Finite Group Databasebeta

← #11889734

Subgroups — #11889734

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595428C211yesmaximal, characteristic
2#10594536C211yesmaximal, characteristic, complemented
3#10592510C211yesmaximal, characteristic, complemented
4C3×#4803C211yesmaximal, characteristic, complemented
5C3×#4798C211yesmaximal, characteristic, complemented
6#10591624C211yesmaximal, characteristic, complemented
7#10591601C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10590943C211yesmaximal, characteristic, complemented
10#10590833C211yesmaximal, characteristic, complemented
11#10590762C211yesmaximal, characteristic, complemented
12#10590738C211yesmaximal, characteristic, complemented
13#10590593C211yesmaximal, characteristic, complemented
14#10590498C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#80619—31nomaximal
17#78898—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20#64155C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic, complemented
24C2×C3×#204C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
26C3×D3×C4⋊C4C2211yescharacteristic, complemented
27C3×#887C2211yescharacteristic, complemented
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63918C2211yescharacteristic, complemented
31#63908C2211yescharacteristic
32#63905—21no—
33C4×#626—21no—
34C4×#626C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63885—21no—
37#63871C2211yescharacteristic
38#63867—21no—
39#63865—21no—
40#63856C2211yescharacteristic, complemented
41#63851—21no—
42C2×#3715C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63647C2211yescharacteristic
47#63645C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5829—31no—
62#5676—31no—
63#5579—31no—
64#5511—31no—
65C3×#464—31no—
66C3×#417—31no—
67#5239—31no—
68#5188—31no—
69#5187—31no—
70#5174—31no—
71#5169—31no—
72#5134—31no—
73#5127—31no—
74#5055—31no—
75#5026—31no—
76#4967—31no—
77#4846—31no—
78#4836—31no—
79#4813—31no—
80#4811—31no—
81#4811—31no—
82#4811—61no—
83#4803D311yescharacteristic, complemented
84#4798D311yescharacteristic, complemented
85#4794—31no—
86#4776—31no—
87#4774—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4759—31no—
91#4757—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#626D411yescharacteristic
107C2×#625—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110#3802—22no—
111#3802—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#216—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
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×ΓL(1,𝔽25)—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3715—22no—
143#3710—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C3×#124—31no—
153C3×C4×Q8—31no—
154C2×C3×C4⋊C4—31no—
155#947C2×D311yescharacteristic
156#946—31no—
157#946—31no—
158#946—31no—
159#946—31no—
160#946—61no—
161C2×#216C2×D311yescharacteristic, complemented
162C2×#215—31no—
163#939—61no—
164#938—31no—
165#937—61no—
166D4×Dic3—31no—
167C2×#214—31no—
168#930—31no—
169#929—61no—
170C4×#67—31no—
171C4×#67—61no—
172C2×(C2×D3)⋊C4—61no—
173#924—31no—
174#924—61no—
175C2×#204C2×D311yescharacteristic
176C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179#897—31no—
180#896—61no—
181#896—61no—
182#896—61no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4C2×D311yescharacteristic, complemented
187#889—61no—
188#888—31no—
189#887C2×D311yescharacteristic, complemented
190#884—61no—
191#883—61no—
192#882—61no—
193D3×C22⋊C4—61no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197#870—61no—
198#869—31no—
199C3×C4⋊C8—31no—
200C3×#103—21no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic, complemented
203C3×#103C2×D311yescharacteristic, complemented
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#835C2×D311yescharacteristic, complemented
212#832—31no—
213#832—31no—
214#832—31no—
215#830—31no—
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—61no—
223#818—31no—
224#818—31no—
225#818—31no—
226#818—61no—
227#816—31no—
228#815—31no—
229Dic3⋊C8C2×D311yescharacteristic, complemented
230#809—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237#803—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
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⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—42no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#627—81no—
273#626—22no—
274#625—42no—
275#625—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—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—31no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—31no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C3×#41—62no—
299C3×#41—121no—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C22×Dic3—61no—
316#239—22no—
317#239—41no—
318D3×D4—62no—
319D3×D4—62no—
320D3×D4—121no—
321D3×D4—121no—
322C2×D12—21no—
323C2×D12—31no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C3×Q16—121no—
340C3×SD16—121no—
341C3×M16—121no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356C3×C42—61no—
357#217—31no—
358#217—61no—
359#217—61no—
360#217—61no—
361#216—41no—
362#215—62no—
363#214—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—121no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399Dic3⋊C4—121no—
400C4×Dic3—21no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407#204—41no—
408ΓL(1,𝔽25)—41no—
409D3×C8—121no—
410D3×C8—121no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3#13712yes—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—91no—
439C2×Q16—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C2×M16—31no—
443C22×C8—91no—
444C4⋊Q8—91no—
445#125—181no—
446#124—31no—
447#123—181no—
