Finite Group Databasebeta

← #11889433

Subgroups — #11889433

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 745 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5694C211yesmaximal, characteristic
2Dic6×D12C211yesmaximal, characteristic
3#10592768C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5#10590604C211yesmaximal, characteristic, complemented
6#10590604C211yesmaximal, characteristic, complemented
7#10590600C211yesmaximal, characteristic, complemented
8D3×#810C211yesmaximal, characteristic, complemented
9#10590587C211yesmaximal, characteristic, complemented
10#10590579C211yesmaximal, characteristic, complemented
11#10590429C211yesmaximal, characteristic, complemented
12#10590426C211yesmaximal, characteristic, complemented
13#10590385C211yesmaximal, characteristic, complemented
14#10590381C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic
16#83603—31nomaximal
17#81248—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×#125C2211yescharacteristic
21#64078C2211yescharacteristic
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×C4×Dic6C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63918—21no—
34#63893—21no—
35#63893—21no—
36Dic3×D12—21no—
37#63857C2211yescharacteristic
38#63857C2211yescharacteristic
39C2×#3719C2211yescharacteristic
40C2×#3719C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47#63637C2211yescharacteristic
48#63630C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53C3×C4⋊(C3⋊C8)C2211yescharacteristic
54#63574C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#552—31no—
62#5694D311yescharacteristic
63Q8×D12—31no—
64D4×Dic6—31no—
65C3×#479—31no—
66#5069—31no—
67#5069—31no—
68#5069—61no—
69#5063D311yescharacteristic, complemented
70#5052—31no—
71#5051—31no—
72#5050—31no—
73#5050—31no—
74#5031—31no—
75#5030—31no—
76#5030—31no—
77#5011—31no—
78#5004—31no—
79#4996—31no—
80#4971—31no—
81C2×#810—31no—
82#4888—31no—
83#4887—31no—
84#4867—31no—
85#4862—31no—
86#4849—31no—
87#4836—31no—
88#4809—31no—
89#4809—31no—
90#4802—31no—
91D3×#103—31no—
92C2×#634C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×D12D411yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
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)—21no—
114C4⋊(C3⋊Dic3)—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3719—41no—
140#3719—41no—
141#3718—22no—
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×#126—61no—
150C3×#125—21no—
151C3×#125—61no—
152C3×#125C2×D311yescharacteristic
153C3×#125C2×D311yescharacteristic
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×D4—31no—
160C3×#117—31no—
161C3×#117—61no—
162C2×C3×C4⋊C4—31no—
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—31no—
167D4×Dic3—61no—
168#924—31no—
169#924—31no—
170C2×#208—31no—
171C22×C3⋊C8—31no—
172C2×Dic12—31no—
173C2×Dic12—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×D3×C8—31no—
176#898—21no—
177#897—31no—
178#897—31no—
179#897—61no—
180#897—61no—
181#897C2×D311yescharacteristic
182#897C2×D311yescharacteristic
183#894—21no—
184#892—21no—
185#892C2×D311yescharacteristic
186D3×C4⋊C4C2×D311yescharacteristic
187#890—21no—
188#888—61no—
189#878—61no—
190#878—61no—
191C4×D12—61no—
192C4×D12C2×D311yescharacteristic
193#869—31no—
194#869—31no—
195#869—61no—
196#869—61no—
197C4×Dic6C2×D311yescharacteristic
198C4×Dic6C2×D311yescharacteristic
199C3×#107—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204#835—31no—
205#835—31no—
206#830—31no—
207#830—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210#816—31no—
211#816—31no—
212#810—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#810—61no—
226#810—61no—
227#810—61no—
228#810C2×D311yescharacteristic
229#810C2×D311yescharacteristic
230#808—31no—
231#808—31no—
232#808C2×D311yescharacteristic
233#807C2×D311yescharacteristic
234C4⋊(C3⋊C8)C2×D311yescharacteristic
235#803—31no—
236#803—31no—
237#803—61no—
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—21no—
249#634—21no—
250#634—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—22no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—42no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6#4112yes—
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—91no—
278#485—91no—
279#483—91no—
280#479—31no—
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×D4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298D3×Q8—62no—
299D3×Q8—62no—
300D3×Q8—121no—
301D3×Q8—121no—
302C2×D12#6711yescharacteristic
303C2×C4×D3—21no—
304C2×C4×D3—61no—
305C2×C4×D3—61no—
306C2×C4×D3C22×D311yescharacteristic
307C2×C4×D3C22×D311yescharacteristic
308C2×Dic6—31no—
309C2×Dic6—31no—
310C2×Dic6—31no—
311C2×Dic6—31no—
312C2×Dic6—61no—
313C2×Dic6—61no—
314C2×Dic6—62no—
315C2×Dic6—62no—
316C2×Dic6—61no—
317C2×Dic6—61no—
318C2×Dic6—61no—
319C2×Dic6—61no—
320C2×Dic6—121no—
321C2×Dic6—121no—
322C2×Dic6C22×D311yescharacteristic
323C2×Dic6C22×D311yescharacteristic
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—41no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—21no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357#217—61no—
358#217—61no—
359#216—62no—
360#216—62no—
361#216—121no—
362#216—121no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4#6711yescharacteristic
369(C2×D3)⋊C4#6711yescharacteristic
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—121no—
379C4⋊Dic3—121no—
