Finite Group Databasebeta

← #11887146

Subgroups — #11887146

Order 1152.

988 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595288C211yesmaximal, characteristic
2#10594531C211yesmaximal, characteristic, complemented
3#10592461C211yesmaximal, characteristic, complemented
4C3×#4777C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591460C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591402C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590776C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590460C211yesmaximal, characteristic, complemented
15#10590423C211yesmaximal, characteristic, complemented
16#81342—31nomaximal
17#78758—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21#64149C2211yescharacteristic
22C2×#3754C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic, complemented
24#64096C2211yescharacteristic, complemented
25C3×#938C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29#63983—21no—
30#63977—21no—
31#63971—21no—
32#63919C2211yescharacteristic, complemented
33#63909C2211yescharacteristic
34C4×#625—21no—
35C4×#625C2211yescharacteristic
36#63898C2211yescharacteristic
37#63870—21no—
38#63857C2211yescharacteristic, complemented
39#63857C2211yescharacteristic, complemented
40#63851—21no—
41#63851—21no—
42C2×#3716C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62#5609—31no—
63#5511—31no—
64#5511—31no—
65C3×#481—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5114—31no—
69C8×#67—31no—
70#5041—31no—
71#4968—31no—
72C2×#809—31no—
73#4870—31no—
74#4864—31no—
75#4863—31no—
76#4852—31no—
77#4778—31no—
78#4777D311yescharacteristic, complemented
79#4776—31no—
80#4776—31no—
81D3×#102—31no—
82D3×#102D311yescharacteristic, complemented
83#4762—31no—
84#4762—31no—
85#4762—61no—
86#4761—31no—
87#4760—31no—
88#4760—31no—
89#4758—31no—
90#4731—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108D3×#67—44no—
109C2×#627—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625D411yescharacteristic
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3754—41no—
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3744—41no—
124C3×#217—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133#3724—21no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143#3716—22no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×D3×D4C2×D311yescharacteristic
151C22×D12—31no—
152C22×C3×C8—31no—
153C3×#121—31no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—31no—
156#953—61no—
157#940—31no—
158#940—31no—
159#940—61no—
160#939—61no—
161#938C2×D311yescharacteristic
162#937—61no—
163#937—61no—
164D4×Dic3—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—31no—
168C2×#214—61no—
169#930—31no—
170C4×#67—31no—
171C4×#67—31no—
172C4×#67—61no—
173C4×#67—61no—
174#924—31no—
175#924—31no—
176#924—61no—
177#924—61no—
178C22×C3⋊C8—31no—
179C2×#204—31no—
180C2×#204—31no—
181C2×#204—31no—
182C2×#204—61no—
183C2×D3×C8—31no—
184C2×D3×C8C2×D311yescharacteristic, complemented
185#897—31no—
186#897—31no—
187#896—61no—
188#896—61no—
189#895—31no—
190#893—31no—
191D3×C4⋊C4C2×D311yescharacteristic, complemented
192D3×C4⋊C4C2×D311yescharacteristic, complemented
193#889—61no—
194#889—61no—
195#888—31no—
196#888—31no—
197#887—31no—
198#887—31no—
199#887—61no—
200#884—61no—
201#882—61no—
202C3×#106—31no—
203C3×#106—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic, complemented
210C3×#102C2×D311yescharacteristic, complemented
211C3×C22⋊C8—31no—
212#832—31no—
213#832C2×D311yescharacteristic, complemented
214#832C2×D311yescharacteristic, complemented
215#830—31no—
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8C2×D311yescharacteristic, complemented
221#817C2×D311yescharacteristic, complemented
222#816—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—61no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228#810—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic
236#808—31no—
237#808—31no—
238#808C2×D311yescharacteristic, complemented
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255#638—81no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261#634—21no—
262#634—21no—
263C3×#67—42no—
264C3×#67—42no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—81no—
277C3×C4×D3—81no—
278#627—81no—
279#626—42no—
280#626—42no—
281#625SD1614yescomplemented
282D3×Dic3—42no—
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—91no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—31no—
301C2×#102—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×D4—21no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—62no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—31no—
