Finite Group Databasebeta

← #11867793

Subgroups — #11867793

Order 1152.

1004 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5628C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic, complemented
3#10594894C211yesmaximal, characteristic
4C2×#63814C211yesmaximal, characteristic, complemented
5#10592748C211yesmaximal, characteristic, complemented
6C3×#5051C211yesmaximal, characteristic, complemented
7#10591638C211yesmaximal, characteristic, complemented
8#10591585C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10591189C211yesmaximal, characteristic, complemented
11#10591177C211yesmaximal, characteristic, complemented
12#10590610C211yesmaximal, characteristic, complemented
13#10590585C211yesmaximal, characteristic, complemented
14#10590518C211yesmaximal, characteristic, complemented
15#10590436C211yesmaximal, characteristic, complemented
16#83400—31nomaximal
17#80762—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23#64139C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#924C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#894—21no—
32C3×#892C2211yescharacteristic
33C3×#888—21no—
34C3×#885—21no—
35C3×#883—21no—
36#63971—21no—
37#63958—21no—
38#63948—24no—
39#63909C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41#63888—21no—
42#63886—21no—
43#63856C2211yescharacteristic
44C2×#3718C2211yescharacteristic
45C2×#3717C2211yescharacteristic
46C2×#3711C2211yescharacteristic
47C2×#3711C2211yescharacteristic
48#63814—24no—
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic
52#63636C2211yescharacteristic
53#63634C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#807C2211yescharacteristic
57#63574C2211yescharacteristic
58#63573C2211yescharacteristic
59#63566C2211yescharacteristic
60#63565C2211yescharacteristic
61#63565C2211yescharacteristic
62#63564C2211yescharacteristic
63C3×#536—31no—
64#5833—31no—
65C2×#948—31no—
66C2×#942—31no—
67C2×#918—31no—
68C2×#901—31no—
69#5629—31no—
70#5628D311yescharacteristic, complemented
71C3×#467—31no—
72C2×#835—31no—
73#5189—31no—
74#5114—31no—
75#5052—31no—
76#5052—31no—
77#5052—31no—
78#5051—31no—
79#5051D311yescharacteristic, complemented
80#5049—31no—
81#5049—31no—
82#5049—31no—
83#5049—61no—
84#5048—31no—
85#5048—31no—
86#5002—31no—
87#4995—31no—
88#4886—31no—
89#4881—31no—
90#4813—31no—
91#4807—31no—
92#4804—31no—
93D3×#103—31no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C2×C3×#67D411yescharacteristic
100C3×D3×Q8—22no—
101C3×D3×Q8—22no—
102C3×#235—22no—
103C3×#235—22no—
104C2×C3×D12D411yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6D411yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#624—21no—
115C2×D3×Dic3—21no—
116#3799—22no—
117#3799—22no—
118C32×C4⋊C4—21no—
119C32×C4⋊C4C2311yescharacteristic
120C32×C22⋊C4—21no—
121#3755—22no—
122#3752—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3748—22no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217—21no—
128C3×#217—21no—
129C3×#216—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C2×C3×C3⋊C8—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3724—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147#3718—22no—
148#3717—22no—
149#3711—22no—
150#3711D414yescomplemented
151D3×C3⋊C8—22no—
152D3×C3⋊C8—22no—
153#3063—91noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C2×#239—31no—
157C2×D3×Q8C2×D311yescharacteristic
158C2×#235—31no—
159C2×#235C2×D311yescharacteristic
160C2×C3×Q16—31no—
161C22×C3×C8—31no—
162C3×C4⋊Q8—61no—
163C3×#124—61no—
164C3×#123—61no—
165C3×#123—61no—
166C3×C22⋊Q8—21no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C2×D311yescharacteristic
