Finite Group Databasebeta

← #11889110

Subgroups — #11889110

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
1D12×#67C211yesmaximal, characteristic
2#10594853C211yesmaximal, characteristic, complemented
3#10592435C211yesmaximal, characteristic, complemented
4C3×#4731C211yesmaximal, characteristic, complemented
5C3×#4730C211yesmaximal, characteristic, complemented
6#10591177C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590942C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590882C211yesmaximal, characteristic, complemented
11#10590834C211yesmaximal, characteristic, complemented
12#10590833C211yesmaximal, characteristic, complemented
13#10590799C211yesmaximal, characteristic, complemented
14#10590767C211yesmaximal, characteristic, complemented
15#10590766C211yesmaximal, characteristic, complemented
16#80160—31nomaximal
17#79501—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21#64139C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
23C3×C4×#67C2211yescharacteristic
24C3×#924C2211yescharacteristic, complemented
25C22×C3×C3⋊C8C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29#63977—21no—
30#63962—21no—
31#63957—21no—
32#63922—21no—
33#63911C2211yescharacteristic
34#63908C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63886—21no—
37#63869C2211yescharacteristic, complemented
38#63861—21no—
39#63856C2211yescharacteristic, complemented
40#63845—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42#63841C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63648C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63645C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61D4×#67—31no—
62#5642—31no—
63D4×D12—31no—
64#5541—31no—
65C3×#450—31no—
66C3×#435—31no—
67C2×#832—31no—
68#5174—31no—
69#5169—31no—
70#5164—31no—
71#5163—31no—
72#5134—31no—
73#5131—31no—
74#5114—31no—
75C2×#821—31no—
76#5048—31no—
77#4848—31no—
78#4847—31no—
79#4784—31no—
80#4770—31no—
81#4766—31no—
82#4764—31no—
83#4737—31no—
84#4736—31no—
85#4736—31no—
86#4736—61no—
87#4731—31no—
88#4731D311yescharacteristic, complemented
89#4730D311yescharacteristic, complemented
90#4713—31no—
91#4710—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106D3×#67—44no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#625—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116#3752—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8—41no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—22no—
132C3×#204—41no—
133C3×ΓL(1,𝔽25)—41no—
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143Dic32—21no—
144#3717—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×M16—31no—
155C22×C3×C8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×D4—31no—
158#953—61no—
159#946—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162#940—31no—
163#939—61no—
164#938—31no—
165#937—61no—
166#935—61no—
167D4×Dic3—31no—
168#930—31no—
169#930—31no—
170#930—31no—
171#930—61no—
172C4×#67C2×D311yescharacteristic
173#926—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—61no—
177#924—31no—
178#924C2×D311yescharacteristic, complemented
179C22×C3⋊C8C2×D311yescharacteristic, complemented
180C2×#204—31no—
181C2×#204C2×D311yescharacteristic
182C2×#204C2×D311yescharacteristic, complemented
183C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
184#898—61no—
185#895—61no—
186#892—31no—
187#890—31no—
188#890—61no—
189#889—61no—
190#886—61no—
191#882—61no—
192#882—61no—
193#879—61no—
194#877—61no—
195#877—61no—
196#874—31no—
197C4×D12—31no—
198#870—31no—
199C4×Dic6—31no—
200C3×C4⋊C8—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C22⋊C8—21no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8C2×D311yescharacteristic, complemented
206C3×C22⋊C8C2×D311yescharacteristic, complemented
207C3×#97—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821—61no—
224#821C2×D311yescharacteristic
225#821C2×D311yescharacteristic, complemented
226(C2×D3)⋊C8C2×D311yescharacteristic, complemented
227#818—31no—
228#818—31no—
229#818—31no—
230#818—31no—
231#818—61no—
232#818—61no—
233#817—31no—
234#816—31no—
235#815C2×D311yescharacteristic, complemented
236Dic3⋊C8C2×D311yescharacteristic, complemented
237#809—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
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—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—42no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C3×#67—22no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#626—42no—
277#626—42no—
