Finite Group Databasebeta

← #11775131

Subgroups — #11775131

Order 1152.

833 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 833 conjugacy classes of subgroups — too many to draw. Only its 96 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#10596098C211yesmaximal, characteristic
2#10591370C211yesmaximal, characteristic, complemented
3#10591159C211yesmaximal, characteristic, complemented
4C3×#4538C212yesmaximal, complemented
5#10589151C212yesmaximal, complemented
6#68334—32nomaximal
7C2×#3832C411yescharacteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624—21no—
10C32×C22⋊Q8C2211yescharacteristic
11#64155C411yescharacteristic, complemented
12#64139C2211yescharacteristic
13#64104C411yescharacteristic, complemented
14#64103—21no—
15#64102—21no—
16#64101C411yescharacteristic, complemented
17#64091—21no—
18#64090—21no—
19C2×#3712—21no—
20C3×C3⋊#95C2212yes—
21C3×#830C2212yes—
22#63579—21no—
23#63557—21no—
24#5627—32no—
25#5627—61no—
26#4726—32no—
27D3×#95—32no—
28C3×#328—32no—
29#4538D312yescomplemented
30#4470—32no—
31#4451—32no—
32C23×C3⋊D3D411yescharacteristic
33C2×C32×Q8C2×C411yescharacteristic, complemented
34C22×C32×C4C2311yescharacteristic
35C2×#638—21no—
36C22×C3⋊Dic3D411yescharacteristic
37#3832—42no—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3—42no—
43C2×C4×C3⋊D3C2×C411yescharacteristic
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C22×C3×Dic3—22no—
48C2×#624—24no—
49C2×#624—42no—
50C2×#624—42no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4C2×C411yescharacteristic, complemented
53C32×C22⋊C4—21no—
54#3752—21no—
55#3752—21no—
56#3752—21no—
57#3752—21no—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
59#3750—21no—
60C4×C3⋊Dic3—21no—
61C2×C3×C3⋊C8—22no—
62#3712—42no—
63#1504—91noSylow
64C2×#239—32no—
65C2×#239—61no—
66C22×C4×D3—32no—
67C22×C4×D3—61no—
68C22×C4×D3—62no—
69C3×C22⋊Q8—21no—
70C3×C22⋊Q8C2×D312yes—
71#946—32no—
72#946—61no—
73#930—32no—
74#930—61no—
75C2×ΓL(1,𝔽25)—62no—
76#895—32no—
77#895—61no—
78#894—62no—
79#894—62no—
80#893—62no—
81#893—62no—
82#892—32no—
83#892—61no—
84#882—62no—
85#882—62no—
86#67⋊C4—62no—
87#67⋊C4—62no—
88C3×C22⋊C8—32no—
89C3×#95—32no—
90C3⋊#95—62no—
91C3⋊#95C2×D312yes—
92#830C2×D312yes—
93(C2×D3)⋊C8—62no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—21no—
98C22×C3⋊D3—22no—
99C22×C3⋊D3—22no—
100C22×C3⋊D3C22⋊C411yescharacteristic
101C22×C3⋊D3C22⋊C411yescharacteristic
102C32×Q8—41no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108#638—41no—
109#638—41no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3C22⋊C411yescharacteristic
113C2×C3⋊Dic3C22⋊C411yescharacteristic
114C4⋊(C3⋊D3)—41no—
115C4⋊(C3⋊D3)—42no—
116C4⋊(C3⋊D3)—42no—
117C4×C3⋊D3—22no—
118C4×C3⋊D3—22no—
119C4×C3⋊D3—41no—
120C4×C3⋊D3—41no—
121C4×C3⋊D3—42no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125#624—48no—
126C3×C3⋊C8—42no—
127#525—91no—
128#407—91no—
129C2×#95—91no—
130#328—32no—
131#327—92no—
132C23×D3—32no—
133C23×D3—61no—
134C2×C3×Q8—21no—
135C2×C3×Q8C4×D312yescomplemented
136C22×C3×C4—21no—
137C22×C3×C4—62no—
138C22×C3×C4C22×D312yes—
