Finite Group Databasebeta

← #10848839

Subgroups — #10848839

Order 768.

1094 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5625C211yesmaximal, characteristic, complemented
2C2×#5190C211yesmaximal, characteristic, complemented
3#82821C211yesmaximal, characteristic
4C2×#4800C211yesmaximal, characteristic, complemented
5C3×#2001C211yesmaximal, characteristic, complemented
6#72065C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic
9#70281C211yesmaximal, characteristic, complemented
10#70240C211yesmaximal, characteristic, complemented
11#70225C211yesmaximal, characteristic, complemented
12#69962C211yesmaximal, characteristic
13#69907C211yesmaximal, characteristic, complemented
14#68909C211yesmaximal, characteristic, complemented
15#68805C211yesmaximal, characteristic, complemented
16#25612—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#926C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×#204C2211yescharacteristic
29#5625—24no—
30#5625—24no—
31C2×#890—21no—
32C2×#890C2211yescharacteristic
33C2×#889—21no—
34C2×#887C2211yescharacteristic
35C2×#879—21no—
36C2×#879—21no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5229C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5190—24no—
45C2×#821C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×C8×Dic3C2211yescharacteristic
49#4994—21no—
50#4994—21no—
51#4988C2211yescharacteristic
52#4975C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4959—21no—
56#4959—21no—
57#4800—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#541—31no—
65C2×#497—31no—
66C2×#488—31no—
67#2620—31no—
68#2001—31no—
69#2001D311yescharacteristic, complemented
70#2000—31no—
71#2000—31no—
72#1992—31no—
73#1956—31no—
74#1880—31no—
75#1880—31no—
76#1878—31no—
77#1878—31no—
78#1750—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×D12C2311yescharacteristic
84C22×Dic6C2311yescharacteristic
85C2×C3×Q16—22no—
86C2×C3×Q16—22no—
87C2×C3×Q16—41no—
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—22no—
92C3×C22⋊Q8—41no—
93C3×C22⋊Q8—41no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×#217—21no—
101C2×#217D411yescharacteristic
102C2×#217D411yescharacteristic
103#947—22no—
104#947—22no—
105Q8×Dic3—22no—
106Q8×Dic3—22no—
107#944—22no—
108#944D414yescomplemented
109C2×#216—22no—
110C2×#216—22no—
111C2×#216—41no—
112C2×#215—22no—
113C2×#215—22no—
114C2×#215—41no—
115#930—41no—
116#930—41no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122#926—22no—
123#926—22no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3D411yescharacteristic
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130#924—22no—
131#924—22no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×C4×Dic3—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3C2311yescharacteristic
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×#204—22no—
146C2×#204—22no—
147C2×#204—41no—
148#890—28no—
149#890—22no—
150#890D414yescomplemented
151#889—28no—
152#887—22no—
153#887—22no—
154#879—28no—
155#879—28no—
156C3×#103—22no—
157C3×#103—41no—
158C3×C22⋊C8—22no—
159#835—22no—
160#835—41no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#830—22no—
164#821—22no—
165#816—41no—
166#815—22no—
167C8×Dic3—22no—
168#810—41no—
169#809—22no—
170C22×Q16—31no—
171C22×Q16C2×D311yescharacteristic
172C22×SD16—31no—
173C22×SD16—31no—
174#541—64no—
175#541—64no—
176C2×C4⋊Q8—31no—
177C2×#126—61no—
178C2×#126—61no—
179C2×#125—31no—
180C2×#125—61no—
181C2×#125—61no—
182C2×#124—31no—
183C2×C22⋊Q8—31no—
184C2×C22⋊Q8C2×D311yescharacteristic
185C2×C22⋊Q8C2×D311yescharacteristic
186C2×#121—31no—
187C2×C4×Q8—31no—
188C2×C4×Q8—31no—
189C2×#117—31no—
190#497—64no—
191#488—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103C2×D311yescharacteristic
197C2×#103C2×D311yescharacteristic
198C2×#102—31no—
