Finite Group Databasebeta

← #11887658

Subgroups — #11887658

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595400C211yesmaximal, characteristic
2#10594531C211yesmaximal, characteristic
3#10592494C211yesmaximal, characteristic, complemented
4C3×#4811C211yesmaximal, characteristic, complemented
5C3×D3×#103C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic, complemented
8#10591538C211yesmaximal, characteristic, complemented
9#10590952C211yesmaximal, characteristic, complemented
10#10590852C211yesmaximal, characteristic, complemented
11#10590817C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic
13D3×#810C211yesmaximal, characteristic, complemented
14#10590482C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#81490—31nomaximal
17#78806—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20#64153C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3746C2211yescharacteristic
23#64096C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28#63919C2211yescharacteristic
29C4×#625—21no—
30C4×#625C2211yescharacteristic
31#63887—21no—
32#63879—21no—
33#63870—21no—
34#63857C2211yescharacteristic
35#63857C2211yescharacteristic
36#63857C2211yescharacteristic
37#63851—21no—
38#63851—21no—
39#63851—21no—
40#63843C2211yescharacteristic
41#63839—21no—
42C2×#3719C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63641C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#807C2211yescharacteristic
54#63576C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61Q8×#67—31no—
62#5632—31no—
63#5511—31no—
64#5511—31no—
65C3×#484—31no—
66C2×C3×#103—31no—
67#5228—31no—
68#5116—31no—
69C8×#67—31no—
70#5051—31no—
71#4970—31no—
72C2×#810—31no—
73#4887—31no—
74#4884—31no—
75#4875—31no—
76#4873—31no—
77#4813—31no—
78#4811D311yescharacteristic, complemented
79#4809—31no—
80#4809—31no—
81D3×#103—31no—
82D3×#103D311yescharacteristic, complemented
83#4795—31no—
84#4795—31no—
85#4795—61no—
86#4793—31no—
87#4792—31no—
88#4792—31no—
89#4790—31no—
90#4739—31no—
91#67⋊C8—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#627—21no—
106C2×#625D411yescharacteristic
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3756—41no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3746—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—41no—
130#3724—21no—
131#3724D411yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3719—22no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C22×Dic6—31no—
149C22×C3×C8—31no—
150C3×C22⋊Q8—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153#946—61no—
154#946C2×D311yescharacteristic
155Q8×Dic3—31no—
156#944—31no—
157#944—31no—
158#944—61no—
159#944—61no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#216—31no—
163C2×#216—61no—
164C4×#67—31no—
165C4×#67—31no—
166C4×#67—61no—
167C4×#67—61no—
168C4×#67—61no—
169#924—31no—
170#924—31no—
171#924—31no—
172#924—61no—
173#924—61no—
174#924—61no—
175C22×C3⋊C8—31no—
176C2×Dic12—31no—
177C2×Dic12—31no—
178C2×Dic12—31no—
179C2×Dic12—61no—
180C2×D3×C8—31no—
181C2×D3×C8C2×D311yescharacteristic
182#897—31no—
183#897—31no—
184#897—31no—
185#896—61no—
186#896—61no—
187#896—61no—
188D3×C4⋊C4C2×D311yescharacteristic
189D3×C4⋊C4C2×D311yescharacteristic
190#889—61no—
191#889—61no—
192#888—31no—
193#888—31no—
194#888—61no—
195#887—31no—
196#887—31no—
197#887—31no—
198#887—61no—
199#67⋊C4—61no—
200#878—61no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic
209C3×#103C2×D311yescharacteristic
210C3×C22⋊C8—31no—
211#835—31no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#830—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#818C2×D311yescharacteristic
218#816—31no—
219#816—31no—
220#816—31no—
221#816C2×D311yescharacteristic
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—61no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—61no—
234#810C2×D311yescharacteristic
235#807—31no—
236#807—31no—
237#807C2×D311yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249#634—21no—
250#634—21no—
251#634—21no—
252#634—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6#4112yes—
269#627—42no—
270#627—81no—
271#625Q1614yescomplemented
272D3×Dic3—42no—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—91no—
279#487—91no—
280#484—31no—
281#484—91no—
282#477—91no—
283#467—91no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—31no—
291C2×#103—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—121no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—31no—
305C2×#67—31no—
306C22×Dic3—61no—
307D3×Q8—22no—
308D3×Q8—41no—
309D3×Q8—62no—
310D3×Q8—121no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—61no—
315C2×C4×D3C22×D311yescharacteristic
316C2×C4×D3C22×D311yescharacteristic
317C2×Dic6—21no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6—62no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—121no—
330C2×Dic6C22×D311yescharacteristic
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—121no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347#217—31no—
348#217—31no—
349#217—61no—
350#217—61no—
351#217—61no—
352#216—62no—
353#216—121no—
354#216—121no—
355#216—122no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3C22×D311yescharacteristic
367C4⋊Dic3C22×D311yescharacteristic
368C4⋊Dic3C22×D311yescharacteristic
369Dic3⋊C4—21no—
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387Dic3⋊C4—121no—
