Finite Group Databasebeta

← #11887433

Subgroups — #11887433

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595428C211yesmaximal, characteristic, complemented
2#10594583C211yesmaximal, characteristic, complemented
3#10592510C211yesmaximal, characteristic, complemented
4C3×#4819C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6#10591614C211yesmaximal, characteristic, complemented
7#10591591C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10590945C211yesmaximal, characteristic, complemented
10#10590831C211yesmaximal, characteristic, complemented
11#10590767C211yesmaximal, characteristic, complemented
12#10590720C211yesmaximal, characteristic, complemented
13#10590593C211yesmaximal, characteristic, complemented
14#10590502C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#80559—31nomaximal
17#78846—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20#64155C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic, complemented
24C2×C3×D24C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#893C2211yescharacteristic, complemented
27C3×#892C2211yescharacteristic, complemented
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63916C2211yescharacteristic
31#63912—21no—
32#63908C2211yescharacteristic
33#63908C2211yescharacteristic, complemented
34#63905—21no—
35#63905—21no—
36C4×#626—21no—
37C4×#626C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39#63885—21no—
40#63869C2211yescharacteristic, complemented
41#63859—21no—
42C2×#3713C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63647C2211yescharacteristic
47#63645C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic
54#63573C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5829—31no—
62#5676—31no—
63#5558—31no—
64#5530—31no—
65C3×#463—31no—
66C3×#416—31no—
67#5238—31no—
68#5172—31no—
69#5171—31no—
70#5157—31no—
71#5156—31no—
72#5115—31no—
73C8×#67—31no—
74#5056—31no—
75C4×#213—31no—
76#5003—31no—
77#4847—31no—
78#4834—31no—
79#4819D311yescharacteristic, complemented
80#4811—31no—
81#4811—31no—
82#4811—61no—
83#4807—31no—
84#4804D311yescharacteristic, complemented
85#4800—31no—
86#4779—31no—
87#4773—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4766—31no—
91#4756—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#625—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×D3×Dic3—21no—
111#3802—22no—
112#3802—41no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#215—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D24—41no—
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3713—22no—
143#3710—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C22×C3×C8—31no—
152C3×#124—31no—
153C3×C4×D4—31no—
154C3×#117—31no—
155#947C2×D311yescharacteristic
156#946—31no—
157#946—31no—
158#946—61no—
159C2×#215C2×D311yescharacteristic, complemented
160#939—61no—
161#938—31no—
162#938—31no—
163#938—31no—
164#937—61no—
165D4×Dic3—31no—
166C2×#213—31no—
167C2×#213—31no—
168#930—31no—
169#930—31no—
170#929—61no—
171#929—61no—
172C4×#67—31no—
173C4×#67—61no—
174C2×(C2×D3)⋊C4—61no—
175C2×D24C2×D311yescharacteristic
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8C2×D311yescharacteristic, complemented
179#895—31no—
180#893C2×D311yescharacteristic, complemented
181#892C2×D311yescharacteristic, complemented
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—61no—
185#890—31no—
186#884—61no—
187#884—61no—
188#884—61no—
189#883—61no—
190#883—61no—
191#882—61no—
192D3×C22⋊C4—61no—
193#879—61no—
194#876—61no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198#870—31no—
199C3×C4⋊C8—31no—
200C3×#103—21no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic, complemented
203C3×#103C2×D311yescharacteristic, complemented
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#835—61no—
210#835C2×D311yescharacteristic, complemented
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#830—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—61no—
224#818—31no—
225#818—31no—
226#818—61no—
227#817—31no—
228Dic3⋊C8C2×D311yescharacteristic, complemented
229C8×Dic3—31no—
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#808—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237C4×C3⋊C8—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—42no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—81no—
272#626—22no—
273#626—42no—
274#625—42no—
275#625—81no—
276#625—81no—
277D3×Dic3—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—31no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—31no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—21no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—31no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C22×Dic3—61no—
320#239—22no—
321#239—41no—
322D3×D4—62no—
323D3×D4—62no—
324D3×D4—121no—
325D3×D4—121no—
326C2×D12—21no—
327C2×D12—31no—
328C2×D12—61no—
329C2×D12C22×D311yescharacteristic
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—121no—
341C2×C4×D3C22×D311yescharacteristic
342C3×SD16—121no—
343C3×D8—121no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—121no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359C3×C42—61no—
360#217—31no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#215—41no—
366#213—62no—
367#213—62no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
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—121no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400Dic3⋊C4—121no—
401C4×Dic3—21no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—41no—
409D3×C8—41no—
410D3×C8—121no—
411D3×C8—121no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3#13512yes—
416C2×C3×D3—22no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428D32—84no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C2×#41—31no—
441C22×D4—91no—
442C2×SD16—31no—
443C2×D8—31no—
444C2×D8—91no—
445C22×C8—31no—
446C22×C8—91no—
447#126—181no—
448#125—91no—
449#124—31no—
450#123—181no—
451#123—181no—
452C22⋊Q8—91no—
453#121—91no—
454#121—91no—
455#121—91no—
456#121—181no—
457#121—181no—
458#120—181no—
459C4×D4—31no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463#117—31no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—181no—
