Finite Group Databasebeta

← #11884502

Subgroups — #11884502

Order 1152.

1082 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic, complemented
2C2×#63798C211yesmaximal, characteristic, complemented
3#10594005C211yesmaximal, characteristic, complemented
4#10593900C211yesmaximal, characteristic, complemented
5#10592535C211yesmaximal, characteristic, complemented
6C3×#4845C211yesmaximal, characteristic, complemented
7C3×#4843C211yesmaximal, characteristic, complemented
8#10590965C211yesmaximal, characteristic, complemented
9#10590964C211yesmaximal, characteristic, complemented
10#10590963C211yesmaximal, characteristic, complemented
11#10590945C211yesmaximal, characteristic, complemented
12#10590842C211yesmaximal, characteristic, complemented
13#10590839C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590354C211yesmaximal, characteristic, complemented
16#80628—31nomaximal
17#80348—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C2×#3743C2211yescharacteristic
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C3×#875C2211yescharacteristic
30C3×#874C2211yescharacteristic, complemented
31C3×C4×D12C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63923—21no—
34D3×(C2×D3)⋊C4—21no—
35#63916C2211yescharacteristic
36#63916C2211yescharacteristic
37#63916C2211yescharacteristic, complemented
38#63911—21no—
39#63906—21no—
40Dic3×D12—21no—
41#63891—21no—
42#63886—21no—
43#63886—21no—
44#63871C2211yescharacteristic
45C2×#3715C2211yescharacteristic
46C2×#3715C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3713C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50#63810—24no—
51#63798—24no—
52C32×C4⋊C8C2211yescharacteristic, complemented
53#63647C2211yescharacteristic
54#63647C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic, complemented
58C3×#821C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60#63576C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic
63C2×#919—31no—
64C2×#914—31no—
65C2×#912—31no—
66C2×#911—31no—
67#5718—31no—
68#5676—31no—
69#5577—31no—
70#5554—31no—
71C3×#464—31no—
72C3×#459—31no—
73#5187—31no—
74#5172—31no—
75#5158—31no—
76#5156—31no—
77#5074—31no—
78#5058—31no—
79#5026—31no—
80#5018—31no—
81#4845D311yescharacteristic, complemented
82#4843D311yescharacteristic, complemented
83#4836—31no—
84#4836—31no—
85#4836—61no—
86#4812—31no—
87#4810—31no—
88#4783—31no—
89#4781—31no—
90#4780—31no—
91#4775—31no—
92#4775—31no—
93#4773—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)D411yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802—41no—
119#3796—22no—
120#3796—22no—
121#3796—22no—
122#3796—41no—
123#3796—41no—
124#3796—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C42C2311yescharacteristic
128#3752D411yescharacteristic
129#3752D411yescharacteristic
130C4⋊(C3⋊Dic3)D411yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3743—22no—
134C8×C3⋊D3—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3—21no—
142C3×Dic12—22no—
143C3×D24—22no—
144C3×D24—22no—
145C3×#204—22no—
146Dic3⋊Dic3—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3715—22no—
152#3715—41no—
153#3715D414yescomplemented
154#3713—22no—
155#3713—41no—
156#3268—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#237—31no—
161C2×#237—31no—
162C2×#237—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C2×C3×D8—31no—
169C3×#127—31no—
170C3×#124—31no—
171C3×C4×Q8—31no—
172C3×C4×D4—31no—
173#946—31no—
174C2×#215—31no—
175C2×#215—31no—
176C2×#215—31no—
177#940—61no—
178#939—61no—
179#939—61no—
180#938—31no—
181#938—31no—
182#938—31no—
183D4×Dic3—61no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—31no—
191#930—61no—
