Finite Group Databasebeta

← #11878369

Subgroups — #11878369

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5628C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic
3#10592748C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6#10591594C211yesmaximal, characteristic, complemented
7#10591584C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10591189C211yesmaximal, characteristic, complemented
10#10591177C211yesmaximal, characteristic, complemented
11#10591070C211yesmaximal, characteristic, complemented
12#10590616C211yesmaximal, characteristic, complemented
13#10590521C211yesmaximal, characteristic, complemented
14#10590440C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#83408—31nomaximal
17#80766—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#63909C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63888—21no—
41#63886—21no—
42#63856C2211yescharacteristic
43C2×#3718C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45#63662C2211yescharacteristic
46#63636C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53#63566C2211yescharacteristic
54#63565C2211yescharacteristic
55#63565C2211yescharacteristic
56#63564C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#536—31no—
62#5833—31no—
63#5629—31no—
64#5628D311yescharacteristic, complemented
65C3×#467—31no—
66#5234—31no—
67#5228—31no—
68#5227—31no—
69#5187—31no—
70#5186—31no—
71#5114—31no—
72#5110—31no—
73#5052—31no—
74#5052—31no—
75#5051D311yescharacteristic, complemented
76#5049—31no—
77#5049—31no—
78#5049—61no—
79#5048—31no—
80#5047—31no—
81#5047—31no—
82#5044—31no—
83#5043—31no—
84#5003—31no—
85#4996—31no—
86#4885—31no—
87#4884—31no—
88#4815—31no—
89#4808—31no—
90#4806—31no—
91#4805—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C2×C3×#67D411yescharacteristic
98C3×D3×Q8—41no—
99C3×D3×Q8—41no—
100C3×#235—41no—
101C3×#235—41no—
102C2×C3×D12D411yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6D411yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113C2×D3×Dic3—21no—
114#3799—41no—
115#3799—41no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119#3755—41no—
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3748—41no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#217—21no—
127C3×#216—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3—21no—
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3724—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145#3718—41no—
146#3717—41no—
147#3201—91noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—31no—
150C2×#239—31no—
151C2×D3×Q8C2×D311yescharacteristic
152C2×#235—31no—
153C2×#235C2×D311yescharacteristic
154C2×C3×Q16—31no—
155C22×C3×C8—31no—
156C3×C4⋊Q8—61no—
157C3×#124—61no—
158C3×#123—61no—
159C3×#123—61no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8C2×D311yescharacteristic
166C3×C22⋊Q8C2×D311yescharacteristic
167C3×#117—31no—
168#946—31no—
169#946—61no—
170#946C2×D311yescharacteristic
171C2×#216—31no—
172C2×#216—31no—
173C2×#216C2×D311yescharacteristic
174C2×#215—31no—
175C2×#215—31no—
176C2×#215—31no—
177C2×#215—61no—
178#939—61no—
179#939—61no—
180#938—61no—
181#930—31no—
182#930—31no—
183#930—31no—
184#930—61no—
185C2×C4⋊Dic3—31no—
186#924—31no—
187#924C2×D311yescharacteristic
188#924C2×D311yescharacteristic
189C2×#208—31no—
190C2×#208—31no—
191C2×#208—61no—
192C22×C3⋊C8C2×D311yescharacteristic
193C2×#204—31no—
194#897C2×D311yescharacteristic
195#896—61no—
196#895—31no—
197#895—61no—
198#894—21no—
199#892C2×D311yescharacteristic
200D3×C4⋊C4—31no—
201#888—21no—
202#885—21no—
203#884—61no—
204#884—61no—
205#883—21no—
206C3×#107—31no—
207C3×#103—31no—
208C3×#103—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218#830—31no—
219#830—31no—
220#821—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#817—31no—
226#816—31no—
227#810—31no—
228#810—31no—
229#810C2×D311yescharacteristic
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#808—31no—
235#808—31no—
236#808—31no—
237#807—31no—
238#807—31no—
239#807—61no—
240#807C2×D311yescharacteristic
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253#638—81no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C3×#67—41no—
