Finite Group Databasebeta

← #11889431

Subgroups — #11889431

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 743 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5694C211yesmaximal, characteristic
2#10593904C211yesmaximal, characteristic
3#10592762C211yesmaximal, characteristic, complemented
4C3×#5069C211yesmaximal, characteristic, complemented
5#10590604C211yesmaximal, characteristic, complemented
6#10590604C211yesmaximal, characteristic, complemented
7#10590600C211yesmaximal, characteristic, complemented
8D3×#810C211yesmaximal, characteristic, complemented
9#10590521C211yesmaximal, characteristic, complemented
10#10590520C211yesmaximal, characteristic, complemented
11#10590518C211yesmaximal, characteristic, complemented
12#10590516C211yesmaximal, characteristic, complemented
13#10590384C211yesmaximal, characteristic, complemented
14#10590383C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic
16#83603—31nomaximal
17#81749—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×#125C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×#898—21no—
23C3×#897C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#894—21no—
26C3×#892—21no—
27C3×#892C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29C3×#890—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#869C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63919—21no—
34#63899—21no—
35#63899—21no—
36#63898—21no—
37#63856C2211yescharacteristic
38#63856C2211yescharacteristic
39C2×#3719C2211yescharacteristic
40C2×#3718C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46#63635C2211yescharacteristic
47#63634C2211yescharacteristic
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#552—31no—
62#5727—31no—
63#5694D311yescharacteristic
64D4×Dic6—31no—
65C3×#491—31no—
66#5090—31no—
67#5069D311yescharacteristic, complemented
68#5063—31no—
69#5063—31no—
70#5063—61no—
71#5052—31no—
72#5051—31no—
73#5050—31no—
74#5050—31no—
75#5031—31no—
76#5030—31no—
77#5011—31no—
78#5004—31no—
79#4996—31no—
80#4971—31no—
81C2×#810—31no—
82#4816—31no—
83#4815—31no—
84#4813—31no—
85#4809—31no—
86#4809—31no—
87#4805—31no—
88#4802—31no—
89D3×#103—31no—
90#4716—31no—
91#4706—31no—
92C2×#634C2311yescharacteristic
93C2×C3×D12D411yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#627—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×Dic6—22no—
105D3×Dic6—22no—
106D3×Dic6—41no—
107D3×Dic6—41no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C42C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3719—22no—
140#3718—41no—
141#3718—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C3×C4⋊Q8—31no—
150C3×#126—61no—
151C3×#125—21no—
152C3×#125—61no—
153C3×#125C2×D311yescharacteristic
154C3×#125C2×D311yescharacteristic
155C3×#123—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×D4—31no—
160C3×#117—31no—
161C3×#117—61no—
162C2×C3×C4⋊C4—31no—
163#946—31no—
164#946—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—31no—
170D4×Dic3—61no—
171#924—31no—
172#924—31no—
173C2×#208—31no—
174C22×C3⋊C8—31no—
175C2×Dic12—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×D3×C8—31no—
178#898—21no—
179#897C2×D311yescharacteristic
180#897C2×D311yescharacteristic
181#896—61no—
182#896—61no—
183#894—21no—
184#893—61no—
185#892—21no—
186#892C2×D311yescharacteristic
187D3×C4⋊C4C2×D311yescharacteristic
188#890—21no—
189#888—61no—
190#888—61no—
191#878—61no—
192#878—61no—
193C4×D12C2×D311yescharacteristic
194#869C2×D311yescharacteristic
195C4×Dic6—31no—
196C4×Dic6—31no—
197C4×Dic6—61no—
198C4×Dic6C2×D311yescharacteristic
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#97—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#830—31no—
208#830—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#817—31no—
212#816—31no—
