Finite Group Databasebeta

← #11872757

Subgroups — #11872757

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593994C211yesmaximal, characteristic, complemented
2#10593986C211yesmaximal, characteristic, complemented
3#10592410C211yesmaximal, characteristic, complemented
4C3×#4711C211yesmaximal, characteristic, complemented
5C3×#4709C211yesmaximal, characteristic, complemented
6#10590947C211yesmaximal, characteristic, complemented
7#10590944C211yesmaximal, characteristic, complemented
8#10590837C211yesmaximal, characteristic, complemented
9#10590772C211yesmaximal, characteristic, complemented
10#10590769C211yesmaximal, characteristic, complemented
11#10590765C211yesmaximal, characteristic, complemented
12#10590753C211yesmaximal, characteristic, complemented
13#10590704C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15C4×#3714C211yesmaximal, characteristic, complemented
16#79874—31nomaximal
17#79386—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3745C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×D24C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic, complemented
25C3×#872C2211yescharacteristic
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63912—21no—
29#63911C2211yescharacteristic, complemented
30#63909C2211yescharacteristic
31#63908C2211yescharacteristic
32#63906—21no—
33#63904—21no—
34#63894C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63881—21no—
37#63869C2211yescharacteristic, complemented
38#63853—21no—
39#63850—21no—
40#63841C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#97C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic, complemented
46#63644C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C4×C3⋊C8C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#5562—31no—
62#5545—31no—
63#5535—31no—
64#5521—31no—
65C3×#442—31no—
66C3×#433—31no—
67#5156—31no—
68#5150—31no—
69C4×#213—31no—
70C4×#213—31no—
71#4871—31no—
72#4866—31no—
73#4847—31no—
74#4847—31no—
75#4843—31no—
76#4843—31no—
77#4786—31no—
78#4779—31no—
79#4773—31no—
80#4763—31no—
81#4737—31no—
82#4737—31no—
83#4732—31no—
84#4732—31no—
85#4711—31no—
86#4711—31no—
87#4711—61no—
88#4711D311yescharacteristic, complemented
89#4709D311yescharacteristic, complemented
90C4×D24—31no—
91C4×D24—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3752—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3745—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D24—22no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3714—22no—
140#3714—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×D8—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147C3×#117—31no—
148#940—31no—
149#938—31no—
150D4×Dic3—31no—
151C2×#213—31no—
152C2×#213—31no—
153#930—31no—
154#930—31no—
155#930—61no—
156#929—61no—
157C4×#67—61no—
158C2×(C2×D3)⋊C4—61no—
159#926—31no—
160C2×D24—31no—
161C2×D24—31no—
162C2×D24—31no—
163C2×D24—31no—
164C2×D24—61no—
165C2×D24C2×D311yescharacteristic
166#895—31no—
167#894—61no—
168#894—61no—
169#893—31no—
170#893—61no—
171#893—61no—
172#892—31no—
173#890—31no—
174#884—61no—
175#884—61no—
176#884—61no—
177#883—61no—
178#67⋊C4—61no—
179D3×C22⋊C4—61no—
180D3×C22⋊C4—61no—
181D3×C22⋊C4—61no—
182#874—31no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—61no—
190C4×D12—61no—
191C4×D12C2×D311yescharacteristic
192C4×D12C2×D311yescharacteristic, complemented
193#872C2×D311yescharacteristic
194#870—31no—
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202C3×#97—21no—
203C3×#97C2×D311yescharacteristic, complemented
204C3×#97C2×D311yescharacteristic, complemented
205C3×C4×C8—31no—
206#832—31no—
207#832—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217#821—61no—
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic
222#818—31no—
223#818—31no—
224#817—31no—
225#817—31no—
226#817—61no—
227#817C2×D311yescharacteristic, complemented
228Dic3⋊C8C2×D311yescharacteristic, complemented
229Dic3⋊C8C2×D311yescharacteristic, complemented
230#809—31no—
231#809—31no—