192C2×(C2×D3)⋊C4—61no—
193#919—64no—
194#914—64no—
195#912—64no—
196#911—64no—
197C2×Dic12C2×D311yescharacteristic, complemented
198C2×D24C2×D311yescharacteristic
199C2×D24C2×D311yescharacteristic
200C2×#204C2×D311yescharacteristic
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—61no—
204C2×D3×C8—31no—
205C2×D3×C8—31no—
206C2×D3×C8—61no—
207#897—31no—
208#895—31no—
209#895—31no—
210#895—31no—
211#895—61no—
212#895—61no—
213#886—61no—
214#884—61no—
215#883—61no—
216#882—61no—
217#882—61no—
218D3×C22⋊C4—61no—
219#875C2×D311yescharacteristic
220#874—61no—
221#874C2×D311yescharacteristic, complemented
222C4×D12—31no—
223C4×D12—31no—
224C4×D12—61no—
225C4×D12—61no—
226C4×D12C2×D311yescharacteristic
227C4×Dic6C2×D311yescharacteristic, complemented
228C3×C4⋊C8—21no—
229C3×C4⋊C8C2×D311yescharacteristic, complemented
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×#103—31no—
232C3×#102—31no—
233C3×#102—31no—
234C3×#102—31no—
235#835—31no—
236#832—31no—
237#821C2×D311yescharacteristic
238#821C2×D311yescharacteristic, complemented
239#821C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—61no—
245(C2×D3)⋊C8—61no—
246#816C2×D311yescharacteristic, complemented
247#810—31no—
248#809—31no—
249#807—31no—
250#807—31no—
251#803—31no—
252#803—31no—
253#803—61no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—41no—
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12—81no—
286C3×D12C2×D412yes—
287C3×C4×D3—81no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6C2×D412yes—
292#626—42no—
293#626—42no—
294#626—42no—
295#626—81no—
296#626—81no—
297#626—81no—
298#625—42no—
299D3×Dic3—42no—
300D3×Dic3—42no—
301D3×Dic3—42no—
302C32×C8—21no—
303C32×C8—21no—
304C3⋊(C3⋊C8)—21no—
305C3⋊(C3⋊C8)C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—31no—
314#459—31no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C22×C3×C4—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343#239—62no—
344#239—62no—
345#239—62no—
346#239—121no—
347#239—121no—
348#239—121no—
349#237—62no—
350#237—62no—
351#237—62no—
352#237—121no—
353#237—121no—
354#237—121no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—121no—
358D3×D4—121no—
359C2×D12—21no—
360C2×D12—21no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12C22×D311yescharacteristic
371C2×D12C22×D311yescharacteristic
372C2×D12C22×D311yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×C4×D3—21no—
375C2×C4×D3—31no—
376C2×C4×D3—31no—
377C2×C4×D3—31no—
378C2×C4×D3—31no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×Dic6C22×D311yescharacteristic
385C2×Dic6C22×D311yescharacteristic
386C3×Q16—62no—
387C3×SD16—62no—
388C3×D8—62no—
389C3×D8—62no—
390C2×C3×C8—21no—
391C2×C3×C8—21no—
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C22×D311yescharacteristic
396C3×C4⋊C4—31no—
397C3×C4⋊C4—31no—
398C3×C4⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C42—21no—
403C3×C42—61no—
404C3×C42C22×D311yescharacteristic
405C3×C42C22×D311yescharacteristic
406#217—61no—
407#217—61no—
408#217—61no—
409#215—34no—
410#215—62no—
411#215—121no—
412#214—34no—
413#214—62no—
414#214—121no—
415#213—62no—
416#213—62no—
417#213—121no—
418#213—121no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—61no—
436C4⋊Dic3—61no—
437C4⋊Dic3C22×D311yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—21no—
440Dic3⋊C4—61no—
441C4×Dic3—21no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—61no—
448Dic12—22no—
449D24—22no—
450D24—22no—
451#204—22no—
452ΓL(1,𝔽25)—62no—
453ΓL(1,𝔽25)—62no—
454ΓL(1,𝔽25)—122no—
455D3×C8—62no—
456D3×C8—62no—
