Finite Group Databasebeta

← #11872733

Subgroups — #11872733

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic, complemented
2#10594594C211yesmaximal, characteristic, complemented
3#10592472C211yesmaximal, characteristic, complemented
4C3×#4785C211yesmaximal, characteristic, complemented
5C3×#4763C211yesmaximal, characteristic, complemented
6#10591481C211yesmaximal, characteristic, complemented
7#10591456C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590768C211yesmaximal, characteristic, complemented
10#10590765C211yesmaximal, characteristic, complemented
11#10590652C211yesmaximal, characteristic, complemented
12#10590647C211yesmaximal, characteristic, complemented
13#10590470C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590451C211yesmaximal, characteristic, complemented
16#81146—31nomaximal
17#79874—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3753C2211yescharacteristic
20C2×#3745C2211yescharacteristic
21#64104C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C3×#893C2211yescharacteristic, complemented
26C3×#890C2211yescharacteristic, complemented
27#63974—21no—
28C2×#3722—21no—
29#63952—21no—
30#63952—21no—
31#63916C2211yescharacteristic
32#63911C2211yescharacteristic, complemented
33#63910—21no—
34#63909—21no—
35#63894C2211yescharacteristic
36#63894C2211yescharacteristic
37#63894C2211yescharacteristic, complemented
38#63874C2211yescharacteristic
39#63854—21no—
40#63850—21no—
41#63849C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63647C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#821C2211yescharacteristic, complemented
48C3×#817C2211yescharacteristic, complemented
49C3×#815C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5697—31no—
62#5562—31no—
63#5545—31no—
64#5545—31no—
65C3×#478—31no—
66C3×#442—31no—
67#5156—31no—
68#5150—31no—
69#5066—31no—
70#5015—31no—
71C4×#213—31no—
72C4×#213—31no—
73#4885—31no—
74#4872—31no—
75#4871—31no—
76#4869—31no—
77#4866—31no—
78#4866—31no—
79#4843—31no—
80#4840—31no—
81#4786—31no—
82#4785D311yescharacteristic, complemented
83#4779—31no—
84#4773—31no—
85#4773—31no—
86#4773—31no—
87#4773—61no—
88#4763D311yescharacteristic, complemented
89#4756—31no—
90#4711—31no—
91#4709—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—22no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×#624—21no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3753—22no—
114#3752—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3745—22no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#213—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724D411yescharacteristic
131#3724D411yescharacteristic
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3714—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×C3×D8—31no—
146C3×#125—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150#940—31no—
151#938—31no—
152D4×Dic3C2×D311yescharacteristic
153D4×Dic3C2×D311yescharacteristic
154C2×#213—31no—
155C2×#213—31no—
156C2×#213—31no—
157C2×#213—61no—
158C2×#213C2×D311yescharacteristic
159#930—61no—
160#929—61no—
161C4×#67—61no—
162C4×#67—61no—
163C2×(C2×D3)⋊C4—61no—
164C2×(C2×D3)⋊C4—61no—
165C2×D24—31no—
166C2×D24—31no—
167C2×D24—31no—
168C2×D24—61no—
169#895—31no—
170#895—31no—
171#895—31no—
172#895—61no—
173#895—61no—
174#895—61no—
175#894—61no—
176#894—61no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893C2×D311yescharacteristic, complemented
181#892—31no—
182#892—31no—
183#890C2×D311yescharacteristic, complemented
184#884—61no—
185#883—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190#874—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194#872—31no—
195#872—31no—
196C3×#107—31no—
197C3×#106—31no—
198C3×#106—31no—
199C3×C4⋊C8—31no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102C2×D311yescharacteristic
204C3×#102C2×D311yescharacteristic
205C3×#97—31no—
206#832—31no—
207#832C2×D311yescharacteristic
208#821—31no—
209#821—31no—
210#821—31no—
211#821C2×D311yescharacteristic, complemented
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—61no—
217#817C2×D311yescharacteristic, complemented
218#815C2×D311yescharacteristic, complemented
219Dic3⋊C8—31no—