173C3×#117—31no—
174#948—64no—
175#946—31no—
176#946—61no—
177#946C2×D311yescharacteristic
178C2×#216—31no—
179C2×#216—31no—
180C2×#216C2×D311yescharacteristic
181#942—64no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—61no—
186#939—61no—
187#939—61no—
188#938—61no—
189#930—31no—
190#930—31no—
191#930—31no—
192#930—61no—
193C2×C4⋊Dic3—31no—
194#924—31no—
195#924C2×D311yescharacteristic
196#924C2×D311yescharacteristic
197C2×#208—31no—
198C2×#208—31no—
199C2×#208—31no—
200C2×#208—31no—
201C2×#208—61no—
202C22×C3⋊C8—31no—
203C22×C3⋊C8—31no—
204C22×C3⋊C8C2×D311yescharacteristic
205#918—64no—
206C2×#204—31no—
207#901—64no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211C2×D3×C8—31no—
212#897C2×D311yescharacteristic
213#896—61no—
214#895—31no—
215#895—61no—
216#894—21no—
217#892C2×D311yescharacteristic
218D3×C4⋊C4—31no—
219#888—21no—
220#885—21no—
221#884—61no—
222#884—61no—
223#883—21no—
224C3×#107—31no—
225C3×#103—31no—
226C3×#103—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#835C2×D311yescharacteristic
234#821—31no—
235#817—31no—
236#816—31no—
237#810—31no—
238#810—31no—
239#810C2×D311yescharacteristic
240#809—31no—
241#809—31no—
242#809—31no—
243#809—61no—
244#808—31no—
245#808—31no—
246#808—31no—
247#807—31no—
248#807—31no—
249#807—61no—
250#807C2×D311yescharacteristic
251C23×C32C2×D411yescharacteristic
252C22×C3⋊D3—21no—
253C22×C3×D3C2×D411yescharacteristic
254C22×C3×D3C2×D411yescharacteristic
255C32×Q8—21no—
256C32×Q8—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263#638—81no—
264C2×C3⋊Dic3—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267C3×#67—22no—
268C3×#67—22no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—22no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—42no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—22no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—42no—
287#626—42no—
288#626—81no—
289#624—42no—
290D3×Dic3—81no—
291C3⋊(C3⋊C8)—21no—
292C3⋊(C3⋊C8)C2×D412yes—
293C3×C3⋊C8—21no—
294C3×C3⋊C8C2×D412yes—
295C2×#137—91no—
296C2×#131—91no—
297#537—91no—
298#536—31no—
299#470—91no—
300#470—91no—
301#468—91no—
302#468—91no—
303#467—31no—
304#467—91no—
305#465—91no—
306#465—91no—
307#428—91no—
308#416—91no—
309C2×#103—91no—
310C3×#41—62no—
311C3×#41—62no—
312C2×C3×Q8—21no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8—62no—
318C2×C3×Q8—62no—
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—61no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—121no—
335C2×#67#6711yescharacteristic
336C2×#67#6711yescharacteristic
337C22×Dic3—61no—
338#239—62no—
339#239—62no—
340D3×Q8—22no—
341D3×Q8—22no—
342#235—22no—
343#235—22no—
344#235—62no—
345#235—62no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12#6711yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6—21no—
359C2×Dic6#6711yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C2×Dic6C22×D311yescharacteristic
362C3×Q16—62no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—62no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—41no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—41no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C42—61no—
387#217—21no—
388#217—21no—
389#217—61no—
390#216—22no—
391#216—62no—
392#216—62no—
393#215—62no—
394#215—62no—
395#215—62no—
396#215—122no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—121no—
406C4⋊Dic3—21no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3C22×D311yescharacteristic
412C4⋊Dic3C22×D311yescharacteristic
413Dic3⋊C4—21no—
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419C4×Dic3—21no—
420#208—34no—