457D3×C8—122no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3×D3—22no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477D32—84no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—21no—
483C3⋊Dic3—21no—
484C3×Dic3—22no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—91no—
489C2×#41—91no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—91no—
505#127—31no—
506#127—181no—
507#124—31no—
508#123—181no—
509C22⋊Q8—91no—
510#121—91no—
511#121—91no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121—181no—
516#120—181no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8D3211yescharacteristic, complemented
524#103—31no—
525#103—91no—
526#102—31no—
527#102—31no—
528#102—31no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—31no—
542C22×D3—31no—
543C22×D3—31no—
544C22×D3—31no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—241no—
552C22×D3—241no—
553C3×Q8—32no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—32no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—122no—
566C3×D4—241no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—241no—
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4D3×D411yescharacteristic
578C2×C3×C4D3×D411yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—122no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—122no—
586#67—241no—
587#67—241no—
588#67—241no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—122no—
600C2×Dic3—122no—
601C2×Dic3—122no—
602D12—21no—
603D12—21no—
604D12—21no—
605D12—21no—
606D12—21no—
607D12—21no—
608D12—21no—
609D12—42no—
610D12—81no—
611D12—121no—
612D12—121no—
613D12—122no—
614D12—122no—
615D12—122no—
616D12—122no—
617D12—241no—
618D12—241no—
619D12—241no—
620D12D3×D412yes—
621C4×D3—61no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—61no—
626C4×D3—61no—
627C4×D3—61no—
628C4×D3—61no—
629C4×D3—81no—
630C4×D3—121no—
631C4×D3—121no—
632C4×D3—121no—
633C4×D3—121no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—122no—
637Dic6—21no—
638Dic6—21no—
639Dic6—21no—
640Dic6D3×D412yes—
641C3×C8—21no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—21no—
645C3×C8—41no—
646C3×C8—41no—
647C3⋊C8—32no—
648C3⋊C8—32no—
649C3⋊C8—62no—
650C3⋊C8—61no—
651C3⋊C8—61no—
652C3⋊C8—121no—
653C2×C32D4211yescharacteristic
654C2×C32#57511yescharacteristic
655C2×C32#57611yescharacteristic
656C3⋊D3—41no—
657C3⋊D3—41no—
658C3×D3—42no—
659C3×D3—81no—
660C3×D3—81no—
661C3×D3—81no—
662C24—181no—
663#41—182no—
664#41—182no—
665#41—182no—
666#41—361no—
667#41—361no—
668#41—361no—
669C2×Q8—31no—
670C2×Q8—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—91no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—182no—
686C2×D4—361no—
687C22×C4—61no—
688C22×C4—91no—
689C22×C4—91no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4—181no—
693Q16—62no—
694SD16—62no—
695SD16—94no—
696SD16—182no—
697SD16—361no—
698D8—62no—
699D8—62no—
700D8—182no—
701D8—361no—
702M16—182no—
703C2×C8—91no—
704C2×C8—91no—
705C2×C8—182no—
706C2×C8C2×D3211yescharacteristic
707C2×C8C2×D3211yescharacteristic
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—61no—
711C4⋊C4—91no—
712C4⋊C4—181no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—91no—
717C22⋊C4—91no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C42—61no—
723C42C2×D3211yescharacteristic
724C22×C3—21no—
725C22×C3—62no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3C2×D3×D411yescharacteristic
738C22×C3C2×D3×D411yescharacteristic
739C2×D3—22no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—62no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—61no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—244no—
770C2×D3—244no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—62no—
780C3×C4—121no—
