Finite Group Databasebeta

← #11864597

Subgroups — #11864597

Order 1152.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2C3×#5629C211yesmaximal, characteristic, complemented
3C2×#63949C211yesmaximal, characteristic, complemented
4C2×#63939C211yesmaximal, characteristic, complemented
5#10592745C211yesmaximal, characteristic, complemented
6C3×#5047C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591168C211yesmaximal, characteristic, complemented
10#10591161C211yesmaximal, characteristic, complemented
11#10591145C211yesmaximal, characteristic, complemented
12#10590615C211yesmaximal, characteristic, complemented
13#10590609C211yesmaximal, characteristic, complemented
14#10590595C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16#83424—31nomaximal
17#80231—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×#3811—21no—
23C2×#3811—21no—
24#64308—24no—
25#64308—24no—
26C2×D3×D12—21no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×#3799—21no—
30C2×#3799C2211yescharacteristic
31C2×#3799C2211yescharacteristic
32C32×C22⋊Q8C2211yescharacteristic, complemented
33C2×#3755C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C3×#930C2211yescharacteristic, complemented
39C3×#896—21no—
40C3×#895—21no—
41C3×#895C2211yescharacteristic, complemented
42C3×D3×C4⋊C4C2211yescharacteristic, complemented
43C3×#884—21no—
44C3×#884—21no—
45#63949—24no—
46#63939—24no—
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63657C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1009—31no—
67C3×#537—31no—
68C2×#950—31no—
69C2×#949—31no—
70C2×#919—31no—
71C2×#914—31no—
72#5629D311yescharacteristic, complemented
73C3×#452—31no—
74#5238—31no—
75#5234—31no—
76#5187—31no—
77#5169—31no—
78#5047—31no—
79#5047D311yescharacteristic, complemented
80#5046—31no—
81#5046—31no—
82#5046—31no—
83#5046—61no—
84#5037—31no—
85#5037—31no—
86#5036—31no—
87#5036—31no—
88#4966—31no—
89C2×#809—31no—
90#4810—31no—
91#4803—31no—
92#4773—31no—
93D3×#102—31no—
94#4732—31no—
95#4727—31no—
96C23×C3⋊D3—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—22no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67D411yescharacteristic
109C2×C3×#67D411yescharacteristic
110C3×#239—22no—
111C3×#239—22no—
112C3×#235—22no—
113C3×#235—22no—
114C3×#235—22no—
115C3×#235—22no—
116C2×C3×D12—21no—
117C2×C3×D12—21no—
118C2×C3×D12D411yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×Dic6D411yescharacteristic
127C2×C3×Dic6C2311yescharacteristic
128#3811—28no—
129#3811—28no—
130C2×#626—21no—
131C2×#626—21no—
132C2×#626—21no—
133C2×#626—21no—
134C2×#624—21no—
135C2×#624—21no—
136D3×D12—28no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12D414yescomplemented
141#3799—28no—
142#3799—22no—
143#3799—22no—
144#3799—22no—
145#3799D414yescomplemented
146C32×C4⋊C4—21no—
147C32×C4⋊C4C2311yescharacteristic
148C32×C22⋊C4—21no—
149#3755—22no—
150#3755—22no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153C3×#216—22no—
154C3×#215—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×(C2×D3)⋊C4—21no—
157C3×(C2×D3)⋊C4—21no—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×Dic3⋊C4—21no—
160C3×Dic3⋊C4—21no—
161C2×C3×C3⋊C8C2311yescharacteristic
162C2×C3×C3⋊C8C2311yescharacteristic
163#3715—22no—
164#3714—22no—
165#3714—22no—
166#3713—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C2×C3×#41—31no—
173#1009—64no—
174#1009—64no—
175#1009—64no—
176#1009—64no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239C2×D311yescharacteristic, complemented
181C2×D3×D4—31no—
182C2×D3×D4—31no—
183C2×D3×D4—61no—
184C2×D3×D4—61no—
185C2×D3×D4—61no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×#235—31no—
189C2×#235—31no—
190C2×#235—61no—
191C2×#235C2×D311yescharacteristic
