Finite Group Databasebeta

← #11872190

Subgroups — #11872190

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593994C211yesmaximal, characteristic, complemented
2#10593877C211yesmaximal, characteristic, complemented
3#10592543C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4840C211yesmaximal, characteristic, complemented
6#10590947C211yesmaximal, characteristic
7#10590946C211yesmaximal, characteristic, complemented
8#10590773C211yesmaximal, characteristic, complemented
9#10590763C211yesmaximal, characteristic, complemented
10#10590746C211yesmaximal, characteristic, complemented
11#10590744C211yesmaximal, characteristic, complemented
12#10590708C211yesmaximal, characteristic, complemented
13#10590705C211yesmaximal, characteristic, complemented
14#10590366C211yesmaximal, characteristic, complemented
15#10590300C211yesmaximal, characteristic, complemented
16#80952—31nomaximal
17#79383—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3745C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21#64084C2211yescharacteristic, complemented
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#872C2211yescharacteristic
25C3×#869C2211yescharacteristic, complemented
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63909C2211yescharacteristic
29#63907—21no—
30#63904—21no—
31#63894C2211yescharacteristic
32#63894C2211yescharacteristic, complemented
33Dic3×D12C2211yescharacteristic
34#63888—21no—
35#63881—21no—
36#63857C2211yescharacteristic
37#63854—21no—
38#63848—21no—
39#63844C2211yescharacteristic, complemented
40#63841C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63643C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic, complemented
61#5733—31no—
62#5545—31no—
63#5534—31no—
64#5521—31no—
65C3×#474—31no—
66C3×#433—31no—
67#5084—31no—
68#5016—31no—
69#4889—31no—
70#4888—31no—
71#4885—31no—
72#4872—31no—
73#4846D311yescharacteristic, complemented
74#4844—31no—
75#4844—31no—
76#4844—31no—
77#4844—61no—
78#4842—31no—
79#4840D311yescharacteristic, complemented
80#4785—31no—
81#4776—31no—
82#4773—31no—
83#4758—31no—
84#4737—31no—
85#4732—31no—
86#4731—31no—
87#4723—31no—
88#4711—31no—
89#4710—31no—
90C4×D24—31no—
91C4×#204—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×#626—21no—
102C2×#626—21no—
103C2×#624—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C42C2311yescharacteristic
111#3752—21no—
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3745—22no—
116#3744—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4D411yescharacteristic
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3716—22no—
140#3714—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C3×C4⋊Q8—31no—
145C3×C4×D4—31no—
146C3×#117—31no—
147#947—61no—
148#946—61no—
149D4×Dic3—31no—
150C2×#214—31no—
151C2×#213—31no—
152#930—31no—
153C4×#67—61no—
154C2×(C2×D3)⋊C4—61no—
155#926—31no—
156#924—31no—
157C2×D24—31no—
158C2×D24—31no—
159C2×D24—31no—
160C2×D24—61no—
161C2×#204—31no—
162C2×#204—31no—
163C2×#204—31no—
164C2×#204—61no—
165#898—61no—
166#898—61no—
167#897—31no—
168#896—61no—
169#895—31no—
170#894—61no—
171#893—31no—
172#893—31no—
173#893—61no—
174#893—61no—
175#892—31no—
176#887—31no—
177#885—61no—
178#883—61no—
179#67⋊C4—61no—
180D3×C22⋊C4—61no—
181D3×C22⋊C4—61no—
182D3×C22⋊C4—61no—
183#875—31no—
184#875—31no—
185#875—61no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12C2×D311yescharacteristic
193#872C2×D311yescharacteristic
194#869C2×D311yescharacteristic, complemented
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#107—31no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8—31no—
200C3×C4⋊C8C2×D311yescharacteristic, complemented
201C3×C4⋊C8C2×D311yescharacteristic, complemented
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207C3×C4×C8—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818C2×D311yescharacteristic, complemented
219#818C2×D311yescharacteristic, complemented
220#817—31no—
221#817—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#815C2×D311yescharacteristic, complemented
