Finite Group Databasebeta

← #11872357

Subgroups — #11872357

Order 1152.

939 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#10595975C211yesmaximal, characteristic, complemented
2#10595041C211yesmaximal, characteristic, complemented
3C3×#4968C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic, complemented
5#10591182C211yesmaximal, characteristic, complemented
6#10591182C211yesmaximal, characteristic, complemented
7#10591062C211yesmaximal, characteristic, complemented
8#10590553C211yesmaximal, characteristic, complemented
9#10590551C211yesmaximal, characteristic, complemented
10#10590462C211yesmaximal, characteristic, complemented
11#10590461C211yesmaximal, characteristic, complemented
12#10590460C211yesmaximal, characteristic, complemented
13#10590459C211yesmaximal, characteristic, complemented
14#10590435C211yesmaximal, characteristic, complemented
15#10590434C211yesmaximal, characteristic, complemented
16#81312—31nomaximal
17#81272—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C4×#638—21no—
21C4×#638—21no—
22#64135C2211yescharacteristic
23#64102C2211yescharacteristic
24#64102C2211yescharacteristic
25#64101—21no—
26C4⋊C4×C3⋊D3—21no—
27#64096C2211yescharacteristic
28#64096C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#930C2211yescharacteristic
31#63970—21no—
32#63970—21no—
33#63914C2211yescharacteristic
34#63898C2211yescharacteristic
35#63898C2211yescharacteristic
36#63891—21no—
37#63891—21no—
38#63872C2211yescharacteristic
39C2×#3716C2211yescharacteristic
40C2×#3716C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#830C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63572C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5619—31no—
62#5619—31no—
63#5504—31no—
64#5504—31no—
65#5504—61no—
66C3×#481—31no—
67C3×#480—31no—
68#5037—31no—
69#5037—31no—
70#4968D311yescharacteristic, complemented
71#4967D311yescharacteristic, complemented
72#4891—31no—
73#4889—31no—
74#4877—31no—
75#4872—31no—
76#4871—31no—
77#4869—31no—
78#4857—31no—
79#4852—31no—
80#4786—31no—
81#4786—31no—
82#4785—31no—
83#4762—31no—
84#4762—31no—
85#4758—31no—
86#4757—31no—
87#4756—31no—
88#4734—31no—
89#4734—31no—
90#4720—31no—
91#4720—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—22no—
96#3828—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3757D411yescharacteristic
114#3757D411yescharacteristic
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)D411yescharacteristic
118C4⋊(C3⋊Dic3)D411yescharacteristic
119#3750—21no—
120#3750—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137#3716—22no—
138#3716—22no—
139#3714—22no—
140#3714—22no—
141#3119—91noSylow
142C2×#235—31no—
143C2×#235—31no—
144C2×#235—61no—
145C3×#121—31no—
146C3×#121—31no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D311yescharacteristic
150#940—31no—
151#940—31no—
152#939—61no—
153#939—61no—
154#938—61no—
155#938—61no—
156D4×Dic3—31no—
157D4×Dic3—31no—
158C2×#214—31no—
159C2×#214—31no—
160C2×#213—31no—
161C2×#213—31no—
162#930C2×D311yescharacteristic
163#930C2×D311yescharacteristic
164C4×#67—61no—
165C4×#67—61no—
166C4×#67—61no—
167C4×#67—61no—
168C4×#67—62no—
169C4×#67—62no—
170#926—31no—
171#926—31no—
172#926—61no—
173C2×D24—31no—
174C2×D24—31no—
175C2×#204—31no—
176C2×#204—31no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—31no—
181#893—31no—
182#893—31no—
183#893—61no—
184#893—61no—
185#892—61no—
186#892—61no—
187#892—62no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4—62no—
191#890—31no—
192#890—31no—
193#887—31no—
194#887—31no—
195#887—31no—
196#887—31no—
197#887—61no—
198#887—61no—
199#886—61no—
200#886—61no—
201#883—61no—
202#883—61no—
203C3×#107—31no—
204C3×#107—31no—
205C3×#106—31no—
206C3×#106—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—31no—
212C3×C22⋊C8—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217#816—31no—
218#816—31no—
219#815—31no—
220#815—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227#810—31no—
228#810—31no—
229#809—31no—
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic
235#808C2×D311yescharacteristic
236#808C2×D311yescharacteristic
237#807C2×D311yescharacteristic
238#807C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—81no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—24no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)#4112yes—
258C4×C3⋊D3—24no—
259C4×C3⋊D3—81no—
260C4×C3⋊D3—81no—
261#634—21no—
262#634#4112yes—
263C3×#67—81no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271#625—81no—
272#625—81no—
273D3×Dic3—81no—
274D3×Dic3—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#540—91no—
280#520—91no—
281#481—31no—
282#480—31no—
283#479—91no—
284#478—91no—
285#460—91no—
286#459—91no—
287#449—91no—
288#449—91no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—91no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C22×C3×C4—22no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—21no—
305C2×#67—21no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—62no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#235—62no—
316#235—62no—
317#235—62no—
318#235—62no—
319#235—64no—
320#235—64no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—62no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×Dic6—31no—
338C2×Dic6—31no—
339C2×Dic6—61no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357#217—31no—
358#217—31no—
359#217—31no—
360#217—31no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#214—62no—
366#214—62no—
367#213—62no—
368#213—62no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
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—62no—
