Finite Group Databasebeta

← #11887167

Subgroups — #11887167

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594621C211yesmaximal, characteristic
2#10594537C211yesmaximal, characteristic, complemented
3#10592563C211yesmaximal, characteristic, complemented
4C3×#4870C211yesmaximal, characteristic, complemented
5C3×#4863C211yesmaximal, characteristic, complemented
6#10590946C211yesmaximal, characteristic, complemented
7#10590940C211yesmaximal, characteristic, complemented
8#10590906C211yesmaximal, characteristic, complemented
9#10590879C211yesmaximal, characteristic, complemented
10#10590597C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590578C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic, complemented
14#10590479C211yesmaximal, characteristic, complemented
15#10590445C211yesmaximal, characteristic, complemented
16#81342—31nomaximal
17#81075—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3744C2211yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23#64106C2211yescharacteristic, complemented
24#64104C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28C3×#888C2211yescharacteristic, complemented
29#63923—21no—
30#63922—21no—
31#63911C2211yescharacteristic
32#63906—21no—
33#63904—21no—
34C4×#626C2211yescharacteristic
35#63900C2211yescharacteristic, complemented
36#63888—21no—
37#63857C2211yescharacteristic, complemented
38#63856—21no—
39#63845—21no—
40#63844C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic, complemented
53C3×#808C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5730—31no—
62#5609—31no—
63D4×D12—31no—
64#5511—31no—
65C3×#481—31no—
66C3×#476—31no—
67#5088—31no—
68#5041—31no—
69C4×#214—31no—
70C2×#809—31no—
71#4870D311yescharacteristic, complemented
72#4864—31no—
73#4864—31no—
74#4864—31no—
75#4864—61no—
76#4863—31no—
77#4863—31no—
78#4863D311yescharacteristic, complemented
79#4852—31no—
80#4848—31no—
81#4834—31no—
82#4776—31no—
83#4776—31no—
84#4776—31no—
85D3×#102—31no—
86D3×#102—31no—
87D3×#102—31no—
88#4762—31no—
89#4760—31no—
90#4731—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626D411yescharacteristic
109C2×#625—21no—
110C2×#624—21no—
111#3802—22no—
112#3802—41no—
113D3×D12—22no—
114D3×D12—41no—
115D3×D12—44no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3752—21no—
120#3752—21no—
121C4⋊(C3⋊Dic3)—21no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3744—41no—
124C8×C3⋊D3—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3716—22no—
143#3716—41no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—61no—
152C3×C4⋊Q8—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155C2×C3×C4⋊C4—31no—
156#946—61no—
157#946—61no—
158#940—31no—
159#937—61no—
160C2×#214—31no—
161C2×#214—31no—
162#930—61no—
163C4×#67—31no—
164C4×#67—61no—
165#924—31no—
166#924—61no—
167C22×C3⋊C8—31no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—31no—
171C2×#204—31no—
172C2×#204—61no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8—61no—
177#897—31no—
178#897—31no—
179#897—31no—
180#897—61no—
181#896—61no—
182#895—31no—
183#895—31no—
184#895—61no—
185#895C2×D311yescharacteristic
186#893—61no—
187#893C2×D311yescharacteristic
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4C2×D311yescharacteristic, complemented
191#890—61no—
192#889—61no—
193#888C2×D311yescharacteristic, complemented
194#887—31no—
195#884—61no—
196#882—61no—
197#882—61no—
198#882—61no—
199#874—31no—
200C4×D12—31no—
201C4×Dic6—31no—
202C3×#106—21no—
203C3×#106—31no—
204C3×#106—31no—
205C3×#106C2×D311yescharacteristic, complemented
206C3×#106C2×D311yescharacteristic, complemented
207C3×C4⋊C8—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×C22⋊C8—31no—
213#832—31no—
214#832—31no—
215#821—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218#821C2×D311yescharacteristic, complemented
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8C2×D311yescharacteristic, complemented
222Dic3⋊C8C2×D311yescharacteristic, complemented
223C8×Dic3—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#809C2×D311yescharacteristic, complemented
236#808C2×D311yescharacteristic, complemented
237#808C2×D311yescharacteristic, complemented
238C4×C3⋊C8—31no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—42no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260#634—21no—
261#634—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—42no—
275C3×C4×D3—81no—
276C3×Dic6—81no—
277#626—42no—
278#626—42no—
279#626—81no—