192C2×#235C2×D311yescharacteristic
193C22×D12—31no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—61no—
198C22×D12—61no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C3×C22⋊Q8—21no—
202C3×C22⋊Q8—31no—
203C3×C22⋊Q8—61no—
204C3×C22⋊Q8C2×D311yescharacteristic, complemented
205C3×C22⋊Q8C2×D311yescharacteristic, complemented
206C3×#121—31no—
207C3×#121—31no—
208C3×#121—61no—
209C3×#121—61no—
210C3×#121—61no—
211C2×C3×C4⋊C4—31no—
212#950—64no—
213#949—64no—
214#946C2×D311yescharacteristic, complemented
215C2×#216C2×D311yescharacteristic, complemented
216C2×#215—31no—
217C2×#215—31no—
218C2×#215—31no—
219C2×#215—31no—
220C2×#215—31no—
221C2×#215—61no—
222C2×#215—61no—
223C2×#215C2×D311yescharacteristic, complemented
224C2×#214—31no—
225C2×#213—31no—
226C2×#213—31no—
227C2×#213—31no—
228C2×#213—31no—
229#930C2×D311yescharacteristic, complemented
230C2×#208—31no—
231C22×C3⋊C8—31no—
232#919—64no—
233#914—64no—
234C2×D24—31no—
235C2×D24—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×D3×C8—31no—
238#896—21no—
239#895—21no—
240#895C2×D311yescharacteristic, complemented
241D3×C4⋊C4C2×D311yescharacteristic, complemented
242#884—21no—
243#884—21no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#832—31no—
249#830—31no—
250#830—31no—
251#830—31no—
252#830—31no—
253#830—61no—
254#830C2×D311yescharacteristic, complemented
255#821—31no—
256#821—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259#810—31no—
260#810C2×D311yescharacteristic, complemented
261#809—31no—
262#809—31no—
263#809—31no—
264#809—31no—
265#809—31no—
266#809—31no—
267#809—31no—
268#809—61no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3—21no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3—24no—
275C22×C3⋊D3—81no—
276C22×C3⋊D3—81no—
277C22×C3×D3—21no—
278C22×C3×D3—21no—
279C22×C3×D3C2×D411yescharacteristic
280C22×C3×D3C2×D411yescharacteristic
281C2×D32—24no—
282C2×D32—24no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C32×Q8—21no—
288C32×Q8—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C2×D411yescharacteristic
294C2×C32×C4C2411yescharacteristic
295C4⋊(C3⋊D3)—24no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)C2×D412yes—
299C4⋊(C3⋊D3)C2×D412yes—
300C3×#67—24no—
301C3×#67—22no—
302C3×#67—22no—
303C3×#67—81no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—22no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—42no—
313C3×D12—81no—
314C3×D12C2×D412yes—
315C3×C4×D3—24no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—42no—
319C3×C4×D3—81no—
320C3×C4×D3C2×D412yes—
321C3×C4×D3C2×D412yes—
322C3×Dic6—21no—
323C3×Dic6—22no—
324C3×Dic6C2×D412yes—
325#626—24no—
326#626—24no—
327#626—24no—
328#626—24no—
329#624—24no—
330#624—24no—
331C3⋊(C3⋊C8)—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—31no—
339#452—31no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C23×D3—121no—
357C3×#41—62no—
358C3×#41—62no—
359C3×#41—62no—
360C3×#41—62no—
361C3×#41—62no—
362C3×#41—62no—
363C2×C3×Q8—21no—
364C2×C3×Q8—31no—
365C2×C3×Q8—31no—
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4—61no—
376C2×C3×D4—61no—
377C22×C3×C4—21no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—61no—
381C22×C3×C4—61no—
382C22×C3×C4—61no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C2×#67—21no—
386C2×#67—21no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67#6711yescharacteristic
392C2×#67#6711yescharacteristic
393#239—22no—
394#239—22no—
395#239—34no—
396#239—62no—
397#239—62no—
398#239—68no—
399#239—62no—
400D3×D4—34no—
401D3×D4—62no—
402D3×D4—62no—
403D3×D4—68no—
404D3×D4—68no—
405D3×D4—68no—
406D3×D4—68no—
407D3×D4—68no—
408D3×D4—62no—
409#235—22no—
410#235—22no—
411#235—22no—
412#235—22no—
413#235—34no—
414#235—62no—