388Dic3⋊C4—121no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—121no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—62no—
404Dic12—121no—
405Dic12—121no—
406Dic12—122no—
407D3×C8—41no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3C2×Q1612yes—
415C2×C3×D3C2×Q1612yes—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—21no—
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3⋊Dic3C2×Q1612yes—
424C3×Dic3—22no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C22×Q8—31no—
431C22×Q8—91no—
432C2×Q16—91no—
433C2×Q16—91no—
434C2×Q16—91no—
435C22×C8—31no—
436C22×C8—91no—
437C4⋊Q8—91no—
438C4⋊Q8—91no—
439C4⋊Q8—181no—
440#125—181no—
441C22⋊Q8—31no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—31no—
456#107—31no—
457#107—31no—
458#107—91no—
459C4⋊C8—91no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103D3211yescharacteristic
470C22⋊C8—31no—
471C22⋊C8—91no—
472C4×C8—91no—
473C23×C3—31no—
474C23×C3—31no—
475C22×D3D3×D411yescharacteristic
476C22×D3D3×D411yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—32no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8—61no—
485C3×Q8—122no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—122no—
504C2×C3×C4—241no—
505C2×C3×C4—241no—
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—34no—
509#67—34no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—122no—
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—42no—
534C4×D3—81no—
535C4×D3—81no—
536C4×D3—122no—
537Dic6—21no—
538Dic6—42no—
539Dic6—62no—
540Dic6—61no—
541Dic6—61no—
542Dic6—61no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—61no—
548Dic6—121no—
549Dic6—121no—
550Dic6—121no—
551Dic6—122no—
552Dic6—122no—
553Dic6—241no—
554Dic6—241no—
555Dic6#23512yes—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C2×C32#54611yescharacteristic
567C2×C32C22×Q1611yescharacteristic
568C2×C32#57711yescharacteristic
569C3×D3—22no—
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—61no—
573C2×Q8—62no—
574C2×Q8—91no—
575C2×Q8—91no—
576C2×Q8—121no—
577C2×Q8—181no—
578C2×Q8—181no—
579C2×Q8—182no—
580C2×Q8—361no—
581C2×Q8C2×D3211yescharacteristic
582C2×D4—91no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—181no—
589Q16—182no—
590Q16—361no—
591Q16—361no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—121no—
596C2×C8—361no—
597C2×C8C2×D3211yescharacteristic
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—61no—
615C22⋊C4—91no—
616C22⋊C4—91no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—91no—
621C42—181no—
622C42—181no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—32no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3D3×Q1612yes—
637C2×D3D3×Q1612yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—62no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4C2×#23511yescharacteristic
653C3×C4#100411yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4#100911yescharacteristic
656Dic3—21no—
657Dic3—22no—
658Dic3—21no—
659Dic3—32no—
660Dic3—32no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—62no—
665Dic3—61no—
666Dic3—61no—
667Dic3—121no—
668Dic3—122no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674C32#329911yescharacteristic, complemented, Sylow
675C23—31no—
676C23—31no—
677Q8—21no—
678Q8—21no—
679Q8—32no—
680Q8—61no—
681Q8—122no—
682Q8—181no—
683Q8—181no—
684Q8—181no—
685Q8—181no—
686Q8—362no—
687Q8—721no—
688D4—94no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—122no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—241no—
707C2×C4—241no—
708C2×C4—362no—
709C2×C4C22×D3211yescharacteristic
710C8—21no—
711C8—61no—
712C8—61no—
713C8—181no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—62no—
718C2×C3—62no—
719C2×C3#549011yescharacteristic
720C2×C3#565411yescharacteristic
721C2×C3#576211yescharacteristic
722C2×C3C2×D3×Q1611yescharacteristic
723C2×C3C2×D3×Q1611yescharacteristic
724C2×C3#577511yescharacteristic
725D3—22no—
726D3—22no—
727C22—32no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22D32×D411yescharacteristic
734C4—41no—
735C4—41no—
736C4—61no—
737C4—61no—
738C4—62no—
739C4—92no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—181no—
744C4—361no—
745C4—361no—
746C4D3×#23511yescharacteristic
747C4#6431411yescharacteristic
748C3—21no—
749C3#7880611yescharacteristic, complemented
750C3#8149011yescharacteristic, complemented
751C2—62no—
752C2—62no—
753C2#1059427211yescharacteristic
754C2#1059474911yescharacteristic
755C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#625D4
hypercenter#103D32
hypocenterC32#3299
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
3. #10592494C2semidirect
4. C3×#4811C2semidirect
5. C3×D3×#103C2semidirect
6. #10591596C2semidirect
7. #10591595C2semidirect
8. #10591538C2semidirect
9. #10590952C2semidirect
10. #10590852C2semidirect
11. #10590817C2semidirect
13. D3×#810C2semidirect
14. #10590482C2semidirect
15. #10590427C2semidirect
78. #4811D3semidirect
82. D3×#103D3semidirect
271. #625Q16semidirect
674. C32#3299semidirect
749. C3#78806semidirect
750. C3#81490semidirect

Maximal subgroups

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

subgroupindex
#105954002
#105945312
#105924942
C3×#48112
C3×D3×#1032
#105915962
#105915952
#105915382
#105909522
#105908522
#105908172
#105907172
D3×#8102
#105904822
#105904272
#814903
#788063