Finite Group Databasebeta

← #11889144

Subgroups — #11889144

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595293C211yesmaximal, characteristic
2#10594333C211yesmaximal, characteristic, complemented
3#10592478C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4762C211yesmaximal, characteristic, complemented
6#10591477C211yesmaximal, characteristic, complemented
7#10591464C211yesmaximal, characteristic, complemented
8#10591458C211yesmaximal, characteristic, complemented
9#10590943C211yesmaximal, characteristic, complemented
10#10590829C211yesmaximal, characteristic, complemented
11#10590772C211yesmaximal, characteristic, complemented
12#10590727C211yesmaximal, characteristic, complemented
13#10590594C211yesmaximal, characteristic, complemented
14#10590498C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#80397—31nomaximal
17#78762—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21#64147C2211yescharacteristic
22#64101C2211yescharacteristic, complemented
23C3×#940C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic, complemented
25C2×C3×#204C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28C3×#887C2211yescharacteristic, complemented
29#63983—21no—
30#63976—21no—
31#63970—21no—
32#63908C2211yescharacteristic
33C4×#626C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63871C2211yescharacteristic, complemented
36#63870—21no—
37#63869C2211yescharacteristic, complemented
38#63868—21no—
39#63856C2211yescharacteristic, complemented
40#63855—21no—
41#63850—21no—
42C2×#3715C2211yescharacteristic
43C2×#3712C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63644C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61D4×#67—31no—
62#5717—31no—
63#5581—31no—
64#5513—31no—
65C3×#460—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5174—31no—
69#5171—31no—
70#5169—31no—
71#5169—31no—
72#5114—31no—
73#5111—31no—
74#5071—31no—
75#5026—31no—
76#4967—31no—
77#4847—31no—
78#4836—31no—
79#4780—31no—
80#4779—31no—
81#4779—31no—
82#4779—61no—
83#4776—31no—
84#4774—31no—
85#4770—31no—
86#4770—31no—
87D3×#102D311yescharacteristic, complemented
88#4764—31no—
89#4763—31no—
90#4762D311yescharacteristic, complemented
91#4757—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107D3×#67—44no—
108C2×#626D411yescharacteristic
109C2×#625—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112#3802—22no—
113#3802—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3757—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4×C3⋊Dic3—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#214—41no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×#204—41no—
131C3×D3×C8—41no—
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143#3715—22no—
144#3712—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×#127—31no—
156C3×C4×Q8—31no—
157C2×C3×C4⋊C4—31no—
158#953—61no—
159#946—31no—
160#946—31no—
161C2×#215—31no—
162#940C2×D311yescharacteristic
163#939—61no—
164#938—31no—
165#938—31no—
166#938—31no—
167#938—61no—
168#938—61no—
169#937—61no—
170#937—61no—
171#937—61no—
172D4×Dic3—31no—
173C2×#214—31no—
174C2×#214C2×D311yescharacteristic, complemented
175#930—31no—
176#929—61no—
177C4×#67—31no—
178#926—61no—
179#924—31no—
180C2×#204C2×D311yescharacteristic, complemented
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×D3×C8C2×D311yescharacteristic, complemented
184#898—61no—
185#897—31no—
186#894—61no—
187#892—31no—
188#892—31no—
189#892—61no—
190D3×C4⋊C4C2×D311yescharacteristic, complemented
191#890—31no—
192#889—61no—
193#889—61no—
194#887C2×D311yescharacteristic, complemented
195#876—61no—
196C4×D12—31no—
197C4×D12—31no—
198#872—61no—
199#870—31no—
200C3×C4⋊C8—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic, complemented
207C3×#102C2×D311yescharacteristic, complemented
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic, complemented
216#830—31no—
217#821—31no—
218#821—31no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—61no—
224#818—31no—
225#817—31no—
226#817—31no—
227#817—61no—
228#816—31no—
229#815—31no—
230Dic3⋊C8C2×D311yescharacteristic, complemented
231#809—31no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236#807—31no—
237#807—61no—
238#803—31no—
239C23×C32—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