415#235—62no—
416#235—68no—
417#235—62no—
418C2×D12—21no—
419C2×D12—21no—
420C2×D12—31no—
421C2×D12—31no—
422C2×D12—31no—
423C2×D12—31no—
424C2×D12—34no—
425C2×D12—61no—
426C2×D12—61no—
427C2×D12—62no—
428C2×D12—62no—
429C2×D12—68no—
430C2×D12—62no—
431C2×D12—62no—
432C2×D12—62no—
433C2×D12—62no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—62no—
441C2×D12—122no—
442C2×D12—122no—
443C2×D12—121no—
444C2×D12#6711yescharacteristic
445C2×D12C22×D311yescharacteristic
446C2×D12C22×D311yescharacteristic
447C2×C4×D3—21no—
448C2×C4×D3—21no—
449C2×C4×D3—21no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3C22×D311yescharacteristic
455C2×C4×D3C22×D311yescharacteristic
456C2×Dic6#6711yescharacteristic
457C2×Dic6C22×D311yescharacteristic
458C3×Q16—62no—
459C3×SD16—62no—
460C2×C3×C8—31no—
461C2×C3×C8—31no—
462C3×C4⋊C4—21no—
463C3×C4⋊C4—21no—
464C3×C4⋊C4—21no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—41no—
467C3×C4⋊C4—61no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4C22×D311yescharacteristic
470C3×C4⋊C4C22×D311yescharacteristic
471C3×C22⋊C4—21no—
472C3×C22⋊C4—21no—
473C3×C22⋊C4—41no—
474C3×C22⋊C4—61no—
475C3×C22⋊C4—61no—
476C3×C22⋊C4—61no—
477#216—22no—
478#215—22no—
479#215—62no—
480#215—62no—
481#215—62no—
482#215—62no—
483#215—62no—
484#215—122no—
485#215—122no—
486#214—62no—
487#213—62no—
488#213—62no—
489#213—62no—
490#213—62no—
491(C2×D3)⋊C4—21no—
492(C2×D3)⋊C4—21no—
493(C2×D3)⋊C4—21no—
494C4⋊Dic3C22×D311yescharacteristic
495Dic3⋊C4—21no—
496Dic3⋊C4—21no—
497#208—62no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8—62no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507D24—62no—
508D24—62no—
509ΓL(1,𝔽25)—62no—
510D3×C8—62no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—22no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—41no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—84no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—22no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3#12012yes—
534D32—84no—
535D32—84no—
536C32×C4—21no—
537C32×C4—41no—
538C32×C4—41no—
539C32×C4C22×D411yescharacteristic
540C32×C4C22×D411yescharacteristic
541C3×Dic3—21no—
542C3×Dic3—22no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—31no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—31no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—91no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—91no—
571C22⋊Q8—31no—
572C22⋊Q8—61no—
573C22⋊Q8D3211yescharacteristic, complemented
574#121—31no—
575#121—31no—
576#121—61no—
577#121—61no—
578#121—61no—
579C2×C4⋊C4—31no—
580#103—31no—
581#103—91no—
582#102—31no—
583#102—91no—
584#102—91no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—21no—
593C23×C3—31no—
594C23×C3—31no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3D3×D411yescharacteristic
598C23×C3C2×#6711yescharacteristic
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—64no—
602C22×D3—64no—
603C22×D3—64no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—64no—
609C22×D3—64no—
610C22×D3—64no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—124no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3—241no—
626C22×D3—242no—
627C22×D3—242no—
628C22×D3C2×#6711yescharacteristic
629C22×D3C2×#6711yescharacteristic
630C3×Q8—21no—
631C3×Q8—21no—
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—32no—
635C3×Q8—41no—
636C3×Q8—41no—
637C3×Q8—62no—
638C3×Q8—61no—
639C3×D4—32no—
640C3×D4—62no—
641C3×D4—62no—
642C3×D4—62no—
643C3×D4—64no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—61no—
647C3×D4—122no—
648C3×D4—241no—
649C3×D4—241no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—31no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—31no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—64no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—122no—