139C2×#67—62no—
140C2×#67—62no—
141C22×Dic3—22no—
142C22×Dic3—32no—
143C22×Dic3—61no—
144#239—124no—
145#239—124no—
146C2×D12—32no—
147C2×D12—61no—
148C2×D12—62no—
149C2×D12—62no—
150C2×D12—62no—
151C2×D12—62no—
152C2×C4×D3—32no—
153C2×C4×D3—32no—
154C2×C4×D3—32no—
155C2×C4×D3—32no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—68no—
161C2×C4×D3—62no—
162C2×C4×D3—62no—
163C2×C4×D3—124no—
164C2×C4×D3—124no—
165C2×C4×D3—124no—
166C2×C4×D3—124no—
167C2×C3×C8—62no—
168C3×C4⋊C4—22no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4C4×D312yescomplemented
172C3×C22⋊C4—22no—
173C3×C22⋊C4—22no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—62no—
182C4⋊Dic3—32no—
183C4⋊Dic3—61no—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186C4×Dic3—62no—
187C4×Dic3—62no—
188C2×C3⋊C8—22no—
189ΓL(1,𝔽25)—124no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32C2×C22⋊C411yescharacteristic
193C22×C32AGL(1,ℤ/8)11yescharacteristic
194C22×C32#13711yescharacteristic
195C2×C3⋊D3—24no—
196C2×C3⋊D3—24no—
197C2×C3⋊D3—21no—
198C2×C3⋊D3—21no—
199C2×C3⋊D3—21no—
200C2×C3⋊D3—21no—
201C2×C3⋊D3—41no—
202C2×C3⋊D3—41no—
203C2×C3⋊D3—41no—
204C2×C3⋊D3#9912yes—
205C2×C3⋊D3#10412yes—
206C32×C4—21no—
207C32×C4—21no—
208C32×C4—41no—
209C32×C4—41no—
210C3⋊Dic3—21no—
211C3⋊Dic3—21no—
212C3⋊Dic3—41no—
213C3×Dic3—44no—
214C2×#41—91no—
215C23×C4—91no—
216C23×C4—181no—
217C2×M16—181no—
218#123—181no—
219C22⋊Q8—91no—
220C22⋊Q8D3211yescharacteristic
221#121—91no—
222#121—91no—
223#120—181no—
224C4×D4—181no—
225C4×D4—181no—
226#117—91no—
227C22⋊C8—32no—
228C22⋊C8—181no—
229#95—32no—
230#95—181no—
231C23×C3—21no—
232C23×C3D3×D412yes—
233C22×D3—32no—
234C22×D3—32no—
235C22×D3—61no—
236C22×D3—61no—
237C22×D3—64no—
238C22×D3—64no—
239C22×D3—62no—
240C22×D3—62no—
241C22×D3—62no—
242C22×D3—62no—
243C22×D3—122no—
244C22×D3—122no—
245C22×D3—121no—
246C22×D3—121no—
247C3×Q8—42no—
248C3×Q8—42no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—64no—
258C2×C3×C4—122no—
259C2×C3×C4—122no—
260C2×C3×C4C2×C4×D312yes—
261C2×C3×C4D3×D412yes—
262#67—122no—
263#67—122no—
264#67—122no—
265#67—122no—
266C2×Dic3—24no—
267C2×Dic3—32no—
268C2×Dic3—32no—
269C2×Dic3—42no—
270C2×Dic3—42no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—122no—
276C2×Dic3—122no—
277D12—122no—
278D12—122no—
279D12—124no—
280D12—124no—
281D12—124no—
282D12—124no—
283C4×D3—64no—
284C4×D3—64no—
285C4×D3—64no—
286C4×D3—122no—
287C4×D3—1216no—
288C4×D3—122no—
289C4×D3—122no—
290C4×D3—122no—
291C4×D3—124no—
292C4×D3—124no—
293C4×D3—122no—
294C3×C8—122no—
295C3⋊C8—42no—
296C2×C32—21no—
297C2×C32—21no—
298C2×C32C2×#9911yescharacteristic
299C2×C32#41711yescharacteristic
300C2×C32C2×#10411yescharacteristic
301C3⋊D3—22no—
302C3⋊D3—22no—
303C3⋊D3—81no—
304C24—91no—
305#41—362no—
306C2×Q8#62411yescharacteristic, complemented
307C2×D4—91no—
308C2×D4—181no—
309C2×D4—181no—
310C2×D4—181no—
311C22×C4—62no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—181no—
318C22×C4—184no—
319C22×C4—362no—
320C22×C4—362no—
321C22×C4—362no—
322C22×C4C2×D3211yescharacteristic
323M16—362no—