227C8×Dic3C2×D311yescharacteristic, complemented
228#810—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#808—31no—
233#808—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—81no—
252#634—21no—
253#634—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×Dic6—81no—
266#626—24no—
267#626—81no—
268#624—81no—
269#624—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—31no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—31no—
290C23×D3—61no—
291C23×D3—61no—
292C2×C3×Q8—61no—
293C2×C3×D4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C2×#67—61no—
297C2×#67—61no—
298C22×Dic3—61no—
299D3×D4—62no—
300D3×D4—62no—
301C2×D12—31no—
302C2×D12—31no—
303C2×D12—31no—
304C2×D12—31no—
305C2×D12—61no—
306C2×D12—61no—
307C2×D12—62no—
308C2×D12—61no—
309C2×D12—62no—
310C2×D12—61no—
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—121no—
321C2×C4×D3C22×D311yescharacteristic
322C2×Dic6—21no—
323C2×Dic6—31no—
324C2×Dic6—31no—
325C2×Dic6—61no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—31no—
342C3×C22⋊C4—61no—
343C3×C42—21no—
344C3×C42—31no—
345C3×C42C22×D311yescharacteristic
346C3×C42C22×D311yescharacteristic
347#217—61no—
348#217—61no—
349#217—61no—
350#214—62no—
351#213—62no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—121no—
369(C2×D3)⋊C4—121no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4D1211yescharacteristic
372(C2×D3)⋊C4D1211yescharacteristic
373C4⋊Dic3—21no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4D1211yescharacteristic
385Dic3⋊C4D1211yescharacteristic
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393D24—62no—
394D24—62no—
395D24—62no—
396D24—122no—
397#204—62no—
398#204—62no—
399#204—62no—
400#204—122no—
401C22×C32C22×D411yescharacteristic
402C2×C3⋊D3—22no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—22no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414D32—84no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—91no—
428C2×SD16—91no—
429C2×SD16—91no—
430C2×D8—91no—
431C2×D8—91no—
432C4⋊Q8—31no—
433#126—181no—
434#124—91no—
435#124—181no—
436#123—181no—
437C22⋊Q8—91no—
438C22⋊Q8—181no—
439#121—91no—
440C4×Q8—91no—
441C4×D4—31no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—181no—
447C4×D4—181no—
448#117—31no—
449#117—91no—
450C2×C22⋊C4—181no—
451C2×C22⋊C4—181no—
452#107—31no—
453#107—31no—
454#106—91no—
455#106—91no—
456C4⋊C8—31no—
457C4⋊C8D3211yescharacteristic, complemented
458#103—91no—
459#103—91no—
460#102—31no—
461#102—31no—
462#102—91no—
463#102—91no—
464#102—91no—
465#102—91no—
466C22⋊C8—31no—
467C22⋊C8—31no—
468#97—31no—
469C4×C8—31no—
470C23×C3—31no—
471C23×C3—61no—
472C22×D3—21no—
473C22×D3—64no—
474C22×D3—64no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—121no—
480C22×D3—121no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—241no—
484C22×D3—241no—
485C22×D3C2×D1211yescharacteristic
486C3×Q8—241no—
487C3×D4—32no—
488C3×D4—61no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—241no—
501C2×C3×C4C2×D1211yescharacteristic
502C2×C3×C4C2×D1211yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—64no—
508#67—241no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—121no—
517C2×Dic3—121no—
518C2×Dic3—241no—
519C2×Dic3C2×D1211yescharacteristic
520C2×Dic3C2×D1211yescharacteristic
521C2×Dic3C2×D1211yescharacteristic
522D12—21no—
523D12—32no—
524D12—32no—
525D12—62no—
526D12—64no—
527D12—61no—
528D12—61no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—121no—
534D12—121no—
535D12—121no—
536D12—241no—
537D12#23912yes—
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—81no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—242no—
549Dic6—61no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—81no—
554Dic6—121no—
555Dic6—121no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—41no—
561C3×C8—41no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C2×C32#52511yescharacteristic
567C2×C32#57611yescharacteristic
568C2×C32#57711yescharacteristic
569C3⋊D3—42no—
570C3⋊D3—81no—
571C3×D3—41no—
572C3×D3—42no—
573C24—181no—
574C2×Q8—61no—