278#626—81no—
279#625—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C32×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—91no—
294#450—31no—
295#450—91no—
296#440—91no—
297#435—31no—
298#418—91no—
299C2×#102—91no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—121no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—121no—
323C2×#67—124no—
324C2×#67D1211yescharacteristic
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—121no—
329D3×D4—62no—
330D3×D4—121no—
331D3×D4—124no—
332C2×D12—22no—
333C2×D12—21no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—41no—
337C2×D12—61no—
338C2×D12—62no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—121no—
343C2×D12C22×D311yescharacteristic
344C2×D12C22×D311yescharacteristic
345C2×C4×D3—61no—
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—62no—
349C3×SD16—121no—
350C3×M16—121no—
351C2×C3×C8—21no—
352C2×C3×C8—21no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—121no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367#217—21no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217D1211yescharacteristic
373#215—121no—
374(C2×D3)⋊C4—61no—
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—121no—
381(C2×D3)⋊C4D1211yescharacteristic
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—121no—
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4D1211yescharacteristic
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—41no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—22no—
414#204—41no—
415#204—121no—
416ΓL(1,𝔽25)—41no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32AGL(1,ℤ/8)12yes—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
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—
433C2×C3×D3—84no—
434D32—84no—
435C32×C4—21no—
436C32×C4C2×#4111yescharacteristic
437C32×C4H(5,𝔽2)11yescharacteristic
438C3⋊Dic3—41no—
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—31no—
453C22×C8—31no—
454#127—91no—
455#126—181no—
456#125—91no—
457#125—181no—
458#123—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461#121—91no—
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#107—91no—
474#106—91no—
475C4⋊C8—31no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486C22⋊C8—31no—
487C22⋊C8D3211yescharacteristic, complemented
488#97—31no—
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—122no—
494C23×C3—122no—
495C23×C3—241no—
496C23×C3C2×D1211yescharacteristic
497C23×C3D3×D411yescharacteristic
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—42no—
501C22×D3—42no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—81no—
505C22×D3—121no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3C2×D1211yescharacteristic
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—32no—
516C3×D4—62no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—122no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4C2×D1211yescharacteristic
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—22no—
541#67—122no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—242no—
548#67—241no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—122no—
561C2×Dic3—122no—
562C2×Dic3—122no—
563C2×Dic3—242no—
564C2×Dic3C2×D1211yescharacteristic
565C2×Dic3C2×D1211yescharacteristic
566C2×Dic3C2×D1211yescharacteristic
567D12—21no—
568D12—21no—
569D12—21no—
570D12—42no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—121no—
576D12—121no—
577D12—122no—
578D12—122no—
579D12—241no—
580D12#23712yes—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—122no—
584Dic6—21no—
585Dic6—21no—
586C3×C8—21no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—21no—
590C3×C8—41no—
591C3×C8—41no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C2×C32—22no—
597C2×C32#54611yescharacteristic
598C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
599C2×C32#57711yescharacteristic
600C3⋊D3—81no—
601C3×D3—41no—
602C3×D3—42no—
603C3×D3—81no—
604C24—61no—
605C24—181no—
606C2×Q8—31no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—62no—
611C2×D4—61no—
612C2×D4—91no—
613C2×D4—121no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—182no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—361no—
621C2×D4—364no—
622C22×C4—31no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4C2×D3211yescharacteristic
626SD16—62no—
627SD16—121no—
628SD16—361no—
629M16—121no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—121no—
633C2×C8C2×D3211yescharacteristic
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C22⋊C4—31no—
