Finite Group Databasebeta

← #11884037

Subgroups — #11884037

Order 1152.

1154 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63798C211yesmaximal, characteristic, complemented
2C2×#63796C211yesmaximal, characteristic, complemented
3#10594004C211yesmaximal, characteristic, complemented
4#10593901C211yesmaximal, characteristic, complemented
5#10592535C211yesmaximal, characteristic, complemented
6C3×#4848C211yesmaximal, characteristic, complemented
7C3×#4844C211yesmaximal, characteristic, complemented
8#10590964C211yesmaximal, characteristic, complemented
9#10590945C211yesmaximal, characteristic, complemented
10#10590943C211yesmaximal, characteristic, complemented
11#10590842C211yesmaximal, characteristic, complemented
12#10590839C211yesmaximal, characteristic, complemented
13#10590824C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590354C211yesmaximal, characteristic, complemented
16#80553—31nomaximal
17#80404—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×D3×D12—21no—
21C2×#3797C2211yescharacteristic, complemented
22C2×#3796C2211yescharacteristic, complemented
23C2×#3743C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic, complemented
30C3×#875C2211yescharacteristic, complemented
31C3×#874C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63922—21no—
35#63922—21no—
36#63916C2211yescharacteristic
37#63916C2211yescharacteristic
38#63916C2211yescharacteristic, complemented
39#63910—21no—
40#63908—21no—
41#63893—21no—
42#63880—21no—
43#63871C2211yescharacteristic, complemented
44#63852—21no—
45C2×#3715C2211yescharacteristic
46C2×#3715C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3713C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50#63798—24no—
51#63796—24no—
52C32×C4⋊C8C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×#821C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60#63576C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×D3×SD16—31no—
66C2×#911—31no—
67#5717—31no—
68#5677—31no—
69#5576—31no—
70D4×D12—31no—
71C3×#463—31no—
72C3×#460—31no—
73#5172—31no—
74#5170—31no—
75#5169—31no—
76#5156—31no—
77#5074—31no—
78#5058—31no—
79#5026—31no—
80#5018—31no—
81#4848D311yescharacteristic, complemented
82#4844D311yescharacteristic, complemented
83#4836—31no—
84#4836—31no—
85#4836—61no—
86#4812—31no—
87#4806—31no—
88#4781—31no—
89#4780—31no—
90#4776—31no—
91#4775—31no—
92#4775—31no—
93#4773—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)D411yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802—22no—
119#3802—41no—
120#3802—41no—
121D3×D12—44no—
122#3797—22no—
123#3797—41no—
124#3796—22no—
125#3796—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C32×C42C2311yescharacteristic
129#3752D411yescharacteristic
130#3752D411yescharacteristic
131C4⋊(C3⋊Dic3)D411yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3743—22no—
135C8×C3⋊D3—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×C4×Dic3—21no—
143C3×D24—22no—
144C3×#204—22no—
145C3×#204—22no—
146C3×#204—22no—
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3715—22no—
153#3715—41no—
154#3715D414yescomplemented
155#3713—22no—
156#3713—41no—
157#3265—91noSylow
158C2×#239—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C22×D12—61no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×D8—31no—
172C3×#127—31no—
173C3×#124—31no—
174C3×C4×Q8—31no—
175C3×C4×D4—31no—
176#946—31no—
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—31no—
180#938—31no—
181#938—31no—
182#938—31no—
183#938—61no—
184#937—61no—
185#937—61no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193#930—61no—
194#914—64no—
195D3×SD16—64no—
196D3×SD16—64no—
197#911—64no—
198C2×D24C2×D311yescharacteristic
199C2×#204C2×D311yescharacteristic
200C2×#204C2×D311yescharacteristic, complemented
201C2×#204C2×D311yescharacteristic, complemented
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—61no—
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207C2×D3×C8—61no—
208#897—31no—
209#897—61no—
210#895—31no—
211#895—31no—
212#895—31no—
213#895—61no—
214#885—61no—
215#884—61no—
216#882—61no—
217#882—61no—
218#67⋊C4—61no—
219#878—61no—
220#875—61no—
221#875C2×D311yescharacteristic, complemented
222#874C2×D311yescharacteristic
223C4×D12—31no—
224C4×D12—31no—
225C4×D12—61no—
226C4×D12—61no—
227C4×D12C2×D311yescharacteristic
228C4×Dic6C2×D311yescharacteristic, complemented
229C3×C4⋊C8—21no—
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×#103—31no—
233C3×#102—31no—
234C3×#102—31no—
235C3×#102—31no—
236#835—31no—
237#832—31no—
238#821C2×D311yescharacteristic, complemented
239#821C2×D311yescharacteristic, complemented
240#821C2×D311yescharacteristic, complemented
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—61no—
246(C2×D3)⋊C8—61no—
247#816C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250#807—31no—
251#807—31no—