232#807—31no—
233#807—31no—
234C4×C3⋊C8C2×D311yescharacteristic, complemented
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C2×D32—24no—
241C2×D32—81no—
242C2×D32—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)#4112yes—
252C4×C3⋊D3—81no—
253C4×C3⋊D3—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267#626—24no—
268#626—81no—
269#626—81no—
270#626—81no—
271#625—81no—
272#624—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C32×C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—31no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—31no—
293C23×D3—61no—
294C23×D3—61no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C22×Dic3—61no—
307D3×D4—62no—
308D3×D4—62no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—62no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—121no—
333C2×C4×D3—121no—
334C2×C4×D3C22×D311yescharacteristic
335C3×D8—62no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42—31no—
354C3×C42C22×D311yescharacteristic
355C3×C42C22×D311yescharacteristic
356#217—61no—
357#217—61no—
358#217—61no—
359#213—62no—
360#213—62no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4—121no—
376(C2×D3)⋊C4D1211yescharacteristic
377(C2×D3)⋊C4D1211yescharacteristic
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4D1211yescharacteristic
391Dic3⋊C4D1211yescharacteristic
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397D24—22no—
398D24—62no—
399D24—62no—
400D24—64no—
401D24—62no—
402D24—62no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—22no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3×D3—22no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419D32—84no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4C2×#4111yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C22×D4—91no—
432C2×D8—31no—
433C2×D8—91no—
434C2×D8—91no—
435C2×D8—91no—
436#127—91no—
437#125—91no—
438#123—181no—
439#123—181no—
440#121—91no—
441#121—91no—
442#121—181no—
443#121—181no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—181no—
451C4×D4—181no—
452#117—31no—
453#117—91no—
454C2×C22⋊C4—181no—
455C2×C22⋊C4—181no—
456#107—91no—
457#107—91no—
458#106—31no—
459#106—91no—
460C4⋊C8—31no—
461C4⋊C8—31no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469#102—91no—
470C22⋊C8—31no—
471C22⋊C8—31no—
472#97D3211yescharacteristic, complemented
473C4×C8—31no—
474C23×C3—31no—
475C23×C3—61no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—64no—
480C22×D3—64no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3—121no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3C2×D1211yescharacteristic
492C3×D4—32no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—241no—
507C2×C3×C4—241no—
508C2×C3×C4C2×D1211yescharacteristic
509C2×C3×C4C2×D1211yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—64no—
515#67—241no—
516#67—241no—
517#67—241no—
518#67—241no—
519#67—241no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—241no—
529C2×Dic3C2×D1211yescharacteristic
530C2×Dic3C2×D1211yescharacteristic
531C2×Dic3C2×D1211yescharacteristic
532D12—21no—
533D12—21no—
534D12—21no—
535D12—32no—
536D12—32no—
537D12—62no—
538D12—62no—
539D12—64no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—61no—
545D12—61no—
546D12—121no—
547D12—121no—
548D12—241no—
549D12—241no—
550D12—241no—
551D12#23512yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—81no—
555C4×D3—81no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—241no—
563C4×D3—242no—
564C4×D3—242no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C2×C32#52511yescharacteristic
576C2×C32#57611yescharacteristic
577C2×C32#57611yescharacteristic
578C3⋊D3—42no—
579C3⋊D3—81no—
580C3×D3—41no—
581C3×D3—42no—
582C3×D3—81no—
583C24—181no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—91no—
587C2×D4—91no—
588C2×D4—181no—
589C2×D4—181no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—182no—
593C2×D4—181no—
594C2×D4—181no—
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602D8—62no—
603D8—182no—
