Finite Group Databasebeta

← #11796553

Subgroups — #11796553

Order 1152.

556 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595426C211yesmaximal, characteristic
2C3×#4751C211yesmaximal, characteristic, complemented
3#10591637C211yesmaximal, characteristic, complemented
4#10589343C211yesmaximal, characteristic, complemented
5C3×#4477C211yesmaximal, characteristic, complemented
6#10589183C211yesmaximal, characteristic, complemented
7#10589182C211yesmaximal, characteristic, complemented
8#70149—31nomaximal
9#69166—31nomaximal
10C2×C3×#239C2211yescharacteristic
11C2×D3×D12C411yescharacteristic
12#64156C2211yescharacteristic
13C3×#947C2211yescharacteristic
14C3×D3×M16—21no—
15#63922—21no—
16#63922—21no—
17#63914C411yescharacteristic
18#63911C411yescharacteristic
19#63906—21no—
20#63906—21no—
21#63855C411yescharacteristic
22D3×#208—21no—
23C32×#101C2211yescharacteristic, complemented
24#63663C2211yescharacteristic, complemented
25C3×#836C2211yescharacteristic, complemented
26C3×#836C2211yescharacteristic, complemented
27C3×#823—21no—
28#63558—21no—
29#5830—31no—
30#5674—31no—
31C3×#413—31no—
32#5237—31no—
33#4751—31no—
34#4751D311yescharacteristic, complemented
35C3×#355—31no—
36#4542—31no—
37#4477—31no—
38#4477—31no—
39#4477—31no—
40#4477—31no—
41#4477—31no—
42#4477—61no—
43#4477D311yescharacteristic, complemented
44C22×D32—21no—
45C2×C32×Q8C2311yescharacteristic
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C3×#239—41no—
48C3×#239—41no—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×D12C2×C411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3C2×C411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×#626—21no—
57C2×#626—21no—
58C2×#626—21no—
59C2×#625—21no—
60C2×#625—21no—
61D3×D12—41no—
62D3×D12—41no—
63C32×M16—21no—
64#3752—21no—
65#3752—21no—
66C4×C3⋊Dic3C2×C411yescharacteristic
67#3748—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×C4×Dic3C2×C411yescharacteristic
71C3×#208—21no—
72C3×#208—21no—
73C3×ΓL(1,𝔽25)—41no—
74C3×D3×C8—41no—
75Dic3⋊Dic3—21no—
76(C2×D3)⋊Dic3—21no—
77#3711—41no—
78D3×C3⋊C8—41no—
79#2134—91noSylow
80C2×C3×#41—31no—
81C2×#239C2×D311yescharacteristic
82C2×D3×D4—31no—
83C22×D12—31no—
84C2×C3×M16—61no—
85C3×#124—31no—
86#947—31no—
87#947—31no—
88#947—61no—
89#947C2×D311yescharacteristic
90#940—31no—
91#940—31no—
92#940—31no—
93#937—61no—
94#937—61no—
95#930—61no—
96#930—61no—
97#926—31no—
98C2×#208—61no—
99D3×M16—21no—
100D3×M16—61no—
101#884—61no—
102#884—61no—
103#882—61no—
104#882—61no—
105#874—31no—
106#872—31no—
107C3×#101—21no—
108C3×#101—31no—
109C3×#101—31no—
110C3×#101C2×D311yescharacteristic, complemented
111C3×#101C2×D311yescharacteristic, complemented
112C3×#100—61no—
113#836—31no—
114#836—31no—
115#836—61no—
116#836C2×D311yescharacteristic, complemented
117#836C2×D311yescharacteristic, complemented
118#833—61no—
119#823—21no—
120#823—61no—
121C22×C3⋊D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3C22⋊C411yescharacteristic
124C22×C3×D3C22⋊C411yescharacteristic
125C22×C3×D3C22⋊C411yescharacteristic
126C2×D32—42no—
127C2×D32—81no—
128C2×D32—81no—
129C32×Q8—41no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C3⋊Dic3—21no—
134C4⋊(C3⋊D3)—41no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3C22⋊C411yescharacteristic
137C3×D12—41no—
138C3×D12—41no—
139C3×D12—41no—
140C3×D12—41no—
141C3×C4×D3—21no—
142C3×C4×D3—21no—
143C3×C4×D3—21no—
144C3×C4×D3—21no—
145C3×C4×D3—21no—
146C3×C4×D3—21no—
147#626—41no—
148#626—41no—
149#626—81no—
150#626—81no—
151#625—81no—
152#625—81no—
153C32×C8—41no—
