Finite Group Databasebeta

← #11889736

Subgroups — #11889736

Order 1152.

901 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic
2#10594393C211yesmaximal, characteristic, complemented
3#10592502C211yesmaximal, characteristic, complemented
4C3×#4813C211yesmaximal, characteristic, complemented
5C3×#4794C211yesmaximal, characteristic, complemented
6#10591602C211yesmaximal, characteristic, complemented
7#10591578C211yesmaximal, characteristic, complemented
8#10591551C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590842C211yesmaximal, characteristic, complemented
11#10590795C211yesmaximal, characteristic, complemented
12#10590726C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590510C211yesmaximal, characteristic, complemented
15#10590464C211yesmaximal, characteristic, complemented
16#81700—31nomaximal
17#80777—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3743C2211yescharacteristic, complemented
21C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic
26C3×#897C2211yescharacteristic
27C3×#888C2211yescharacteristic, complemented
28#63923—21no—
29#63921—21no—
30#63916C2211yescharacteristic
31#63910—21no—
32C4×#626C2211yescharacteristic
33#63894C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63887—21no—
36#63881—21no—
37#63871—21no—
38#63871C2211yescharacteristic, complemented
39#63853—21no—
40#63846—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63648C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5730—31no—
62#5676—31no—
63#5635—31no—
64#5630—31no—
65C3×#489—31no—
66C3×#467—31no—
67#5187—31no—
68#5185—31no—
69C2×#821—31no—
70#5111—31no—
71#5087—31no—
72#5054—31no—
73#5046—31no—
74#5044—31no—
75#4890—31no—
76#4882—31no—
77#4817—31no—
78#4813D311yescharacteristic, complemented
79#4812—31no—
80#4811—31no—
81#4808—31no—
82#4803—31no—
83#4803—31no—
84#4803—61no—
85#4794D311yescharacteristic, complemented
86#4780—31no—
87#4776—31no—
88#4774—31no—
89D3×#102—31no—
90#4710—31no—
91#4706—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832—41no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#626D411yescharacteristic
108C2×#624—21no—
109C2×D3×Dic3—21no—
110D3×D12—22no—
111D3×D12—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3743—41no—
118C3×#216—41no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3717—22no—
143#3715—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C2×C3×Q16—31no—
151C22×C3×C8—31no—
152C3×C4⋊Q8—31no—
153C3×#124—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156#947C2×D311yescharacteristic
157#946—31no—
158#946—61no—
159#946—61no—
160#946C2×D311yescharacteristic
161Q8×Dic3—31no—
162C2×#216C2×D311yescharacteristic, complemented
163C2×#215—31no—
164C2×#215—31no—
165#938—31no—
166C2×#214—31no—
167C4×#67—31no—
168C2×C4⋊Dic3—31no—
169C2×#204—31no—
170C2×ΓL(1,𝔽25)—31no—
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—61no—
173C2×D3×C8C2×D311yescharacteristic
174#897—31no—
175#897—61no—
176#897C2×D311yescharacteristic
177#895—31no—
178#895—61no—
179#894—61no—
180#893—31no—
181#893—61no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186#890—61no—
187#889—61no—
188#888C2×D311yescharacteristic, complemented
189#884—61no—
190#883—61no—
191#882—61no—
192#882—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195D3×C22⋊C4—61no—
196#878—61no—
197C4×D12—31no—
198C4×D12—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103C2×D311yescharacteristic, complemented
205C3×#103C2×D311yescharacteristic, complemented
206C3×#102—31no—
207C3×#102—31no—
208C3×#97—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#818—31no—
225#816C2×D311yescharacteristic, complemented
226#815C2×D311yescharacteristic, complemented
227Dic3⋊C8—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—42no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—42no—
258C4×C3⋊D3—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—81no—
272#626—22no—
273#626—42no—
274#626—81no—
275#624—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—31no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—31no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8—61no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—31no—
304C22×C3×C4—31no—
305C2×#67—31no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—61no—
309#239—62no—
310#239—62no—
311#239—64no—
312#239—121no—
313#239—121no—
314#239—122no—
315D3×D4—62no—
316D3×D4—121no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—62no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—121no—
327C2×D12—121no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—121no—
340C2×C4×D3—121no—
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6—21no—
343C2×Dic6C22×D311yescharacteristic
344C3×Q16—121no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—121no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364#217—31no—
365#217—61no—
366#216—41no—
367#215—62no—
368#215—121no—
369#214—121no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
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—
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—121no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—62no—
410ΓL(1,𝔽25)—121no—
411ΓL(1,𝔽25)—121no—
412ΓL(1,𝔽25)—122no—
413D3×C8—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3#13712yes—
427D32—84no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—91no—
442C2×Q16—31no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×M16—91no—
446C22×C8—31no—
447C4⋊Q8—31no—
448#125—181no—
449#124—31no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—91no—
457#121—181no—
458#120—181no—
459C4×Q8—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#107—91no—
469C4⋊C8—91no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103D3211yescharacteristic, complemented
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482#97—31no—
483C23×C3—31no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3—31no—
