Finite Group Databasebeta

← #11887235

Subgroups — #11887235

Order 1152.

867 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595244C211yesmaximal, characteristic
2#10594551C211yesmaximal, characteristic, complemented
3#10592465C211yesmaximal, characteristic, complemented
4C3×#4783C211yesmaximal, characteristic, complemented
5C3×D3×#102C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591445C211yesmaximal, characteristic, complemented
8#10591420C211yesmaximal, characteristic, complemented
9#10590851C211yesmaximal, characteristic, complemented
10#10590834C211yesmaximal, characteristic, complemented
11#10590797C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic, complemented
13#10590539C211yesmaximal, characteristic, complemented
14#10590516C211yesmaximal, characteristic, complemented
15#10590501C211yesmaximal, characteristic, complemented
16#80246—31nomaximal
17#78759—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21#64099C2211yescharacteristic, complemented
22C2×C3×#214C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic, complemented
24C2×C3×D3×C8C2211yescharacteristic
25C3×#897C2211yescharacteristic, complemented
26C3×D3×C4⋊C4C2211yescharacteristic
27#63980—21no—
28#63976—21no—
29#63961—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63908C2211yescharacteristic
32#63905—21no—
33C4×#625C2211yescharacteristic
34#63863C2211yescharacteristic
35#63861—21no—
36#63856C2211yescharacteristic
37#63856C2211yescharacteristic
38#63847—21no—
39#63843C2211yescharacteristic, complemented
40#63841—21no—
41#63841C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63645C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5829—31no—
62#5806—31no—
63#5639—31no—
64#5513—31no—
65C3×#452—31no—
66C2×C3×#102—31no—
67#5233—31no—
68#5218—31no—
69#5188—31no—
70#5185—31no—
71#5169—31no—
72Dic3×SD16—31no—
73#5116—31no—
74C8×#67—31no—
75#5048—31no—
76#4971—31no—
77#4805—31no—
78#4800—31no—
79#4784—31no—
80#4783D311yescharacteristic, complemented
81#4778—31no—
82#4772—31no—
83D3×#102D311yescharacteristic, complemented
84#4768—31no—
85#4767—31no—
86#4766—31no—
87#4766—31no—
88#4766—61no—
89#4758—31no—
90#4737—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×#237—22no—
99C3×#237—41no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#625—21no—
109C2×#625D411yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#214—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×Dic12—41no—
127C3×D3×C8—41no—
128#3724—21no—
129#3724—21no—
130#3724D411yescharacteristic
131Dic3⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142#3715—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C2×C3×C4⋊C4—31no—
154#953—61no—
155C2×#217—61no—
156#947—31no—
157#946—31no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#215—31no—
161#939—61no—
162#939—61no—
163#938—31no—
164#937—61no—
165#936—31no—
166#935—61no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—61no—
170C2×#214—31no—
171C2×#214C2×D311yescharacteristic
172#930—31no—
173#929—61no—
174#929—61no—
175C4×#67—31no—
176C4×#67—31no—
177C2×(C2×D3)⋊C4—61no—
178#926—31no—
179#926—61no—
180#924—31no—
181#924—31no—
182C22×C3⋊C8—31no—
183C2×Dic12C2×D311yescharacteristic, complemented
184C2×D3×C8—31no—
185C2×D3×C8C2×D311yescharacteristic
186#898—61no—
187#897C2×D311yescharacteristic, complemented
188#892—31no—
189#892—61no—
190D3×C4⋊C4C2×D311yescharacteristic
191#890—31no—
192#890—31no—
193#890—61no—
194#889—61no—
195#889—61no—
196#887—31no—
197#883—61no—
198#879—61no—
199C3×#103—31no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic
205C3×#102C2×D311yescharacteristic
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic, complemented
220#818—31no—
221#818—31no—
222#818—61no—
223#817—31no—
224#816—31no—
225#816—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—61no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810—31no—
232#810C2×D311yescharacteristic, complemented
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#808—61no—
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—81no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C3×#67—42no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#625—22no—
274#625—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—31no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—121no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—31no—
315C2×#67—31no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322#237—22no—
323#237—41no—
324D3×D4—22no—
325D3×D4—41no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3C22×D311yescharacteristic
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C3×Q16—121no—
333C3×SD16—62no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—121no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347#217—31no—
348#217—31no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—121no—
358#215—121no—
359#214—22no—
360#214—121no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370C4⋊Dic3—21no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—121no—
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—121no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—41no—
407D3×C8—41no—
408D3×C8—121no—
409C22×C32—22no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—84no—
422C2×C3×D3#13512yes—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—31no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—91no—
