Finite Group Databasebeta

← #11889126

Subgroups — #11889126

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594004C211yesmaximal, characteristic
2#10593917C211yesmaximal, characteristic, complemented
3#10592546C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×#4836C211yesmaximal, characteristic, complemented
6#10590942C211yesmaximal, characteristic, complemented
7#10590942C211yesmaximal, characteristic, complemented
8#10590939C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590837C211yesmaximal, characteristic, complemented
11#10590833C211yesmaximal, characteristic, complemented
12#10590829C211yesmaximal, characteristic, complemented
13#10590680C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590275C211yesmaximal, characteristic, complemented
16#80397—31nomaximal
17#79501—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22#64079C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic, complemented
24C2×C3×#204C2211yescharacteristic, complemented
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×#874C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic, complemented
30#63922—21no—
31#63922—21no—
32#63916—21no—
33#63908C2211yescharacteristic
34#63908C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic, complemented
36#63884—21no—
37#63877—21no—
38#63859—21no—
39#63856C2211yescharacteristic, complemented
40#63856C2211yescharacteristic, complemented
41#63847—21no—
42#63841C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63645C2211yescharacteristic, complemented
48#63644C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5717—31no—
62#5581—31no—
63D4×D12—31no—
64#5541—31no—
65C3×#460—31no—
66C3×#435—31no—
67#5174—31no—
68#5171—31no—
69#5169—31no—
70#5169—31no—
71#5134—31no—
72#5131—31no—
73#5114—31no—
74C2×#821—31no—
75#5071—31no—
76#5026—31no—
77#4848D311yescharacteristic, complemented
78#4847—31no—
79#4847—31no—
80#4847—61no—
81#4836D311yescharacteristic, complemented
82#4779—31no—
83#4774—31no—
84#4770—31no—
85D3×#102—31no—
86#4737—31no—
87#4736—31no—
88#4731—31no—
89#4731—31no—
90#4713—31no—
91#4710—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12D411yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109#3802—44no—
110D3×D12—22no—
111D3×D12—22no—
112D3×D12—41no—
113D3×D12—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C42C2311yescharacteristic
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132C3×#204—41no—
133C3×ΓL(1,𝔽25)—41no—
134C3×D3×C8—41no—
135#3724—21no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144#3717—22no—
145#3310—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—31no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×M16—31no—
155C22×C3×C8—31no—
156C3×#127—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159#946—31no—
160#946—31no—
161C2×#215—31no—
162#938—31no—
163#938—31no—
164#938—61no—
165#937—61no—
166#937—61no—
167#935—61no—
168#930—31no—
169#930—31no—
170#926—31no—
171C2×C4⋊Dic3—31no—
172#924—31no—
173#924—31no—
174C2×#204—31no—
175C2×#204C2×D311yescharacteristic, complemented
176C2×#204C2×D311yescharacteristic, complemented
177C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
178C2×D3×C8C2×D311yescharacteristic, complemented
179#895—61no—
180#894—61no—
181#892—31no—
182D3×C4⋊C4—31no—
183#889—61no—
184#889—61no—
185#882—61no—
186#882—61no—
187#879—61no—
188#877—61no—
189#876—61no—
190#874C2×D311yescharacteristic
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—61no—
194C4×D12C2×D311yescharacteristic
195#872—61no—
196#870—31no—
197#870—31no—
198#870—61no—
199C4×Dic6C2×D311yescharacteristic, complemented
200C3×C4⋊C8—21no—
201C3×C4⋊C8C2×D311yescharacteristic, complemented
202C3×C4⋊C8C2×D311yescharacteristic, complemented
203C3×#102—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
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, complemented
225#821C2×D311yescharacteristic, complemented
226(C2×D3)⋊C8C2×D311yescharacteristic, complemented
227(C2×D3)⋊C8C2×D311yescharacteristic, complemented
228#818—31no—
229#818—31no—
230#818—31no—
231#818—61no—
232#817—31no—
233#817—31no—
234#817—61no—
235#816—31no—
236#809—31no—
237#807—31no—
238#803C2×D311yescharacteristic, complemented
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)#4112yes—