220Dic3⋊C8C2×D311yescharacteristic, complemented
221C8×Dic3—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#808C2×D311yescharacteristic, complemented
230#807—31no—
231#807—31no—
232#807C2×D311yescharacteristic, complemented
233C4⋊(C3⋊C8)—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—24no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—81no—
240C22×C3⋊D3—81no—
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247#638—24no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—81no—
253C4⋊(C3⋊D3)#4112yes—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×C4×D3—81no—
268#626—81no—
269#626—81no—
270#626—81no—
271#624—81no—
272#624—81no—
273#624—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—31no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C23×D3—61no—
294C23×D3—61no—
295C23×D3—121no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—121no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311D3×D4—62no—
312D3×D4—62no—
313D3×D4—62no—
314D3×D4—62no—
315D3×D4—122no—
316D3×D4—122no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—121no—
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C3×D8—62no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—31no—
359#217—21no—
360#217—21no—
361#217—61no—
362#213—22no—
363#213—62no—
364#213—62no—
365#213—62no—
366#213—122no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
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—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—121no—
384C4⋊Dic3—21no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3C22×D311yescharacteristic
396C4×Dic3C22×D311yescharacteristic
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402D24—62no—
403D24—62no—
404D24—62no—
405D24—122no—
406C22×C32—22no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—22no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—84no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3⋊Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C22×D4—91no—
435C2×D8—31no—
436C2×D8—91no—
437C2×D8—91no—
438C2×D8—91no—
439#127—91no—
440#125—31no—
441#123—181no—
442#123—181no—
443#121—91no—
444#121—91no—
445#121—181no—
446#121—181no—
447C4×D4—31no—
448C4×D4—31no—
449C4×D4—31no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—91no—
457C2×C22⋊C4—181no—
458C2×C22⋊C4—181no—
459#107—31no—
460#107—91no—
461#106—31no—
462#106—31no—
463C4⋊C8—31no—
464C4⋊C8—91no—
465#102—31no—
466#102—31no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471#102—91no—
472#102D3211yescharacteristic
473C22⋊C8—91no—
474C22⋊C8—91no—
475#97—31no—
476C4×C8—91no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—41no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—64no—
488C22×D3—64no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—121no—
492C22×D3—124no—
493C22×D3—121no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3—241no—
497C22×D3—241no—
498C22×D3—242no—
499C22×D3—242no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—22no—
503C3×D4—41no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4#23512yes—
507C3×D4#23912yes—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—241no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—64no—
525#67—64no—
526#67—124no—
527#67—241no—
528#67—241no—
529#67—241no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—61no—
536C2×Dic3—81no—
537C2×Dic3—81no—
538C2×Dic3D3×D411yescharacteristic
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—21no—
543D12—21no—
544D12—32no—
545D12—32no—
546D12—62no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—121no—
554D12—121no—
555D12—121no—
556D12—241no—
557D12—241no—
558D12—241no—
559D12—241no—
560D12—242no—
561D12—241no—
562C4×D3—61no—
563C4×D3—61no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—81no—
567C4×D3—121no—
568C4×D3—121no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—61no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—121no—
585C2×C32—42no—
586C2×C32#52511yescharacteristic
587C2×C32#57611yescharacteristic
588C2×C32#57611yescharacteristic
589C3⋊D3—41no—
590C3⋊D3—42no—
591C3⋊D3—81no—
592C3×D3—81no—
593C24—181no—
594C2×D4—31no—
595C2×D4—91no—