258C3×#67—41no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—41no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—41no—
276C3×Dic6—42no—
277#626—42no—
278#626—81no—
279#624—42no—
280D3×Dic3—81no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#537—91no—
286#536—31no—
287#485—91no—
288#484—91no—
289#483—91no—
290#482—91no—
291#470—91no—
292#468—91no—
293#467—31no—
294#465—91no—
295#452—91no—
296#452—91no—
297#451—91no—
298#448—91no—
299#408—91no—
300C3×#41—121no—
301C3×#41—121no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8—31no—
305C2×C3×Q8—31no—
306C2×C3×Q8—61no—
307C2×C3×Q8—121no—
308C2×C3×Q8—121no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—121no—
325C2×#67#6711yescharacteristic
326C2×#67#6711yescharacteristic
327C22×Dic3—61no—
328#239—121no—
329#239—121no—
330D3×Q8—41no—
331D3×Q8—41no—
332#235—41no—
333#235—41no—
334#235—121no—
335#235—121no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12#6711yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3C22×D311yescharacteristic
347C2×C4×D3C22×D311yescharacteristic
348C2×Dic6—21no—
349C2×Dic6#6711yescharacteristic
350C2×Dic6C22×D311yescharacteristic
351C2×Dic6C22×D311yescharacteristic
352C3×Q16—121no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—121no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—41no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—41no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C42—61no—
377#217—21no—
378#217—21no—
379#217—61no—
380#216—41no—
381#216—121no—
382#216—121no—
383#215—121no—
384#215—121no—
385#215—121no—
386#215—122no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—121no—
396C4⋊Dic3—21no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3C22×D311yescharacteristic
402C4⋊Dic3C22×D311yescharacteristic
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409C4×Dic3—21no—
410#208—121no—
411#208—121no—
412#208—122no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—41no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422#204—121no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32C22×D411yescharacteristic
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C32×C4—21no—
437C32×C4—41no—
438C32×C4—41no—
439C32×C4H(5,𝔽2)11yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—41no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C2×#41—31no—
449C2×#41—91no—
450C22×Q8—31no—
451C2×Q16—31no—
452C2×Q16—91no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×M16—91no—
456C22×C8—31no—
457C4⋊Q8—61no—
458#124—61no—
459#123—61no—
460#123—61no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465C22⋊Q8—91no—
466C22⋊Q8—181no—
467C22⋊Q8D3211yescharacteristic
468#121—91no—
469#121—91no—
470#121—181no—
471#121—181no—
472#121—181no—
473#117—31no—
474C2×C4⋊C4—91no—
475#107—31no—
476#107—91no—
477#106—91no—
478#106—91no—
479#103—31no—
480#103—31no—
481#103—91no—
482#103—91no—
483#103—91no—
484#103—91no—
485#102—91no—
486#102—91no—
487C22⋊C8—91no—
488C22⋊C8—91no—
489C22⋊C8—91no—
490C22⋊C8—91no—
491C23×C3—21no—
492C23×C3—31no—
493C23×C3—31no—
494C23×C3D3×D411yescharacteristic
495C23×C3C2×#6711yescharacteristic
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—121no—
499C22×D3C2×#6711yescharacteristic
500C22×D3C2×#6711yescharacteristic
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—41no—
506C3×Q8—41no—
507C3×Q8—61no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×Q8—61no—
511C3×Q8—121no—
512C3×Q8—122no—
513C3×D4—121no—
514C3×D4—121no—
515C3×D4—121no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—122no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—41no—
546#67—41no—
547#67—122no—
548#67—241no—
549#67—241no—
550#67—241no—
551#67—242no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—121no—
559C2×Dic3—241no—
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562D12—41no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—121no—
568D12—121no—
569D12—122no—
570D12—241no—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—42no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—241no—
579Dic6—21no—
580Dic6—21no—
581Dic6—21no—