421#208—62no—
422#208—62no—
423#208—62no—
424#208—122no—
425C2×C3⋊C8—22no—
426C2×C3⋊C8—31no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—61no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8—62no—
433C2×C3⋊C8—62no—
434C2×C3⋊C8C22×D311yescharacteristic
435C2×C3⋊C8C22×D311yescharacteristic
436#204—62no—
437ΓL(1,𝔽25)—34no—
438ΓL(1,𝔽25)—62no—
439D3×C8—62no—
440D3×C8—62no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32C22×D411yescharacteristic
445C2×C3⋊D3—41no—
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3#12112yes—
454C32×C4—21no—
455C32×C4—41no—
456C32×C4—41no—
457C32×C4C22×D411yescharacteristic
458C32×C4C2×#4111yescharacteristic
459C3⋊Dic3—41no—
460C3×Dic3—21no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C2×#41—31no—
467C2×#41—91no—
468C22×Q8—31no—
469#137—184no—
470C2×Q16—31no—
471C2×Q16—91no—
472C2×SD16—91no—
473C2×SD16—91no—
474#131—184no—
475C2×M16—91no—
476C2×M16—91no—
477C2×M16—91no—
478C22×C8—31no—
479C22×C8—91no—
480C22×C8—91no—
481C4⋊Q8—61no—
482#124—61no—
483#123—61no—
484#123—61no—
485C22⋊Q8—31no—
486C22⋊Q8—31no—
487C22⋊Q8—31no—
488C22⋊Q8—31no—
489C22⋊Q8—91no—
490C22⋊Q8—181no—
491C22⋊Q8D3211yescharacteristic
492#121—91no—
493#121—91no—
494#121—181no—
495#121—181no—
496#121—181no—
497#117—31no—
498C2×C4⋊C4—91no—
499#107—31no—
500#107—91no—
501#106—91no—
502#106—91no—
503#103—31no—
504#103—31no—
505#103—91no—
506#103—91no—
507#103—91no—
508#103—91no—
509#102—91no—
510#102—91no—
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—31no—
514C23×C3D3×D411yescharacteristic
515C23×C3C2×#6711yescharacteristic
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—121no—
519C22×D3C2×#6711yescharacteristic
520C22×D3C2×#6711yescharacteristic
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—41no—
526C3×Q8—41no—
527C3×Q8—62no—
528C3×Q8—61no—
529C3×Q8—61no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—122no—
533C3×D4—62no—
534C3×D4—62no—
535C3×D4—62no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—31no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—122no—
561C2×C3×C4D3×D411yescharacteristic
562C2×C3×C4C2×#6711yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565#67—22no—
566#67—22no—
567#67—122no—
568#67—241no—
569#67—241no—
570#67—241no—
571#67—242no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—121no—
579C2×Dic3—241no—
580C2×Dic3C2×#6711yescharacteristic
581C2×Dic3C2×#6711yescharacteristic
582D12—22no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—121no—
588D12—121no—
589D12—122no—
590D12—241no—
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—42no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3—241no—
597C4×D3D3×D412yes—
598C4×D3#23712yes—
599Dic6—22no—
600Dic6—21no—
601Dic6—21no—
602Dic6—21no—
603Dic6—21no—
604Dic6—42no—
605C3×C8—32no—
606C3×C8—61no—
607C3⋊C8—21no—
608C3⋊C8—32no—
609C3⋊C8—32no—
610C3⋊C8—62no—
611C3⋊C8—61no—
612C3⋊C8—61no—
613C3⋊C8—121no—
614C3⋊C8D3×D412yes—
615C2×C32—41no—
616C2×C32C2×#12111yescharacteristic
617C2×C32#57711yescharacteristic
618C2×C32#57811yescharacteristic
619C3⋊D3—81no—
620C3×D3—22no—
621C3×D3—41no—
622#41—62no—
623#41—62no—
624#41—182no—
625#41—182no—
626C2×Q8—31no—
627C2×Q8—31no—
628C2×Q8—31no—
629C2×Q8—61no—
630C2×Q8—62no—
631C2×Q8—62no—
632C2×Q8C2×D3211yescharacteristic
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—91no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4—181no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—61no—
643C22×C4—181no—
644C22×C4—181no—
645C22×C4C2×D3211yescharacteristic
646Q16—62no—
647Q16—182no—
648SD16—182no—
649SD16—182no—
650M16—94no—
651M16—182no—