321C2×#67—31no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—121no—
329C2×#67—121no—
330C2×#67—124no—
331C22×Dic3—61no—
332D3×D4—22no—
333D3×D4—41no—
334D3×D4—62no—
335D3×D4—121no—
336D3×D4—124no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—62no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—121no—
344C2×D12C22×D311yescharacteristic
345C2×C4×D3—21no—
346C2×C4×D3—21no—
347C2×C4×D3—61no—
348C2×C4×D3C22×D311yescharacteristic
349C2×C4×D3C22×D311yescharacteristic
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—61no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—121no—
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C3×C4⋊C4—21no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C22⋊C4—61no—
370#217—21no—
371#217—31no—
372#217—31no—
373#217—61no—
374#217—61no—
375#217—61no—
376#214—62no—
377#214—121no—
378#214—121no—
379#214—122no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—121no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—121no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—121no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415#204—62no—
416#204—121no—
417#204—121no—
418#204—122no—
419D3×C8—41no—
420D3×C8—121no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—22no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—84no—
436C2×C3×D3C2×SD1612yes—
437C2×C3×D3C2×SD1612yes—
438D32—84no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—21no—
443C3⋊Dic3—41no—
444C3⋊Dic3C2×SD1612yes—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—31no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C22×C8—31no—
457C22×C8—91no—
458C4⋊Q8—91no—
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—91no—
472C4×D4—91no—
473C4×D4—181no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—31no—
476#106—31no—
477#106—31no—
478#106—91no—
479C4⋊C8—91no—
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#102D3211yescharacteristic, complemented
490C22⋊C8—31no—
491C22⋊C8—91no—
492C4×C8—91no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—31no—
497C23×C3—41no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C23×C3—241no—
502C22×D3—21no—
503C22×D3—42no—
504C22×D3—42no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—81no—
508C22×D3—121no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—241no—
514C22×D3—241no—
515C22×D3D3×D411yescharacteristic
516C22×D3D3×D411yescharacteristic
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—32no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—61no—
525C3×D4—122no—
526C3×D4—122no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—41no—
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—241no—
541C2×C3×C4—241no—
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544#67—34no—
545#67—34no—
546#67—42no—
547#67—42no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—242no—
553#67—241no—
554#67—241no—
555#67—242no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3—122no—
569C2×Dic3D3×D411yescharacteristic
570C2×Dic3D3×D411yescharacteristic
571D12—21no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—121no—
577D12—121no—
578D12—122no—
579D12—122no—
580D12#23512yes—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—21no—
585C4×D3—81no—
586C4×D3—81no—
587C4×D3—122no—
588Dic6—62no—
589Dic6—61no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—121no—
594Dic6—241no—
595Dic6—241no—
596C3×C8—21no—
597C3×C8—21no—
598C3×C8—41no—
599C3×C8—61no—
600C3×C8—61no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C3⋊C8—61no—
604C3⋊C8—61no—
605C3⋊C8—121no—
606C2×C32—81no—
607C2×C32#54611yescharacteristic
608C2×C32C22×SD1611yescharacteristic
609C2×C32#57611yescharacteristic
610C3⋊D3—81no—
611C3×D3—22no—
612C3×D3—22no—
613C3×D3—42no—
614C24—61no—
615C24—181no—
616C2×Q8—91no—
617C2×Q8—181no—
618C2×D4—31no—
619C2×D4—61no—
620C2×D4—62no—
621C2×D4—61no—
622C2×D4—91no—
623C2×D4—91no—
624C2×D4—121no—
625C2×D4—181no—
626C2×D4—182no—
627C2×D4—181no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4—361no—
631C2×D4—364no—
632C2×D4C2×D3211yescharacteristic
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—181no—
638SD16—182no—
639SD16—361no—
640SD16—361no—
641C2×C8—31no—
642C2×C8—31no—
643C2×C8—91no—
644C2×C8—121no—
645C2×C8—361no—
646C2×C8C2×D3211yescharacteristic
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—31no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—91no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4—181no—