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—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C3×#67—42no—
261C3×#67—42no—
262C3×#67—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—42no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277#626—22no—
278#625—42no—
279#625—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—31no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—31no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—62no—
312C2×C3×D4—121no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—31no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—121no—
328C2×#67—124no—
329C22×Dic3—61no—
330D3×D4—22no—
331D3×D4—41no—
332D3×D4—62no—
333D3×D4—62no—
334D3×D4—121no—
335D3×D4—121no—
336D3×D4—124no—
337C2×D12—31no—
338C2×D12C22×D311yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C3×SD16—121no—
348C3×SD16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C42—31no—
362C3×C42—61no—
363#217—31no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—121no—
370#215—62no—
371#214—41no—
372#214—62no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—121no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—31no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403C4×Dic3—21no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—121no—
407C4×Dic3C22×D311yescharacteristic
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—41no—
414ΓL(1,𝔽25)—121no—
415ΓL(1,𝔽25)—121no—
416D3×C8—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—84no—
433C2×C3×D3AGL(1,ℤ/8)12yes—
434D32—84no—
435C32×C4—41no—
436C32×C4C2×#4111yescharacteristic
437C32×C4H(5,𝔽2)11yescharacteristic
438C3⋊Dic3—21no—
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—31no—
447C22×D4—91no—
448C22×D4—181no—
449C2×SD16—31no—
450C2×SD16—31no—
451C2×SD16—91no—
452C2×M16—91no—
453C22×C8—31no—
454#127—31no—
455#126—181no—
456#125—91no—
457#125—181no—
458#123—181no—
459C22⋊Q8—91no—
460C22⋊Q8—91no—
461#121—91no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—31no—
467C4×D4—91no—
468C4×D4—91no—
469#117—91no—
470#117—181no—
471C2×C4⋊C4—31no—
472#107—91no—
473#107—91no—
474#106—91no—
475C4⋊C8—31no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102D3211yescharacteristic, complemented
486C22⋊C8—91no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—41no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C23×C3—241no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—31no—
501C22×D3—31no—
502C22×D3—42no—
503C22×D3—42no—
504C22×D3—61no—
505C22×D3—81no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3D3×D411yescharacteristic
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—32no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—122no—
526C3×D4—122no—
527C3×D4—241no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—122no—
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542#67—42no—
543#67—42no—
544#67—62no—
545#67—81no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—242no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568D12—21no—
569D12—21no—
570D12—21no—
571D12—62no—
572D12#23512yes—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—42no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—121no—
581C4×D3—121no—
582C4×D3—122no—
583Dic6—21no—
584Dic6—21no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—41no—
588C3×C8—61no—
589C3×C8—61no—
590C3⋊C8—21no—
591C3⋊C8—21no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—121no—
595C2×C32—81no—
596C2×C32#54611yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—41no—
600C3×D3—22no—
601C3×D3—42no—
602C3×D3—81no—
603C24—61no—
604C24—181no—
605C2×Q8—31no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—62no—
612C2×D4—91no—
613C2×D4—121no—
614C2×D4—181no—
615C2×D4—182no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4—361no—
619C2×D4—364no—
620C2×D4C2×D3211yescharacteristic
621C22×C4—31no—
622C22×C4—61no—
623C22×C4—91no—
624C22×C4—181no—
625SD16—121no—
626SD16—121no—
627SD16—182no—
628M16—361no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—91no—
632C2×C8—121no—
633C2×C8C2×D3211yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4C2×D3211yescharacteristic
645C22⋊C4—91no—
646C22⋊C4—91no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C42—31no—