781C3×C4—121no—
782C3×C4—121no—
783C3×C4C2×D3×D411yescharacteristic
784C3×C4C2×D3×D411yescharacteristic
785C3×C4#100911yescharacteristic
786C3×C4#100911yescharacteristic
787Dic3—22no—
788Dic3—41no—
789Dic3—41no—
790Dic3—41no—
791Dic3—61no—
792Dic3—61no—
793Dic3—61no—
794Dic3—61no—
795Dic3—121no—
796Dic3—121no—
797C32#326811yescharacteristic, complemented, Sylow
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—91no—
803C23—91no—
804C23—362no—
805C23—362no—
806C23—721no—
807Q8—32no—
808Q8—61no—
809Q8—61no—
810Q8—61no—
811D4—32no—
812D4—61no—
813D4—61no—
814D4—61no—
815D4—61no—
816D4—61no—
817D4—61no—
818D4—61no—
819D4—122no—
820D4—241no—
821D4—361no—
822D4—362no—
823D4—362no—
824D4—362no—
825D4—362no—
826D4—721no—
827D4—721no—
828D4—721no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—91no—
834C2×C4—91no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—241no—
840C2×C4—362no—
841C2×C4—362no—
842C2×C4—362no—
843C2×C4#380211yescharacteristic
844C2×C4#380211yescharacteristic
845C2×C4C22×D3211yescharacteristic
846C8—21no—
847C8—21no—
848C8—92no—
849C8—181no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—122no—
854C2×C3—241no—
855C2×C3—241no—
856C2×C3—241no—
857C2×C3#560911yescharacteristic
858C2×C3#560911yescharacteristic
859C2×C3#575711yescharacteristic
860C2×C3#576911yescharacteristic
861C2×C3#577311yescharacteristic
862C2×C3#577711yescharacteristic
863D3—42no—
864D3—81no—
865D3—81no—
866D3—81no—
867D3—122no—
868D3—121no—
869D3—121no—
870D3—121no—
871D3—121no—
872D3—241no—
873C22—62no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—181no—
886C22—181no—
887C22—181no—
888C22—181no—
889C22—181no—
890C22—181no—
891C22—724no—
892C22C2×#380211yescharacteristic
893C4—21no—
894C4—21no—
895C4—62no—
896C4—121no—
897C4—121no—
898C4—121no—
899C4—181no—
900C4—181no—
901C4D32×D411yescharacteristic
902C4#6432011yescharacteristic
903C3—21no—
904C3#8034811yescharacteristic, complemented
905C3#8062811yescharacteristic, complemented
906C2—122no—
907C2—241no—
908C2—241no—
909C2—241no—
910C2—361no—
911C2—361no—
912C2#1059461811yescharacteristic
913C2#1059468711yescharacteristic
914C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3268
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×#63810C2semidirect
2. C2×#63798C2semidirect
3. #10594005C2semidirect
4. #10593900C2semidirect
5. #10592535C2semidirect
6. C3×#4845C2semidirect
7. C3×#4843C2semidirect
8. #10590965C2semidirect
9. #10590964C2semidirect
10. #10590963C2semidirect
11. #10590945C2semidirect
12. #10590842C2semidirect
13. #10590839C2semidirect
14. #10590358C2semidirect
15. #10590354C2semidirect
21. C2×#3796C22semidirect
23. C2×C8×C3⋊D3C22semidirect
25. C2×C3×Dic12C22semidirect
30. C3×#874C22semidirect
32. C3×C4×Dic6C22semidirect
37. #63916C22semidirect
46. C2×#3715C22semidirect
47. C2×#3715C22semidirect
52. C32×C4⋊C8C22semidirect
54. #63647C22semidirect
55. #63630C22semidirect
57. C3×#821C22semidirect
58. C3×#821C22semidirect
59. C3×#816C22semidirect
60. #63576C22semidirect
61. #63565C22semidirect
81. #4845D3semidirect
82. #4843D3semidirect
153. #3715D4semidirect
197. C2×Dic12C2×D3semidirect
221. #874C2×D3semidirect
227. C4×Dic6C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
230. C3×C4⋊C8C2×D3semidirect
238. #821C2×D3semidirect
239. #821C2×D3semidirect
246. #816C2×D3semidirect
523. C4⋊C8D32semidirect
797. C32#3268semidirect
904. C3#80348semidirect
905. C3#80628semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
C2×#637982
#105940052
#105939002
#105925352
C3×#48452
C3×#48432
#105909652
#105909642
#105909632
#105909452
#105908422
#105908392
#105903582
#105903542
#806283
#803483