Finite Group Databasebeta

← #11872773

Subgroups — #11872773

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594606C211yesmaximal, characteristic, complemented
2#10594594C211yesmaximal, characteristic, complemented
3#10592584C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4872C211yesmaximal, characteristic, complemented
6#10590945C211yesmaximal, characteristic, complemented
7#10590753C211yesmaximal, characteristic, complemented
8#10590745C211yesmaximal, characteristic, complemented
9#10590648C211yesmaximal, characteristic, complemented
10#10590598C211yesmaximal, characteristic, complemented
11#10590589C211yesmaximal, characteristic, complemented
12#10590547C211yesmaximal, characteristic, complemented
13#10590513C211yesmaximal, characteristic, complemented
14#10590469C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#81146—31nomaximal
17#79596—31nomaximal
18C2×#3802C2211yescharacteristic
19#64104C2211yescharacteristic
20#64101C2211yescharacteristic
21C2×C3×D24C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#893C2211yescharacteristic, complemented
25C3×#890C2211yescharacteristic, complemented
26D3×(C2×D3)⋊C4—21no—
27D3×(C2×D3)⋊C4—21no—
28#63916C2211yescharacteristic
29#63911C2211yescharacteristic, complemented
30#63910—21no—
31#63909—21no—
32#63902—21no—
33C4×#625—21no—
34#63894C2211yescharacteristic, complemented
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63874C2211yescharacteristic
38#63854—21no—
39#63850—21no—
40C2×#3714C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×#107C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63636C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5697—31no—
62#5562—31no—
63#5545—31no—
64#5545—31no—
65C3×#478—31no—
66C3×C4×D8—31no—
67#5156—31no—
68#5150—31no—
69#5066—31no—
70#5015—31no—
71#5014—31no—
72#5014—31no—
73#4891D311yescharacteristic, complemented
74#4885—31no—
75#4885—31no—
76#4885—61no—
77#4872D311yescharacteristic, complemented
78#4869—31no—
79#4866—31no—
80#4843—31no—
81#4840—31no—
82#4786—31no—
83#4785—31no—
84#4784—31no—
85#4773—31no—
86#4773—31no—
87#4773—31no—
88#4766—31no—
89#4756—31no—
90C4×D24—31no—
91#4690—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#625—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3802—22no—
110#3802—22no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D24—22no—
130#3724D411yescharacteristic
131#3724D411yescharacteristic
132#3722—21no—
133#3722D411yescharacteristic
134#3722D411yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138#3714—22no—
139#3714—22no—
140#3713—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×C3×D8—31no—
145C3×#125—31no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149#940—31no—
150#938—31no—
151D4×Dic3—31no—
152D4×Dic3—31no—
153C2×#213—31no—
154C2×#213—31no—
155C2×#213—31no—
156C2×#213—31no—
157#930—61no—
158#929—61no—
159C4×#67—61no—
160C4×#67—61no—
161C2×(C2×D3)⋊C4—61no—
162C2×(C2×D3)⋊C4—61no—
163C2×D24—31no—
164C2×D24—31no—
165C2×D24C2×D311yescharacteristic
166#895—31no—
167#895—31no—
168#895—31no—
169#895—61no—
170#895—61no—
171#895—61no—
172#894—61no—
173#894—61no—
174#893—31no—
175#893C2×D311yescharacteristic
176#893C2×D311yescharacteristic
177#893C2×D311yescharacteristic, complemented
178#892—31no—
179#892—31no—
180#892—61no—
181#890C2×D311yescharacteristic, complemented
182#884—61no—
183#883—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#874—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192#872—31no—
193#872—31no—
194C3×#107—21no—
195C3×#107C2×D311yescharacteristic, complemented
196C3×#107C2×D311yescharacteristic, complemented
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C4×C8—31no—
204#832—31no—
205#832—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210#821C2×D311yescharacteristic
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—61no—
216#818—31no—
217#815—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8C2×D311yescharacteristic, complemented
220C8×Dic3C2×D311yescharacteristic, complemented
221#809—31no—
222#809—31no—
223#809—31no—
224#809—61no—
225#809C2×D311yescharacteristic
226#809C2×D311yescharacteristic
227#809C2×D311yescharacteristic, complemented
228#808—31no—
229#808—31no—
230#808—61no—
231#808C2×D311yescharacteristic, complemented
232#807—31no—
233C4⋊(C3⋊C8)—31no—
234#803—31no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C2×D32—24no—
241C2×D32—81no—
242C2×D32—81no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—81no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12#4112yes—
263C3×D12#4112yes—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267#626—81no—
268#626—81no—
269#626—81no—
270#625—24no—
271#624—81no—
272D3×Dic3—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—31no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—31no—
291C4×D8—91no—
292#433—91no—
293C23×D3—61no—
294C23×D3—61no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308D3×D4—62no—
309D3×D4—62no—
310D3×D4—62no—
311D3×D4—62no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—121no—
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C3×D8—62no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#213—62no—
358#213—62no—
359#213—62no—
360#213—62no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
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—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392C4×Dic3C22×D311yescharacteristic
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399D24—22no—
400D24—62no—
401D24—62no—
402C22×C32C22×D411yescharacteristic
403C2×C3⋊D3—21no—
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418D32—84no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4C2×#4111yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—21no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—91no—
