Finite Group Databasebeta

← #11872279

Subgroups — #11872279

Order 1152.

912 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596090C211yesmaximal, characteristic, complemented
2#10594986C211yesmaximal, characteristic, complemented
3C3×#5037C211yesmaximal, characteristic, complemented
4C3×#5034C211yesmaximal, characteristic, complemented
5#10591446C211yesmaximal, characteristic, complemented
6#10591444C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591433C211yesmaximal, characteristic, complemented
9#10591163C211yesmaximal, characteristic, complemented
10#10591133C211yesmaximal, characteristic, complemented
11#10591062C211yesmaximal, characteristic, complemented
12#10590495C211yesmaximal, characteristic, complemented
13#10590483C211yesmaximal, characteristic, complemented
14#10590474C211yesmaximal, characteristic, complemented
15#10590462C211yesmaximal, characteristic, complemented
16#81312—31nomaximal
17#80072—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C32×#121C2211yescharacteristic
20#64149C2211yescharacteristic
21#64148—21no—
22#64147—21no—
23D4×C3⋊Dic3C2211yescharacteristic
24#64139C2211yescharacteristic
25#64135C2211yescharacteristic
26#64102C2211yescharacteristic
27#64099C2211yescharacteristic
28#64095—21no—
29#64092—21no—
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33Dic3×#67—21no—
34Dic3×#67—21no—
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic
37D3×C4⋊Dic3—21no—
38#63843C2211yescharacteristic
39#63843C2211yescharacteristic
40#63841—21no—
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#832C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#808C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63572C2211yescharacteristic
54#63572C2211yescharacteristic
55#63566C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5827—31no—
62#5619—31no—
63#5619—31no—
64#5619—61no—
65#5504—31no—
66C3×#481—31no—
67C3×#449—31no—
68#5238—31no—
69#5164—31no—
70#5163—31no—
71#5150—31no—
72Dic3×D8—31no—
73#5037D311yescharacteristic, complemented
74#5034D311yescharacteristic, complemented
75#4967—31no—
76#4871—31no—
77#4869—31no—
78#4857—31no—
79#4852—31no—
80#4796—31no—
81#4788—31no—
82#4786—31no—
83#4785—31no—
84#4766—31no—
85#4762—31no—
86#4757—31no—
87#4756—31no—
88#4736—31no—
89#4734—31no—
90#4720—31no—
91#4720—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#235—22no—
104C3×#235—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112#3757—21no—
113#3757D411yescharacteristic
114#3757D411yescharacteristic
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)D411yescharacteristic
119C4⋊(C3⋊Dic3)D411yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C3×#214—22no—
125C3×#213—22no—
126C3×C4⋊Dic3—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—
137Dic32—21no—
138Dic32—21no—
139#3717—22no—
140#3714—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C3×#121—21no—
147C3×#121C2×D311yescharacteristic
148C3×#121C2×D311yescharacteristic
149C2×C3×C4⋊C4—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152C2×#215—31no—
153#940—31no—
154#940—31no—
155#940—61no—
156#939—61no—
157#939—61no—
158#939—62no—
159#938—61no—
160#938—61no—
161#938—62no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3—61no—
169C2×#214C2×D311yescharacteristic
170C2×#213—31no—
171C2×#213C2×D311yescharacteristic
172#930—31no—
173#930—31no—
174#930—61no—
175C4×#67—61no—
176C4×#67—61no—
177#926—31no—
178#926—31no—
179#926—61no—
180#926—61no—
181C2×C4⋊Dic3—61no—
182C2×C4⋊Dic3C2×D311yescharacteristic
183C2×D24—31no—
184C2×#204—31no—
185#893—31no—
186#893—31no—
187#893—31no—
188#893—31no—
189#893—61no—
190#892—61no—
191D3×C4⋊C4—61no—
192#890—31no—
193#890—31no—
194#890—61no—
195#887—31no—
196#887—31no—
197#886—61no—
198#886—61no—
199#886—62no—
200#883—61no—
201#883—61no—
202#883—62no—
203C3×#106—31no—
204C3×#106—31no—
205C3×#103—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211#835—31no—
212#832—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#830C2×D311yescharacteristic
216#830C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#818—31no—
221#818—31no—
222#816—31no—
223#815—31no—
224#815—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810C2×D311yescharacteristic
232#809—31no—
233#809—31no—
234#809C2×D311yescharacteristic
235#808C2×D311yescharacteristic
236#808C2×D311yescharacteristic
237#807—31no—
238#807—31no—
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3×D3—21no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251#638—81no—
252#638—81no—
253#638—81no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—81no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C4×C3⋊D3—81no—
263C3×#67—24no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—81no—
268C3×D12—21no—
269C3×D12#4112yes—
270C3×C4×D3—24no—
271C3×Dic6—21no—
272C3×Dic6#4112yes—
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—91no—
283#479—91no—
284#478—91no—
285#460—91no—
286#459—91no—
287#449—31no—
288#449—91no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—91no—
294C3×#41—62no—
295C3×#41—62no—
296C2×C3×Q8—31no—
297C2×C3×D4—22no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—21no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—62no—
316C2×#67—62no—
317C2×#67—62no—
318C2×#67—61no—
319C2×#67—61no—
320C22×Dic3—21no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—62no—
326#235—22no—
327#235—22no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—62no—
338C2×Dic6C22×D311yescharacteristic
339C3×SD16—62no—
340C3×D8—62no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—22no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354#217—31no—
355#217—31no—
356#217—31no—
357#217—31no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—62no—
365#215—62no—
366#214—22no—
367#213—22no—
