Finite Group Databasebeta

← #11904520

Subgroups — #11904520

Order 1152.

2314 conjugacy classes of subgroups; only the 449 normal subgroups are shown.

normal subgroups only

This group has 2314 conjugacy classes of subgroups — too many to draw. Only its 449 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#10596687C211yesmaximal, characteristic, complemented
2C2×D32×Q8C211yesmaximal, characteristic, complemented
3#10596646C211yesmaximal, characteristic, complemented
4#10596524C218yesmaximal, complemented
5Q8×GO+(4,𝔽2)C218yesmaximal, complemented
6#10596510C216yesmaximal, complemented
7#10596494C216yesmaximal, complemented
8C2×Q8×C3⋊D3C2211yescharacteristic
9C3×#1007—21no—
10C2×C3×D3×Q8—21no—
11#64319C2214yescomplemented
12D32×Q8—24no—
13D32×Q8C2218yes—
14D32×Q8C2214yescomplemented
15#64315—24no—
16#64306C2216yes—
17C2×C4×D32C2213yes—
18C2×#3797C2213yes—
19#64298—23no—
20C2×D3×Dic6—23no—
21Q8×#157C2218yescomplemented
22#64286C2216yes—
23#64241C2214yes—
24#64233C22112yes—
25#64230C22112yes—
26C4×GO+(4,𝔽2)C22124yes—
27#64222C22112yescomplemented
28#64221C22112yescomplemented
29D32⋊Q8C22112yes—
30D32⋊Q8C22124yescomplemented
31D3×2−1+4—61no—
32C22×D3×Q8—61no—
33C22×D32C2311yescharacteristic
34C2×GO+(4,𝔽2)C2318yes—
35C2×C32×Q8D411yescharacteristic, complemented
36Q8×C3⋊D3D414yescomplemented
37Q8×C3⋊D3C2314yes—
38C2×C4×C3⋊D3C2313yes—
39C2×#634D413yescomplemented
40C3×#239—24no—
41C3×D3×Q8—24no—
42C3×D3×Q8—28no—
43C3×#235—26no—
44C2×C3×C4×D3—23no—
45C2×C3×Dic6—23no—
46#3811C2314yes—
47C2×#627—23no—
48C2×#624C2313yes—
49#3805—26no—
50C2×D3×Dic3—23no—
51#3802C2316yes—
52C4×D32—26no—
53C4×D32C23112yes—
54C4×D32C23112yes—
55#3798—26no—
56#3797—26no—
57#3797C23112yes—
58#3797C2316yes—
59#3796—26no—
60#3795—212no—
61D3×Dic6—224no—
62D3×Dic6—212no—
63C22⋊#157C2314yes—
64C4⋊#157C23112yes—
65C4×#157C23112yes—
66#3773C23124yes—
67D32⋊C4C2318yes—
68D32⋊C4C23124yes—
69#3486—91nomaximal, Sylow
70C3×2−1+4—61no—
71C22×C3×Q8—61no—
72#1010—66no—
73#1010—64no—
74D3×#41—66no—
75D3×#41—64no—
76#1007—21no—
77#1007—64no—
78C2×D3×Q8—21no—
79C2×D3×Q8—63no—
80C2×D3×Q8—68no—
81C2×D3×Q8—64no—
82C2×D3×Q8—61no—
83C2×D3×Q8—61no—
84C2×D3×Q8—63no—
85C2×D3×Q8—68no—
86C22×C4×D3—63no—
87C22×Dic6—63no—
88C22×C3⋊D3C2411yescharacteristic
89C22×C3×D3—21no—
90C2×D32—21no—
91C2×D32—24no—
92C2×D32C2414yes—
93C2×D32C2412yes—
94C2×#157C2418yes—
95GO+(4,𝔽2)—216no—
96C32×Q8C2×D414yes—
97C2×C32×C4C2×D413yes—
98C2×C3⋊Dic3C2×D413yes—
99C4×C3⋊D3C2×D416yes—
100C4×C3⋊D3C2416yes—
101#634C2×D4112yes—
102C3×#67—24no—
103C2×C3×Dic3—23no—
104C3×D12—26no—
105C3×C4×D3—212no—
106C3×C4×D3—212no—
107C3×Dic6—26no—
108C3×Dic6—212no—
109#627—212no—
110#627—26no—
111#626—24no—
112#625—26no—
113#624—23no—
