Finite Group Databasebeta

← #11870459

Subgroups — #11870459

Order 1152.

1051 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595133C211yesmaximal, characteristic, complemented
2D3×#893C211yesmaximal, characteristic, complemented
3#10592455C211yesmaximal, characteristic, complemented
4C3×#4786C211yesmaximal, characteristic, complemented
5C3×#4774C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591429C211yesmaximal, characteristic, complemented
9#10590944C211yesmaximal, characteristic, complemented
10#10590777C211yesmaximal, characteristic, complemented
11#10590764C211yesmaximal, characteristic, complemented
12#10590656C211yesmaximal, characteristic, complemented
13#10590555C211yesmaximal, characteristic, complemented
14#10590498C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#81268—31nomaximal
17#80312—31nomaximal
18C2×#3805—21no—
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21D4×C3⋊Dic3C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23#64102C2211yescharacteristic
24C3×#940C2211yescharacteristic, complemented
25C3×#938C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28C3×#893C2211yescharacteristic
29C3×D3×C4⋊C4C2211yescharacteristic
30#67⋊Dic3—21no—
31#63970—21no—
32#63959—21no—
33D3×(C2×D3)⋊C4—21no—
34#63918C2211yescharacteristic, complemented
35#63908C2211yescharacteristic
36#63904—21no—
37#63898C2211yescharacteristic
38#63898C2211yescharacteristic, complemented
39#63894C2211yescharacteristic
40#63881—21no—
41C4×D3×Dic3C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#102C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5716—31no—
62#5596—31no—
63C4×D3×D4—31no—
64C2×#893—31no—
65C3×#480—31no—
66C3×#459—31no—
67#5156—31no—
68#5156—31no—
69Dic3×D8—31no—
70Dic3×D8—31no—
71#5072—31no—
72#5036—31no—
73#5007—31no—
74#4967—31no—
75#4890—31no—
76#4890—31no—
77#4872—31no—
78#4872—31no—
79#4846—31no—
80#4833—31no—
81#4786—31no—
82#4786D311yescharacteristic, complemented
83#4774—31no—
84#4774D311yescharacteristic, complemented
85#4756—31no—
86#4756—31no—
87#4756—31no—
88#4756—31no—
89#4756—61no—
90#4732—31no—
91#4718—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×#627—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#624—21no—
109#3805—44no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3D411yescharacteristic
113C2×D3×Dic3D411yescharacteristic
114D3×D12—22no—
115D3×D12—22no—
116C4×D32—44no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3757—21no—
120#3753—22no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D24—22no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32D411yescharacteristic
141Dic32D411yescharacteristic
142#3714—22no—
143#3100—91noSylow
144C2×#237—61no—
145C2×#237—61no—
146C2×D3×D4—31no—
147C22×D12—31no—
148C22×C4×D3—61no—
149C22×C4×D3—61no—
150C2×C3×D8—31no—
151C2×C3×D8—31no—
152C3×#127—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155C2×C3×C4⋊C4—31no—
156#940C2×D311yescharacteristic, complemented
157#939—61no—
158#938—31no—
159#938—61no—
160#938C2×D311yescharacteristic
161#936—61no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172C2×#213C2×D311yescharacteristic
173#930—31no—
174C4×#67—61no—
175C2×(C2×D3)⋊C4—61no—
176C2×C4×Dic3—31no—
177C2×D24—31no—
178C2×D24C2×D311yescharacteristic
179#893—31no—
180#893—31no—
181#893—31no—
182#893—31no—
183#893—31no—
184#893—61no—
185#893—61no—
186#893—61no—
187#893C2×D311yescharacteristic
188D3×C4⋊C4C2×D311yescharacteristic
189#888—31no—
190#885—61no—
191#67⋊C4—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194C4×D12—31no—
195C42×D3—31no—
196#869—31no—
197C3×#107—31no—
198C3×#107—31no—
199C3×C4⋊C8—31no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102C2×D311yescharacteristic, complemented
204C3×#102C2×D311yescharacteristic, complemented
205C3×C22⋊C8—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832C2×D311yescharacteristic, complemented
210#830—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#818C2×D311yescharacteristic, complemented
220Dic3⋊C8—31no—
221Dic3⋊C8C2×D311yescharacteristic, complemented
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—31no—
226C8×Dic3—61no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237C23×C32—21no—
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—24no—
243C2×D32—42no—
244C2×D32—42no—
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yescomplemented
255C4×C3⋊D3—42no—
