Finite Group Databasebeta

← #11889752

Subgroups — #11889752

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595243C211yesmaximal, characteristic
2#10594393C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic, complemented
4C3×#4780C211yesmaximal, characteristic, complemented
5C3×#4765C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7#10591442C211yesmaximal, characteristic, complemented
8#10591413C211yesmaximal, characteristic, complemented
9#10590855C211yesmaximal, characteristic, complemented
10#10590795C211yesmaximal, characteristic, complemented
11#10590736C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13#10590616C211yesmaximal, characteristic, complemented
14#10590528C211yesmaximal, characteristic, complemented
15#10590464C211yesmaximal, characteristic, complemented
16#81700—31nomaximal
17#80823—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C3×#936C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
26C3×#897C2211yescharacteristic, complemented
27C3×#888C2211yescharacteristic, complemented
28#63981—21no—
29#63975—21no—
30#63974—21no—
31#63958—21no—
32C4×#626C2211yescharacteristic
33#63894C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic, complemented
35#63887—21no—
36#63881—21no—
37#63871—21no—
38#63871C2211yescharacteristic
39#63871C2211yescharacteristic
40#63846—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3718C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63648C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61#5730—31no—
62#5676—31no—
63#5635—31no—
64#5612—31no—
65C3×#489—31no—
66C3×#468—31no—
67#5169—31no—
68#5166—31no—
69#5133—31no—
70#5127—31no—
71#5087—31no—
72#5054—31no—
73#5047—31no—
74#5033—31no—
75#4890—31no—
76#4884—31no—
77#4817—31no—
78#4813—31no—
79#4813—31no—
80#4811—31no—
81#4808—31no—
82#4803—31no—
83#4780D311yescharacteristic, complemented
84#4776—31no—
85#4774—31no—
86D3×#102—31no—
87D3×#102—31no—
88D3×#102—61no—
89#4765D311yescharacteristic, complemented
90#4710—31no—
91#4706—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110#3799—22no—
111#3799—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C8×C3⋊D3—41no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#214—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×ΓL(1,𝔽25)—41no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3718—41no—
143#3717—22no—
144#3314—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×#235—31no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C3×C4⋊Q8—31no—
153C3×#124—31no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156#946—31no—
157#946—31no—
158#946—61no—
159#946—61no—
160Q8×Dic3—31no—
161C2×#216—31no—
162C2×#216—31no—
163C2×#215—31no—
164#938—61no—
165#938C2×D311yescharacteristic
166#937—61no—
167#936C2×D311yescharacteristic
168C2×#214C2×D311yescharacteristic
169C4×#67—31no—
170C2×C4⋊Dic3—31no—
171C2×#204—31no—
172C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—61no—
176#897—31no—
177#897—31no—
178#897—61no—
179#897C2×D311yescharacteristic, complemented
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#883—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—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×#97—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832C2×D311yescharacteristic
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#818—31no—
223#816—31no—
224#816C2×D311yescharacteristic, complemented
225#816C2×D311yescharacteristic, complemented
226#815C2×D311yescharacteristic, complemented
227Dic3⋊C8—31no—
228#810C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#807—31no—
234#807—31no—
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
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—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yes—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—81no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
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×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—81no—
272#626—22no—
273#626—42no—
274#624—42no—
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—31no—
288#467—91no—
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—
298C23×D3—121no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×D4—21no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C2×#67—21no—
308C2×#67—31no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—121no—
313C22×Dic3—61no—
314#239—62no—
315#239—121no—
316D3×D4—62no—
317D3×D4—62no—
318D3×D4—64no—
319D3×D4—121no—
320D3×D4—121no—
321D3×D4—122no—
322#235—62no—
323#235—121no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12—61no—
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×D3C22×D311yescharacteristic
341C2×Dic6—21no—
342C2×Dic6C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C3×SD16—121no—
345C3×M16—121no—
346C2×C3×C8—21no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
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⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—31no—
363#217—21no—
364#217—21no—
365#217—21no—
366#217—31no—
367#216—121no—
368#216—121no—
369#215—62no—
370#214—41no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—61no—
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—
381C4⋊Dic3—21no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—61no—
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)—41no—
411D3×C8—121no—
412D3×C8—121no—
413D3×C8—122no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—22no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—84no—
424C2×C3⋊D3#13712yes—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—91no—
442C2×Q16—91no—
443C2×SD16—31no—
444C2×SD16—91no—
445C2×M16—31no—
446C22×C8—91no—
447C4⋊Q8—31no—
448#125—181no—
449#124—31no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—31no—
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—31no—