114#624C2416yes—
115#624C2414yes—
116D3×Dic3—212no—
117D3×Dic3—212no—
118C2×2−1+4—91no—
119C23×Q8—91no—
120D4×Q8—98no—
121#548—98no—
122#536—96no—
123#525—96no—
124#519—91no—
125C23×D3—61no—
126C3×#41—66no—
127C3×#41—64no—
128C2×C3×Q8—21no—
129C2×C3×Q8—21no—
130C2×C3×Q8—63no—
131C2×C3×Q8—68no—
132C2×C3×Q8—64no—
133C22×C3×C4—63no—
134C22×Dic3—63no—
135#239—24no—
136#239—66no—
137D3×Q8—28no—
138D3×Q8—24no—
139D3×Q8—612no—
140D3×Q8—66no—
141D3×Q8—64no—
142D3×Q8—64no—
143D3×Q8—64no—
144D3×Q8—64no—
145D3×Q8—612no—
146D3×Q8—624no—
147D3×Q8—612no—
148#237—66no—
149#237—612no—
150#237—612no—
151D3×D4—66no—
152D3×D4—64no—
153#235—26no—
154#235—612no—
155#235—612no—
156C2×C4×D3—23no—
157C2×C4×D3—612no—
158C2×C4×D3—612no—
159C2×C4×D3—63no—
160C2×C4×D3—63no—
161C2×C4×D3—63no—
162C2×C4×D3—612no—
163C2×C4×D3—63no—
164C2×Dic6—23no—
165C2×Dic6—63no—
166C2×Dic6—63no—
167C2×Dic6—624no—
168C2×Dic6—612no—
169C2×Dic6—66no—
170C22×C32C22×D411yescharacteristic
171C2×C3⋊D3—22no—
172C2×C3⋊D3C22×D411yescharacteristic
173C2×C3⋊D3C2511yescharacteristic
174C2×C3×D3—24no—
175C2×C3×D3—22no—
176C2×C3×D3—24no—
177D32—24no—
178D32—22no—
179D32—28no—
180D322−1+414yescomplemented
181#157—28no—
182C32×C4C22×D416yes—
183C3⋊Dic3C22×D416yes—
184C3×Dic3—24no—
185C3×Dic3—26no—
1862−1+4—61no—
1872−1+4—184no—
1882−1+4—183no—
189C2×#41—96no—
190C2×#41—94no—
191C22×Q8—61no—
192C22×Q8—93no—
193C22×Q8—98no—
194C22×Q8—94no—
195C22×Q8—91no—
196C22×Q8—183no—
197C22×Q8—184no—
198C23×C4—93no—
199C4⋊Q8—912no—
200#124—912no—
201#123—912no—
202C22⋊Q8—912no—
203C22⋊Q8—924no—
204#121—912no—
205#120—94no—
206C4×Q8—98no—
207C4×D4—924no—
208#117—96no—
209C23×C3—61no—
210C22×D3—21no—
211C22×D3—62no—
212C22×D3—64no—
213C22×D3—61no—
214C22×D3—61no—
215C22×D3—62no—
216C22×D3—68no—
217C3×Q8—24no—
218C3×Q8—24no—
219C3×Q8—612no—
220C3×Q8—66no—
221C3×D4—66no—
222C3×D4—64no—
223C2×C3×C4—23no—
224C2×C3×C4—23no—
225C2×C3×C4—612no—
226C2×C3×C4—612no—
227C2×C3×C4—63no—
228#67—24no—
229#67—64no—
230#67—612no—
231C2×Dic3—23no—
232C2×Dic3—63no—
233C2×Dic3—63no—
234C2×Dic3—612no—
235C2×Dic3—612no—
236D12—26no—
237D12—64no—
238C4×D3—212no—
239C4×D3—212no—
240C4×D3—64no—
241C4×D3—66no—
242C4×D3—66no—
243C4×D3—66no—
244C4×D3—66no—
245C4×D3—66no—
246C4×D3—66no—
247C4×D3—612no—
248C4×D3—612no—
249Dic6—212no—
250Dic6—26no—
251Dic6—612no—
252Dic6—612no—
253Dic6—624no—
254Dic6—612no—
255C2×C32—21no—
256C2×C32C23×D411yescharacteristic
257C3⋊D3—21no—
258C3⋊D3C2×2−1+412yes—
259C3×D3—24no—
260C3×D3—44no—
261C24—91no—
262#41—64no—
263#41—66no—
264#41—186no—
265#41—1812no—
266#41—186no—
267#41—186no—
268C2×Q8—68no—
269C2×Q8—64no—
270C2×Q8—63no—
271C2×Q8—912no—
272C2×Q8—96no—
273C2×Q8—94no—
274C2×Q8—94no—
275C2×Q8—93no—
276C2×Q8—183no—