380C4⋊Dic3#6711yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391#208—121no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—121no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401Dic12—121no—
402Dic12—121no—
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—41no—
419C3⋊Dic3—41no—
420C3×Dic3—22no—
421C3×Dic3—21no—
422C3×Dic3—21no—
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—91no—
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—31no—
447C4×D4—31no—
448C4×D4—181no—
449#117—31no—
450#117—61no—
451C2×C4⋊C4—31no—
452#107—31no—
453#106—31no—
454#106—91no—
455C4⋊C8—31no—
456#103—31no—
457#103—31no—
458#103—91no—
459#103—91no—
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—91no—
469C23×C3—31no—
470C23×C3—31no—
471C22×D3C2×#6711yescharacteristic
472C22×D3C2×#6711yescharacteristic
473C3×Q8—32no—
474C3×Q8—61no—
475C3×Q8—61no—
476C3×Q8—61no—
477C3×D4—62no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
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—122no—
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4C2×#6711yescharacteristic
501C2×C3×C4C2×#6711yescharacteristic
502C2×C3×C4C23×D311yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—121no—
513C2×Dic3—121no—
514C2×Dic3—122no—
515C2×Dic3—122no—
516C2×Dic3C2×#6711yescharacteristic
517C2×Dic3C2×#6711yescharacteristic
518D12—22no—
519C4×D3—21no—
520C4×D3—21no—
521C4×D3—21no—
522C4×D3—21no—
523C4×D3—42no—
524C4×D3—122no—
525C4×D3—122no—
526Dic6—21no—
527Dic6—21no—
528Dic6—21no—
529Dic6—61no—
530Dic6—61no—
531Dic6—61no—
532Dic6—61no—
533Dic6—61no—
534Dic6—61no—
535Dic6—61no—
536Dic6—61no—
537Dic6—121no—
538Dic6—121no—
539Dic6—121no—
540Dic6—121no—
541Dic6—122no—
542Dic6—122no—
543Dic6—122no—
544Dic6—122no—
545Dic6#23912yes—
546C3×C8—61no—
547C3×C8—61no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—121no—
555C3⋊C8—121no—
556C2×C32#54611yescharacteristic
557C2×C32C2×#13711yescharacteristic
558C2×C32#57811yescharacteristic
559C3×D3—22no—
560C3×D3—41no—
561C2×Q8—31no—
562C2×Q8—31no—
563C2×Q8—91no—
564C2×Q8—91no—
565C2×Q8—181no—
566C2×Q8—181no—
567C2×Q8—182no—
568C2×Q8—182no—
569C2×Q8—361no—
570C2×Q8—361no—
571C2×D4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—61no—
575C22×C4—181no—
576C22×C4—181no—
577Q16—182no—
578Q16—361no—
579Q16—361no—
580M16—361no—
581C2×C8—31no—
582C2×C8—31no—
583C2×C8—91no—
584C2×C8—91no—
585C2×C8—361no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—31no—
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4C2×D3211yescharacteristic
601C4⋊C4C2×D3211yescharacteristic
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C42—61no—
610C42—61no—
611C42—61no—
612C42C2×D3211yescharacteristic
613C22×C3—21no—
614C22×C3—32no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C22×#6711yescharacteristic
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3#95112yes—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—62no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—81no—
644C3×C4—81no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4C2×#23911yescharacteristic
649C3×C4D3×#4111yescharacteristic
650C3×C4#100911yescharacteristic
651C3×C4#100911yescharacteristic
652Dic3—21no—
653Dic3—21no—
654Dic3—22no—
655Dic3—41no—
656Dic3—41no—
657Dic3—41no—
658Dic3—121no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662Dic3—241no—
663Dic3—241no—
664C32#331211yescharacteristic, complemented, Sylow
665C23—31no—
666C23—31no—
667Q8—32no—
668Q8—61no—
669Q8—61no—
670Q8—61no—
671Q8—181no—
672Q8—181no—
673Q8—181no—
674Q8—181no—
675Q8—362no—
676Q8—362no—
677D4—62no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—122no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—362no—
694C2×C4—362no—
695C2×C4D3×#6711yescharacteristic
696C2×C4D3×#6711yescharacteristic
697C2×C4C22×D3211yescharacteristic
698C8—61no—
699C8—61no—
700C8—181no—
701C8—181no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—62no—
706C2×C3—121no—
707C2×C3#563011yescharacteristic
708C2×C3#577111yescharacteristic
709C2×C3D3×#13711yescharacteristic
710C2×C3C2×#95111yescharacteristic
711C2×C3#582911yescharacteristic
712C2×C3#583811yescharacteristic
713D3—22no—
714D3—41no—
715C22—32no—
716C22—61no—
717C22—61no—
718C22—61no—
719C22—61no—
720C22—61no—
721C22C2×D3×#6711yescharacteristic
722C4—21no—
723C4—21no—
724C4—41no—
725C4—41no—
726C4—61no—
727C4—61no—
728C4—62no—
729C4—121no—
730C4—121no—
731C4—121no—
732C4—361no—
733C4—361no—
734C4D3×#23911yescharacteristic
735C4#6432011yescharacteristic
736C3—21no—
737C3#8124811yescharacteristic, complemented
738C3#8360311yescharacteristic, complemented
739C2—62no—
740C2—121no—
741C2#1059542711yescharacteristic
742C2D3×#95111yescharacteristic
743C2#1059546711yescharacteristic
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. #10592768C2semidirect
4. C3×#5063C2semidirect
5. #10590604C2semidirect
6. #10590604C2semidirect
7. #10590600C2semidirect
8. D3×#810C2semidirect
9. #10590587C2semidirect
10. #10590579C2semidirect
11. #10590429C2semidirect
12. #10590426C2semidirect
13. #10590385C2semidirect
14. #10590381C2semidirect
69. #5063D3semidirect
664. C32#3312semidirect
737. C3#81248semidirect
738. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C3×#56942
Dic6×D122
#105927682
C3×#50632
#105906042
#105906002
D3×#8102
#105905872
#105905792
#105904292
#105904262
#105903852
#105903812
#105903302
#836033
#812483