Finite Group Databasebeta

← #11889154

Subgroups — #11889154

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594621C211yesmaximal, characteristic
2#10594579C211yesmaximal, characteristic, complemented
3#10592581C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4886C211yesmaximal, characteristic, complemented
6#10590943C211yesmaximal, characteristic, complemented
7#10590939C211yesmaximal, characteristic, complemented
8#10590799C211yesmaximal, characteristic, complemented
9#10590738C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11#10590593C211yesmaximal, characteristic, complemented
12#10590550C211yesmaximal, characteristic, complemented
13#10590523C211yesmaximal, characteristic, complemented
14#10590478C211yesmaximal, characteristic, complemented
15#10590449C211yesmaximal, characteristic, complemented
16#81189—31nomaximal
17#80821—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21#64104C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic, complemented
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
25C3×#897C2211yescharacteristic, complemented
26C3×#895C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×#890C2211yescharacteristic, complemented
29#63923—21no—
30#63922—21no—
31#63911C2211yescharacteristic
32#63906—21no—
33C4×#626C2211yescharacteristic
34#63871C2211yescharacteristic, complemented
35#63858—21no—
36#63853—21no—
37#63849—21no—
38#63846—21no—
39Dic3×Dic6C2211yescharacteristic, complemented
40#63841C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5694—31no—
62#5639—31no—
63#5609—31no—
64D4×D12—31no—
65C3×#478—31no—
66C3×#468—31no—
67#5169—31no—
68#5163—31no—
69#5131—31no—
70#5127—31no—
71#5067—31no—
72#5046—31no—
73#5035—31no—
74#5018—31no—
75#4891D311yescharacteristic, complemented
76#4886D311yescharacteristic, complemented
77#4882—31no—
78#4882—31no—
79#4882—61no—
80#4866—31no—
81#4864—31no—
82#4848—31no—
83#4836—31no—
84#4817—31no—
85#4807—31no—
86#4776—31no—
87#4776—31no—
88#4770—31no—
89D3×#102—31no—
90D3×#102—31no—
91#4764—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626D411yescharacteristic
108C2×#625—21no—
109#3802—22no—
110#3802—41no—
111D3×D12—22no—
112D3×D12—44no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132C3×ΓL(1,𝔽25)—41no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142#3717—41no—
143#3715—22no—
144#3710—41no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—61no—
152C2×C3×SD16—31no—
153C2×C3×M16—31no—
154C3×#125—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#215—31no—
161C2×#215—31no—
162#940—31no—
163#937—61no—
164C2×#214—31no—
165#930—61no—
166C4×#67—31no—
167#926—31no—
168C2×#204—31no—
169C2×#204C2×D311yescharacteristic, complemented
170C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
171C2×D3×C8—31no—
172C2×D3×C8—31no—
173#898—61no—
174#897—31no—
175#897C2×D311yescharacteristic, complemented
176#895—31no—
177#895—31no—
178#895—61no—
179#895C2×D311yescharacteristic
180#894—61no—
181#893C2×D311yescharacteristic
182#892—31no—
183#892—61no—
184#892—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—61no—
188#890—61no—
189#890C2×D311yescharacteristic, complemented
190#889—61no—
191#884—61no—
192#883—61no—
193#882—61no—
194#882—61no—
195#882—61no—
196#879—61no—
197#874—31no—
198C4×D12—31no—
199C4×Dic6—31no—
200C3×#107—21no—
201C3×#107C2×D311yescharacteristic, complemented
202C3×#107C2×D311yescharacteristic, complemented
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#103—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#830—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—61no—
224#815—31no—
225Dic3⋊C8C2×D311yescharacteristic, complemented
226#810C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237#807—61no—
238#803—31no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—42no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—42no—
270C3×D12#4112yes—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—42no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#626—22no—
277#626—42no—
278#626—42no—
279#626—81no—
280#625—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—31no—