154C3⋊(C3⋊C8)—41no—
155C3×C3⋊C8—41no—
156C3×C3⋊C8—41no—
157#535—91no—
158#413—31no—
159#413—91no—
160#355—31no—
161#355—91no—
162#355—91no—
163#355—91no—
164C23×D3—61no—
165C23×D3—61no—
166C3×#41—121no—
167C3×#41—121no—
168C2×C3×Q8—21no—
169C2×C3×Q8C22×D311yescharacteristic
170C2×C3×Q8C22×D311yescharacteristic
171C2×C3×D4—31no—
172C2×C3×D4—31no—
173C2×C3×D4—31no—
174C2×C3×D4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C2×#67—61no—
179C2×#67—61no—
180C2×#67—61no—
181C2×#67—61no—
182C2×#67—61no—
183C2×#67—61no—
184C2×#67—61no—
185#239—41no—
186#239—41no—
187D3×D4—121no—
188D3×D4—121no—
189C2×D12—31no—
190C2×D12—31no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—121no—
196C2×D12—121no—
197C2×D12C4×D311yescharacteristic
198C2×D12C4×D311yescharacteristic
199C2×D12D1211yescharacteristic
200C2×D12#6711yescharacteristic
201C2×C4×D3C4×D311yescharacteristic
202C2×C4×D3D1211yescharacteristic
203C2×C4×D3#6711yescharacteristic
204C3×M16—21no—
205C3×M16—21no—
206C3×M16—41no—
207C3×M16—61no—
208C3×M16—61no—
209C3×M16—121no—
210C2×C3×C8—121no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C42—31no—
214#217—61no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—61no—
222(C2×D3)⋊C4—121no—
223(C2×D3)⋊C4—121no—
224C4⋊Dic3—61no—
225Dic3⋊C4—61no—
226C4×Dic3—31no—
227C4×Dic3—31no—
228C4×Dic3—61no—
229C4×Dic3C4×D311yescharacteristic
230#208—21no—
231#208—21no—
232#208—61no—
233#208—61no—
234#208—121no—
235#208—121no—
236C2×C3⋊C8—121no—
237ΓL(1,𝔽25)—41no—
238ΓL(1,𝔽25)—121no—
239D3×C8—41no—
240D3×C8—121no—
241C22×C32C2×C22⋊C411yescharacteristic
242C2×C3⋊D3—41no—
243C2×C3⋊D3—41no—
244C2×C3⋊D3—41no—
245C2×C3×D3—21no—
246C2×C3×D3—21no—
247C2×C3×D3—21no—
248C2×C3×D3—41no—
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254D32—84no—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4—21no—
258C3⋊Dic3—41no—
259C3×Dic3—41no—
260C3×Dic3#9911yescharacteristic
261C3×Dic3#9911yescharacteristic
262C2×#41—31no—
263C22×D4—91no—
264C2×M16—61no—
265C2×M16—181no—
266#127—91no—
267#127—91no—
268#124—31no—
269#124—91no—
270#121—181no—
271#121—181no—
272#120—181no—
273#120—181no—
274#117—91no—
275#101—31no—
276#101—31no—
277#101—91no—
278#101D3211yescharacteristic, complemented
279#100—61no—
280#100—181no—
281C23×C3—31no—
282C23×C3—31no—
283C23×C3—31no—
284C23×C3—61no—
285C22×D3—21no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—121no—
289C22×D3—122no—
290C22×D3—122no—
291C22×D3—241no—
292C22×D3—241no—
293C22×D3—241no—
294C22×D3—241no—
295C22×D3(C2×D3)⋊C411yescharacteristic
296C22×D3(C2×D3)⋊C411yescharacteristic
297C22×D3(C2×D3)⋊C411yescharacteristic
298C3×Q8—41no—
299C3×Q8—41no—
300C3×Q8—81no—
301C3×D4—121no—
302C3×D4—121no—
303C3×D4—121no—
304C3×D4—121no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—31no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322#67—121no—
323#67—121no—
324#67—241no—
325#67—241no—
326#67—241no—
327#67—241no—
328#67—241no—
329#67—241no—
330C2×Dic3—21no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—121no—
334C2×Dic3(C2×D3)⋊C411yescharacteristic
335D12—41no—
336D12—41no—
337D12—41no—
338D12—41no—
339D12—121no—
340D12—121no—
341D12—121no—
342D12—121no—
343D12—241no—
344D12—241no—
345D12—241no—
346C4×D3—21no—
347C4×D3—21no—
348C4×D3—21no—
349C4×D3—21no—
350C4×D3—21no—
351C4×D3—21no—
352C3×C8—41no—
353C3×C8—41no—
354C3×C8—81no—
355C3×C8—121no—
356C3×C8—121no—
357C3⋊C8—41no—
358C3⋊C8—41no—
359C3⋊C8—121no—
360C3⋊C8—121no—
361C3⋊C8—241no—
362C2×C32—21no—
363C2×C32C2×#9911yescharacteristic
364C3⋊D3—81no—
365C3×D3—41no—
366C3×D3—41no—
367C3×D3—41no—