487C22×D3—31no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—121no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—241no—
497C22×D3—241no—
498C22×D3D3×D411yescharacteristic
499C3×Q8—22no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—41no—
505C3×Q8—61no—
506C3×Q8—61no—
507C3×Q8—241no—
508C3×D4—61no—
509C3×D4—61no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—62no—
528#67—122no—
529#67—241no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—241no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543D12—21no—
544D12—21no—
545D12—32no—
546D12—32no—
547D12—62no—
548D12—62no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—122no—
553D12—122no—
554D12—124no—
555D12—122no—
556D12—241no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—62no—
560C4×D3—62no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—61no—
564C4×D3—61no—
565C4×D3—122no—
566C4×D3—122no—
567C4×D3—124no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—242no—
574Dic6—21no—
575Dic6—21no—
576Dic6—81no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—41no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—121no—
587C2×C32#54611yescharacteristic
588C2×C32C2×#13711yescharacteristic
589C2×C32#57611yescharacteristic
590C3⋊D3—41no—
591C3⋊D3—42no—
592C3×D3—22no—
593C3×D3—81no—
594C24—181no—
595#41—182no—
596#41—361no—
597C2×Q8—31no—
598C2×Q8—61no—
599C2×Q8C2×D3211yescharacteristic
600C2×D4—31no—
601C2×D4—91no—
602C2×D4—91no—
603C2×D4—181no—
604C2×D4—181no—
605C2×D4—182no—
606C2×D4—181no—
607C2×D4—361no—
608C22×C4—31no—
609C22×C4—91no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614Q16—121no—
615SD16—182no—
616SD16—361no—
617M16—361no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—91no—
621C2×C8—121no—
622C2×C8C2×D3211yescharacteristic
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—91no—
629C4⋊C4—91no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4C2×D3211yescharacteristic
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—91no—
640C22⋊C4—91no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C42—31no—
645C42—181no—
646C22×C3—21no—
647C22×C3—32no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—62no—
661C2×D3—61no—
662C2×D3—62no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—62no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—122no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—244no—
679C2×D3—244no—
680C2×D3#91812yes—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—42no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—61no—
691C3×C4—81no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4#100411yescharacteristic
696C3×C4D3×#4111yescharacteristic
697C3×C4D3×#4111yescharacteristic
698C3×C4#100911yescharacteristic
699Dic3—21no—
700Dic3—21no—
701Dic3—21no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3—62no—
706Dic3—61no—
707Dic3—61no—
708Dic3—121no—
709Dic3—121no—
710Dic3—241no—
711C32#331411yescharacteristic, complemented, Sylow
712C23—31no—
713C23—61no—
714C23—91no—
715C23—181no—
716C23—362no—
717C23—362no—
718C23—721no—
719Q8—21no—
720Q8—21no—
721Q8—61no—
722Q8—61no—
723Q8—241no—
724D4—61no—
725D4—61no—
726D4—92no—
727D4—182no—
728D4—181no—
729D4—362no—
730D4—362no—
731D4—721no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—91no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—362no—
747C2×C4—721no—
748C2×C4—721no—
749C2×C4—721no—
750C2×C4C22×D3211yescharacteristic
751C8—21no—
752C8—61no—
753C8—61no—
754C8—181no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—62no—
759C2×C3—241no—
760C2×C3#561011yescharacteristic
761C2×C3#567611yescharacteristic
762C2×C3C2×#91811yescharacteristic
763C2×C3#576911yescharacteristic
764C2×C3#577411yescharacteristic
765C2×C3D3×#13711yescharacteristic
766D3—22no—
767D3—81no—
768D3—122no—
769D3—121no—
770D3—122no—
771D3—121no—
772D3—122no—
773D3—242no—
774C22—32no—
775C22—61no—
776C22—61no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—182no—
784C22—361no—
785C22—361no—
786C22—724no—
787C22D32×D411yescharacteristic
788C4—41no—
789C4—41no—
790C4—61no—
791C4—61no—
792C4—61no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—181no—
797C4—361no—
798C4#6430611yescharacteristic
799C4#6431411yescharacteristic
800C3—21no—
801C3#8077711yescharacteristic, complemented
802C3#8170011yescharacteristic, complemented
803C2—62no—
804C2—241no—
805C2—361no—
806C2—362no—
807C2#1059428511yescharacteristic
808C2#1059475511yescharacteristic
809C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595431C2
hypercenter#103D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594393C2semidirect
3. #10592502C2semidirect
4. C3×#4813C2semidirect
5. C3×#4794C2semidirect
6. #10591602C2semidirect
7. #10591578C2semidirect
8. #10591551C2semidirect
9. D3×#821C2semidirect
10. #10590842C2semidirect
11. #10590795C2semidirect
12. #10590726C2semidirect
13. #10590596C2semidirect
14. #10590510C2semidirect
15. #10590464C2semidirect
20. C2×#3743C22semidirect
21. C4⋊C4×C3⋊D3C22semidirect
24. C2×C3×#216C22semidirect
27. C3×#888C22semidirect
38. #63871C22semidirect
41. Dic3×Dic6C22semidirect
44. C32×#103C22semidirect
45. #63662C22semidirect
48. C3×#835C22semidirect
50. C3×#816C22semidirect
51. C3×#815C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
59. #63557C22semidirect
78. #4813D3semidirect
85. #4794D3semidirect
162. C2×#216C2×D3semidirect
188. #888C2×D3semidirect
204. C3×#103C2×D3semidirect
205. C3×#103C2×D3semidirect
212. #835C2×D3semidirect
225. #816C2×D3semidirect
226. #815C2×D3semidirect
236. #807C2×D3semidirect
473. #103D32semidirect
711. C32#3314semidirect
801. C3#80777semidirect
802. C3#81700semidirect

Maximal subgroups

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

subgroupindex
#105954312
#105943932
#105925022
C3×#48132
C3×#47942
#105916022
#105915782
#105915512
D3×#8212
#105908422
#105907952
#105907262
#105905962
#105905102
#105904642
#817003
#807773