596C2×D4—91no—
597C2×D4—181no—
598C2×D4—181no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—182no—
603C2×D4—182no—
604C2×D4C2×D3211yescharacteristic
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—91no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612D8—62no—
613D8—182no—
614D8—182no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—91no—
619C2×C8C2×D3211yescharacteristic
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4C2×D3211yescharacteristic
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—31no—
641C42—181no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—62no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—62no—
667C2×D3—61no—
668C2×D3—62no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—122no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3—244no—
688C2×D3—244no—
689C2×D3—248no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—81no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4C2×#23511yescharacteristic
703C3×C4C2×#23911yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4D3×#4111yescharacteristic
706Dic3—21no—
707Dic3—21no—
708Dic3—21no—
709Dic3—21no—
710Dic3—41no—
711Dic3—41no—
712Dic3—41no—
713Dic3—61no—
714Dic3—61no—
715Dic3—121no—
716C32#312211yescharacteristic, complemented, Sylow
717C23—21no—
718C23—61no—
719C23—91no—
720C23—184no—
721C23—181no—
722C23—181no—
723C23—721no—
724C23—721no—
725D4—21no—
726D4—61no—
727D4—61no—
728D4—92no—
729D4—184no—
730D4—181no—
731D4—181no—
732D4—181no—
733D4—721no—
734D4—721no—
735D4—721no—
736D4—721no—
737D4#379912yes—
738C2×C4—21no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—91no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—241no—
750C2×C4—241no—
751C2×C4—241no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4—721no—
755C2×C4C22×D3211yescharacteristic
756C8—21no—
757C8—61no—
758C8—61no—
759C8—181no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—42no—
765C2×C3—82no—
766C2×C3—241no—
767C2×C3#554711yescharacteristic
768C2×C3#562711yescharacteristic
769C2×C3#576911yescharacteristic
770C2×C3#577411yescharacteristic
771C2×C3#577411yescharacteristic
772C2×C3#577411yescharacteristic
773D3—81no—
774D3—122no—
775D3—121no—
776D3—122no—
777D3—121no—
778D3—122no—
779D3—242no—
780D3—241no—
781D3—241no—
782D3—481no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—181no—
790C22—182no—
791C22—181no—
792C22—181no—
793C22—361no—
794C22—361no—
795C22—361no—
796C22—361no—
797C22—361no—
798C22—724no—
799C22D32×D411yescharacteristic
800C4—41no—
801C4—61no—
802C4—61no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—181no—
809C4C2×#379911yescharacteristic
810C4#6431211yescharacteristic
811C3—21no—
812C3#7987411yescharacteristic, complemented
813C3#8114611yescharacteristic, complemented
814C2—42no—
815C2—241no—
816C2—361no—
817C2—362no—
818C2—721no—
819C2#1059406611yescharacteristic
820C2#1059473511yescharacteristic
821C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595223C2semidirect
2. #10594594C2semidirect
3. #10592472C2semidirect
4. C3×#4785C2semidirect
5. C3×#4763C2semidirect
6. #10591481C2semidirect
7. #10591456C2semidirect
8. #10591400C2semidirect
9. #10590768C2semidirect
10. #10590765C2semidirect
11. #10590652C2semidirect
12. #10590647C2semidirect
13. #10590470C2semidirect
14. #10590456C2semidirect
15. #10590451C2semidirect
25. C3×#893C22semidirect
26. C3×#890C22semidirect
32. #63911C22semidirect
37. #63894C22semidirect
47. C3×#821C22semidirect
48. C3×#817C22semidirect
49. C3×#815C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
82. #4785D3semidirect
88. #4763D3semidirect
180. #893C2×D3semidirect
183. #890C2×D3semidirect
211. #821C2×D3semidirect
217. #817C2×D3semidirect
218. #815C2×D3semidirect
220. Dic3⋊C8C2×D3semidirect
229. #808C2×D3semidirect
232. #807C2×D3semidirect
716. C32#3122semidirect
812. C3#79874semidirect
813. C3#81146semidirect

Maximal subgroups

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

subgroupindex
#105952232
#105945942
#105924722
C3×#47852
C3×#47632
#105914812
#105914562
#105914002
#105907682
#105907652
#105906522
#105906472
#105904702
#105904562
#105904512
#811463
#798743