604D8—182no—
605D8—182no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8C2×D3211yescharacteristic
609C2×C8C2×D3211yescharacteristic
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—31no—
630C42—181no—
631C42C2×D3211yescharacteristic
632C22×C3—21no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—62no—
636C22×C3—61no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C22×D1211yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—22no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—122no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—122no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—244no—
672C2×D3—244no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23511yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4D3×#4111yescharacteristic
689C3×C4D3×#4111yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—241no—
700Dic3—241no—
701C32#312211yescharacteristic, complemented, Sylow
702C23—31no—
703C23—61no—
704C23—61no—
705C23—184no—
706C23—181no—
707C23—181no—
708C23—721no—
709C23—721no—
710D4—32no—
711D4—61no—
712D4—61no—
713D4—61no—
714D4—92no—
715D4—184no—
716D4—181no—
717D4—181no—
718D4—181no—
719D4—721no—
720D4—721no—
721D4—721no—
722D4—721no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—241no—
733C2×C4—241no—
734C2×C4—721no—
735C2×C4—721no—
736C2×C4—721no—
737C2×C4—721no—
738C2×C4D3×D1211yescharacteristic
739C2×C4D3×D1211yescharacteristic
740C2×C4C22×D3211yescharacteristic
741C8—21no—
742C8—21no—
743C8—61no—
744C8—61no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—121no—
749C2×C3—122no—
750C2×C3—241no—
751C2×C3#552411yescharacteristic
752C2×C3#554711yescharacteristic
753C2×C3#575211yescharacteristic
754C2×C3#575211yescharacteristic
755C2×C3#577411yescharacteristic
756C2×C3#577411yescharacteristic
757D3—42no—
758D3—41no—
759D3—81no—
760D3—122no—
761D3—122no—
762D3—242no—
763D3—242no—
764D3—241no—
765D3—241no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—62no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—182no—
776C22—361no—
777C22—361no—
778C22—361no—
779C22—361no—
780C22—361no—
781C22—724no—
782C22C2×D3×D1211yescharacteristic
783C4—21no—
784C4—21no—
785C4—61no—
786C4—61no—
787C4—61no—
788C4—121no—
789C4—121no—
790C4—361no—
791C4—361no—
792C4D3×#23511yescharacteristic
793C4#6430611yescharacteristic
794C3—21no—
795C3#7938611yescharacteristic, complemented
796C3#7987411yescharacteristic, complemented
797C2—121no—
798C2—122no—
799C2—241no—
800C2—362no—
801C2—721no—
802C2#1059399711yescharacteristic
803C2#1059471411yescharacteristic
804C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593994C2semidirect
2. #10593986C2semidirect
3. #10592410C2semidirect
4. C3×#4711C2semidirect
5. C3×#4709C2semidirect
6. #10590947C2semidirect
7. #10590944C2semidirect
8. #10590837C2semidirect
9. #10590772C2semidirect
10. #10590769C2semidirect
11. #10590765C2semidirect
12. #10590753C2semidirect
13. #10590704C2semidirect
14. C4×#3714C2semidirect
15. C4×#3714C2semidirect
21. C4×C4⋊(C3⋊D3)C22semidirect
24. C3×C4×D12C22semidirect
29. #63911C22semidirect
37. #63869C22semidirect
43. C32×#97C22semidirect
45. #63648C22semidirect
46. #63644C22semidirect
48. C3×#821C22semidirect
51. C3×#817C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C4×C3⋊C8C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
58. #63564C22semidirect
60. #63563C22semidirect
88. #4711D3semidirect
89. #4709D3semidirect
192. C4×D12C2×D3semidirect
203. C3×#97C2×D3semidirect
204. C3×#97C2×D3semidirect
219. #821C2×D3semidirect
227. #817C2×D3semidirect
228. Dic3⋊C8C2×D3semidirect
229. Dic3⋊C8C2×D3semidirect
234. C4×C3⋊C8C2×D3semidirect
472. #97D32semidirect
701. C32#3122semidirect
795. C3#79386semidirect
796. C3#79874semidirect

Maximal subgroups

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

subgroupindex
#105939942
#105939862
#105924102
C3×#47112
C3×#47092
#105909472
#105909442
#105908372
#105907722
#105907692
#105907652
#105907532
#105907042
C4×#37142
#798743
#793863