291#468—31no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316D3×D4—62no—
317D3×D4—62no—
318D3×D4—62no—
319D3×D4—121no—
320D3×D4—124no—
321D3×D4—121no—
322D3×D4—121no—
323C2×D12—21no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—121no—
335C2×D12—121no—
336C2×D12—124no—
337C2×D12C22×D311yescharacteristic
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—121no—
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—121no—
349C3×M16—121no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—31no—
369#217—31no—
370#217—61no—
371#215—62no—
372#215—121no—
373#214—62no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—121no—
386C4⋊Dic3—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—31no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—121no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412#204—41no—
413#204—121no—
414ΓL(1,𝔽25)—41no—
415D3×C8—121no—
416D3×C8—121no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3AGL(1,ℤ/8)12yes—
424C2×C3×D3—22no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433D32—84no—
434D32—84no—
435C32×C4—41no—
436C32×C4—41no—
437C32×C4C2×#4111yescharacteristic
438C32×C4H(5,𝔽2)11yescharacteristic
439C3⋊Dic3—21no—
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—91no—
447C22×D4—91no—
448C22×D4—181no—
449C2×SD16—31no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×M16—31no—
453C22×C8—91no—
454#127—91no—
455#126—181no—
456#125—31no—
457#125—181no—
458#123—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461#121—31no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—91no—
467C4×D4—31no—
468C4×D4—91no—
469#117—91no—
470#117—181no—
471C2×C4⋊C4—91no—
472#107—91no—
473#107D3211yescharacteristic, complemented
474#106—31no—
475C4⋊C8—31no—
476#103—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486C22⋊C8—91no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—31no—
490C23×C3—61no—
491C23×C3—61no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—121no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3D3×D411yescharacteristic
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—32no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—122no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—62no—
538#67—122no—
539#67—122no—
540#67—122no—
541#67—122no—
542#67—241no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—121no—
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554D12—21no—
555D12—21no—
556D12—21no—
557D12—42no—
558D12—62no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—121no—
564D12—121no—
565D12—122no—
566D12—122no—
567D12—122no—
568D12—122no—
569D12—242no—
570D12—241no—
571D12#23912yes—
572C4×D3—21no—
573C4×D3—21no—
574C4×D3—42no—
575C4×D3—61no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—121no—
580C4×D3—121no—
581C4×D3—122no—
582C4×D3—122no—
583C4×D3—242no—
584Dic6—21no—
585Dic6—21no—
586C3×C8—21no—
587C3×C8—21no—
588C3×C8—41no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—61no—
594C3⋊C8—61no—
595C3⋊C8—121no—
596C2×C32#54611yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—22no—
600C3⋊D3—81no—
601C3×D3—41no—
602C3×D3—42no—
603C3×D3—81no—
604C24—181no—
605C24—181no—
606C2×Q8—31no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—61no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—182no—
617C2×D4—181no—
618C2×D4—182no—
619C2×D4—361no—
620C2×D4—364no—
621C2×D4—361no—
622C22×C4—31no—
623C22×C4—61no—
624C22×C4—91no—
625C22×C4—181no—
626SD16—121no—
627SD16—182no—
628SD16—361no—
629M16—121no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—361no—
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4C2×D3211yescharacteristic
645C4⋊C4C2×D3211yescharacteristic
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—91no—
650C22⋊C4—91no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—31no—
655C42—181no—
656C42—181no—
657C22×C3—21no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—62no—
661C22×C3—61no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3C2×D3×D411yescharacteristic
668C22×C3C2×D3×D411yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—22no—