199C2×#102—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202C2×#97—31no—
203C2×C4×C8—31no—
204#396—61no—
205#396—61no—
206#394—61no—
207#394—61no—
208#391—31no—
209#390—31no—
210#384—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8C2×D412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C2×#67—42no—
244C2×#67—81no—
245C2×#67—81no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6C2×D412yes—
265C3×Q16—44no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8#4112yes—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—42no—
277C3×C4⋊C4C2×D412yes—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—42no—
280#217—24no—
281#217—22no—
282#217—22no—
283#216—44no—
284#215—44no—
285(C2×D3)⋊C4—42no—
286(C2×D3)⋊C4—42no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—81no—
289(C2×D3)⋊C4—81no—
290C4⋊Dic3—24no—
291C4⋊Dic3—21no—
292C4⋊Dic3—24no—
293C4⋊Dic3—22no—
294C4⋊Dic3—22no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3C2×D412yes—
298Dic3⋊C4—24no—
299Dic3⋊C4—24no—
300Dic3⋊C4—24no—
301Dic3⋊C4—24no—
302Dic3⋊C4—24no—
303Dic3⋊C4—81no—
304Dic3⋊C4—81no—
305C4×Dic3—24no—
306C4×Dic3—24no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309C4×Dic3C2×D412yes—
310C4×Dic3C2×D412yes—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8#4112yes—
317#204—44no—
318C22×Q8—31no—
319C22×Q8C22×D311yescharacteristic
320C22×Q8C22×D311yescharacteristic
321C22×D4—31no—
322C22×D4—61no—
323C23×C4C22×D311yescharacteristic
324C2×Q16—22no—
325C2×Q16—22no—
326C2×Q16—41no—
327C2×Q16—62no—
328C2×Q16—62no—
329C2×Q16—121no—
330C2×SD16—62no—
331C2×SD16—62no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—121no—
335C2×SD16—121no—
336C22×C8—31no—
337C22×C8—31no—
338C22×C8C22×D311yescharacteristic
339C22×C8C22×D311yescharacteristic
340C4⋊Q8—34no—
341C4⋊Q8—62no—
342#126—68no—
343#126—68no—
344#125—34no—
345#125—62no—
346#125—68no—
347#125—68no—
348#124—62no—
349#124—62no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—41no—
353C22⋊Q8—41no—
354C22⋊Q8—62no—
355C22⋊Q8—62no—
356#121—121no—
357#121—121no—
358C4×Q8—62no—
359C4×Q8—62no—
360C4×Q8—62no—
361C4×Q8—62no—
362#117—62no—
363#117—62no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
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—31no—
384C2×C22⋊C4—31no—
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×C42—31no—
392C2×C42—31no—
393C2×C42—61no—
394C2×C42—61no—
395#103—22no—
396#103—41no—
397#103—62no—
398#103—121no—
399#103—121no—
400#103—121no—
401#102—62no—
402#102—62no—
403C22⋊C8—22no—
404C22⋊C8—62no—
405#97—62no—
406C4×C8—62no—
407#95—61no—
408#95—61no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3C22×D411yescharacteristic
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×Q8—41no—
429C3×Q8—41no—
430C3×Q8—41no—
431C3×Q8—41no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4C22×D411yescharacteristic
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4H(5,𝔽2)11yescharacteristic
456C2×C3×C4H(5,𝔽2)11yescharacteristic
457#67—84no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3#12012yes—
478C2×Dic3#12012yes—
479D12—41no—
480D12—41no—
481D12—41no—
482D12—41no—
483Dic6—22no—
484Dic6—22no—
485Dic6—41no—
486Dic6—41no—
487C3×C8—22no—
488C3×C8—41no—
489C3⋊C8—22no—
490C3⋊C8—41no—
491C24—61no—
492C24D3×D411yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—32no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8D3×D412yes—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—122no—
518C2×D4—241no—
519C2×D4—241no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4D3×D411yescharacteristic
538C22×C4C23×D311yescharacteristic
539Q16—44no—
540Q16—124no—
541SD16—124no—
542SD16—124no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—32no—
549C2×C8—61no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8#23712yes—