280#626SD1614yescomplemented
281#625—42no—
282#624—81no—
283C32×C8—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—91no—
289#486—91no—
290#481—31no—
291#481—91no—
292#476—31no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—91no—
301C2×#102—91no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—61no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—62no—
322D3×D4—121no—
323D3×D4—124no—
324D3×D4—121no—
325D3×D4—121no—
326C2×D12—21no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—121no—
338C2×D12—121no—
339C2×D12—124no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3C22×D311yescharacteristic
350C2×Dic6—21no—
351C2×Dic6—31no—
352C2×Dic6—31no—
353C2×Dic6—61no—
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—31no—
372#217—31no—
373#217—61no—
374#214—62no—
375#214—121no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—121no—
387(C2×D3)⋊C4—121no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—121no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—31no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412#204—62no—
413#204—121no—
414#204—121no—
415#204—122no—
416#204—121no—
417D3×C8—121no—
418D3×C8—121no—
419D3×C8—121no—
420D3×C8—122no—
421C22×C32C22×D411yescharacteristic
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3C2×SD1612yes—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—22no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3C2×SD1612yes—
437D32—84no—
438D32—84no—
439C32×C4—41no—
440C32×C4—41no—
441C32×C4C2×#4111yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
443C3⋊Dic3—21no—
444C3⋊Dic3—41no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3C2×SD1612yes—
450C22×D4—91no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C22×C8—91no—
457C22×C8—91no—
458C4⋊Q8—31no—
459#127—91no—
460#125—181no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—181no—
464C22⋊Q8—181no—
465#121—31no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—91no—
471C4×D4—31no—
472C4×D4—91no—
473C4×D4—181no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—91no—
476#106—31no—
477#106—31no—
478#106D3211yescharacteristic, complemented
479C4⋊C8—31no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—31no—
491C22⋊C8—91no—
492C4×C8—91no—
493C23×C3—31no—
494C23×C3—61no—
495C23×C3—61no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—121no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3D3×D411yescharacteristic
517C3×Q8—241no—
518C3×D4—32no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—122no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—122no—
538C2×C3×C4—241no—
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—34no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—122no—
546#67—241no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—121no—
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557C2×Dic3D3×D411yescharacteristic
558D12—21no—
559D12—21no—
560D12—21no—
561D12—34no—
562D12—42no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—121no—
568D12—121no—
569D12—122no—
570D12—122no—
571D12—122no—
572D12—122no—
573D12—242no—
574D12—241no—
575D12#23912yes—
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—42no—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—61no—
583C4×D3—81no—
584C4×D3—121no—
585C4×D3—121no—
586C4×D3—241no—
587C4×D3—241no—
588Dic6—61no—
589Dic6—61no—
590Dic6—61no—
591Dic6—61no—
592Dic6—81no—
593Dic6—121no—
594Dic6—121no—
595C3×C8—22no—
596C3×C8—21no—
597C3×C8—21no—
598C3×C8—61no—
599C3×C8—61no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C3⋊C8—61no—
603C3⋊C8—61no—
604C3⋊C8—121no—
605C2×C32#54611yescharacteristic
606C2×C32C22×SD1611yescharacteristic
607C2×C32#57611yescharacteristic
608C3⋊D3—22no—
609C3⋊D3—81no—
610C3×D3—22no—
611C3×D3—42no—
612C3×D3—81no—
613C24—181no—
614C24—181no—
615C2×Q8—61no—
616C2×Q8—91no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—61no—
620C2×D4—91no—
621C2×D4—91no—
622C2×D4—181no—
623C2×D4—181no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—182no—
627C2×D4—181no—
628C2×D4—182no—
629C2×D4—361no—
630C2×D4—364no—
631C2×D4—361no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—91no—
636C22×C4—181no—
637SD16—182no—
638SD16—361no—
639SD16—361no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8—361no—
644C2×C8—361no—
645C2×C8C2×D3211yescharacteristic
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4C2×D3211yescharacteristic
656C4⋊C4C2×D3211yescharacteristic
