Finite Group Databasebeta

← #11889394

Subgroups — #11889394

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic
2#10593920C211yesmaximal, characteristic
3#10592729C211yesmaximal, characteristic, complemented
4C3×#5022C211yesmaximal, characteristic, complemented
5#10591595C211yesmaximal, characteristic, complemented
6#10591595C211yesmaximal, characteristic, complemented
7#10591557C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10590587C211yesmaximal, characteristic, complemented
10#10590579C211yesmaximal, characteristic, complemented
11#10590448C211yesmaximal, characteristic, complemented
12#10590439C211yesmaximal, characteristic, complemented
13#10590388C211yesmaximal, characteristic, complemented
14#10590330C211yesmaximal, characteristic
15#10590291C211yesmaximal, characteristic, complemented
16#83552—31nomaximal
17#81248—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#897—21no—
24C3×#897—21no—
25C3×#897C2211yescharacteristic
26C3×#897C2211yescharacteristic
27C3×C4×D12—21no—
28C3×C4×D12C2211yescharacteristic
29C3×#870C2211yescharacteristic
30C3×#869—21no—
31C3×#869C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33#63884—21no—
34#63878—21no—
35#63862—21no—
36#63857C2211yescharacteristic
37#63857C2211yescharacteristic
38#63846—21no—
39#63841C2211yescharacteristic
40C2×#3719C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63637C2211yescharacteristic
46#63635C2211yescharacteristic
47#63630C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×C4⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×D4×Q8—31no—
62#5694—31no—
63Q8×D12D311yescharacteristic
64#5541—31no—
65C3×#479—31no—
66#5228—31no—
67#5228—31no—
68#5225—31no—
69C2×#835—31no—
70#5090—31no—
71#5082—31no—
72#5069—31no—
73#5052—31no—
74#5051—31no—
75#5045—31no—
76#5043—31no—
77#5030—31no—
78#5030—31no—
79#5030—61no—
80#5022D311yescharacteristic, complemented
81#5011—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×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C3×D3×Q8—41no—
98C2×C3×D12D411yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×D3×Dic3—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112#3756—22no—
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)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3719—41no—
141#3719—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C2×D3×Q8C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×C4⋊Q8—61no—
151C3×#125—31no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8—61no—
156C3×C4×Q8—21no—
157C3×C4×Q8C2×D311yescharacteristic
158C3×C4×Q8C2×D311yescharacteristic
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161C2×#216—31no—
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—61no—
166#935—61no—
167#926—31no—
168C2×C4⋊Dic3—31no—
169#924—31no—
170#924—31no—
171C2×#208—31no—
172C22×C3⋊C8—31no—
173C2×Dic12—31no—
174C2×Dic12—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×D3×C8—31no—
177#898—61no—
178#897—21no—
179#897—21no—
180#897—31no—
181#897—31no—
182#897C2×D311yescharacteristic
183#897C2×D311yescharacteristic
184#894—61no—
185#892—31no—
186#892—61no—
187D3×C4⋊C4—31no—
188#890—61no—
189#889—61no—
190#879—61no—
191#877—61no—
192C4×D12—21no—
193C4×D12C2×D311yescharacteristic
194#870C2×D311yescharacteristic
195#869—21no—
196#869C2×D311yescharacteristic
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—61no—
200C3×#107—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#835C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220#816—31no—
221#816—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#808—31no—
230#808—31no—
231#808—61no—
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
240C32×Q8—21no—
241C32×Q8#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—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×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269C3×Dic6—42no—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—91no—
276D4×Q8—31no—
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—21no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—62no—
297C2×C3×Q8—121no—
298C2×C3×Q8—121no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×Dic3—61no—
307D3×Q8—22no—
308D3×Q8—22no—
309D3×Q8—41no—
310D3×Q8—41no—
311C2×D12#6711yescharacteristic
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—21no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—61no—
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—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—41no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C22⋊C4—31no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—41no—
349C3×C42C22×D311yescharacteristic
350C3×C42C22×D311yescharacteristic
351#217—61no—
352#217—61no—
353#217—61no—
354#216—64no—
355#216—62no—
356#216—62no—
357#216—121no—
358#216—121no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4#6711yescharacteristic
365(C2×D3)⋊C4#6711yescharacteristic
366C4⋊Dic3—21no—
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3#6711yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387C4×Dic3—61no—
388C4×Dic3—61no—
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—121no—
403Dic12—121no—
404ΓL(1,𝔽25)—121no—
405D3×C8—121no—
406C22×C32C22×D411yescharacteristic