252#803—31no—
253#803—31no—
254#803—61no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3C2×D411yescharacteristic
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4⋊(C3⋊D3)—22no—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12—81no—
290C3×D12C2×D412yes—
291C3×C4×D3—42no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6C2×D412yescomplemented
296#627—42no—
297#626—42no—
298#626—42no—
299#626—42no—
300#626—42no—
301#625—42no—
302#625—42no—
303#624—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C32×C8—21no—
307C3⋊(C3⋊C8)—21no—
308C3⋊(C3⋊C8)C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—31no—
317#460—31no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×Q8—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C22×C3×C4—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C22×Dic3—61no—
346#239—62no—
347#239—121no—
348D3×Q8—62no—
349D3×Q8—62no—
350D3×Q8—121no—
351D3×Q8—121no—
352#237—62no—
353#237—121no—
354D3×D4—62no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4—124no—
359D3×D4—121no—
360D3×D4—121no—
361D3×D4—121no—
362D3×D4—121no—
363C2×D12—21no—
364C2×D12—21no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—124no—
373C2×D12C22×D311yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×Dic6—61no—
388C2×Dic6—61no—
389C2×Dic6C22×D311yescharacteristic
390C2×Dic6C22×D311yescharacteristic
391C3×SD16—62no—
392C3×SD16—62no—
393C3×SD16—62no—
394C3×D8—62no—
395C2×C3×C8—21no—
396C2×C3×C8—21no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—31no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C42—21no—
408C3×C42—61no—
409C3×C42C22×D311yescharacteristic
410C3×C42C22×D311yescharacteristic
411#217—61no—
412#217—61no—
413#217—61no—
414#215—34no—
415#215—62no—
416#215—121no—
417#214—34no—
418#214—62no—
419#214—121no—
420#213—62no—
421#213—62no—
422#213—121no—
423#213—121no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—61no—
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D311yescharacteristic
443C4⋊Dic3C22×D311yescharacteristic
444Dic3⋊C4—21no—
445Dic3⋊C4—61no—
446C4×Dic3—21no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—61no—
453D24—22no—
454#204—22no—
455#204—22no—
456#204—22no—
457ΓL(1,𝔽25)—62no—
458ΓL(1,𝔽25)—62no—
459ΓL(1,𝔽25)—122no—
460D3×C8—62no—
461D3×C8—62no—
462D3×C8—122no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
470C2×C3×D3—22no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482D32—84no—
483D32—84no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3×Dic3—22no—
491C3×Dic3—41no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—91no—
496C22×D4—91no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127—31no—
513#124—31no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—91no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—31no—
525C4×D4—31no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8D3211yescharacteristic, complemented
530#103—31no—
531#103—91no—
532#102—31no—
533#102—31no—
534#102—31no—
535#102—91no—
536C22⋊C8—91no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—31no—
550C22×D3—31no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—241no—
565C3×Q8—32no—
566C3×Q8—61no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×D4—32no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—122no—
578C3×D4—241no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—122no—
587C2×C3×C4D3×D411yescharacteristic
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4D3×D411yescharacteristic
590C2×C3×C4D3×D411yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—122no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—42no—
620D12—62no—
621D12—62no—
622D12—81no—
623D12—122no—
624D12—122no—
625D12—122no—
626D12—122no—
627D12—122no—
628D12D3×D412yes—
629C4×D3—42no—
630C4×D3—61no—
631C4×D3—61no—
632C4×D3—61no—
633C4×D3—61no—
634C4×D3—61no—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—121no—
639C4×D3—121no—
640C4×D3—121no—
641C4×D3—121no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—122no—
645Dic6—21no—
646Dic6—21no—
647Dic6—21no—
648Dic6—122no—
649Dic6—122no—
650Dic6D3×D412yescomplemented
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—41no—
656C3×C8—41no—
657C3⋊C8—32no—
658C3⋊C8—32no—
659C3⋊C8—62no—
660C3⋊C8—61no—
661C3⋊C8—61no—
662C3⋊C8—121no—
663C2×C32D4211yescharacteristic
664C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
665C2×C32#57711yescharacteristic
666C3⋊D3—22no—
667C3⋊D3—41no—
668C3×D3—42no—
669C3×D3—81no—
670C3×D3—81no—
671C3×D3—81no—
672C24—181no—
673C24—181no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8—31no—
678C2×Q8—181no—
679C2×Q8—182no—
680C2×Q8—361no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—182no—
695C2×D4—182no—
696C2×D4—364no—
697C2×D4—361no—
698C2×D4—361no—
699C22×C4—61no—
700C22×C4—91no—
701C22×C4—91no—
702C22×C4—181no—
703C22×C4—181no—