431C2×D8—31no—
432C2×D8—91no—
433C2×D8—91no—
434C2×D8—91no—
435#127—91no—
436#125—31no—
437#123—181no—
438#123—181no—
439#121—91no—
440#121—91no—
441#121—181no—
442#121—181no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—181no—
450C4×D4—181no—
451#117—91no—
452#117—91no—
453C2×C22⋊C4—181no—
454C2×C22⋊C4—181no—
455#107—91no—
456#107D3211yescharacteristic, complemented
457#106—31no—
458#106—91no—
459C4⋊C8—31no—
460C4⋊C8—91no—
461#102—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471#97—91no—
472C4×C8—31no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—61no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—61no—
482C22×D3—64no—
483C22×D3—64no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—241no—
491C3×D4—32no—
492C3×D4—32no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—61no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—241no—
510C2×C3×C4—241no—
511C2×C3×C4—241no—
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—64no—
515#67—64no—
516#67—241no—
517#67—241no—
518#67—241no—
519C2×Dic3—21no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532D12—21no—
533D12—21no—
534D12—21no—
535D12—21no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—121no—
541D12—121no—
542D12—241no—
543D12—241no—
544D12—241no—
545D12—241no—
546D12—242no—
547D12—241no—
548D12#23512yes—
549D12#23912yes—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—81no—
555C4×D3—81no—
556C4×D3—81no—
557C4×D3—121no—
558C4×D3—121no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—241no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C2×C32#52511yescharacteristic
574C2×C32#57611yescharacteristic
575C2×C32#57611yescharacteristic
576C3⋊D3—41no—
577C3⋊D3—81no—
578C3×D3—42no—
579C3×D3—42no—
580C3×D3—81no—
581C24—181no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—91no—
586C2×D4—181no—
587C2×D4—181no—
588C2×D4—181no—
589C2×D4—181no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—182no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—91no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600D8—62no—
601D8—182no—
602D8—182no—
603D8—182no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—91no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4C2×D3211yescharacteristic
615C4⋊C4C2×D3211yescharacteristic
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C42—31no—
628C42—31no—
629C42—181no—
630C22×C3—21no—
631C22×C3—62no—
632C22×C3—62no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—241no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4C2×#23511yescharacteristic
685C3×C4C2×#23911yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4D3×#4111yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—41no—
693Dic3—61no—
694Dic3—61no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—241no—
699C32#312211yescharacteristic, complemented, Sylow
700C23—61no—
701C23—61no—
702C23—61no—
703C23—91no—
704C23—184no—
705C23—181no—
706C23—721no—
707C23—721no—
708D4—32no—
709D4—32no—
710D4—61no—
711D4—61no—
712D4—61no—
713D4—61no—
714D4—184no—
715D4—181no—
716D4—181no—
717D4—721no—
718D4—721no—
719D4—721no—
720D4—721no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—241no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4—721no—
736C2×C4—721no—
737C2×C4—721no—
738C2×C4C22×D3211yescharacteristic
739C8—21no—
740C8—61no—
741C8—61no—
742C8—181no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—122no—
747C2×C3—122no—
748C2×C3—241no—
749C2×C3#554711yescharacteristic
750C2×C3#562711yescharacteristic
751C2×C3#575711yescharacteristic
752C2×C3#576911yescharacteristic
753C2×C3#576911yescharacteristic
754C2×C3#577411yescharacteristic
755D3—42no—
756D3—42no—
757D3—81no—
758D3—121no—
759D3—121no—
760D3—241no—
761D3—241no—
762D3—241no—
763D3—481no—
764C22—62no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—181no—
774C22—181no—
775C22—181no—
776C22—361no—
777C22—361no—
778C22—361no—
779C22—724no—
780C22D32×D411yescharacteristic
781C4—41no—
782C4—41no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—181no—
789C4—361no—
790C4D3×#23511yescharacteristic
791C4D3×#23911yescharacteristic
792C3—21no—
793C3#7959611yescharacteristic, complemented
794C3#8114611yescharacteristic, complemented
795C2—122no—
796C2—122no—
797C2—241no—
798C2—361no—
799C2—721no—
800C2#1059462311yescharacteristic
801C2#1059473211yescharacteristic
802C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594606C2semidirect
2. #10594594C2semidirect
3. #10592584C2semidirect
4. C3×#4891C2semidirect
5. C3×#4872C2semidirect
6. #10590945C2semidirect
7. #10590753C2semidirect
8. #10590745C2semidirect
9. #10590648C2semidirect
10. #10590598C2semidirect
11. #10590589C2semidirect
12. #10590547C2semidirect
13. #10590513C2semidirect
14. #10590469C2semidirect
15. #10590455C2semidirect
24. C3×#893C22semidirect
25. C3×#890C22semidirect
29. #63911C22semidirect
34. #63894C22semidirect
43. C32×#107C22semidirect
44. #63648C22semidirect
46. #63636C22semidirect
47. #63635C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×C8×Dic3C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63563C22semidirect
60. #63554C22semidirect
73. #4891D3semidirect
77. #4872D3semidirect
177. #893C2×D3semidirect
181. #890C2×D3semidirect
195. C3×#107C2×D3semidirect
196. C3×#107C2×D3semidirect
219. Dic3⋊C8C2×D3semidirect
220. C8×Dic3C2×D3semidirect
227. #809C2×D3semidirect
231. #808C2×D3semidirect
456. #107D32semidirect
699. C32#3122semidirect
793. C3#79596semidirect
794. C3#81146semidirect

Maximal subgroups

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

subgroupindex
#105946062
#105945942
#105925842
C3×#48912
C3×#48722
#105909452
#105907532
#105907452
#105906482
#105905982
#105905892
#105905472
#105905132
#105904692
#105904552
#811463
#795963