654C42—61no—
655C42—181no—
656C22×C3—21no—
657C22×C3—32no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—62no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—244no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C2×D3×D411yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—22no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—84no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3#91112yes—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4C2×#23511yescharacteristic
710C3×C4#100411yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4D3×#4111yescharacteristic
713Dic3—21no—
714Dic3—21no—
715Dic3—21no—
716Dic3—41no—
717Dic3—41no—
718Dic3—61no—
719Dic3—61no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726Dic3—241no—
727C32#331011yescharacteristic, complemented, Sylow
728C23—21no—
729C23—31no—
730C23—61no—
731C23—61no—
732C23—91no—
733C23—122no—
734C23—122no—
735C23—241no—
736C23—362no—
737C23—362no—
738C23—721no—
739Q8—61no—
740Q8—61no—
741D4—21no—
742D4—21no—
743D4—32no—
744D4—61no—
745D4—61no—
746D4—61no—
747D4—122no—
748D4—122no—
749D4—182no—
750D4—241no—
751D4—362no—
752D4—362no—
753D4—362no—
754C2×C4—21no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—91no—
763C2×C4—122no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—362no—
769C2×C4C22×D3211yescharacteristic
770C8—21no—
771C8—61no—
772C8—61no—
773C8—181no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—62no—
778C2×C3—81no—
779C2×C3—81no—
780C2×C3—122no—
781C2×C3—161no—
782C2×C3—241no—
783C2×C3#549011yescharacteristic
784C2×C3#561211yescharacteristic
785C2×C3C2×#91111yescharacteristic
786C2×C3#576211yescharacteristic
787C2×C3#576211yescharacteristic
788C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
789D3—22no—
790D3—42no—
791D3—81no—
792D3—121no—
793D3—121no—
794D3—241no—
795C22—32no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—61no—
800C22—61no—
801C22—62no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—181no—
808C22—181no—
809C22—181no—
810C22—244no—
811C22—724no—
812C22D32×D411yescharacteristic
813C4—41no—
814C4—61no—
815C4—61no—
816C4—61no—
817C4—121no—
818C4—121no—
819C4—181no—
820C4—361no—
821C4—361no—
822C4D3×#23511yescharacteristic
823C4#6431311yescharacteristic
824C3—21no—
825C3#7876211yescharacteristic, complemented
826C3#8039711yescharacteristic, complemented
827C2—62no—
828C2—81no—
829C2—122no—
830C2—241no—
831C2—361no—
832C2#1059427811yescharacteristic
833C2D3×#91111yescharacteristic
834C2#1059474811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595293C2
hypercenter#102D32
hypocenterC32#3310
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. #10594333C2semidirect
3. #10592478C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4762C2semidirect
6. #10591477C2semidirect
7. #10591464C2semidirect
8. #10591458C2semidirect
9. #10590943C2semidirect
10. #10590829C2semidirect
11. #10590772C2semidirect
12. #10590727C2semidirect
13. #10590594C2semidirect
14. #10590498C2semidirect
15. #10590454C2semidirect
22. #64101C22semidirect
24. C2×C3×#214C22semidirect
25. C2×C3×#204C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×D3×C4⋊C4C22semidirect
28. C3×#887C22semidirect
35. #63871C22semidirect
37. #63869C22semidirect
39. #63856C22semidirect
43. C2×#3712C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
46. #63647C22semidirect
47. #63644C22semidirect
48. #63634C22semidirect
49. C3×#832C22semidirect
51. C3×Dic3⋊C8C22semidirect
53. C3×#809C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
87. D3×#102D3semidirect
90. #4762D3semidirect
174. C2×#214C2×D3semidirect
180. C2×#204C2×D3semidirect
183. C2×D3×C8C2×D3semidirect
190. D3×C4⋊C4C2×D3semidirect
194. #887C2×D3semidirect
206. C3×#102C2×D3semidirect
207. C3×#102C2×D3semidirect
215. #832C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
233. #809C2×D3semidirect
485. #102D32semidirect
727. C32#3310semidirect
825. C3#78762semidirect
826. C3#80397semidirect

Maximal subgroups

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

subgroupindex
#105952932
#105943332
#105924782
C3×D3×#1022
C3×#47622
#105914772
#105914642
#105914582
#105909432
#105908292
#105907722
#105907272
#105905942
#105904982
#105904542
#803973
#787623