Finite Group Databasebeta

← #11870586

Subgroups — #11870586

Order 1152.

909 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596071C211yesmaximal, characteristic, complemented
2#10594958C211yesmaximal, characteristic, complemented
3C3×#5037C211yesmaximal, characteristic
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591445C211yesmaximal, characteristic, complemented
6#10591443C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591434C211yesmaximal, characteristic, complemented
9#10591173C211yesmaximal, characteristic, complemented
10#10591134C211yesmaximal, characteristic, complemented
11#10591061C211yesmaximal, characteristic, complemented
12#10590495C211yesmaximal, characteristic, complemented
13#10590482C211yesmaximal, characteristic, complemented
14#10590473C211yesmaximal, characteristic, complemented
15#10590460C211yesmaximal, characteristic, complemented
16#81348—31nomaximal
17#80068—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C32×#121C2211yescharacteristic
20#64145C2211yescharacteristic
21#64144—21no—
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3C2211yescharacteristic
24#64133C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64099C2211yescharacteristic
27#64096C2211yescharacteristic
28#64088—21no—
29#64086—21no—
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#926C2211yescharacteristic
33#67⋊Dic3—21no—
34#67⋊Dic3—21no—
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic
37C4×D3×Dic3—21no—
38#63855—21no—
39#63843C2211yescharacteristic
40#63843C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C3×#832C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63572C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63563C2211yescharacteristic
59#63553C2211yescharacteristic
60#63553C2211yescharacteristic
61Dic3×#41—31no—
62#5600—31no—
63#5600—31no—
64#5600—61no—
65#5522—31no—
66C3×#482—31no—
67C3×#449—31no—
68#5239—31no—
69#5166—31no—
70Dic3×SD16—31no—
71#5153—31no—
72Dic3×D8—31no—
73#5037D311yescharacteristic
74#5035D311yescharacteristic, complemented
75#4996—31no—
76#4891—31no—
77#4873—31no—
78#4857—31no—
79#4852—31no—
80#4796—31no—
81#4790—31no—
82#4787—31no—
83#4767—31no—
84#4763—31no—
85#4758—31no—
86#4758—31no—
87#4756—31no—
88#4733—31no—
89#4723—31no—
90#4718—31no—
91#4718—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C22×C3⋊Dic3D411yescharacteristic
97C22×C3⋊Dic3D411yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C3×#235—22no—
101C3×#235—22no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109#3757—21no—
110#3757—21no—
111#3757—21no—
112#3757—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3D411yescharacteristic
120C4×C3⋊Dic3D411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C3×#217—21no—
124C3×#214—22no—
125C3×#213—22no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4×Dic3—21no—
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#3719—22no—
140#3716—22no—
141#3102—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
149C3×#117—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152C2×#216—31no—
153#936—31no—
154#936—31no—
155#936—61no—
156#935—61no—
157#935—61no—
158#935—62no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3—62no—
169C2×#214—31no—
170C2×#214C2×D311yescharacteristic
171C2×#213C2×D311yescharacteristic
172#926—61no—
173#926C2×D311yescharacteristic
174#924—31no—
175#924—31no—
176#924—61no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—61no—
180C2×C4×Dic3—61no—
181C2×Dic12—31no—
182C2×#204—31no—
183#893—31no—
184#893—31no—
185#890—31no—
186#890—31no—
187#890—61no—
188#887—31no—
189#887—31no—
190#887—31no—
191#887—31no—
192#887—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195#879—61no—
196#879—61no—
197#879—62no—
198#877—61no—
199#877—61no—
200#877—62no—
201#872—61no—
202C42×D3—61no—
203C3×#107—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#818—31no—
219#817—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810—31no—
232#810—31no—
233#810C2×D311yescharacteristic
234#809C2×D311yescharacteristic
235#808—31no—
236#808C2×D311yescharacteristic
237#807—31no—
238#807C2×D311yescharacteristic
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—42no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—22no—
253C2×C3⋊Dic3—41no—
254C2×C3⋊Dic3—42no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259#634—21no—
260#634—21no—
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—24no—
268C3×Dic6—21no—
269C3×Dic6#4112yes—
270D3×Dic3—42no—
271D3×Dic3—42no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#529—91no—
277C4×#41—91no—
278#485—91no—
279#482—31no—
280#479—91no—
281#478—91no—
282#464—91no—
283#463—91no—
284#452—91no—
285#449—31no—
286C4×Q16—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289C4×D8—91no—
290#431—91no—
291C3×#41—62no—
292C3×#41—62no—
293C2×C3×Q8—31no—
294C2×C3×D4—22no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C22×C3×C4—21no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—21no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—62no—
318#235—22no—
319#235—22no—
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—21no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×Dic6—31no—
325C2×Dic6—31no—
326C2×Dic6—61no—
327C2×Dic6C22×D311yescharacteristic
328C3×SD16—62no—
329C3×D8—62no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C22⋊C4—22no—
340C3×C22⋊C4—21no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—61no—
343C3×C42—61no—
344#217—21no—
345#217—61no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—62no—
354#217—62no—
355#217—62no—
356#217—62no—
357#217—61no—
358#217—61no—
359#216—62no—
360#214—22no—
361#214—62no—
