Finite Group Databasebeta

← #11889439

Subgroups — #11889439

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 749 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5581C211yesmaximal, characteristic
2Dic6×D12C211yesmaximal, characteristic
3#10592730C211yesmaximal, characteristic, complemented
4C3×#5030C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591598C211yesmaximal, characteristic, complemented
8#10591596C211yesmaximal, characteristic, complemented
9#10590600C211yesmaximal, characteristic, complemented
10D3×#810C211yesmaximal, characteristic, complemented
11#10590428C211yesmaximal, characteristic, complemented
12#10590426C211yesmaximal, characteristic, complemented
13#10590326C211yesmaximal, characteristic
14#10590295C211yesmaximal, characteristic, complemented
15#10590286C211yesmaximal, characteristic, complemented
16#83603—31nomaximal
17#79841—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23#64078C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#894—21no—
28C3×#892C2211yescharacteristic
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×#889—21no—
31C3×#876—21no—
32C3×C4×D12C2211yescharacteristic
33C3×#872—21no—
34C3×#870C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic
36#63918—21no—
37#63893—21no—
38#63893—21no—
39Dic3×D12—21no—
40#63857C2211yescharacteristic
41#63857C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#803C2211yescharacteristic
51#63576C2211yescharacteristic
52#63574C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#552—31no—
62#5581D311yescharacteristic
63Q8×D12—31no—
64D4×Dic6—31no—
65C3×#441—31no—
66#5186—31no—
67#5186—31no—
68#5069—31no—
69#5063—31no—
70#5052—31no—
71#5051—31no—
72#5050—31no—
73#5050—31no—
74#5031—31no—
75#5031—31no—
76#5031—61no—
77#5030D311yescharacteristic, complemented
78#5022—31no—
79#5011—31no—
80#5004—31no—
81#4996—31no—
82#4971—31no—
83C2×#810—31no—
84#4868—31no—
85#4862—31no—
86#4816—31no—
87#4813—31no—
88#4802—31no—
89D3×#103—31no—
90#4706—31no—
91#4703—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12D411yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
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⋊C4C2311yescharacteristic
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112#3756—41no—
113#3756—41no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#216—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C2×C3×Q16—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—21no—
157C3×C4×Q8—31no—
158C3×C4×Q8C2×D311yescharacteristic
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×D4—31no—
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C4⋊C4—31no—
164#946C2×D311yescharacteristic
165#946C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—61no—
171C2×#216—61no—
172C2×#216C2×D311yescharacteristic
173D4×Dic3—61no—
174#924—31no—
175#924—31no—
176C2×#208—31no—
177C22×C3⋊C8—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8—31no—
180#897—31no—
181#897—31no—
182#897—61no—
183#897—61no—
184#894—21no—
185#892C2×D311yescharacteristic
186D3×C4⋊C4C2×D311yescharacteristic
187#889—21no—
188#888—61no—
189#878—61no—
190#878—61no—
191#876—21no—
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194#872—21no—
195#870C2×D311yescharacteristic
196#869—31no—
197#869—31no—
198#869—61no—
199#869—61no—
200C4×Dic6C2×D311yescharacteristic
201C3×#106—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#97—31no—
205#835—31no—
206#835—31no—
207#835C2×D311yescharacteristic
208#830—31no—
209#830—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#816—31no—
213#816—31no—
214#816—31no—
215#816—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—31no—
225#810—31no—
226#810—61no—
227#810—61no—
228#810C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808C2×D311yescharacteristic
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×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×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
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×D12—22no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
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—91no—
281#470—91no—
282#467—91no—
283#462—91no—
284#451—91no—
285#451—91no—
286#441—31no—
287#435—91no—
288#419—91no—
289C2×#103—91no—
290C2×C3×Q8—21no—
291C2×C3×Q8—31no—
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×D4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300D3×Q8—62no—
301D3×Q8—62no—
302D3×Q8—121no—
303D3×Q8—121no—
304C2×D12#6711yescharacteristic
305C2×C4×D3—21no—
306C2×C4×D3—61no—
307C2×C4×D3—61no—
308C2×C4×D3C22×D311yescharacteristic
309C2×C4×D3C22×D311yescharacteristic
310C2×Dic6—31no—
311C2×Dic6—31no—
312C2×Dic6—31no—
313C2×Dic6—31no—
314C2×Dic6—61no—
315C2×Dic6—61no—
316C2×Dic6—62no—
317C2×Dic6—62no—
318C2×Dic6—61no—
319C2×Dic6—61no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C2×Dic6—121no—
323C2×Dic6—121no—
324C2×Dic6C22×D311yescharacteristic
325C3×Q16—62no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—61no—
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×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—41no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357#217—61no—
358#217—61no—
359#216—22no—
360#216—121no—
361#216—121no—
362#216—121no—
363#216—121no—
364#216—122no—