368#213—62no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—62no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—62no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413D24—62no—
414#204—62no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32C22×D411yescharacteristic
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4C2×#4111yescharacteristic
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—41no—
437C3×Dic3—22no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—31no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×D8—31no—
444C2×D8—91no—
445#127—91no—
446#125—91no—
447#123—181no—
448#123—181no—
449#121—91no—
450#121—181no—
451#121—181no—
452#121D3211yescharacteristic
453C4×Q8—91no—
454C4×Q8—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C4×D4—181no—
461#117—91no—
462#117—181no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4—181no—
465#107—91no—
466#107—91no—
467#106—31no—
468#106—31no—
469C4⋊C8—91no—
470C4⋊C8—91no—
471#103—31no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—31no—
481#97—91no—
482C4×C8—91no—
483C23×C3—22no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—61no—
488C23×C3D3×D411yescharacteristic
489C23×C3D3×D411yescharacteristic
490C22×D3—21no—
491C22×D3—62no—
492C22×D3—61no—
493C22×D3—61no—
494C3×Q8—32no—
495C3×Q8—61no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—32no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—64no—
504C3×D4—61no—
505C3×D4—81no—
506C3×D4—81no—
507C3×D4—82no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—64no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—241no—
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—24no—
529#67—241no—
530#67—241no—
531#67—241no—
532#67—241no—
533#67—241no—
534#67—241no—
535#67—242no—
536#67—242no—
537#67—242no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—62no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—81no—
557C2×Dic3—241no—
558C2×Dic3—241no—
559C2×Dic3—241no—
560C2×Dic3—241no—
561C2×Dic3—242no—
562D12—21no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—121no—
568D12—121no—
569D12#23712yes—
570C4×D3—24no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C4×D3—242no—
576Dic6—21no—
577Dic6#23712yes—
578C3×C8—61no—
579C3×C8—61no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C2×C32—41no—
587C2×C32—81no—
588C2×C32#52511yescharacteristic
589C2×C32#57611yescharacteristic
590C2×C32#57711yescharacteristic
591C3⋊D3—81no—
592C3×D3—42no—
593#41—62no—
594#41—62no—
595C2×Q8—31no—
596C2×D4—21no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4C2×D3211yescharacteristic
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4C2×D3211yescharacteristic
611SD16—62no—
612SD16—182no—
613D8—62no—
614D8—182no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4C2×D3211yescharacteristic
630C22⋊C4—21no—
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—91no—
639C42—91no—
640C42—181no—
641C42—181no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—62no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C2×D3×D411yescharacteristic
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—122no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—42no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—62no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×#23711yescharacteristic
690C3×C4C2×#23711yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4D3×#4111yescharacteristic
693Dic3—22no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—122no—
709Dic3—121no—
710Dic3—121no—
711C32#311911yescharacteristic, complemented, Sylow
712C23—21no—
713C23—61no—
714C23—181no—
715C23#381111yescharacteristic
716Q8—32no—
717Q8—61no—
718D4—21no—
719D4—21no—
720D4—32no—
721D4—64no—
722D4—61no—
723D4—81no—
724D4—181no—
725D4—181no—
726D4—721no—
727D4—721no—
728D4—721no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—64no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—91no—
739C2×C4—91no—
740C2×C4—181no—
741C2×C4—241no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4—721no—
745C2×C4—721no—
746C2×C4#381111yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—61no—
749C8—61no—
750C8—61no—
751C8—61no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—81no—
758C2×C3—82no—
759C2×C3—81no—
760C2×C3—81no—
761C2×C3—122no—
762C2×C3#558611yescharacteristic
763C2×C3#565611yescharacteristic
764C2×C3#576211yescharacteristic
765C2×C3#576911yescharacteristic
766C2×C3#577411yescharacteristic
767C2×C3#577511yescharacteristic
768D3—42no—
769D3—242no—
770D3—241no—
771D3—241no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—62no—
779C22—121no—
780C22—121no—
781C22—361no—
782C22—361no—
783C22—361no—
784C22C2×#381111yescharacteristic
785C4—21no—
786C4—41no—
787C4—62no—
788C4—121no—
789C4—121no—
790C4—181no—
791C4—181no—
792C4—181no—
793C4—181no—
794C4—361no—
795C4D3×#23711yescharacteristic
796C4D3×#23711yescharacteristic
797C3—21no—
798C3#8007211yescharacteristic, complemented
799C3#8131211yescharacteristic, complemented
800C2—41no—
801C2—81no—
802C2—122no—
803C2—721no—
804C2#1059511511yescharacteristic
805C2#1059516011yescharacteristic
806C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596090C2semidirect
2. #10594986C2semidirect
3. C3×#5037C2semidirect
4. C3×#5034C2semidirect
5. #10591446C2semidirect
6. #10591444C2semidirect
7. #10591435C2semidirect
8. #10591433C2semidirect
9. #10591163C2semidirect
10. #10591133C2semidirect
11. #10591062C2semidirect
12. #10590495C2semidirect
13. #10590483C2semidirect
14. #10590474C2semidirect
15. #10590462C2semidirect
73. #5037D3semidirect
74. #5034D3semidirect
711. C32#3119semidirect
798. C3#80072semidirect
799. C3#81312semidirect

Maximal subgroups

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

subgroupindex
#105960902
#105949862
C3×#50372
C3×#50342
#105914462
#105914442
#105914352
#105914332
#105911632
#105911332
#105910622
#105904952
#105904832
#105904742
#105904622
#813123
#800723