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#13712yes—
413C32×C4—22no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4H(5,𝔽2)11yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×Q8—31no—
428C22×Q8—31no—
429C2×Q16—91no—
430C2×Q16—91no—
431C2×Q16—91no—
432C2×M16—91no—
433C22×C8—91no—
434C4⋊Q8—31no—
435C4⋊Q8—61no—
436#126—181no—
437#125—31no—
438#125—181no—
439#123—181no—
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442C22⋊Q8—61no—
443C22⋊Q8—61no—
444C22⋊Q8—91no—
445C22⋊Q8—91no—
446C4×Q8—91no—
447C4×Q8D3211yescharacteristic
448C4×D4—31no—
449C4×D4—61no—
450#117—91no—
451#117—181no—
452C2×C4⋊C4—91no—
453#107—31no—
454#106—31no—
455#106—91no—
456C4⋊C8—31no—
457#103—31no—
458#103—31no—
459#103—91no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469#97—91no—
470C23×C3—31no—
471C23×C3—31no—
472C22×D3C2×#6711yescharacteristic
473C22×D3C2×#6711yescharacteristic
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—22no—
477C3×Q8—41no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—122no—
483C3×Q8—122no—
484C3×Q8#23712yes—
485C3×Q8#23912yes—
486C3×D4—62no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—122no—
507C2×C3×C4—122no—
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4C2×#6711yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—122no—
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527D12—22no—
528C4×D3—21no—
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—42no—
533C4×D3—42no—
534C4×D3—122no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6—21no—
539Dic6—42no—
540Dic6—42no—
541Dic6—62no—
542Dic6—61no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—121no—
547C3×C8—61no—
548C3×C8—61no—
549C3⋊C8—21no—
550C3⋊C8—21no—
551C3⋊C8—62no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—121no—
557C2×C32#54611yescharacteristic
558C2×C32C2×#13711yescharacteristic
559C2×C32#57811yescharacteristic
560C3×D3—22no—
561C3×D3—41no—
562C2×Q8—31no—
563C2×Q8—31no—
564C2×Q8—61no—
565C2×Q8—61no—
566C2×Q8—62no—
567C2×Q8—62no—
568C2×Q8—91no—
569C2×Q8—121no—
570C2×Q8—121no—
571C2×Q8C2×D3211yescharacteristic
572C2×D4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—181no—
578Q16—182no—
579Q16—361no—
580Q16—361no—
581M16—361no—
582C2×C8—31no—
583C2×C8—31no—
584C2×C8—91no—
585C2×C8—91no—
586C2×C8—361no—
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—61no—
597C4⋊C4—91no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—21no—
611C42—181no—
612C42—181no—
613C42C2×D3211yescharacteristic
614C22×C3—21no—
615C22×C3—32no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C22×#6711yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—21no—
628C2×D3#94212yes—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—22no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—22no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—42no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—81no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4C2×#23711yescharacteristic
650C3×C4#100411yescharacteristic
651C3×C4C2×#23911yescharacteristic
652C3×C4#100911yescharacteristic
653Dic3—21no—
654Dic3—21no—
655Dic3—41no—
656Dic3—41no—
657Dic3—41no—
658Dic3—41no—
659Dic3—122no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—241no—
665C32#331211yescharacteristic, complemented, Sylow
666C23—31no—
667C23—31no—
668Q8—21no—
669Q8—61no—
670Q8—61no—
671Q8—61no—
672Q8—61no—
673Q8—122no—
674Q8—122no—
675Q8—181no—
676Q8—181no—
677Q8#379612yes—
678D4—62no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—122no—
692C2×C4—122no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—362no—
696C2×C4D3×#6711yescharacteristic
697C2×C4D3×#6711yescharacteristic
698C2×C4C22×D3211yescharacteristic
699C8—61no—
700C8—61no—
701C8—181no—
702C8—181no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—62no—
707C2×C3—121no—
708C2×C3#563011yescharacteristic
709C2×C3#577111yescharacteristic
710C2×C3D3×#13711yescharacteristic
711C2×C3#580611yescharacteristic
712C2×C3C2×#94211yescharacteristic
713C2×C3#583811yescharacteristic
714D3—22no—
715D3—41no—
716C22—32no—
717C22—61no—
718C22—61no—
719C22—61no—
720C22—61no—
721C22—61no—
722C22C2×D3×#6711yescharacteristic
723C4—22no—
724C4—21no—
725C4—21no—
726C4—41no—
727C4—61no—
728C4—61no—
729C4—121no—
730C4—121no—
731C4—121no—
732C4—121no—
733C4—361no—
734C4—361no—
735C4C2×#379611yescharacteristic
736C4#6430711yescharacteristic
737C3—21no—
738C3#8124811yescharacteristic, complemented
739C3#8355211yescharacteristic, complemented
740C2—62no—
741C2—121no—
742C2#1059488911yescharacteristic
743C2D3×#94211yescharacteristic
744C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4×Q8D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10592729C2semidirect
4. C3×#5022C2semidirect
5. #10591595C2semidirect
6. #10591595C2semidirect
7. #10591557C2semidirect
8. D3×#835C2semidirect
9. #10590587C2semidirect
10. #10590579C2semidirect
11. #10590448C2semidirect
12. #10590439C2semidirect
13. #10590388C2semidirect
15. #10590291C2semidirect
80. #5022D3semidirect
665. C32#3312semidirect
738. C3#81248semidirect
739. C3#83552semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
#105939202
#105927292
C3×#50222
#105915952
#105915572
D3×#8352
#105905872
#105905792
#105904482
#105904392
#105903882
#105903302
#105902912
#835523
#812483