324C2×C8—62no—
325C4⋊C4—21no—
326C4⋊C4—91no—
327C4⋊C4—181no—
328C4⋊C4#62411yescharacteristic, complemented
329C22⋊C4—21no—
330C22⋊C4—181no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C22⋊C4—181no—
334C42—181no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3D3×C22⋊C412yes—
343C22×C3#91412yes—
344C22×C3#91812yes—
345C2×D3—34no—
346C2×D3—34no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—68no—
350C2×D3—68no—
351C2×D3—62no—
352C2×D3—62no—
353C2×D3—62no—
354C2×D3—62no—
355C2×D3—121no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—124no—
360C2×D3—124no—
361C2×D3—122no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—122no—
366C2×D3—122no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—41no—
371C3×C4—42no—
372C3×C4—42no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—124no—
376Dic3—44no—
377Dic3—62no—
378Dic3—62no—
379Dic3—62no—
380Dic3—121no—
381Dic3—122no—
382Dic3—122no—
383C32#150411yescharacteristic, complemented, Sylow
384C23—91no—
385C23—91no—
386C23—182no—
387C23—182no—
388C23—181no—
389C23—181no—
390C23—181no—
391C23#381111yescharacteristic
392Q8—41no—
393D4—361no—
394D4—362no—
395D4—362no—
396D4—361no—
397D4—361no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—64no—
402C2×C4—91no—
403C2×C4—91no—
404C2×C4—122no—
405C2×C4—122no—
406C2×C4—182no—
407C2×C4—182no—
408C2×C4—181no—
409C2×C4—361no—
410C2×C4—361no—
411C2×C4—362no—
412C2×C4—368no—
413C2×C4—361no—
414C2×C4C2×#62411yescharacteristic
415C2×C4#381111yescharacteristic
416C8—122no—
417C2×C3—22no—
418C2×C3—22no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3D3×#9912yes—
425C2×C3#480312yes—
426C2×C3D3×#10412yes—
427D3—64no—
428D3—64no—
429D3—122no—
430D3—122no—
431D3—242no—
432D3—242no—
433C22—21no—
434C22—21no—
435C22—92no—
436C22—92no—
437C22—184no—
438C22—184no—
439C22—181no—
440C22—181no—
441C22—181no—
442C22—181no—
443C22—361no—
444C22—361no—
445C22—361no—
446C22#6394111yescharacteristic
447C22#6394511yescharacteristic
448C22#6397411yescharacteristic
449C4—21no—
450C4—21no—
451C4—41no—
452C4—41no—
453C4—124no—
454C4—181no—
455C4—181no—
456C4—361no—
457C3—21no—
458C3#6833412yescomplemented
459C2—21no—
460C2—21no—
461C2—182no—
462C2—182no—
463C2—721no—
464C2#1059152711yescharacteristic
465C2#1059155411yescharacteristic
466C2#1059167111yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radical#10596098C2
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10591370C2semidirect
3. #10591159C2semidirect
4. C3×#4538C2semidirect
5. #10589151C2semidirect
7. C2×#3832C4semidirect
11. #64155C4semidirect
13. #64104C4semidirect
16. #64101C4semidirect
29. #4538D3semidirect
33. C2×C32×Q8C2×C4semidirect
40. C2×C4⋊(C3⋊D3)C2×C4semidirect
52. C32×C4⋊C4C2×C4semidirect
58. C4⋊(C3⋊Dic3)C2×C4semidirect
135. C2×C3×Q8C4×D3semidirect
171. C3×C4⋊C4C4×D3semidirect
306. C2×Q8#624semidirect
328. C4⋊C4#624semidirect
383. C32#1504semidirect
458. C3#68334semidirect

Maximal subgroups

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

subgroupindex
#105960982
#105913702
#105911592
C3×#45382
#105891512
#683343