256C3×#67—42no—
257C3×#67—42no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12#4112yescomplemented
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272#627—42no—
273#626—24no—
274#625—42no—
275#624—42no—
276D3×Dic3—41no—
277D3×Dic3—42no—
278D3×Dic3—42no—
279D3×Dic3D814yescomplemented
280C32×C8—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—91no—
285C2×C4×D4—91no—
286#480—31no—
287#480—91no—
288#474—91no—
289#474—91no—
290#459—31no—
291#459—91no—
292#447—91no—
293#447—91no—
294C4×D8—91no—
295C4×D8—91no—
296C4×D8—91no—
297C4×D8—91no—
298#431—91no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325#237—124no—
326#237—124no—
327D3×D4—62no—
328D3×D4—62no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—61no—
332C2×D12—62no—
333C2×D12—61no—
334C2×D12—62no—
335C2×D12C22×D311yescharacteristic
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—121no—
348C2×C4×D3—124no—
349C2×C4×D3—124no—
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6—61no—
352C2×Dic6—61no—
353C3×D8—62no—
354C3×D8—62no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—31no—
369#217—21no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—121no—
376#213—22no—
377#213—62no—
378#213—62no—
379#213—62no—
380#213—64no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—121no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—61no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—22no—
412D24—62no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3C2×D812yes—
429D32—48no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4C2×#4111yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—41no—
435C3⋊Dic3C2×D812yes—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3C2×D812yes—
441C2×#41—181no—
442C22×D4—91no—
443C23×C4—181no—
444C2×D8—31no—
445C2×D8—31no—
446C2×D8—91no—
447C2×D8—91no—
448C4⋊Q8—91no—
449#127—31no—
450#124—181no—
451#121—31no—
452#121—91no—
453#121—181no—
454C4×D4—31no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462C4×D4—181no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—181no—
465C2×C42—91no—
466#107—31no—
467#107—31no—
468#107—91no—
469#107—91no—
470C4⋊C8—31no—
471C4⋊C8—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102D3211yescharacteristic, complemented
480C22⋊C8—31no—
481C22⋊C8—91no—
482C4×C8—91no—
483C4×C8—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—61no—
489C23×C3—61no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—64no—
493C22×D3—64no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—121no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3D3×D411yescharacteristic
502C3×D4—22no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—122no—
513C3×D4—122no—
514C3×D4—122no—
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—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
527C2×C3×C4—122no—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—42no—
531#67—42no—
532#67—42no—
533#67—64no—
534#67—122no—
535#67—122no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—34no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—122no—
550C2×Dic3—122no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C2×Dic3—242no—
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557D12—21no—
558D12—21no—
559D12—21no—
560D12—32no—
561D12—32no—
562D12—62no—
563D12—64no—
564D12—61no—
565D12—61no—
566D12—121no—
567D12#23712yescomplemented
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—34no—
571C4×D3—42no—
572C4×D3—42no—
573C4×D3—122no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—121no—
579C4×D3—122no—
580C4×D3—242no—
581Dic6—122no—
582Dic6—122no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—41no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—62no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C2×C32—81no—
594C2×C32#52511yescharacteristic
595C2×C32C22×D811yescharacteristic
596C2×C32#57511yescharacteristic
597C3⋊D3—42no—
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—81no—
601C24—181no—
602#41—364no—
603C2×Q8—181no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—91no—
610C2×D4—181no—
611C2×D4—182no—
612C2×D4—182no—
613C2×D4—181no—
614C2×D4C2×D3211yescharacteristic
615C22×C4—31no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—91no—
619C22×C4—91no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4—364no—
626D8—62no—
627D8—62no—
628D8—182no—