378(C2×D3)⋊C4—62no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—62no—
396Dic3⋊C4—62no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—62no—
408C4×Dic3—62no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413D24—62no—
414D24—62no—
415#204—62no—
416#204—62no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—22no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—22no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447#127—91no—
448#125—91no—
449#123—181no—
450#123—181no—
451#121—31no—
452#121—31no—
453#121—181no—
454#121—181no—
455C4×Q8—91no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463#117—91no—
464#117—181no—
465C2×C4⋊C4—181no—
466C2×C4⋊C4D3211yescharacteristic
467#107—31no—
468#107—31no—
469#106—31no—
470#106—31no—
471C4⋊C8—91no—
472C4⋊C8—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481C22⋊C8—31no—
482C22⋊C8—31no—
483#97—91no—
484C4×C8—91no—
485C23×C3—21no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3D3×D411yescharacteristic
489C23×C3D3×D411yescharacteristic
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—62no—
493C22×D3—61no—
494C22×D3—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—241no—
500C3×D4—241no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—81no—
518C2×C3×C4—81no—
519C2×C3×C4—82no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—68no—
525#67—64no—
526#67—64no—
527#67—81no—
528#67—81no—
529#67—241no—
530#67—241no—
531#67—241no—
532#67—241no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—62no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552D12—21no—
553D12—21no—
554D12—21no—
555D12—21no—
556D12—32no—
557D12—32no—
558D12—62no—
559D12—62no—
560D12—61no—
561D12—61no—
562C4×D3—68no—
563C4×D3—64no—
564C4×D3—64no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—242no—
572C4×D3—242no—
573Dic6—32no—
574Dic6—32no—
575Dic6—62no—
576Dic6—62no—
577Dic6—61no—
578Dic6—61no—
579C3×C8—61no—
580C3×C8—61no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C2×C32—41no—
588C2×C32#52511yescharacteristic
589C2×C32#57611yescharacteristic
590C2×C32#57711yescharacteristic
591C3⋊D3—42no—
592C3×D3—81no—
593C3×D3—81no—
594#41—182no—
595#41—182no—
596C2×Q8—91no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—91no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4—181no—
605C22×C4—21no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4C2×D3211yescharacteristic
612SD16—182no—
613SD16—182no—
614D8—182no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—31no—
620C4⋊C4—21no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4C2×D3211yescharacteristic
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—91no—
640C42—91no—
641C42—181no—
642C42—181no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—64no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C3×C4—22no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—42no—
682C3×C4—42no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4D3×#4111yescharacteristic
690C3×C4D3×#4111yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4D3×#4111yescharacteristic
693Dic3—41no—
694Dic3—41no—
695Dic3—64no—
696Dic3—62no—
697Dic3—62no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—61no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710C32#311911yescharacteristic, complemented, Sylow
711C23—61no—
712C23—61no—
713C23—181no—
714C23#381111yescharacteristic
715Q8—92no—
716Q8—181no—
717D4—61no—
718D4—61no—
719D4—61no—
720D4—61no—
721D4—92no—
722D4—184no—
723D4—181no—
724D4—241no—
725D4—241no—
726D4—721no—
727D4—721no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—81no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—91no—
739C2×C4—184no—
740C2×C4—181no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4—721no—
745C2×C4#381111yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—61no—
748C8—61no—
749C8—61no—
750C8—61no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—241no—
758C2×C3—241no—
759C2×C3#565611yescharacteristic
760C2×C3#565611yescharacteristic
761C2×C3#575711yescharacteristic
762C2×C3#576211yescharacteristic
763C2×C3#577411yescharacteristic
764C2×C3#577811yescharacteristic
765D3—81no—
766D3—81no—
767D3—124no—
768D3—122no—
769D3—122no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—182no—
780C22—361no—
781C22—361no—
782C22C2×#381111yescharacteristic
783C4—21no—
784C4—41no—
785C4—41no—
786C4—121no—
787C4—121no—
788C4—181no—
789C4—181no—
790C4—182no—
791C4—181no—
792C4—181no—
793C4#6430611yescharacteristic
794C4#6430611yescharacteristic
795C3—21no—
796C3#8127211yescharacteristic, complemented
797C3#8131211yescharacteristic, complemented
798C2—41no—
799C2—241no—
800C2—241no—
801C2—362no—
802C2#1059492011yescharacteristic
803C2#1059510211yescharacteristic
804C2#1059532411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595975C2semidirect
2. #10595041C2semidirect
3. C3×#4968C2semidirect
4. C3×#4967C2semidirect
5. #10591182C2semidirect
6. #10591182C2semidirect
7. #10591062C2semidirect
8. #10590553C2semidirect
9. #10590551C2semidirect
10. #10590462C2semidirect
11. #10590461C2semidirect
12. #10590460C2semidirect
13. #10590459C2semidirect
14. #10590435C2semidirect
15. #10590434C2semidirect
70. #4968D3semidirect
71. #4967D3semidirect
710. C32#3119semidirect
796. C3#81272semidirect
797. C3#81312semidirect

Maximal subgroups

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

subgroupindex
#105959752
#105950412
C3×#49682
C3×#49672
#105911822
#105910622
#105905532
#105905512
#105904622
#105904612
#105904602
#105904592
#105904352
#105904342
#813123
#812723