277C2×Q8—1824no—
278C2×Q8—1812no—
279C2×Q8—186no—
280C2×Q8GO+(4,𝔽2)11yescharacteristic, complemented
281C2×D4—94no—
282C2×D4—96no—
283C2×D4—98no—
284C22×C4—63no—
285C22×C4—912no—
286C22×C4—912no—
287C22×C4—93no—
288C22×C4—93no—
289C22×C4—186no—
290C22×C4—183no—
291C4⋊C4—912no—
292C4⋊C4—924no—
293C22⋊C4—94no—
294C22⋊C4—98no—
295C22⋊C4—924no—
296C42—912no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—62no—
300C22×C3—64no—
301C22×C3—64no—
302C2×D3—22no—
303C2×D3—24no—
304C2×D3—24no—
305C2×D3—64no—
306C2×D3—61no—
307C2×D3—61no—
308C2×D3—61no—
309C2×D3—61no—
310C2×D3—64no—
311C2×D3—68no—
312C2×D3—64no—
313C2×D3—128no—
314C2×D3—122no—
315C3×C4—26no—
316C3×C4—26no—
317C3×C4—66no—
318C3×C4—64no—
319Dic3—26no—
320Dic3—24no—
321Dic3—66no—
322Dic3—66no—
323C32#348611yescharacteristic, complemented, Sylow
324C23—61no—
325C23—92no—
326C23—94no—
327C23—91no—
328C23—181no—
329C23—184no—
330Q8—612no—
331Q8—66no—
332Q8—912no—
333Q8—1812no—
334Q8—186no—
335Q8C2×GO+(4,𝔽2)14yes—
336D4—64no—
337D4—66no—
338D4—184no—
339D4—186no—
340D4—1816no—
341C2×C4—63no—
342C2×C4—612no—
343C2×C4—612no—
344C2×C4—96no—
345C2×C4—94no—
346C2×C4—93no—
347C2×C4—96no—
348C2×C4—96no—
349C2×C4—98no—
350C2×C4—183no—
351C2×C4—1812no—
352C2×C4—1812no—
353C2×C4C2×GO+(4,𝔽2)13yes—
354C2×C3—22no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—41no—
358C2×C3—64no—
359C2×C3—124no—
360D3—24no—
361D3—44no—
362D3—62no—
363D3—62no—
364D3—62no—
365D3—121no—
366C22—64no—
367C22—62no—
368C22—64no—
369C22—94no—
370C22—91no—
371C22—91no—
372C22—182no—
373C22—182no—
374C22—184no—
375C22—188no—
376C22C22×GO+(4,𝔽2)11yescharacteristic
377C4—64no—
378C4—66no—
379C4—96no—
380C4—188no—
381C4C22×GO+(4,𝔽2)16yes—
382C3—21no—
383C3—21no—
384C2—21no—
385C2—64no—
386C2—92no—
387C2—124no—
388C2—181no—
389C2C23×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC2C23×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C25
FittingC2×C32×Q8D4
socleC2×C32C23×D4
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#3486
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #10596687C2semidirect
2. C2×D32×Q8C2semidirect
3. #10596646C2semidirect
4. #10596524C2semidirect
5. Q8×GO+(4,𝔽2)C2semidirect
6. #10596510C2semidirect
7. #10596494C2semidirect
11. #64319C22semidirect
14. D32×Q8C22semidirect
21. Q8×#157C22semidirect
27. #64222C22semidirect
28. #64221C22semidirect
30. D32⋊Q8C22semidirect
35. C2×C32×Q8D4semidirect
36. Q8×C3⋊D3D4semidirect
39. C2×#634D4semidirect
180. D322−1+4semidirect
280. C2×Q8GO+(4,𝔽2)semidirect
323. C32#3486semidirect

Maximal subgroups

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

subgroupindex
#105966872
C2×D32×Q82
#105966462
#105965242
Q8×GO+(4,𝔽2)2
#105965102
#105964942
#34869