673C2×D3—32no—
674C2×D3—32no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—62no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—241no—
694C2×D3—241no—
695C2×D3—241no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3—244no—
699C2×D3—244no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—81no—
710C3×C4—81no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4#100411yescharacteristic
714C3×C4C2×#23911yescharacteristic
715C3×C4D3×#4111yescharacteristic
716C3×C4#100911yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—41no—
721Dic3—41no—
722Dic3—61no—
723Dic3—61no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—241no—
728C32#331011yescharacteristic, complemented, Sylow
729C23—31no—
730C23—61no—
731C23—61no—
732C23—91no—
733C23—181no—
734C23—362no—
735C23—362no—
736C23—362no—
737C23—362no—
738C23—721no—
739C23—721no—
740Q8—61no—
741Q8—61no—
742D4—32no—
743D4—61no—
744D4—61no—
745D4—61no—
746D4—122no—
747D4—182no—
748D4—181no—
749D4—181no—
750D4—362no—
751D4—362no—
752D4—362no—
753D4—362no—
754D4—721no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—91no—
765C2×C4—122no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—362no—
770C2×C4C22×D3211yescharacteristic
771C8—21no—
772C8—61no—
773C8—61no—
774C8—181no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—121no—
779C2×C3—122no—
780C2×C3—241no—
781C2×C3#561011yescharacteristic
782C2×C3#563011yescharacteristic
783C2×C3#577011yescharacteristic
784C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
785C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
786C2×C3#577811yescharacteristic
787D3—42no—
788D3—41no—
789D3—62no—
790D3—62no—
791D3—81no—
792D3—122no—
793D3—241no—
794D3—241no—
795D3—481no—
796C22—61no—
797C22—62no—
798C22—61no—
799C22—61no—
800C22—92no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—181no—
807C22—181no—
808C22—361no—
809C22—361no—
810C22—361no—
811C22—724no—
812C22—724no—
813C22D32×D411yescharacteristic
814C4—41no—
815C4—41no—
816C4—61no—
817C4—61no—
818C4—61no—
819C4—121no—
820C4—121no—
821C4—181no—
822C4—361no—
823C4#6430711yescharacteristic
824C4D3×#23911yescharacteristic
825C3—21no—
826C3#8082111yescharacteristic, complemented
827C3#8118911yescharacteristic, complemented
828C2—121no—
829C2—122no—
830C2—182no—
831C2—241no—
832C2—721no—
833C2#1059462211yescharacteristic
834C2#1059472611yescharacteristic
835C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594621C2
hypercenter#107D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594579C2semidirect
3. #10592581C2semidirect
4. C3×#4891C2semidirect
5. C3×#4886C2semidirect
6. #10590943C2semidirect
7. #10590939C2semidirect
8. #10590799C2semidirect
9. #10590738C2semidirect
10. #10590596C2semidirect
11. #10590593C2semidirect
12. #10590550C2semidirect
13. #10590523C2semidirect
14. #10590478C2semidirect
15. #10590449C2semidirect
22. C4⋊C4×C3⋊D3C22semidirect
23. C2×C3×#204C22semidirect
24. C2×C3×ΓL(1,𝔽25)C22semidirect
25. C3×#897C22semidirect
28. C3×#890C22semidirect
34. #63871C22semidirect
39. Dic3×Dic6C22semidirect
40. #63841C22semidirect
41. C2×#3717C22semidirect
43. C2×#3710C22semidirect
44. C32×#107C22semidirect
45. #63648C22semidirect
46. #63647C22semidirect
47. #63636C22semidirect
48. #63634C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#810C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
55. #63564C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
75. #4891D3semidirect
76. #4886D3semidirect
169. C2×#204C2×D3semidirect
170. C2×ΓL(1,𝔽25)C2×D3semidirect
175. #897C2×D3semidirect
189. #890C2×D3semidirect
201. C3×#107C2×D3semidirect
202. C3×#107C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
226. #810C2×D3semidirect
233. #809C2×D3semidirect
234. #808C2×D3semidirect
473. #107D32semidirect
728. C32#3310semidirect
826. C3#80821semidirect
827. C3#81189semidirect

Maximal subgroups

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

subgroupindex
#105946212
#105945792
#105925812
C3×#48912
C3×#48862
#105909432
#105909392
#105907992
#105907382
#105905962
#105905932
#105905502
#105905232
#105904782
#105904492
#811893
#808213