440C22×C8—31no—
441C22×C8—91no—
442#126—181no—
443#125—91no—
444#125—181no—
445#124—91no—
446#123—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—91no—
455C4×D4—91no—
456C4×D4—91no—
457#117—91no—
458#117—181no—
459C2×C4⋊C4—31no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—91no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102D3211yescharacteristic
475C22⋊C8—31no—
476C22⋊C8—91no—
477C4×C8—91no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C22×D3—21no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—81no—
491C22×D3D3×D411yescharacteristic
492C22×D3D3×D411yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—41no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—122no—
504C3×D4—122no—
505C3×D4#23512yes—
506C3×D4#23712yes—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4—122no—
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—42no—
525#67—42no—
526#67—62no—
527#67—62no—
528#67—241no—
529#67—241no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—42no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—241no—
547C2×Dic3—241no—
548C2×Dic3—242no—
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551D12—21no—
552D12—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C2×C32—42no—
573C2×C32#54611yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32#57711yescharacteristic
576C3×D3—22no—
577C3×D3—41no—
578C3×D3—81no—
579C24—61no—
580#41—62no—
581#41—121no—
582C2×Q8—31no—
583C2×Q8—31no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4—62no—
587C2×D4—61no—
588C2×D4—91no—
589C2×D4—121no—
590C2×D4—181no—
591C2×D4C2×D3211yescharacteristic
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—181no—
597Q16—121no—
598SD16—62no—
599SD16—361no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—91no—
603C2×C8—121no—
604C2×C8—361no—
605C2×C8C2×D3211yescharacteristic
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—61no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C42—91no—
629C42—181no—
630C42—181no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—244no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C2×D3×D411yescharacteristic
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—84no—
662C2×D3#91212yes—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—81no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4C2×#23511yescharacteristic
674C3×C4C2×#23711yescharacteristic
675C3×C4#100411yescharacteristic
676C3×C4#100411yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—241no—
693Dic3—241no—
694C32#329611yescharacteristic, complemented, Sylow
695C23—21no—
696C23—31no—
697C23—31no—
698C23—61no—
699C23—122no—
700C23—122no—
701C23—241no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706D4—21no—
707D4—61no—
708D4—61no—
709D4—122no—
710D4—122no—
711D4—182no—
712D4—721no—
713D4#379512yes—
714C2×C4—21no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—91no—
725C2×C4—91no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—721no—
731C2×C4C22×D3211yescharacteristic
732C8—21no—
733C8—61no—
734C8—61no—
735C8—181no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—42no—
740C2×C3—42no—
741C2×C3—62no—
742C2×C3—82no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3#549011yescharacteristic
746C2×C3#559111yescharacteristic
747C2×C3C2×#91211yescharacteristic
748C2×C3#576211yescharacteristic
749C2×C3D3×#13511yescharacteristic
750C2×C3#577811yescharacteristic
751D3—22no—
752D3—41no—
753D3—81no—
754C22—22no—
755C22—32no—
756C22—41no—
757C22—41no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—244no—
767C22D32×D411yescharacteristic
768C4—41no—
769C4—61no—
770C4—61no—
771C4—121no—
772C4—121no—
773C4—121no—
774C4—181no—
775C4—181no—
776C4—361no—
777C4—361no—
778C4C2×#379511yescharacteristic
779C4#6431311yescharacteristic
780C3—21no—
781C3#7875911yescharacteristic, complemented
782C3#8024611yescharacteristic, complemented
783C2—42no—
784C2—62no—
785C2—121no—
786C2—241no—
787C2#1059418411yescharacteristic
788C2D3×#91211yescharacteristic
789C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595244C2
hypercenter#102D32
hypocenterC32#3296
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. #10594551C2semidirect
3. #10592465C2semidirect
4. C3×#4783C2semidirect
5. C3×D3×#102C2semidirect
6. #10591458C2semidirect
7. #10591445C2semidirect
8. #10591420C2semidirect
9. #10590851C2semidirect
10. #10590834C2semidirect
11. #10590797C2semidirect
12. #10590717C2semidirect
13. #10590539C2semidirect
14. #10590516C2semidirect
15. #10590501C2semidirect
21. #64099C22semidirect
23. C2×C3×Dic12C22semidirect
25. C3×#897C22semidirect
39. #63843C22semidirect
41. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63645C22semidirect
47. #63641C22semidirect
48. #63635C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#810C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
60. #63553C22semidirect
80. #4783D3semidirect
83. D3×#102D3semidirect
183. C2×Dic12C2×D3semidirect
187. #897C2×D3semidirect
219. (C2×D3)⋊C8C2×D3semidirect
232. #810C2×D3semidirect
694. C32#3296semidirect
781. C3#78759semidirect
782. C3#80246semidirect

Maximal subgroups

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

subgroupindex
#105952442
#105945512
#105924652
C3×#47832
C3×D3×#1022
#105914582
#105914452
#105914202
#105908512
#105908342
#105907972
#105907172
#105905392
#105905162
#105905012
#802463
#787593