365#216—122no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4#6711yescharacteristic
372(C2×D3)⋊C4#6711yescharacteristic
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—121no—
380C4⋊Dic3—121no—
381C4⋊Dic3#6711yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395#208—121no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405ΓL(1,𝔽25)—121no—
406D3×C8—121no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3#13712yes—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×Q8—91no—
429C22×Q8—91no—
430C2×Q16—31no—
431C2×Q16—91no—
432C2×Q16—91no—
433C2×M16—91no—
434C22×C8—91no—
435C4⋊Q8—91no—
436C4⋊Q8—181no—
437#126—61no—
438#125—31no—
439#125—61no—
440#123—61no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C4×Q8—31no—
448C4×Q8D3211yescharacteristic
449C4×D4—31no—
450C4×D4—181no—
451#117—31no—
452#117—61no—
453C2×C4⋊C4—31no—
454#107—91no—
455#106—31no—
456#106—91no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470#97—31no—
471C23×C3—31no—
472C23×C3—31no—
473C22×D3C2×#6711yescharacteristic
474C22×D3C2×#6711yescharacteristic
475C3×Q8—22no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—32no—
481C3×Q8—41no—
482C3×Q8—61no—
483C3×D4—62no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
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×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4C2×#6711yescharacteristic
507C2×C3×C4C2×#6711yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—122no—
521C2×Dic3—122no—
522C2×Dic3C2×#6711yescharacteristic
523C2×Dic3C2×#6711yescharacteristic
524D12—22no—
525C4×D3—21no—
526C4×D3—21no—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—42no—
530C4×D3—122no—
531C4×D3—122no—
532Dic6—21no—
533Dic6—61no—
534Dic6—61no—
535Dic6—61no—
536Dic6—61no—
537Dic6—61no—
538Dic6—61no—
539Dic6—61no—
540Dic6—61no—
541Dic6—121no—
542Dic6—121no—
543Dic6—121no—
544Dic6—121no—
545Dic6—122no—
546Dic6—122no—
547Dic6—122no—
548Dic6—122no—
549Dic6#23512yes—
550C3×C8—61no—
551C3×C8—61no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—121no—
559C3⋊C8—121no—
560C2×C32#54611yescharacteristic
561C2×C32C2×#13711yescharacteristic
562C2×C32#57811yescharacteristic
563C3×D3—22no—
564C3×D3—41no—
565C2×Q8—31no—
566C2×Q8—91no—
567C2×Q8—91no—
568C2×Q8—181no—
569C2×Q8—181no—
570C2×Q8—182no—
571C2×Q8—182no—
572C2×Q8—361no—
573C2×Q8—361no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—61no—
579C22×C4—181no—
580C22×C4—181no—
581Q16—62no—
582Q16—361no—
583Q16—361no—
584M16—361no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8—91no—
589C2×C8—361no—
590C4⋊C4—21no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—21no—
614C42—61no—
615C42—61no—
616C42C2×D3211yescharacteristic
617C22×C3—21no—
618C22×C3—32no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C22×#6711yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3#95112yes—
632C3×C4—22no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—42no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—62no—
648C3×C4—81no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4C2×#23511yescharacteristic
653C3×C4D3×#4111yescharacteristic
654C3×C4#100911yescharacteristic
655C3×C4#100911yescharacteristic
656Dic3—22no—
657Dic3—21no—
658Dic3—21no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—241no—
667Dic3—241no—
668C32#331211yescharacteristic, complemented, Sylow
669C23—31no—
670C23—31no—
671Q8—21no—
672Q8—21no—
673Q8—32no—
674Q8—61no—
675Q8—181no—
676Q8—181no—
677Q8—181no—
678Q8—181no—
679Q8—362no—
680Q8—362no—
681D4—62no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—122no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—362no—
698C2×C4—362no—
699C2×C4D3×#6711yescharacteristic
700C2×C4D3×#6711yescharacteristic
701C2×C4C22×D3211yescharacteristic
702C8—61no—
703C8—61no—
704C8—181no—
705C8—181no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—62no—
710C2×C3—121no—
711C2×C3#555011yescharacteristic
712C2×C3D3×#13711yescharacteristic
713C2×C3#577911yescharacteristic
714C2×C3C2×#95111yescharacteristic
715C2×C3#582911yescharacteristic
716C2×C3#583811yescharacteristic
717D3—22no—
718D3—41no—
719C22—32no—
720C22—61no—
721C22—61no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22C2×D3×#6711yescharacteristic
726C4—21no—
727C4—21no—
728C4—41no—
729C4—41no—
730C4—61no—
731C4—61no—
732C4—62no—
733C4—121no—
734C4—121no—
735C4—121no—
736C4—361no—
737C4—361no—
738C4D3×#23511yescharacteristic
739C4#6430811yescharacteristic
740C3—21no—
741C3#7984111yescharacteristic, complemented
742C3#8360311yescharacteristic, complemented
743C2—62no—
744C2—121no—
745C2#1059506711yescharacteristic
746C2#1059532811yescharacteristic
747C2D3×#95111yescharacteristic
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. #10592730C2semidirect
4. C3×#5030C2semidirect
5. #10591653C2semidirect
6. #10591653C2semidirect
7. #10591598C2semidirect
8. #10591596C2semidirect
9. #10590600C2semidirect
10. D3×#810C2semidirect
11. #10590428C2semidirect
12. #10590426C2semidirect
14. #10590295C2semidirect
15. #10590286C2semidirect
77. #5030D3semidirect
668. C32#3312semidirect
741. C3#79841semidirect
742. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C3×#55812
Dic6×D122
#105927302
C3×#50302
#105916532
#105915982
#105915962
#105906002
D3×#8102
#105904282
#105904262
#105903262
#105902952
#105902862
#836033
#798413