368C3×D3—81no—
369C24—181no—
370#41—121no—
371#41—121no—
372C2×Q8C2×D3211yescharacteristic
373C2×D4—31no—
374C2×D4—31no—
375C2×D4—31no—
376C2×D4—31no—
377C2×D4—91no—
378C2×D4—181no—
379C2×D4—181no—
380C2×D4—181no—
381C2×D4—181no—
382C2×D4—181no—
383C2×D4—361no—
384C2×D4—361no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388M16—21no—
389M16—61no—
390M16—61no—
391M16—121no—
392M16—181no—
393M16—361no—
394C2×C8—121no—
395C2×C8—361no—
396C4⋊C4—181no—
397C22⋊C4—61no—
398C22⋊C4—61no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—181no—
402C42—31no—
403C42—91no—
404C22×C3—21no—
405C22×C3—61no—
406C22×C3—61no—
407C22×C3—61no—
408C22×C3—121no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3—121no—
413C22×C3—121no—
414C22×C3D3×C22⋊C411yescharacteristic
415C22×C3C2×(C2×D3)⋊C411yescharacteristic
416C2×D3—21no—
417C2×D3—21no—
418C2×D3—21no—
419C2×D3—41no—
420C2×D3—41no—
421C2×D3—41no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—241no—
432C2×D3—241no—
433C2×D3—241no—
434C2×D3—244no—
435C2×D3—244no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—31no—
443C3×C4—31no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—121no—
448Dic3—41no—
449Dic3—121no—
450Dic3—121no—
451Dic3—241no—
452Dic3#80611yescharacteristic
453Dic3#80611yescharacteristic
454C32#213411yescharacteristic, complemented, Sylow
455C23—31no—
456C23—31no—
457C23—31no—
458C23—61no—
459C23—181no—
460C23—362no—
461C23—721no—
462C23—721no—
463Q8—41no—
464D4—121no—
465D4—121no—
466D4—121no—
467D4—121no—
468D4—361no—
469D4—361no—
470D4—361no—
471D4—721no—
472D4—721no—
473D4—721no—
474D4—721no—
475C2×C4—31no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—181no—
484C2×C4C4×D3211yescharacteristic
485C2×C4D3×D1211yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C8—41no—
488C8—121no—
489C8—121no—
490C8—361no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—41no—
495C2×C3—121no—
496C2×C3—121no—
497C2×C3—121no—
498C2×C3—241no—
499C2×C3D3×#9911yescharacteristic
500C2×C3C2×#80611yescharacteristic
501D3—41no—
502D3—41no—
503D3—41no—
504D3—81no—
505D3—241no—
506D3—241no—
507D3—481no—
508C22—61no—
509C22—61no—
510C22—61no—
511C22—121no—
512C22—121no—
513C22—121no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—361no—
518C22—361no—
519C22—361no—
520C22—724no—
521C22D3×(C2×D3)⋊C411yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—31no—
526C4—31no—
527C4—121no—
528C4—361no—
529C3—21no—
530C3#6916611yescharacteristic, complemented
531C3#7014911yescharacteristic, complemented
532C2—21no—
533C2—121no—
534C2—121no—
535C2—121no—
536C2—241no—
537C2—721no—
538C2D3×#80611yescharacteristic
subgroupG/H
centerC2D3×#806
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC32×#101C22
socleC2×C32C2×#99
prime radical#10595426C2
cosocleC2×C32×Q8C23
hypercenter#101D32
hypocenterC32#2134
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
2. C3×#4751C2semidirect
3. #10591637C2semidirect
4. #10589343C2semidirect
5. C3×#4477C2semidirect
6. #10589183C2semidirect
7. #10589182C2semidirect
23. C32×#101C22semidirect
24. #63663C22semidirect
25. C3×#836C22semidirect
26. C3×#836C22semidirect
34. #4751D3semidirect
43. #4477D3semidirect
110. C3×#101C2×D3semidirect
111. C3×#101C2×D3semidirect
116. #836C2×D3semidirect
117. #836C2×D3semidirect
278. #101D32semidirect
454. C32#2134semidirect
530. C3#69166semidirect
531. C3#70149semidirect

Maximal subgroups

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

subgroupindex
#105954262
C3×#47512
#105916372
#105893432
C3×#44772
#105891832
#105891822
#701493
#691663