466#107—91no—
467#107—91no—
468#106—91no—
469C4⋊C8—31no—
470#103—31no—
471#103—91no—
472#103D3211yescharacteristic, complemented
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482C4×C8—91no—
483C23×C3—31no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—31no—
491C22×D3—31no—
492C22×D3—61no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3D3×D411yescharacteristic
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—32no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—122no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
527C2×C3×C4—241no—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—62no—
531#67—122no—
532#67—122no—
533#67—122no—
534#67—241no—
535#67—241no—
536#67—241no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—241no—
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552D12—21no—
553D12—21no—
554D12—21no—
555D12—21no—
556D12—21no—
557D12—42no—
558D12—62no—
559D12—122no—
560D12#23512yes—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—42no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—81no—
569C4×D3—121no—
570C4×D3—121no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—242no—
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#54611yescharacteristic
586C2×C32C2×#13511yescharacteristic
587C2×C32#57611yescharacteristic
588C3⋊D3—22no—
589C3×D3—42no—
590C3×D3—41no—
591C3×D3—81no—
592C3×D3—81no—
593C24—181no—
594#41—62no—
595#41—121no—
596C2×Q8C2×D3211yescharacteristic
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—61no—
601C2×D4—91no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4—182no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4—361no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—91no—
612C22×C4—181no—
613C22×C4—181no—
614SD16—121no—
615D8—121no—
616D8—182no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—91no—
620C2×C8—121no—
621C2×C8—361no—
622C2×C8C2×D3211yescharacteristic
623C4⋊C4—31no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—91no—
637C22⋊C4—91no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C42—31no—
644C42—61no—
645C22×C3—21no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—62no—
649C22×C3—61no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3C2×D3×D411yescharacteristic
659C22×C3C2×D3×D411yescharacteristic
660C2×D3—21no—
661C2×D3—22no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—32no—
665C2×D3—32no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—62no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—244no—
682C2×D3—244no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—61no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—81no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4C2×#23511yescharacteristic
696C3×C4#100411yescharacteristic
697C3×C4#100411yescharacteristic
698C3×C4D3×#4111yescharacteristic
699Dic3—21no—
700Dic3—21no—
701Dic3—21no—
702Dic3—41no—
703Dic3—61no—
704Dic3—61no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—241no—
711Dic3—241no—
712C32#329711yescharacteristic, complemented, Sylow
713C23—31no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—91no—
718C23—362no—
719C23—362no—
720C23—721no—
721Q8—21no—
722Q8—21no—
723D4—32no—
724D4—61no—
725D4—61no—
726D4—61no—
727D4—61no—
728D4—61no—
729D4—122no—
730D4—182no—
731D4—362no—
732D4—362no—
733D4—721no—
734D4—721no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—91no—
744C2×C4—122no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—241no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4C22×D3211yescharacteristic
753C8—21no—
754C8—61no—
755C8—61no—
756C8—181no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—122no—
761C2×C3—121no—
762C2×C3—241no—
763C2×C3—241no—
764C2×C3#549011yescharacteristic
765C2×C3#561211yescharacteristic
766C2×C3D3×#13511yescharacteristic
767C2×C3D3×#13511yescharacteristic
768C2×C3#576911yescharacteristic
769C2×C3#577411yescharacteristic
770D3—41no—
771D3—42no—
772D3—62no—
773D3—62no—
774D3—81no—
775D3—81no—
776D3—122no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—62no—
781C22—92no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—181no—
791C22—181no—
792C22—724no—
793C22D32×D411yescharacteristic
794C4—41no—
795C4—41no—
796C4—61no—
797C4—61no—
798C4—61no—
799C4—121no—
800C4—181no—
801C4—361no—
802C4—361no—
803C4D3×#23511yescharacteristic
804C4#6431311yescharacteristic
805C3—21no—
806C3#7884611yescharacteristic, complemented
807C3#8055911yescharacteristic, complemented
808C2—121no—
809C2—122no—
810C2—182no—
811C2—241no—
812C2—241no—
813C2#1059427811yescharacteristic
814C2#1059475511yescharacteristic
815C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595428C2semidirect
2. #10594583C2semidirect
3. #10592510C2semidirect
4. C3×#4819C2semidirect
5. C3×#4804C2semidirect
6. #10591614C2semidirect
7. #10591591C2semidirect
8. #10591586C2semidirect
9. #10590945C2semidirect
10. #10590831C2semidirect
11. #10590767C2semidirect
12. #10590720C2semidirect
13. #10590593C2semidirect
14. #10590502C2semidirect
15. #10590452C2semidirect
23. C2×C3×#215C22semidirect
25. C2×C3×D3×C8C22semidirect
26. C3×#893C22semidirect
27. C3×#892C22semidirect
33. #63908C22semidirect
40. #63869C22semidirect
44. C32×#103C22semidirect
45. #63662C22semidirect
47. #63645C22semidirect
48. #63634C22semidirect
49. C3×#835C22semidirect
51. C3×Dic3⋊C8C22semidirect
54. #63573C22semidirect
57. #63563C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
79. #4819D3semidirect
84. #4804D3semidirect
159. C2×#215C2×D3semidirect
178. C2×D3×C8C2×D3semidirect
180. #893C2×D3semidirect
181. #892C2×D3semidirect
202. C3×#103C2×D3semidirect
203. C3×#103C2×D3semidirect
210. #835C2×D3semidirect
228. Dic3⋊C8C2×D3semidirect
472. #103D32semidirect
712. C32#3297semidirect
806. C3#78846semidirect
807. C3#80559semidirect

Maximal subgroups

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

subgroupindex
#105954282
#105945832
#105925102
C3×#48192
C3×#48042
#105916142
#105915912
#105915862
#105909452
#105908312
#105907672
#105907202
#105905932
#105905022
#105904522
#805593
#788463