652M16—182no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—62no—
656C2×C8—91no—
657C2×C8—91no—
658C2×C8—182no—
659C2×C8—182no—
660C4⋊C4—21no—
661C4⋊C4—31no—
662C4⋊C4—31no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—91no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4C2×D3211yescharacteristic
671C22⋊C4—21no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C42—61no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—32no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3C2×D3×D411yescharacteristic
698C22×C3C22×#6711yescharacteristic
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3#93912yes—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—32no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—61no—
725C3×C4—81no—
726C3×C4—81no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4C2×D3×D411yescharacteristic
732C3×C4C2×D3×D411yescharacteristic
733C3×C4C2×#23711yescharacteristic
734C3×C4D3×#4111yescharacteristic
735Dic3—21no—
736Dic3—41no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—121no—
741Dic3—121no—
742Dic3—241no—
743Dic3#93912yes—
744C32#306311yescharacteristic, complemented, Sylow
745C23—31no—
746C23—31no—
747C23—181no—
748C23D3×#6711yescharacteristic
749Q8—21no—
750Q8—21no—
751Q8—62no—
752Q8—61no—
753Q8—61no—
754Q8—61no—
755Q8—61no—
756Q8—122no—
757D4—62no—
758D4—62no—
759D4—62no—
760D4—181no—
761D4—181no—
762D4—362no—
763D4—721no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—31no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—31no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—122no—
780C2×C4—181no—
781C2×C4—362no—
782C2×C4—721no—
783C2×C4D3×#6711yescharacteristic
784C2×C4C22×D3211yescharacteristic
785C8—32no—
786C8—61no—
787C8—92no—
788C8—181no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—62no—
795C2×C3—81no—
796C2×C3—121no—
797C2×C3D3×#12111yescharacteristic
798C2×C3#576611yescharacteristic
799C2×C3#577011yescharacteristic
800C2×C3C2×#93911yescharacteristic
801C2×C3#583711yescharacteristic
802C2×C3#583811yescharacteristic
803D3—22no—
804D3—41no—
805D3—241no—
806D3—241no—
807D3—481no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—32no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—361no—
818C22—361no—
819C22—361no—
820C22C2×D3×#6711yescharacteristic
821C4—21no—
822C4—32no—
823C4—41no—
824C4—41no—
825C4—61no—
826C4—121no—
827C4—121no—
828C4—121no—
829C4—121no—
830C4—361no—
831C4D32×D411yescharacteristic
832C4D3×#23711yescharacteristic
833C3—21no—
834C3#8076211yescharacteristic, complemented
835C3#8340011yescharacteristic, complemented
836C2—41no—
837C2—62no—
838C2—121no—
839C2—721no—
840C2D3×#93911yescharacteristic
841C2#1059532711yescharacteristic
842C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10594894C2
hypercenterC22⋊Q8D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5628C2semidirect
2. C2×#63948C2semidirect
4. C2×#63814C2semidirect
5. #10592748C2semidirect
6. C3×#5051C2semidirect
7. #10591638C2semidirect
8. #10591585C2semidirect
9. D3×#835C2semidirect
10. #10591189C2semidirect
11. #10591177C2semidirect
12. #10590610C2semidirect
13. #10590585C2semidirect
14. #10590518C2semidirect
15. #10590436C2semidirect
70. #5628D3semidirect
79. #5051D3semidirect
150. #3711D4semidirect
744. C32#3063semidirect
834. C3#80762semidirect
835. C3#83400semidirect

Maximal subgroups

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

subgroupindex
C3×#56282
C2×#639482
#105948942
C2×#638142
#105927482
C3×#50512
#105916382
#105915852
D3×#8352
#105911892
#105911772
#105906102
#105905852
#105905182
#105904362
#834003
#807623