704SD16—62no—
705SD16—62no—
706SD16—62no—
707SD16—94no—
708SD16—182no—
709SD16—361no—
710D8—62no—
711D8—182no—
712D8—361no—
713M16—182no—
714C2×C8—91no—
715C2×C8—91no—
716C2×C8—182no—
717C2×C8C2×D3211yescharacteristic
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—31no—
720C4⋊C4—31no—
721C4⋊C4—61no—
722C4⋊C4—91no—
723C4⋊C4—181no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—91no—
728C22⋊C4—91no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—61no—
734C42C2×D3211yescharacteristic
735C22×C3—21no—
736C22×C3—62no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—22no—
751C2×D3—32no—
752C2×D3—32no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—62no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3—244no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—62no—
793C3×C4—121no—
794C3×C4—121no—
795C3×C4—121no—
796C3×C4C2×D3×D411yescharacteristic
797C3×C4C2×D3×D411yescharacteristic
798C3×C4#100911yescharacteristic
799C3×C4#100911yescharacteristic
800Dic3—22no—
801Dic3—41no—
802Dic3—41no—
803Dic3—41no—
804Dic3—61no—
805Dic3—61no—
806Dic3—61no—
807Dic3—61no—
808Dic3—121no—
809Dic3—121no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—91no—
816C23—91no—
817C23—362no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23—721no—
823Q8—32no—
824Q8—61no—
825Q8—61no—
826Q8—61no—
827Q8—362no—
828D4—32no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—122no—
837D4—182no—
838D4—241no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—91no—
850C2×C4—91no—
851C2×C4—122no—
852C2×C4—181no—
853C2×C4—181no—
854C2×C4—181no—
855C2×C4—181no—
856C2×C4—362no—
857C2×C4—362no—
858C2×C4#380211yescharacteristic
859C2×C4#380211yescharacteristic
860C2×C4C22×D3211yescharacteristic
861C8—21no—
862C8—21no—
863C8—92no—
864C8—181no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—122no—
869C2×C3—241no—
870C2×C3—241no—
871C2×C3—241no—
872C2×C3#560911yescharacteristic
873C2×C3#560911yescharacteristic
874C2×C3#576211yescharacteristic
875C2×C3#577011yescharacteristic
876C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
877C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
878D3—42no—
879D3—62no—
880D3—62no—
881D3—81no—
882D3—81no—
883D3—81no—
884D3—122no—
885D3—121no—
886D3—121no—
887D3—241no—
888C22—62no—
889C22—92no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—181no—
902C22—181no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—724no—
907C22—724no—
908C22C2×#380211yescharacteristic
909C4—21no—
910C4—21no—
911C4—62no—
912C4—121no—
913C4—121no—
914C4—121no—
915C4—181no—
916C4—181no—
917C4D32×D411yescharacteristic
918C4#6432011yescharacteristic
919C3—21no—
920C3#8040411yescharacteristic, complemented
921C3#8055311yescharacteristic, complemented
922C2—122no—
923C2—182no—
924C2—241no—
925C2—241no—
926C2—241no—
927C2—361no—
928C2#1059461811yescharacteristic
929C2#1059468611yescharacteristic
930C2#1059471611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3265
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
1. C2×#63798C2semidirect
2. C2×#63796C2semidirect
3. #10594004C2semidirect
4. #10593901C2semidirect
5. #10592535C2semidirect
6. C3×#4848C2semidirect
7. C3×#4844C2semidirect
8. #10590964C2semidirect
9. #10590945C2semidirect
10. #10590943C2semidirect
11. #10590842C2semidirect
12. #10590839C2semidirect
13. #10590824C2semidirect
14. #10590358C2semidirect
15. #10590354C2semidirect
21. C2×#3797C22semidirect
22. C2×#3796C22semidirect
23. C2×#3743C22semidirect
24. C2×C8×C3⋊D3C22semidirect
28. C2×C3×#204C22semidirect
29. C2×C3×#204C22semidirect
30. C3×#875C22semidirect
33. C3×C4×Dic6C22semidirect
38. #63916C22semidirect
43. #63871C22semidirect
46. C2×#3715C22semidirect
47. C2×#3715C22semidirect
48. C2×#3713C22semidirect
49. C2×#3713C22semidirect
52. C32×C4⋊C8C22semidirect
53. #63647C22semidirect
54. #63647C22semidirect
55. #63630C22semidirect
56. C3×#821C22semidirect
57. C3×#821C22semidirect
58. C3×#821C22semidirect
59. C3×#816C22semidirect
60. #63576C22semidirect
61. #63565C22semidirect
81. #4848D3semidirect
82. #4844D3semidirect
154. #3715D4semidirect
200. C2×#204C2×D3semidirect
201. C2×#204C2×D3semidirect
221. #875C2×D3semidirect
228. C4×Dic6C2×D3semidirect
230. C3×C4⋊C8C2×D3semidirect
231. C3×C4⋊C8C2×D3semidirect
238. #821C2×D3semidirect
239. #821C2×D3semidirect
240. #821C2×D3semidirect
247. #816C2×D3semidirect
295. C3×Dic6C2×D4semidirect
308. C3⋊(C3⋊C8)C2×D4semidirect
469. C2×C3⋊D3AGL(1,ℤ/8)semidirect
529. C4⋊C8D32semidirect
650. Dic6D3×D4semidirect
810. C32#3265semidirect
920. C3#80404semidirect
921. C3#80553semidirect

Maximal subgroups

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

subgroupindex
C2×#637982
C2×#637962
#105940042
#105939012
#105925352
C3×#48482
C3×#48442
#105909642
#105909452
#105909432
#105908422
#105908392
#105908242
#105903582
#105903542
#805533
#804043