258C4×C3⋊D3—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—22no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12—81no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#626—42no—
277#626—42no—
278#625—42no—
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—31no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—31no—
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—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—61no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—121no—
322D3×D4—121no—
323D3×D4—124no—
324D3×D4—124no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—121no—
335C2×D12—121no—
336C2×D12D1211yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—121no—
343C2×C4×D3C22×D311yescharacteristic
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6C22×D311yescharacteristic
346C3×SD16—121no—
347C3×SD16—121no—
348C3×M16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—121no—
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—61no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C42—21no—
364C3×C42—61no—
365C3×C42C22×D311yescharacteristic
366C3×C42C22×D311yescharacteristic
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#215—62no—
373(C2×D3)⋊C4—61no—
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
382(C2×D3)⋊C4D1211yescharacteristic
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3D1211yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—121no—
406Dic3⋊C4—121no—
407C4×Dic3—21no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412#204—41no—
413#204—41no—
414#204—62no—
415ΓL(1,𝔽25)—41no—
416D3×C8—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3AGL(1,ℤ/8)12yes—
433D32—84no—
434D32—84no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4C2×#4111yescharacteristic
438C32×C4H(5,𝔽2)11yescharacteristic
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3⋊Dic3—41no—
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—31no—
451C2×SD16—91no—
452C2×M16—31no—
453C22×C8—31no—
454#127—31no—
455#126—181no—
456#125—91no—
457#125—181no—
458#123—181no—
459C22⋊Q8—91no—
460C22⋊Q8—91no—
461#121—91no—
462#121—91no—
463#121—181no—
464#120—181no—
465#120—181no—
466C4×Q8—31no—
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⋊C8D3211yescharacteristic, complemented
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⋊C8—31no—
488#97—31no—
489C23×C3—31no—
490C23×C3—31no—
491C23×C3—61no—
492C23×C3—61no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—121no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—241no—
507C22×D3—241no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3C2×D1211yescharacteristic
511C22×D3C2×D1211yescharacteristic
512C3×Q8—61no—
513C3×Q8—61no—
514C3×D4—62no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—122no—
520C3×D4—241no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4C2×D1211yescharacteristic
533C2×C3×C4C2×D1211yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538#67—122no—
539#67—122no—
540#67—122no—
541#67—122no—
542#67—122no—
543#67—122no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3—122no—
556C2×Dic3C2×D1211yescharacteristic
557C2×Dic3C2×D1211yescharacteristic
558D12—22no—
559D12—21no—
560D12—21no—
561D12—21no—
562D12—21no—
563D12—32no—
564D12—32no—
565D12—42no—
566D12—62no—
567D12—61no—
568D12—61no—
569D12—81no—
570D12—121no—
571D12—122no—
572D12—122no—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—242no—
581Dic6—21no—
582Dic6—21no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—41no—
588C3×C8—41no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C2×C32#54611yescharacteristic
594C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
595C2×C32#57711yescharacteristic
596C3⋊D3—42no—
597C3×D3—22no—
598C3×D3—41no—
599C3×D3—81no—
600C3×D3—81no—
601C24—181no—
602C24—181no—
603C2×Q8—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—31no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—91no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4—182no—
613C2×D4—182no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—361no—
617C2×D4—361no—
618C2×D4—364no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—181no—
622C22×C4—181no—
623SD16—121no—
624SD16—121no—
625SD16—182no—
626M16—121no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—121no—