575C2×Q8—91no—
576C2×D4—31no—
577C2×D4—91no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4—182no—
581C2×D4—182no—
582C2×D4—181no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589SD16—182no—
590SD16—182no—
591D8—182no—
592D8—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8C2×D3211yescharacteristic
596C2×C8C2×D3211yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—31no—
619C42—181no—
620C42—181no—
621C42C2×D3211yescharacteristic
622C22×C3—21no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—62no—
626C22×C3—61no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C22×D1211yescharacteristic
630C22×C3C2×D3×D411yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—122no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3—241no—
654C2×D3—241no—
655C2×D3—244no—
656C2×D3—244no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C2×#23911yescharacteristic
672C3×C4D3×#4111yescharacteristic
673C3×C4D3×#4111yescharacteristic
674C3×C4D3×#4111yescharacteristic
675Dic3—21no—
676Dic3—21no—
677Dic3—21no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—241no—
686Dic3—241no—
687C32#311811yescharacteristic, complemented, Sylow
688C23—31no—
689C23—61no—
690C23—184no—
691C23—181no—
692C23—181no—
693C23—721no—
694C23—721no—
695Q8—181no—
696Q8—181no—
697Q8—241no—
698D4—32no—
699D4—61no—
700D4—92no—
701D4—184no—
702D4—181no—
703D4—181no—
704D4—181no—
705D4—721no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4D3×D1211yescharacteristic
722C2×C4D3×D1211yescharacteristic
723C2×C4C22×D3211yescharacteristic
724C8—21no—
725C8—21no—
726C8—61no—
727C8—61no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—122no—
732C2×C3—121no—
733C2×C3#552411yescharacteristic
734C2×C3#562711yescharacteristic
735C2×C3#575111yescharacteristic
736C2×C3#575211yescharacteristic
737C2×C3#575711yescharacteristic
738C2×C3#577811yescharacteristic
739D3—41no—
740D3—42no—
741D3—122no—
742D3—122no—
743D3—242no—
744D3—241no—
745D3—241no—
746D3—481no—
747C22—61no—
748C22—62no—
749C22—61no—
750C22—61no—
751C22—121no—
752C22—121no—
753C22—182no—
754C22—361no—
755C22—361no—
756C22—361no—
757C22—361no—
758C22—361no—
759C22—724no—
760C22C2×D3×D1211yescharacteristic
761C4—21no—
762C4—21no—
763C4—61no—
764C4—61no—
765C4—61no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—361no—
770C4—361no—
771C4#6431211yescharacteristic
772C4D3×#23911yescharacteristic
773C3—21no—
774C3#7938311yescharacteristic, complemented
775C3#8095211yescharacteristic, complemented
776C2—121no—
777C2—122no—
778C2—362no—
779C2—721no—
780C2#1059462711yescharacteristic
781C2#1059467811yescharacteristic
782C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10590947C2
hypercenterC4⋊C8D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593994C2semidirect
2. #10593877C2semidirect
3. #10592543C2semidirect
4. C3×#4846C2semidirect
5. C3×#4840C2semidirect
7. #10590946C2semidirect
8. #10590773C2semidirect
9. #10590763C2semidirect
10. #10590746C2semidirect
11. #10590744C2semidirect
12. #10590708C2semidirect
13. #10590705C2semidirect
14. #10590366C2semidirect
15. #10590300C2semidirect
21. #64084C22semidirect
25. C3×#869C22semidirect
32. #63894C22semidirect
39. #63844C22semidirect
43. C32×C4⋊C8C22semidirect
44. #63648C22semidirect
45. #63643C22semidirect
50. C3×#818C22semidirect
51. C3×#818C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
60. #63564C22semidirect
73. #4846D3semidirect
79. #4840D3semidirect
194. #869C2×D3semidirect
200. C3×C4⋊C8C2×D3semidirect
201. C3×C4⋊C8C2×D3semidirect
218. #818C2×D3semidirect
219. #818C2×D3semidirect
226. #815C2×D3semidirect
227. C8×Dic3C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
457. C4⋊C8D32semidirect
687. C32#3118semidirect
774. C3#79383semidirect
775. C3#80952semidirect

Maximal subgroups

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

subgroupindex
#105939942
#105938772
#105925432
C3×#48462
C3×#48402
#105909472
#105909462
#105907732
#105907632
#105907462
#105907442
#105907082
#105907052
#105903662
#105903002
#809523
#793833