582Dic6—21no—
583Dic6—41no—
584Dic6—42no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—62no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—121no—
595C2×C32—41no—
596C2×C32#53411yescharacteristic
597C2×C32#57711yescharacteristic
598C2×C32#57811yescharacteristic
599C3⋊D3—81no—
600C3×D3—41no—
601C3×D3—41no—
602#41—121no—
603#41—121no—
604#41—361no—
605#41—361no—
606C2×Q8—31no—
607C2×Q8—31no—
608C2×Q8—31no—
609C2×Q8—61no—
610C2×Q8—121no—
611C2×Q8—121no—
612C2×Q8C2×D3211yescharacteristic
613C2×D4—31no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—91no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—181no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—61no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4C2×D3211yescharacteristic
626Q16—121no—
627Q16—361no—
628SD16—361no—
629SD16—361no—
630M16—361no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8—91no—
634C2×C8—91no—
635C2×C8—121no—
636C4⋊C4—21no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—91no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C4⋊C4C2×D3211yescharacteristic
647C22⋊C4—21no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C42—61no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3C2×D3×D411yescharacteristic
674C22×C3C22×#6711yescharacteristic
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—241no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—61no—
700C3×C4—61no—
701C3×C4—81no—
702C3×C4—81no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4—121no—
707C3×C4#100411yescharacteristic
708C3×C4#100411yescharacteristic
709C3×C4#100411yescharacteristic
710C3×C4#100911yescharacteristic
711Dic3—21no—
712Dic3—21no—
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716Dic3—41no—
717Dic3—121no—
718Dic3—121no—
719Dic3—241no—
720C32#320111yescharacteristic, complemented, Sylow
721C23—31no—
722C23—31no—
723C23—181no—
724C23D3×#6711yescharacteristic
725Q8—21no—
726Q8—21no—
727Q8—61no—
728Q8—61no—
729Q8—61no—
730Q8—61no—
731Q8—121no—
732Q8—122no—
733D4—121no—
734D4—121no—
735D4—121no—
736D4—181no—
737D4—181no—
738D4—362no—
739D4—721no—
740D4—721no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—122no—
756C2×C4—181no—
757C2×C4—362no—
758C2×C4—721no—
759C2×C4D3×#6711yescharacteristic
760C2×C4C22×D3211yescharacteristic
761C8—61no—
762C8—61no—
763C8—181no—
764C8—181no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—41no—
769C2×C3—41no—
770C2×C3—81no—
771C2×C3—121no—
772C2×C3—121no—
773C2×C3#560511yescharacteristic
774C2×C3#576611yescharacteristic
775C2×C3#577011yescharacteristic
776C2×C3#580411yescharacteristic
777C2×C3#583711yescharacteristic
778C2×C3#583811yescharacteristic
779D3—41no—
780D3—41no—
781D3—241no—
782D3—241no—
783D3—481no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—61no—
792C22—61no—
793C22—361no—
794C22—361no—
795C22—361no—
796C22C2×D3×#6711yescharacteristic
797C4—21no—
798C4—41no—
799C4—41no—
800C4—61no—
801C4—61no—
802C4—121no—
803C4—121no—
804C4—121no—
805C4—121no—
806C4—361no—
807C4#6431311yescharacteristic
808C4#6431411yescharacteristic
809C3—21no—
810C3#8076611yescharacteristic, complemented
811C3#8340811yescharacteristic, complemented
812C2—41no—
813C2—121no—
814C2—121no—
815C2—721no—
816C2#1059530211yescharacteristic
817C2#1059532711yescharacteristic
818C2#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#3201
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
3. #10592748C2semidirect
4. C3×#5051C2semidirect
5. #10591657C2semidirect
6. #10591594C2semidirect
7. #10591584C2semidirect
8. #10591549C2semidirect
9. #10591189C2semidirect
10. #10591177C2semidirect
11. #10591070C2semidirect
12. #10590616C2semidirect
13. #10590521C2semidirect
14. #10590440C2semidirect
15. #10590424C2semidirect
64. #5628D3semidirect
75. #5051D3semidirect
720. C32#3201semidirect
810. C3#80766semidirect
811. C3#83408semidirect

Maximal subgroups

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

subgroupindex
C3×#56282
#105948942
#105927482
C3×#50512
#105916572
#105915942
#105915842
#105915492
#105911892
#105911772
#105910702
#105906162
#105905212
#105904402
#105904242
#834083
#807663