657C4⋊C4C2×D3211yescharacteristic
658C22⋊C4—61no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C42—91no—
666C42—181no—
667C22×C3—21no—
668C22×C3—32no—
669C22×C3—32no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—62no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—244no—
687C22×C3C2×D3×D411yescharacteristic
688C22×C3C2×D3×D411yescharacteristic
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—22no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—84no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—241no—
704C2×D3—241no—
705C2×D3—241no—
706C2×D3—244no—
707C2×D3—244no—
708C2×D3D3×SD1612yes—
709C2×D3D3×SD1612yes—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—81no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4C2×#23511yescharacteristic
721C3×C4#100411yescharacteristic
722C3×C4D3×#4111yescharacteristic
723C3×C4#100911yescharacteristic
724Dic3—21no—
725Dic3—21no—
726Dic3—32no—
727Dic3—32no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731Dic3—62no—
732Dic3—61no—
733Dic3—61no—
734Dic3—121no—
735Dic3—122no—
736Dic3—121no—
737Dic3—121no—
738C32#329511yescharacteristic, complemented, Sylow
739C23—21no—
740C23—31no—
741C23—31no—
742C23—61no—
743C23—122no—
744C23—122no—
745C23—181no—
746C23—241no—
747C23—362no—
748C23—362no—
749C23—721no—
750Q8—181no—
751Q8—181no—
752Q8—721no—
753D4—21no—
754D4—21no—
755D4—32no—
756D4—61no—
757D4—94no—
758D4—122no—
759D4—122no—
760D4—181no—
761D4—181no—
762D4—362no—
763D4—362no—
764D4—362no—
765D4—721no—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—91no—
777C2×C4—91no—
778C2×C4—181no—
779C2×C4—241no—
780C2×C4—241no—
781C2×C4—362no—
782C2×C4C22×D3211yescharacteristic
783C8—21no—
784C8—61no—
785C8—61no—
786C8—181no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—62no—
791C2×C3—62no—
792C2×C3—81no—
793C2×C3—81no—
794C2×C3—122no—
795C2×C3—161no—
796C2×C3#549011yescharacteristic
797C2×C3#565411yescharacteristic
798C2×C3#575711yescharacteristic
799C2×C3C2×D3×SD1611yescharacteristic
800C2×C3C2×D3×SD1611yescharacteristic
801C2×C3#577411yescharacteristic
802D3—22no—
803D3—22no—
804D3—42no—
805D3—241no—
806D3—241no—
807D3—481no—
808C22—32no—
809C22—32no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—62no—
818C22—121no—
819C22—121no—
820C22—244no—
821C22—361no—
822C22—361no—
823C22—361no—
824C22—724no—
825C22D32×D411yescharacteristic
826C4—41no—
827C4—61no—
828C4—61no—
829C4—92no—
830C4—121no—
831C4—121no—
832C4—121no—
833C4—181no—
834C4—361no—
835C4D3×#23511yescharacteristic
836C4#6431411yescharacteristic
837C3—21no—
838C3#7875811yescharacteristic, complemented
839C3#8134211yescharacteristic, complemented
840C2—62no—
841C2—62no—
842C2—81no—
843C2—122no—
844C2—721no—
845C2#1059427211yescharacteristic
846C2#1059473211yescharacteristic
847C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595288C2
hypercenter#102D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594531C2semidirect
3. #10592461C2semidirect
4. C3×#4777C2semidirect
5. C3×D3×#102C2semidirect
6. #10591460C2semidirect
7. #10591459C2semidirect
8. #10591402C2semidirect
9. #10590946C2semidirect
10. #10590830C2semidirect
11. #10590776C2semidirect
12. #10590717C2semidirect
13. D3×#809C2semidirect
14. #10590460C2semidirect
15. #10590423C2semidirect
22. C2×#3754C22semidirect
23. C2×#3744C22semidirect
24. #64096C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×D3×C4⋊C4C22semidirect
28. C3×D3×C4⋊C4C22semidirect
32. #63919C22semidirect
38. #63857C22semidirect
39. #63857C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#102C22semidirect
45. #63641C22semidirect
46. #63636C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#817C22semidirect
53. C3×#808C22semidirect
54. #63574C22semidirect
55. #63567C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63553C22semidirect
78. #4777D3semidirect
82. D3×#102D3semidirect
184. C2×D3×C8C2×D3semidirect
191. D3×C4⋊C4C2×D3semidirect
192. D3×C4⋊C4C2×D3semidirect
209. C3×#102C2×D3semidirect
210. C3×#102C2×D3semidirect
213. #832C2×D3semidirect
214. #832C2×D3semidirect
220. (C2×D3)⋊C8C2×D3semidirect
221. #817C2×D3semidirect
238. #808C2×D3semidirect
281. #625SD16semidirect
489. #102D32semidirect
738. C32#3295semidirect
838. C3#78758semidirect
839. C3#81342semidirect

Maximal subgroups

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

subgroupindex
#105952882
#105945312
#105924612
C3×#47772
C3×D3×#1022
#105914602
#105914592
#105914022
#105909462
#105908302
#105907762
#105907172
D3×#8092
#105904602
#105904232
#813423
#787583