555C4⋊C4—24no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—32no—
560C4⋊C4—42no—
561C4⋊C4—62no—
562C4⋊C4—62no—
563C4⋊C4—64no—
564C4⋊C4—64no—
565C4⋊C4—64no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—241no—
574C4⋊C4—241no—
575C4⋊C4D3×D412yes—
576C22⋊C4—24no—
577C22⋊C4—42no—
578C22⋊C4—62no—
579C22⋊C4—62no—
580C22⋊C4—64no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—241no—
585C22⋊C4—241no—
586C42—32no—
587C42—32no—
588C42—64no—
589C42—64no—
590C42—61no—
591C42—61no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3C2×#12011yescharacteristic
600C22×C3#53211yescharacteristic
601C22×C3#53511yescharacteristic
602C22×C3#57711yescharacteristic
603C22×C3#57711yescharacteristic
604C22×C3#57811yescharacteristic
605C22×C3#57811yescharacteristic
606C2×D3—81no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C2×D3—81no—
611C2×D3—81no—
612C2×D3—81no—
613C3×C4—41no—
614C3×C4—42no—
615C3×C4—42no—
616C3×C4—81no—
617C3×C4—81no—
618C3×C4#54611yescharacteristic
619C3×C4#54611yescharacteristic
620C3×C4#55011yescharacteristic
621C3×C4#55011yescharacteristic
622Dic3—22no—
623Dic3—22no—
624Dic3—42no—
625Dic3—41no—
626Dic3—41no—
627Dic3—42no—
628Dic3—81no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—121no—
637C23—121no—
638C23—121no—
639C23—121no—
640C23—121no—
641C23—121no—
642C23—121no—
643C23C2×D3×D411yescharacteristic
644Q8—22no—
645Q8—22no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—62no—
653Q8—62no—
654Q8—121no—
655Q8—121no—
656D4—121no—
657D4—121no—
658D4—121no—
659D4—121no—
660D4—244no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4C2×D3×D411yescharacteristic
702C2×C4C2×D3×D411yescharacteristic
703C2×C4C2×#23711yescharacteristic
704C2×C4#100411yescharacteristic
705C2×C4#100411yescharacteristic
706C2×C4D3×#4111yescharacteristic
707C8—22no—
708C8—41no—
709C8—62no—
710C8—121no—
711C2×C3—81no—
712C2×C3#243111yescharacteristic
713C2×C3#301311yescharacteristic
714C2×C3#301311yescharacteristic
715C2×C3#317811yescharacteristic
716C2×C3#317811yescharacteristic
717C2×C3#322211yescharacteristic
718C2×C3#322311yescharacteristic
719D3—161no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—241no—
728C22—241no—
729C22—241no—
730C22—241no—
731C22—241no—
732C22—241no—
733C22—241no—
734C22D3×#12011yescharacteristic
735C22#559211yescharacteristic
736C22#559611yescharacteristic
737C22#576611yescharacteristic
738C22#577011yescharacteristic
739C22#577811yescharacteristic
740C22#577911yescharacteristic
741C4—42no—
742C4—41no—
743C4—42no—
744C4—62no—
745C4—62no—
746C4—81no—
747C4—81no—
748C4—121no—
749C4—122no—
750C4—121no—
751C4—122no—
752C4—241no—
753C4#559111yescharacteristic
754C4#559911yescharacteristic
755C4#561011yescharacteristic
756C4#571811yescharacteristic
757C3#2561211yescharacteristic, complemented, Sylow
758C2—81no—
759C2—481no—
760C2#7667211yescharacteristic
761C2#8018011yescharacteristic
762C2#8018611yescharacteristic
763C2#8023211yescharacteristic
764C2#8026211yescharacteristic
765C2#8074411yescharacteristic
766C2#8089111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2001C2
socleC23×C3C22×D4
prime radicalC2×#930C22
hypercenter#2001D3
hypocenterC3#25612
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
1. C2×#5625C2semidirect
2. C2×#5190C2semidirect
4. C2×#4800C2semidirect
5. C3×#2001C2semidirect
6. #72065C2semidirect
7. #71700C2semidirect
9. #70281C2semidirect
10. #70240C2semidirect
11. #70225C2semidirect
13. #69907C2semidirect
14. #68909C2semidirect
15. #68805C2semidirect
69. #2001D3semidirect
108. #944D4semidirect
150. #890D4semidirect
757. C3#25612semidirect

Maximal subgroups

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

subgroupindex
C2×#56252
C2×#51902
#828212
C2×#48002
C3×#20012
#720652
#717002
#716992
#702812
#702402
#702252
#699622
#699072
#689092
#688052
#256123