674C2×C3×C4—241no—
675C2×C3×C4D3×D411yescharacteristic
676C2×C3×C4C2×#6711yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679#67—24no—
680#67—22no—
681#67—22no—
682#67—64no—
683#67—64no—
684#67—64no—
685#67—64no—
686#67—81no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3C2×#6711yescharacteristic
690C2×Dic3C2×#6711yescharacteristic
691D12—22no—
692D12—21no—
693D12—21no—
694D12—21no—
695D12—32no—
696D12—32no—
697D12—32no—
698D12—32no—
699D12—42no—
700D12—62no—
701D12—62no—
702D12—64no—
703D12—64no—
704D12—64no—
705D12—64no—
706D12—64no—
707D12—64no—
708D12—61no—
709D12—61no—
710D12—61no—
711D12—61no—
712D12—81no—
713D12—121no—
714D12—121no—
715D12—124no—
716D12D3×D412yes—
717C4×D3—24no—
718C4×D3—21no—
719C4×D3—21no—
720C4×D3—42no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—64no—
724C4×D3—64no—
725C4×D3—81no—
726C4×D3D3×D412yes—
727C4×D3D3×D412yes—
728Dic6—21no—
729Dic6—22no—
730Dic6D3×D412yes—
731C3×C8—61no—
732C3×C8—61no—
733C3⋊C8—21no—
734C3⋊C8—21no—
735C3⋊C8—61no—
736C3⋊C8—61no—
737C3⋊C8—61no—
738C3⋊C8—61no—
739C3⋊C8—121no—
740C3⋊C8—121no—
741C2×C32—41no—
742C2×C32C2×#12011yescharacteristic
743C2×C32#57611yescharacteristic
744C2×C32#57711yescharacteristic
745C3⋊D3—42no—
746C3⋊D3—42no—
747C3×D3—22no—
748C3×D3—41no—
749C3×D3—42no—
750C3×D3—81no—
751C24—181no—
752C24—181no—
753C24—181no—
754#41—62no—
755#41—62no—
756#41—62no—
757#41—62no—
758#41—62no—
759#41—62no—
760#41—94no—
761#41—182no—
762#41—182no—
763#41—182no—
764#41—188no—
765C2×Q8—31no—
766C2×Q8—31no—
767C2×Q8C2×D3211yescharacteristic
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—31no—
773C2×D4—61no—
774C2×D4—61no—
775C2×D4—61no—
776C2×D4—61no—
777C2×D4—94no—
778C2×D4—91no—
779C2×D4—91no—
780C2×D4—182no—
781C2×D4—182no—
782C2×D4—182no—
783C2×D4—181no—
784C2×D4—181no—
785C2×D4—182no—
786C2×D4—182no—
787C2×D4—188no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—188no—
791C2×D4—188no—
792C2×D4—181no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—181no—
799C22×C4—181no—
800C22×C4C2×D3211yescharacteristic
801Q16—62no—
802SD16—62no—
803SD16—182no—
804SD16—182no—
805SD16—182no—
806D8—182no—
807D8—182no—
808D8—182no—
809M16—182no—
810C2×C8—31no—
811C2×C8—31no—
812C2×C8—91no—
813C2×C8—91no—
814C2×C8—182no—
815C4⋊C4—21no—
816C4⋊C4—31no—
817C4⋊C4—61no—
818C4⋊C4—61no—
819C4⋊C4C2×D3211yescharacteristic
820C22⋊C4—21no—
821C22⋊C4—61no—
822C22⋊C4—61no—
823C22⋊C4—61no—
824C22×C3—22no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—32no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—61no—
836C22×C3—61no—
837C22×C3—61no—
838C22×C3—61no—
839C22×C3—62no—
840C22×C3—61no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3C2×D3×D411yescharacteristic
847C22×C3C22×#6711yescharacteristic
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—22no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—122no—
864C2×D3—122no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—241no—
874C2×D3—241no—
875C2×D3—241no—
876C2×D3—241no—
877C2×D3—244no—
878C2×D3—244no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3—244no—
883C2×D3—248no—
884C2×D3#93712yes—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—32no—
890C3×C4—41no—
891C3×C4—41no—
892C3×C4—41no—
893C3×C4—41no—
894C3×C4—41no—
895C3×C4—62no—
896C3×C4—61no—
897C3×C4—81no—
898C3×C4—81no—
899C3×C4—121no—
900C3×C4C2×D3×D411yescharacteristic
901C3×C4C2×D3×D411yescharacteristic
902C3×C4C2×D3×D411yescharacteristic
903C3×C4C2×D3×D411yescharacteristic
904Dic3—21no—
905Dic3—22no—
906Dic3—41no—
907Dic3#93712yes—
908C32#301211yescharacteristic, complemented, Sylow
909C23—31no—
910C23—31no—