473#103—91no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102D3211yescharacteristic
480C22⋊C8—91no—
481C22⋊C8—91no—
482#97—31no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—41no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—121no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—124no—
498C22×D3—242no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3—242no—
502C22×D3D3×D411yescharacteristic
503C3×Q8—61no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×Q8—61no—
507C3×Q8—241no—
508C3×D4—22no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—41no—
514C3×D4—241no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—62no—
531#67—81no—
532#67—122no—
533#67—122no—
534#67—122no—
535#67—124no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—241no—
547C2×Dic3D3×D411yescharacteristic
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550D12—32no—
551D12—32no—
552D12—62no—
553D12—62no—
554D12—61no—
555D12—61no—
556D12—121no—
557D12—122no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—61no—
563C4×D3—61no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—122no—
567C4×D3—122no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—242no—
574Dic6—21no—
575Dic6—21no—
576Dic6—21no—
577Dic6—21no—
578Dic6—81no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—41no—
582C3×C8—61no—
583C3×C8—61no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—121no—
589C2×C32—81no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13711yescharacteristic
592C2×C32#57611yescharacteristic
593C3⋊D3—22no—
594C3⋊D3—42no—
595C3×D3—41no—
596C24—181no—
597#41—182no—
598#41—361no—
599C2×Q8—31no—
600C2×Q8—31no—
601C2×Q8—61no—
602C2×D4—61no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4—182no—
608C2×D4—361no—
609C2×D4C2×D3211yescharacteristic
610C22×C4—31no—
611C22×C4—91no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4—181no—
616Q16—361no—
617SD16—121no—
618SD16—182no—
619M16—121no—
620C2×C8—31no—
621C2×C8—31no—
622C2×C8—91no—
623C2×C8—361no—
624C2×C8C2×D3211yescharacteristic
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—91no—
630C4⋊C4—91no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—91no—
642C22⋊C4—91no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C42—31no—
647C42—181no—
648C22×C3—21no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—32no—
667C2×D3—32no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—122no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—244no—
685C2×D3—244no—
686C2×D3—248no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—81no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4#100411yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4#100911yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710Dic3—62no—
711Dic3—61no—
712Dic3—61no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716C32#331411yescharacteristic, complemented, Sylow
717C23—21no—
718C23—31no—
719C23—91no—
720C23—181no—
721C23—362no—
722C23—362no—
723C23—721no—
724Q8—61no—
725Q8—61no—
726Q8—61no—
727Q8—61no—
728Q8—241no—
729D4—21no—
730D4—21no—
731D4—92no—
732D4—182no—
733D4—181no—
734D4—241no—
735D4—362no—
736D4—362no—
737C2×C4—21no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—91no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—362no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4—721no—
755C2×C4C22×D3211yescharacteristic
756C8—21no—
757C8—61no—
758C8—61no—
759C8—181no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—82no—
764C2×C3—81no—
765C2×C3—81no—
766C2×C3—121no—
767C2×C3#561011yescharacteristic
768C2×C3#567611yescharacteristic
769C2×C3#577411yescharacteristic
770C2×C3#577411yescharacteristic
771C2×C3D3×#13711yescharacteristic
772C2×C3D3×#13711yescharacteristic
773D3—41no—
774D3—64no—
775D3—62no—
776D3—62no—
777D3—122no—
778D3—122no—
779D3—242no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—92no—
787C22—181no—
788C22—181no—
789C22—182no—
790C22—361no—
791C22—361no—
792C22—724no—
793C22D32×D411yescharacteristic
794C4—41no—
795C4—61no—
796C4—61no—
797C4—61no—
798C4—121no—
799C4—121no—
800C4—121no—
801C4—121no—
802C4—181no—
803C4—361no—
804C4#6430611yescharacteristic
805C4#6431411yescharacteristic
806C3—21no—
807C3#8082311yescharacteristic, complemented
808C3#8170011yescharacteristic, complemented
809C2—81no—
810C2—121no—
811C2—182no—
812C2—362no—
813C2#1059428511yescharacteristic
814C2#1059473511yescharacteristic
815C2#1059474211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595243C2
hypercenter#102D32
hypocenterC32#3314
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. #10594393C2semidirect
3. C3⋊D3×#102C2semidirect
4. C3×#4780C2semidirect
5. C3×#4765C2semidirect
6. #10591467C2semidirect
7. #10591442C2semidirect
8. #10591413C2semidirect
9. #10590855C2semidirect
10. #10590795C2semidirect
11. #10590736C2semidirect
12. #10590671C2semidirect
13. #10590616C2semidirect
14. #10590528C2semidirect
15. #10590464C2semidirect
25. C2×C3×ΓL(1,𝔽25)C22semidirect
26. C3×#897C22semidirect
27. C3×#888C22semidirect
34. D3×C4⋊Dic3C22semidirect
41. Dic3×Dic6C22semidirect
42. C2×#3718C22semidirect
49. C3×#816C22semidirect
50. C3×#816C22semidirect
51. C3×#815C22semidirect
52. C3×#810C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
83. #4780D3semidirect
89. #4765D3semidirect
172. C2×ΓL(1,𝔽25)C2×D3semidirect
179. #897C2×D3semidirect
188. #888C2×D3semidirect
224. #816C2×D3semidirect
225. #816C2×D3semidirect
226. #815C2×D3semidirect
228. #810C2×D3semidirect
236. #807C2×D3semidirect
716. C32#3314semidirect
807. C3#80823semidirect
808. C3#81700semidirect

Maximal subgroups

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

subgroupindex
#105952432
#105943932
C3⋊D3×#1022
C3×#47802
C3×#47652
#105914672
#105914422
#105914132
#105908552
#105907952
#105907362
#105906712
#105906162
#105905282
#105904642
#817003
#808233