629D8—182no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8C2×D3211yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4C2×D3211yescharacteristic
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—91no—
650C42—91no—
651C42—91no—
652C22×C3—21no—
653C22×C3—32no—
654C22×C3—42no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—62no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C2×D3×D411yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—22no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—62no—
682C2×D3—62no—
683C2×D3—122no—
684C2×D3—128no—
685C2×D3—128no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3D3×D812yes—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—32no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4C2×#23711yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4D3×#4111yescharacteristic
706C3×C4D3×#4111yescharacteristic
707Dic3—21no—
708Dic3—21no—
709Dic3—32no—
710Dic3—32no—
711Dic3—41no—
712Dic3—41no—
713Dic3—62no—
714Dic3—61no—
715Dic3—61no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719Dic3—241no—
720Dic3D3×D812yes—
721C32#310011yescharacteristic, complemented, Sylow
722C23—21no—
723C23—31no—
724C23—61no—
725C23—61no—
726C23—184no—
727C23—181no—
728C23—362no—
729C23—362no—
730Q8—362no—
731D4—21no—
732D4—21no—
733D4—32no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—92no—
738D4—122no—
739D4—122no—
740D4—122no—
741D4—184no—
742D4—181no—
743D4—362no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—94no—
753C2×C4—91no—
754C2×C4—91no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—181no—
758C2×C4—362no—
759C2×C4—362no—
760C2×C4—361no—
761C2×C4—362no—
762C2×C4—362no—
763C2×C4—362no—
764C2×C4C22×D3211yescharacteristic
765C8—21no—
766C8—61no—
767C8—61no—
768C8—181no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—62no—
773C2×C3—82no—
774C2×C3—81no—
775C2×C3—81no—
776C2×C3—122no—
777C2×C3—241no—
778C2×C3#560611yescharacteristic
779C2×C3#565611yescharacteristic
780C2×C3C2×D3×D811yescharacteristic
781C2×C3C2×D3×D811yescharacteristic
782C2×C3#577311yescharacteristic
783C2×C3#577711yescharacteristic
784D3—22no—
785D3—42no—
786D3—81no—
787D3—122no—
788D3—122no—
789D3—242no—
790C22—32no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—61no—
795C22—61no—
796C22—62no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—182no—
803C22—368no—
804C22—361no—
805C22—361no—
806C22D32×D411yescharacteristic
807C4—32no—
808C4—41no—
809C4—61no—
810C4—61no—
811C4—92no—
812C4—121no—
813C4—121no—
814C4—181no—
815C4—361no—
816C4#6430611yescharacteristic
817C4D3×#23711yescharacteristic
818C3—21no—
819C3#8031211yescharacteristic, complemented
820C3#8126811yescharacteristic, complemented
821C2—62no—
822C2—81no—
823C2—122no—
824C2—241no—
825C2—362no—
826C2#1059426711yescharacteristic
827C2D32×D811yescharacteristic
828C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3100
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. #10595133C2semidirect
2. D3×#893C2semidirect
3. #10592455C2semidirect
4. C3×#4786C2semidirect
5. C3×#4774C2semidirect
6. #10591515C2semidirect
7. #10591435C2semidirect
8. #10591429C2semidirect
9. #10590944C2semidirect
10. #10590777C2semidirect
11. #10590764C2semidirect
12. #10590656C2semidirect
13. #10590555C2semidirect
14. #10590498C2semidirect
15. #10590459C2semidirect
21. D4×C3⋊Dic3C22semidirect
24. C3×#940C22semidirect
34. #63918C22semidirect
38. #63898C22semidirect
43. C32×#102C22semidirect
45. C8×C3⋊Dic3C22semidirect
46. #63634C22semidirect
47. C3×#832C22semidirect
49. C3×#818C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#809C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
58. #63562C22semidirect
60. #63553C22semidirect
82. #4786D3semidirect
84. #4774D3semidirect
156. #940C2×D3semidirect
203. C3×#102C2×D3semidirect
204. C3×#102C2×D3semidirect
209. #832C2×D3semidirect
219. #818C2×D3semidirect
221. Dic3⋊C8C2×D3semidirect
230. #809C2×D3semidirect
235. #807C2×D3semidirect
254. C4⋊(C3⋊D3)#41semidirect
267. C3×D12#41semidirect
279. D3×Dic3D8semidirect
479. #102D32semidirect
567. D12#237semidirect
721. C32#3100semidirect
819. C3#80312semidirect
820. C3#81268semidirect

Maximal subgroups

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

subgroupindex
#105951332
D3×#8932
#105924552
C3×#47862
C3×#47742
#105915152
#105914352
#105914292
#105909442
#105907772
#105907642
#105906562
#105905552
#105904982
#105904592
#812683
#803123