213#816—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—61no—
222#810—61no—
223#810C2×D311yescharacteristic
224#810C2×D311yescharacteristic
225#810C2×D311yescharacteristic
226#810C2×D311yescharacteristic
227#808—31no—
228#808—31no—
229#808—31no—
230#808—61no—
231#807—31no—
232#807—31no—
233#807—61no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×D311yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247#634—21no—
248#634#4112yes—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—22no—
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—42no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#627—42no—
268#627—42no—
269D3×Dic3—42no—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—91no—
277#491—31no—
278#485—91no—
279#483—91no—
280#479—91no—
281#470—91no—
282#467—91no—
283#462—91no—
284#451—91no—
285#451—91no—
286#441—91no—
287#435—91no—
288#419—91no—
289C2×#103—91no—
290C2×C3×Q8—31no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×D4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299D3×Q8—62no—
300D3×Q8—62no—
301D3×Q8—121no—
302D3×Q8—121no—
303C2×D12#6711yescharacteristic
304C2×C4×D3—21no—
305C2×C4×D3—61no—
306C2×C4×D3—61no—
307C2×C4×D3C22×D311yescharacteristic
308C2×C4×D3C22×D311yescharacteristic
309C2×Dic6—31no—
310C2×Dic6—31no—
311C2×Dic6—61no—
312C2×Dic6—62no—
313C2×Dic6—62no—
314C2×Dic6—61no—
315C2×Dic6—61no—
316C2×Dic6—61no—
317C2×Dic6—61no—
318C2×Dic6—121no—
319C2×Dic6—121no—
320C2×Dic6C22×D311yescharacteristic
321C2×Dic6C22×D311yescharacteristic
322C2×Dic6C22×D311yescharacteristic
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—41no—
334C3×C4⋊C4—41no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—21no—
351C3×C42—61no—
352C3×C42—61no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—61no—
356#217—61no—
357#216—62no—
358#216—121no—
359#216—121no—
360#216—121no—
361#216—121no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4#6711yescharacteristic
368(C2×D3)⋊C4#6711yescharacteristic
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3#6711yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392#208—121no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—121no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402Dic12—62no—
403ΓL(1,𝔽25)—121no—
404D3×C8—121no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3#13712yes—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4H(5,𝔽2)11yescharacteristic
418C3⋊Dic3—22no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×Q8—91no—
427C22×Q8—91no—
428C2×Q16—91no—
429C2×Q16—91no—
430C2×Q16—91no—
431C2×M16—91no—
432C22×C8—91no—
433C4⋊Q8—31no—
434C4⋊Q8—181no—
435#126—61no—
436#125—61no—
437#125D3211yescharacteristic
438#123—61no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—181no—
444C22⋊Q8—181no—
445C4×Q8—31no—
446C4×Q8—91no—
447C4×D4—31no—
448C4×D4—181no—
449#117—31no—
450#117—61no—
451C2×C4⋊C4—31no—
452#107—91no—
453#106—91no—
454#106—91no—
455C4⋊C8—91no—
456#103—31no—
457#103—31no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468#97—31no—
469C23×C3—31no—
470C23×C3—31no—
471C22×D3C2×#6711yescharacteristic
472C22×D3C2×#6711yescharacteristic
473C3×Q8—61no—
474C3×Q8—61no—
475C3×Q8—61no—
476C3×Q8—61no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×D4—62no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—122no—
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4C2×#6711yescharacteristic
503C2×C3×C4C2×#6711yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—121no—
515C2×Dic3—121no—
516C2×Dic3—122no—
517C2×Dic3—122no—
518C2×Dic3C2×#6711yescharacteristic
519C2×Dic3C2×#6711yescharacteristic
520D12—22no—
521C4×D3—21no—
522C4×D3—21no—
523C4×D3—21no—
524C4×D3—21no—
525C4×D3—42no—
526C4×D3—122no—
527C4×D3—122no—
528Dic6—21no—
529Dic6—21no—
530Dic6—21no—
531Dic6—21no—
532Dic6—21no—
533Dic6—21no—
534Dic6—32no—