448C22⋊Q8—91no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—31no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—91no—
464#107—91no—
465#107—91no—
466C4⋊C8—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103D3211yescharacteristic, complemented
471#102—31no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—31no—
481C23×C3—61no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3D3×D411yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×D4—32no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—122no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—122no—
523C2×C3×C4—241no—
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—62no—
527#67—122no—
528#67—122no—
529#67—241no—
530#67—241no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—241no—
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546D12—21no—
547D12—21no—
548D12—21no—
549D12—42no—
550D12—62no—
551D12#23512yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—42no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—81no—
560C4×D3—121no—
561C4×D3—121no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—242no—
566Dic6—21no—
567Dic6—21no—
568Dic6—241no—
569Dic6—241no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—121no—
580C2×C32#54611yescharacteristic
581C2×C32C2×#13711yescharacteristic
582C2×C32#57611yescharacteristic
583C3⋊D3—22no—
584C3×D3—42no—
585C3×D3—41no—
586C3×D3—81no—
587C24—181no—
588#41—62no—
589#41—121no—
590C2×Q8—31no—
591C2×Q8—181no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—91no—
597C2×D4—181no—
598C2×D4—182no—
599C2×D4—181no—
600C2×D4—361no—
601C22×C4—31no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—91no—
605C22×C4—181no—
606C22×C4—181no—
607Q16—121no—
608SD16—121no—
609SD16—182no—
610M16—121no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—361no—
615C2×C8C2×D3211yescharacteristic
616C4⋊C4—31no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4C2×D3211yescharacteristic
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—61no—
639C22×C3—21no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—62no—
643C22×C3—61no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—32no—
656C2×D3—32no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—62no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—244no—
670C2×D3—244no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4C2×#23511yescharacteristic
685C3×C4#100411yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4D3×#4111yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—61no—
694Dic3—61no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701Dic3—241no—
702C32#331411yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—61no—
706C23—91no—
707C23—362no—
708C23—362no—
709C23—721no—
710Q8—21no—
711Q8—21no—
712Q8—61no—
713Q8—61no—
714Q8—721no—
715D4—32no—
716D4—61no—
717D4—61no—
718D4—61no—
719D4—122no—
720D4—182no—
721D4—362no—
722D4—721no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—91no—
733C2×C4—122no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—241no—
739C2×C4—721no—
740C2×C4—721no—
741C2×C4C22×D3211yescharacteristic
742C8—21no—
743C8—61no—
744C8—61no—
745C8—181no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—122no—
750C2×C3—121no—
751C2×C3—241no—
752C2×C3#549011yescharacteristic
753C2×C3#561211yescharacteristic
754C2×C3#576911yescharacteristic
755C2×C3#577411yescharacteristic
756C2×C3D3×#13711yescharacteristic
757C2×C3D3×#13711yescharacteristic
758D3—41no—
759D3—42no—
760D3—62no—
761D3—62no—
762D3—81no—
763D3—122no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—62no—
768C22—92no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—181no—
775C22—181no—
776C22—724no—
777C22D32×D411yescharacteristic
778C4—41no—
779C4—41no—
780C4—61no—
781C4—61no—
782C4—61no—
783C4—121no—
784C4—121no—
785C4—181no—
786C4—361no—
787C4—361no—
788C4D3×#23511yescharacteristic
789C4#6431311yescharacteristic
790C3—21no—
791C3#7889811yescharacteristic, complemented
792C3#8061911yescharacteristic, complemented
793C2—121no—
794C2—122no—
795C2—182no—
796C2—241no—
797C2#1059427811yescharacteristic
798C2#1059475511yescharacteristic
799C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595428C2
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. #10594536C2semidirect
3. #10592510C2semidirect
4. C3×#4803C2semidirect
5. C3×#4798C2semidirect
6. #10591624C2semidirect
7. #10591601C2semidirect
8. #10591597C2semidirect
9. #10590943C2semidirect
10. #10590833C2semidirect
11. #10590762C2semidirect
12. #10590738C2semidirect
13. #10590593C2semidirect
14. #10590498C2semidirect
15. #10590454C2semidirect
23. C2×C3×#216C22semidirect
25. C2×C3×ΓL(1,𝔽25)C22semidirect
26. C3×D3×C4⋊C4C22semidirect
27. C3×#887C22semidirect
30. #63918C22semidirect
40. #63856C22semidirect
44. C32×#103C22semidirect
45. #63662C22semidirect
47. #63645C22semidirect
48. #63634C22semidirect
49. C3×#835C22semidirect
51. C3×Dic3⋊C8C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
83. #4803D3semidirect
84. #4798D3semidirect
161. C2×#216C2×D3semidirect
176. C2×ΓL(1,𝔽25)C2×D3semidirect
186. D3×C4⋊C4C2×D3semidirect
189. #887C2×D3semidirect
202. C3×#103C2×D3semidirect
203. C3×#103C2×D3semidirect
211. #835C2×D3semidirect
229. Dic3⋊C8C2×D3semidirect
470. #103D32semidirect
702. C32#3314semidirect
791. C3#78898semidirect
792. C3#80619semidirect

Maximal subgroups

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

subgroupindex
#105954282
#105945362
#105925102
C3×#48032
C3×#47982
#105916242
#105916012
#105915972
#105909432
#105908332
#105907622
#105907382
#105905932
#105904982
#105904542
#806193
#788983