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—181no—
666C22×C3—21no—
667C22×C3—32no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—62no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C2×D3×D411yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—22no—
681C2×D3—32no—
682C2×D3—32no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—62no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—241no—
702C2×D3—241no—
703C2×D3—241no—
704C2×D3—244no—
705C2×D3—244no—
706C2×D3—244no—
707C2×D3—244no—
708C2×D3D3×SD1612yes—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—32no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—81no—
719C3×C4—81no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4C2×#23911yescharacteristic
723C3×C4D3×#4111yescharacteristic
724C3×C4#100911yescharacteristic
725C3×C4#100911yescharacteristic
726Dic3—21no—
727Dic3—21no—
728Dic3—41no—
729Dic3—41no—
730Dic3—61no—
731Dic3—61no—
732Dic3—121no—
733Dic3—121no—
734Dic3—121no—
735Dic3—241no—
736Dic3D3×SD1612yes—
737C32#329511yescharacteristic, complemented, Sylow
738C23—31no—
739C23—61no—
740C23—61no—
741C23—91no—
742C23—181no—
743C23—362no—
744C23—362no—
745C23—362no—
746C23—362no—
747C23—721no—
748C23—721no—
749Q8—181no—
750Q8—181no—
751Q8—241no—
752D4—32no—
753D4—61no—
754D4—61no—
755D4—61no—
756D4—94no—
757D4—122no—
758D4—181no—
759D4—181no—
760D4—362no—
761D4—362no—
762D4—362no—
763D4—362no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—91no—
775C2×C4—122no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—241no—
780C2×C4—721no—
781C2×C4C22×D3211yescharacteristic
782C8—21no—
783C8—61no—
784C8—61no—
785C8—181no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—62no—
790C2×C3—122no—
791C2×C3—241no—
792C2×C3#563011yescharacteristic
793C2×C3#565411yescharacteristic
794C2×C3C2×D3×SD1611yescharacteristic
795C2×C3C2×D3×SD1611yescharacteristic
796C2×C3#577411yescharacteristic
797C2×C3#577411yescharacteristic
798D3—22no—
799D3—42no—
800D3—62no—
801D3—62no—
802D3—81no—
803D3—122no—
804D3—241no—
805D3—241no—
806D3—481no—
807C22—32no—
808C22—61no—
809C22—61no—
810C22—62no—
811C22—92no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—181no—
818C22—181no—
819C22—361no—
820C22—361no—
821C22—361no—
822C22—724no—
823C22—724no—
824C22D32×D411yescharacteristic
825C4—32no—
826C4—41no—
827C4—41no—
828C4—61no—
829C4—61no—
830C4—121no—
831C4—121no—
832C4—181no—
833C4—361no—
834C4#6430811yescharacteristic
835C4D3×#23911yescharacteristic
836C3—21no—
837C3#8107511yescharacteristic, complemented
838C3#8134211yescharacteristic, complemented
839C2—62no—
840C2—122no—
841C2—182no—
842C2—241no—
843C2—721no—
844C2#1059462011yescharacteristic
845C2D32×SD1611yescharacteristic
846C2#1059475011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594621C2
hypercenter#106D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594537C2semidirect
3. #10592563C2semidirect
4. C3×#4870C2semidirect
5. C3×#4863C2semidirect
6. #10590946C2semidirect
7. #10590940C2semidirect
8. #10590906C2semidirect
9. #10590879C2semidirect
10. #10590597C2semidirect
11. D3×#809C2semidirect
12. #10590578C2semidirect
13. #10590548C2semidirect
14. #10590479C2semidirect
15. #10590445C2semidirect
21. C2×#3744C22semidirect
22. C2×C8×C3⋊D3C22semidirect
23. #64106C22semidirect
27. C3×D3×C4⋊C4C22semidirect
28. C3×#888C22semidirect
35. #63900C22semidirect
37. #63857C22semidirect
40. #63844C22semidirect
42. C2×#3716C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#106C22semidirect
45. #63637C22semidirect
46. #63636C22semidirect
48. C3×#821C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#808C22semidirect
54. C3×#808C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. Dic3×C3⋊C8C22semidirect
71. #4870D3semidirect
78. #4863D3semidirect
190. D3×C4⋊C4C2×D3semidirect
193. #888C2×D3semidirect
205. C3×#106C2×D3semidirect
206. C3×#106C2×D3semidirect
218. #821C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
222. Dic3⋊C8C2×D3semidirect
235. #809C2×D3semidirect
236. #808C2×D3semidirect
237. #808C2×D3semidirect
280. #626SD16semidirect
478. #106D32semidirect
737. C32#3295semidirect
837. C3#81075semidirect
838. C3#81342semidirect

Maximal subgroups

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

subgroupindex
#105946212
#105945372
#105925632
C3×#48702
C3×#48632
#105909462
#105909402
#105909062
#105908792
#105905972
D3×#8092
#105905782
#105905482
#105904792
#105904452
#813423
#810753