535Dic6—32no—
536Dic6—62no—
537Dic6—61no—
538Dic6—61no—
539Dic6—121no—
540Dic6—122no—
541Dic6—122no—
542Dic6—122no—
543Dic6—122no—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—121no—
553C3⋊C8—121no—
554C2×C32#54611yescharacteristic
555C2×C32C2×#13711yescharacteristic
556C2×C32#57811yescharacteristic
557C3×D3—22no—
558C3×D3—41no—
559C2×Q8—31no—
560C2×Q8—31no—
561C2×Q8—31no—
562C2×Q8—91no—
563C2×Q8—181no—
564C2×Q8—181no—
565C2×Q8—182no—
566C2×Q8—182no—
567C2×Q8—361no—
568C2×Q8—361no—
569C2×D4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—61no—
573C22×C4—181no—
574C22×C4—181no—
575Q16—182no—
576Q16—361no—
577Q16—361no—
578M16—361no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—91no—
582C2×C8—91no—
583C2×C8—361no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—91no—
595C4⋊C4—181no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4C2×D3211yescharacteristic
599C4⋊C4C2×D3211yescharacteristic
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C42—61no—
608C42—61no—
609C42—181no—
610C42C2×D3211yescharacteristic
611C22×C3—21no—
612C22×C3—32no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3C2×D3×D411yescharacteristic
619C22×C3C22×#6711yescharacteristic
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—21no—
625C2×D3#95112yes—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—81no—
641C3×C4—81no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4—121no—
645C3×C4—121no—
646C3×C4D3×#4111yescharacteristic
647C3×C4D3×#4111yescharacteristic
648C3×C4#100911yescharacteristic
649C3×C4#100911yescharacteristic
650Dic3—21no—
651Dic3—21no—
652Dic3—41no—
653Dic3—41no—
654Dic3—41no—
655Dic3—41no—
656Dic3—62no—
657Dic3—62no—
658Dic3—122no—
659Dic3—121no—
660Dic3—121no—
661Dic3—241no—
662C32#331211yescharacteristic, complemented, Sylow
663C23—31no—
664C23—31no—
665Q8—61no—
666Q8—61no—
667Q8—61no—
668Q8—61no—
669Q8—61no—
670Q8—61no—
671Q8—92no—
672Q8—181no—
673Q8—362no—
674Q8—362no—
675D4—62no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—122no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—362no—
692C2×C4—362no—
693C2×C4D3×#6711yescharacteristic
694C2×C4D3×#6711yescharacteristic
695C2×C4C22×D3211yescharacteristic
696C8—61no—
697C8—61no—
698C8—181no—
699C8—181no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—62no—
704C2×C3—121no—
705C2×C3#567611yescharacteristic
706C2×C3D3×#13711yescharacteristic
707C2×C3#577911yescharacteristic
708C2×C3C2×#95111yescharacteristic
709C2×C3#582911yescharacteristic
710C2×C3#583811yescharacteristic
711D3—22no—
712D3—41no—
713C22—32no—
714C22—61no—
715C22—61no—
716C22—61no—
717C22—61no—
718C22—61no—
719C22C2×D3×#6711yescharacteristic
720C4—21no—
721C4—21no—
722C4—41no—
723C4—41no—
724C4—61no—
725C4—61no—
726C4—121no—
727C4—121no—
728C4—121no—
729C4—121no—
730C4—182no—
731C4—361no—
732C4#6431911yescharacteristic
733C4#6432011yescharacteristic
734C3—21no—
735C3#8174911yescharacteristic, complemented
736C3#8360311yescharacteristic, complemented
737C2—62no—
738C2—121no—
739C2#1059542811yescharacteristic
740C2D3×#95111yescharacteristic
741C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenter#125D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #10592762C2semidirect
4. C3×#5069C2semidirect
5. #10590604C2semidirect
6. #10590604C2semidirect
7. #10590600C2semidirect
8. D3×#810C2semidirect
9. #10590521C2semidirect
10. #10590520C2semidirect
11. #10590518C2semidirect
12. #10590516C2semidirect
13. #10590384C2semidirect
14. #10590383C2semidirect
67. #5069D3semidirect
662. C32#3312semidirect
735. C3#81749semidirect
736. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C3×#56942
#105939042
#105927622
C3×#50692
#105906042
#105906002
D3×#8102
#105905212
#105905202
#105905182
#105905162
#105903842
#105903832
#105903262
#836033
#817493