C4×Dic3—21no—
313C4×Dic3—22no—
314C4×Dic3—22no—
315C4×Dic3C2×D412yes—
316C4×Dic3C2×D412yes—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8#4112yes—
323#204—44no—
324C22×Q8—31no—
325C22×Q8C22×D311yescharacteristic
326C22×D4—21no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4C22×D311yescharacteristic
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—61no—
333C23×C4C22×D311yescharacteristic
334C2×Q16—62no—
335C2×Q16—62no—
336C2×Q16—121no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—41no—
340C2×SD16—62no—
341C2×SD16—62no—
342C2×SD16—121no—
343C2×D8—62no—
344C2×D8—62no—
345C2×D8—121no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8C22×D311yescharacteristic
349C22×C8C22×D311yescharacteristic
350#126—68no—
351#125—34no—
352#125—62no—
353#124—34no—
354#124—62no—
355#124—62no—
356#124—62no—
357#123—68no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—121no—
361C22⋊Q8—121no—
362#121—41no—
363#121—41no—
364#121—62no—
365#121—62no—
366C4×Q8—62no—
367C4×Q8—62no—
368C4×D4—68no—
369C4×D4—62no—
370C4×D4—62no—
371#117—68no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C4⋊C4C22×D311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C42—31no—
393C2×C42—31no—
394C2×C42—31no—
395C2×C42—31no—
396C2×C42—62no—
397C2×C42—62no—
398C2×C42—61no—
399#103—41no—
400#103—62no—
401#103—62no—
402#103—121no—
403#102—22no—
404#102—62no—
405#102—121no—
406#102—121no—
407C22⋊C8—22no—
408C22⋊C8—62no—
409C4×C8—62no—
410C4×C8—62no—
411#95—61no—
412#95—61no—
413#95—61no—
414#95—61no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3#13512yes—
429C23×C3C22×D411yescharacteristic
430C22×D3—22no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×Q8—22no—
438C3×Q8—22no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—84no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
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—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—44no—
480C2×Dic3—44no—
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#12012yes—
490C2×Dic3#12012yes—
491C2×Dic3#13512yes—
492D12—22no—
493D12—22no—
494D12—41no—
495D12—41no—
496C4×D3—48no—
497Dic6—41no—
498Dic6—41no—
499Dic6—41no—
500Dic6—41no—
501C3×C8—22no—
502C3×C8—41no—
503C3⋊C8—22no—
504C3⋊C8—41no—
505C24—21no—
506C24—61no—
507C24D3×D411yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8D3×D412yes—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—32no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—64no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—122no—
537C2×D4—122no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—64no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—122no—
560C22×C4—122no—
561C22×C4—121no—
562C22×C4—121no—
563C22×C4D3×D411yescharacteristic
564C22×C4C23×D311yescharacteristic
565Q16—124no—
566SD16—44no—
567SD16—124no—
568D8—124no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—32no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8#23712yes—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—32no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—122no—
593C4⋊C4D3×D412yes—
594C22⋊C4—24no—
595C22⋊C4—42no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C42—32no—
606C42—32no—
607C42—62no—
608C42—62no—
609C42—64no—
610C42—61no—
611C42—61no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3C2×#12011yescharacteristic
627C22×C3#53211yescharacteristic
628C22×C3#53511yescharacteristic
629C22×C3C2×#13511yescharacteristic
630C22×C3C2×#13511yescharacteristic
631C22×C3#57511yescharacteristic
632C22×C3#57511yescharacteristic
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C3×C4—41no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4—81no—
644C3×C4#54611yescharacteristic
645C3×C4#54611yescharacteristic
646C3×C4#55011yescharacteristic
647C3×C4#55011yescharacteristic
648Dic3—22no—
649Dic3—22no—
650Dic3—22no—
651Dic3—41no—
652Dic3—42no—
653Dic3—81no—
654Dic3—81no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—62no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23#91612yes—
676C23C2×D3×D411yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681Q8—121no—
682Q8—121no—
683Q8—121no—
684Q8—121no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—62no—
690D4—62no—
691D4—84no—
692D4—128no—
693D4—121no—
694D4—121no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—32no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—62no—
724C2×C4—128no—
725C2×C4—124no—
726C2×C4—124no—
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×C4C2×D3×D411yescharacteristic
736C2×C4C2×D3×D411yescharacteristic
737C2×C4C2×#23711yescharacteristic
738C2×C4#100411yescharacteristic
739C2×C4#100411yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C8—22no—
742C8—41no—
743C8—62no—
744C8—121no—
745C2×C3—42no—
746C2×C3—161no—
747C2×C3#243111yescharacteristic
748C2×C3#300211yescharacteristic
749C2×C3#300211yescharacteristic
750C2×C3#316811yescharacteristic
751C2×C3#318311yescharacteristic
752C2×C3#321111yescharacteristic
753C2×C3#321211yescharacteristic
754D3—82no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—241no—
773C22—241no—
774C22—241no—
775C22—241no—
776C22D3×#12011yescharacteristic
777C22#559211yescharacteristic
778C22#559611yescharacteristic
779C22C2×#91611yescharacteristic
780C22D3×#13511yescharacteristic
781C22#577311yescharacteristic
782C22#577711yescharacteristic
783C4—41no—
784C4—42no—
785C4—42no—
786C4—62no—
787C4—62no—
788C4—62no—
789C4—81no—
790C4—121no—
791C4—122no—
792C4—241no—
793C4—241no—
794C4#559111yescharacteristic
795C4#559911yescharacteristic
796C4#561011yescharacteristic
797C4#571811yescharacteristic
798C3#2560111yescharacteristic, complemented, Sylow
799C2—42no—
800C2—161no—
801C2—242no—
802C2#7667211yescharacteristic
803C2#8003811yescharacteristic
804C2#8008211yescharacteristic
805C2#8013911yescharacteristic
806C2#8022111yescharacteristic
807C2#8063311yescharacteristic
808C2#8079111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radical#71684C2
hypercenter#2000D3
hypocenterC3#25601
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5624C2semidirect
2. C2×#5168C2semidirect
3. #82698C2semidirect
4. C2×#4768C2semidirect
5. C3×#2000C2semidirect
6. #72048C2semidirect
7. #71700C2semidirect
9. #70239C2semidirect
10. #70226C2semidirect
11. #70208C2semidirect
12. #69962C2semidirect
13. Dic3×C22⋊C8C2semidirect
14. #68896C2semidirect
15. #68804C2semidirect
70. #2000D3semidirect
109. #947D4semidirect
151. #890D4semidirect
798. C3#25601semidirect

Maximal subgroups

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

subgroupindex
C2×#56242
C2×#51682
#826982
C2×#47682
C3×#20002
#720482
#717002
#716842
#702392
#702262
#702082
#699622
Dic3×C22⋊C82
#688962
#688042
#256013