647C22⋊C4—31no—
648C22⋊C4—61no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—31no—
655C42—181no—
656C42—181no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—22no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—62no—
668C22×C3—61no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—244no—
675C22×C3#90812yes—
676C22×C3#91412yes—
677C22×C3C22×D1211yescharacteristic
678C22×C3C2×D3×D411yescharacteristic
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—22no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—84no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—241no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3—244no—
699C2×D3—244no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—41no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C2×#23711yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4#100411yescharacteristic
713C3×C4D3×#4111yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—21no—
717Dic3—41no—
718Dic3—41no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726Dic3—241no—
727Dic3—241no—
728C32#331011yescharacteristic, complemented, Sylow
729C23—31no—
730C23—61no—
731C23—61no—
732C23—122no—
733C23—122no—
734C23—181no—
735C23—241no—
736C23—362no—
737C23—362no—
738C23—721no—
739C23D3×D1211yescharacteristic
740Q8—61no—
741Q8—61no—
742D4—32no—
743D4—62no—
744D4—61no—
745D4—61no—
746D4—61no—
747D4—122no—
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—181no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—362no—
768C2×C4—362no—
769C2×C4D3×D1211yescharacteristic
770C2×C4C22×D3211yescharacteristic
771C8—21no—
772C8—21no—
773C8—61no—
774C8—61no—
775C2×C3—22no—
776C2×C3—22no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—42no—
781C2×C3—121no—
782C2×C3—122no—
783C2×C3—241no—
784C2×C3#555411yescharacteristic
785C2×C3#559111yescharacteristic
786C2×C3C2×#90811yescharacteristic
787C2×C3#575111yescharacteristic
788C2×C3C2×#91411yescharacteristic
789C2×C3#577511yescharacteristic
790D3—42no—
791D3—41no—
792D3—81no—
793D3—241no—
794D3—241no—
795D3—481no—
796C22—21no—
797C22—21no—
798C22—61no—
799C22—61no—
800C22—61no—
801C22—62no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—244no—
808C22—361no—
809C22—361no—
810C22—361no—
811C22—724no—
812C22#6379412yes—
813C22C2×D3×D1211yescharacteristic
814C4—21no—
815C4—61no—
816C4—61no—
817C4—61no—
818C4—121no—
819C4—121no—
820C4—361no—
821C4—361no—
822C4—361no—
823C4D3×#23711yescharacteristic
824C4#6431311yescharacteristic
825C3—21no—
826C3#7950111yescharacteristic, complemented
827C3#8016011yescharacteristic, complemented
828C2—22no—
829C2—121no—
830C2—122no—
831C2—241no—
832C2—721no—
833C2#1059429211yescharacteristic
834C2C2×#6379411yescharacteristic
835C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalD12×#67C2
hypercenterC22⋊C8D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594853C2semidirect
3. #10592435C2semidirect
4. C3×#4731C2semidirect
5. C3×#4730C2semidirect
6. #10591177C2semidirect
7. C2×#63563C2semidirect
8. #10590942C2semidirect
9. #10590939C2semidirect
10. #10590882C2semidirect
11. #10590834C2semidirect
12. #10590833C2semidirect
13. #10590799C2semidirect
14. #10590767C2semidirect
15. #10590766C2semidirect
22. C2×C4⋊(C3⋊Dic3)C22semidirect
24. C3×#924C22semidirect
25. C22×C3×C3⋊C8C22semidirect
27. C2×C3×#204C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
37. #63869C22semidirect
39. #63856C22semidirect
41. Dic3×Dic6C22semidirect
42. #63841C22semidirect
43. C2×#3717C22semidirect
44. C32×C22⋊C8C22semidirect
45. #63648C22semidirect
46. #63648C22semidirect
47. #63645C22semidirect
48. #63645C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#815C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
56. #63564C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
88. #4731D3semidirect
89. #4730D3semidirect
178. #924C2×D3semidirect
179. C22×C3⋊C8C2×D3semidirect
182. C2×#204C2×D3semidirect
183. C2×ΓL(1,𝔽25)C2×D3semidirect
205. C3×C22⋊C8C2×D3semidirect
206. C3×C22⋊C8C2×D3semidirect
225. #821C2×D3semidirect
226. (C2×D3)⋊C8C2×D3semidirect
235. #815C2×D3semidirect
236. Dic3⋊C8C2×D3semidirect
487. C22⋊C8D32semidirect
728. C32#3310semidirect
826. C3#79501semidirect
827. C3#80160semidirect

Maximal subgroups

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

subgroupindex
D12×#672
#105948532
#105924352
C3×#47312
C3×#47302
#105911772
C2×#635632
#105909422
#105909392
#105908822
#105908342
#105908332
#105907992
#105907672
#105907662
#801603
#795013