911C23—61no—
912C23—61no—
913C23—184no—
914C23—184no—
915C23—184no—
916C23—181no—
917C23—181no—
918C23—721no—
919C23—721no—
920C23—721no—
921C23—721no—
922C23—721no—
923C23—721no—
924C23D3×#6711yescharacteristic
925Q8—21no—
926Q8—21no—
927Q8—32no—
928Q8—62no—
929Q8—61no—
930D4—32no—
931D4—62no—
932D4—62no—
933D4—62no—
934D4—64no—
935D4—61no—
936D4—61no—
937D4—61no—
938D4—92no—
939D4—92no—
940D4—122no—
941D4—184no—
942D4—184no—
943D4—184no—
944D4—184no—
945D4—184no—
946D4—181no—
947D4—181no—
948D4—241no—
949D4—241no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—31no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—31no—
958C2×C4—64no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—122no—
964C2×C4—184no—
965C2×C4—184no—
966C2×C4—241no—
967C2×C4D3×#6711yescharacteristic
968C2×C4C22×D3211yescharacteristic
969C8—61no—
970C8—61no—
971C8—181no—
972C8—181no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—42no—
977C2×C3—41no—
978C2×C3—41no—
979C2×C3—62no—
980C2×C3—121no—
981C2×C3—122no—
982C2×C3—241no—
983C2×C3D3×#12011yescharacteristic
984C2×C3#576911yescharacteristic
985C2×C3#577811yescharacteristic
986C2×C3C2×#93711yescharacteristic
987C2×C3#583511yescharacteristic
988C2×C3#583711yescharacteristic
989D3—22no—
990D3—42no—
991D3—41no—
992D3—81no—
993D3—122no—
994D3—122no—
995D3—122no—
996D3—122no—
997D3—242no—
998D3—242no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—32no—
1003C22—61no—
1004C22—61no—
1005C22—61no—
1006C22—62no—
1007C22—61no—
1008C22—61no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—182no—
1015C22—182no—
1016C22—361no—
1017C22—361no—
1018C22—361no—
1019C22—361no—
1020C22—724no—
1021C22—724no—
1022C22—724no—
1023C22C2×D3×#6711yescharacteristic
1024C4—21no—
1025C4—32no—
1026C4—41no—
1027C4—41no—
1028C4—61no—
1029C4—62no—
1030C4—121no—
1031C4D32×D411yescharacteristic
1032C4D32×D411yescharacteristic
1033C3—21no—
1034C3#8023111yescharacteristic, complemented
1035C3#8342411yescharacteristic, complemented
1036C2—41no—
1037C2—62no—
1038C2—121no—
1039C2—122no—
1040C2—241no—
1041C2—362no—
1042C2—362no—
1043C2D3×#93711yescharacteristic
1044C2#1059531911yescharacteristic
1045C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64308C2semidirect
2. C3×#5629C2semidirect
3. C2×#63949C2semidirect
4. C2×#63939C2semidirect
5. #10592745C2semidirect
6. C3×#5047C2semidirect
7. #10591657C2semidirect
8. #10591651C2semidirect
9. #10591168C2semidirect
10. #10591161C2semidirect
11. #10591145C2semidirect
12. #10590615C2semidirect
13. #10590609C2semidirect
14. #10590595C2semidirect
15. D3×#809C2semidirect
19. C2×C3×#239C22semidirect
32. C32×C22⋊Q8C22semidirect
33. C2×#3755C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C3×#930C22semidirect
41. C3×#895C22semidirect
42. C3×D3×C4⋊C4C22semidirect
47. C2×#3715C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63657C22semidirect
54. #63636C22semidirect
55. #63636C22semidirect
56. C3×#830C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
72. #5629D3semidirect
79. #5047D3semidirect
140. D3×D12D4semidirect
145. #3799D4semidirect
180. C2×#239C2×D3semidirect
204. C3×C22⋊Q8C2×D3semidirect
205. C3×C22⋊Q8C2×D3semidirect
214. #946C2×D3semidirect
215. C2×#216C2×D3semidirect
223. C2×#215C2×D3semidirect
229. #930C2×D3semidirect
240. #895C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
254. #830C2×D3semidirect
260. #810C2×D3semidirect
270. #809C2×D3semidirect
573. C22⋊Q8D32semidirect
908. C32#3012semidirect
1034. C3#80231semidirect
1035. C3#83424semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
C3×#56292
C2×#639492
C2×#639392
#105927452
C3×#50472
#105916572
#105916512
#105911682
#105911612
#105911452
#105906152
#105906092
#105905952
D3×#8092
#834243
#802313