362#213—22no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—62no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—62no—
382Dic3⋊C4—62no—
383Dic3⋊C4—62no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386C4×Dic3—21no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—62no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410Dic12—62no—
411#204—62no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3×D3—22no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3⋊Dic3#13512yes—
432C3×Dic3—22no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C2×Q16—91no—
437C2×SD16—31no—
438C2×SD16—91no—
439C2×D8—31no—
440#126—181no—
441#125—91no—
442#124—91no—
443#123—181no—
444C22⋊Q8—91no—
445#121D3211yescharacteristic
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454C4×D4—181no—
455#117—31no—
456#117—181no—
457#117—181no—
458C2×C42—91no—
459C2×C42—181no—
460#107—31no—
461#107—91no—
462#106—31no—
463#106—91no—
464C4⋊C8—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102—91no—
474C22⋊C8—31no—
475C22⋊C8—31no—
476C4×C8—91no—
477C4×C8—91no—
478C23×C3—22no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—61no—
483C23×C3D3×D411yescharacteristic
484C23×C3D3×D411yescharacteristic
485C22×D3—21no—
486C3×Q8—32no—
487C3×Q8—61no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—32no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—44no—
496C3×D4—42no—
497C3×D4—42no—
498C3×D4—64no—
499C3×D4—61no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—64no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—24no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—62no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—122no—
544C2×Dic3—122no—
545C2×Dic3—122no—
546C2×Dic3—122no—
547C2×Dic3—122no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—124no—
551C2×Dic3—122no—
552D12—21no—
553D12#23712yes—
554C4×D3—24no—
555C4×D3—122no—
556C4×D3—122no—
557Dic6—21no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—121no—
563Dic6—121no—
564Dic6#23712yes—
565C3×C8—61no—
566C3×C8—61no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—41no—
574C2×C32—81no—
575C2×C32#52511yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32#57511yescharacteristic
578C3×D3—42no—
579#41—62no—
580#41—62no—
581C2×Q8—31no—
582C2×Q8—91no—
583C2×D4—21no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4C2×D3211yescharacteristic
587C22×C4—61no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4—181no—
593C22×C4C2×D3211yescharacteristic
594Q16—182no—
595SD16—62no—
596SD16—182no—
597D8—62no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—31no—
601C2×C8—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—61no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—61no—
621C42—91no—
622C42—91no—
623C42—91no—
624C42—91no—
625C42—181no—
626C42—181no—
627C42—181no—
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—62no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—42no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—62no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4C2×#23711yescharacteristic
667C3×C4C2×#23711yescharacteristic
668C3×C4D3×#4111yescharacteristic
669C3×C4D3×#4111yescharacteristic
670Dic3—22no—
671Dic3—32no—
672Dic3—32no—
673Dic3—41no—
674Dic3—41no—
675Dic3—62no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—122no—
686Dic3—122no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691C32#310211yescharacteristic, complemented, Sylow
692C23—21no—
693C23—61no—
694C23#381111yescharacteristic
695Q8—32no—
696Q8—61no—
697Q8—181no—
698Q8—181no—
699D4—21no—
700D4—21no—
701D4—32no—
702D4—42no—
703D4—64no—
704D4—61no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—64no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—182no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—362no—
720C2×C4—362no—
721C2×C4—362no—
722C2×C4—361no—
723C2×C4#381111yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—61no—
726C8—61no—
727C8—61no—
728C8—61no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—41no—
734C2×C3—41no—
735C2×C3—82no—
736C2×C3—81no—
737C2×C3—81no—
738C2×C3—122no—
739C2×C3#558611yescharacteristic
740C2×C3#565611yescharacteristic
741C2×C3D3×#13511yescharacteristic
742C2×C3D3×#13511yescharacteristic
743C2×C3#577311yescharacteristic
744C2×C3#577311yescharacteristic
745D3—42no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—62no—
753C22—121no—
754C22—121no—
755C22C2×#381111yescharacteristic
756C4—21no—
757C4—41no—
758C4—62no—
759C4—92no—
760C4—121no—
761C4—121no—
762C4—181no—
763C4—181no—
764C4—181no—
765C4—361no—
766C4—361no—
767C4D3×#23711yescharacteristic
768C4D3×#23711yescharacteristic
769C3—21no—
770C3#8006811yescharacteristic, complemented
771C3#8134811yescharacteristic, complemented
772C2—41no—
773C2—81no—
774C2—122no—
775C2#1059510111yescharacteristic
776C2#1059516011yescharacteristic
777C2#1059545911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5037C2
hypercenter#121D32
hypocenterC32#3102
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. #10596071C2semidirect
2. #10594958C2semidirect
4. C3×#5035C2semidirect
5. #10591445C2semidirect
6. #10591443C2semidirect
7. #10591435C2semidirect
8. #10591434C2semidirect
9. #10591173C2semidirect
10. #10591134C2semidirect
11. #10591061C2semidirect
12. #10590495C2semidirect
13. #10590482C2semidirect
14. #10590473C2semidirect
15. #10590460C2semidirect
74. #5035D3semidirect
691. C32#3102semidirect
770. C3#80068semidirect
771. C3#81348semidirect

Maximal subgroups

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

subgroupindex
#105960712
#105949582
C3×#50372
C3×#50352
#105914452
#105914432
#105914352
#105914342
#105911732
#105911342
#105910612
#105904952
#105904822
#105904732
#105904602
#813483
#800683