630C2×C8C2×D3211yescharacteristic
631C2×C8C2×D3211yescharacteristic
632C4⋊C4—31no—
633C4⋊C4—31no—
634C4⋊C4—61no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C22⋊C4—31no—
644C22⋊C4—31no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C42—61no—
652C42—181no—
653C42C2×D3211yescharacteristic
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3C22×D1211yescharacteristic
668C22×C3C2×D3×D411yescharacteristic
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—122no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—244no—
690C2×D3—244no—
691C2×D3—244no—
692C2×D3—244no—
693C2×D3#90812yes—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—61no—
703C3×C4—61no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4#100411yescharacteristic
707C3×C4#100411yescharacteristic
708C3×C4D3×#4111yescharacteristic
709C3×C4D3×#4111yescharacteristic
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719Dic3—121no—
720Dic3—241no—
721Dic3—241no—
722Dic3—241no—
723C32#331011yescharacteristic, complemented, Sylow
724C23—31no—
725C23—31no—
726C23—61no—
727C23—61no—
728C23—181no—
729C23—362no—
730C23—362no—
731C23—362no—
732C23—362no—
733C23—721no—
734C23—721no—
735Q8—61no—
736Q8—61no—
737D4—62no—
738D4—61no—
739D4—61no—
740D4—61no—
741D4—61no—
742D4—92no—
743D4—122no—
744D4—181no—
745D4—241no—
746D4—362no—
747D4—362no—
748D4—362no—
749D4—362no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—362no—
762C2×C4—362no—
763C2×C4D3×D1211yescharacteristic
764C2×C4D3×D1211yescharacteristic
765C2×C4C22×D3211yescharacteristic
766C8—21no—
767C8—21no—
768C8—61no—
769C8—61no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—62no—
774C2×C3—121no—
775C2×C3—241no—
776C2×C3—241no—
777C2×C3#555411yescharacteristic
778C2×C3#561211yescharacteristic
779C2×C3C2×#90811yescharacteristic
780C2×C3#575111yescharacteristic
781C2×C3#576211yescharacteristic
782C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
783D3—22no—
784D3—41no—
785D3—81no—
786D3—81no—
787D3—122no—
788D3—122no—
789D3—242no—
790C22—32no—
791C22—61no—
792C22—61no—
793C22—61no—
794C22—61no—
795C22—61no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—182no—
803C22—361no—
804C22—361no—
805C22—724no—
806C22—724no—
807C22C2×D3×D1211yescharacteristic
808C4—21no—
809C4—21no—
810C4—61no—
811C4—61no—
812C4—121no—
813C4—121no—
814C4—361no—
815C4—361no—
816C4—361no—
817C4#6431311yescharacteristic
818C4#6431911yescharacteristic
819C3—21no—
820C3#7950111yescharacteristic, complemented
821C3#8039711yescharacteristic, complemented
822C2—62no—
823C2—121no—
824C2—241no—
825C2—241no—
826C2—362no—
827C2#1059463011yescharacteristic
828C2#1059467711yescharacteristic
829C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenterC4⋊C8D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593917C2semidirect
3. #10592546C2semidirect
4. C3×#4848C2semidirect
5. C3×#4836C2semidirect
6. #10590942C2semidirect
7. #10590942C2semidirect
8. #10590939C2semidirect
9. D3×#821C2semidirect
10. #10590837C2semidirect
11. #10590833C2semidirect
12. #10590829C2semidirect
13. #10590680C2semidirect
14. #10590362C2semidirect
15. #10590275C2semidirect
22. #64079C22semidirect
23. C2×C3×#204C22semidirect
24. C2×C3×#204C22semidirect
25. C2×C3×ΓL(1,𝔽25)C22semidirect
26. C2×C3×D3×C8C22semidirect
29. C3×C4×Dic6C22semidirect
35. D3×C4⋊Dic3C22semidirect
39. #63856C22semidirect
40. #63856C22semidirect
42. #63841C22semidirect
44. C32×C4⋊C8C22semidirect
47. #63645C22semidirect
48. #63644C22semidirect
49. C3×#821C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
77. #4848D3semidirect
81. #4836D3semidirect
175. C2×#204C2×D3semidirect
176. C2×#204C2×D3semidirect
177. C2×ΓL(1,𝔽25)C2×D3semidirect
178. C2×D3×C8C2×D3semidirect
199. C4×Dic6C2×D3semidirect
201. C3×C4⋊C8C2×D3semidirect
202. C3×C4⋊C8C2×D3semidirect
224. #821C2×D3semidirect
225. #821C2×D3semidirect
226. (C2×D3)⋊C8C2×D3semidirect
227. (C2×D3)⋊C8C2×D3semidirect
238. #803C2×D3semidirect
475. C4⋊C8D32semidirect
723. C32#3310semidirect
820. C3#79501semidirect
821. C3#80397semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105939172
#105925462
C3×#48482
C3×#48362
#105909422
#105909392
D3×#8212
#105908372
#105908332
#105908292
#105906802
#105903622
#105902752
#803973
#795013