Finite Group Databasebeta

← #11875027

Subgroups — #11875027

Order 1152.

913 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 913 conjugacy classes of subgroups — too many to draw. Only its 188 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10593948C211yesmaximal, characteristic
3C3×#5081C212yesmaximal, complemented
4#10590575C212yesmaximal
5#10590573C212yesmaximal
6#10590546C214yesmaximal, complemented
7#10590322C211yesmaximal, characteristic
8#10590306C212yesmaximal, complemented
9D3×#501—32nomaximal
10C2×Q8×C3⋊D3—21no—
11C32×C4⋊Q8C2211yescharacteristic
12#64153—21no—
13C4⋊C4×C3⋊D3—21no—
14C4⋊C4×C3⋊D3C2212yes—
15#64097—21no—
16#64097C2212yes—
17C42×C3⋊D3C2211yescharacteristic
18#64078C2211yescharacteristic
19C3×#870C2212yes—
20#63900C2211yescharacteristic
21#63900C2211yescharacteristic
22#63883—21no—
23#63883—21no—
24#63872C2212yes—
25#63870—21no—
26#63870—21no—
27C2×#3710C2212yes—
28C3×#808C2214yes—
29C3×#807C2214yes—
30C3×#803C2212yes—
31#63575C2214yes—
32#63573C2214yes—
33#63555C2212yes—
34D3×C4⋊Q8—32no—
35D3×C4⋊Q8—61no—
36D3×#125—32no—
37C3×#501—32no—
38#5081D312yescomplemented
39#5064—32no—
40D3×#107—34no—
41#4876—34no—
42D3×#106—34no—
43#4856—34no—
44D3×#97—32no—
45#4702—32no—
46C2×C32×Q8—21no—
47Q8×C3⋊D3—44no—
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3C2311yescharacteristic
52C2×#634—21no—
53C2×#634—22no—
54C2×#624—21no—
55C2×#624—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4C2312yes—
58C32×C42C2311yescharacteristic
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)C2312yes—
61#3750—22no—
62#3750—22no—
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C3×C4⋊Dic3C2312yes—
67C3×C4⋊Dic3C2312yes—
68C3×Dic3⋊C4—22no—
69C3×Dic3⋊C4—22no—
70C2×C3×C3⋊C8C2314yes—
71#3724—21no—
72#3724—21no—
73Dic3⋊Dic3—22no—
74Dic3⋊Dic3—22no—
75#3710Q818yescomplemented
76C2×#501—91noSylow
77C2×D3×Q8—62no—
78C2×D3×Q8—62no—
79C3×C4⋊Q8—21no—
80C3×C4⋊Q8C2×D312yes—
81C3×#125—32no—
82#944—62no—
83#944—62no—
84C2×D3×C8—34no—
85D3×C4⋊C4—34no—
86D3×C4⋊C4—32no—
87D3×C4⋊C4—32no—
88D3×C4⋊C4—62no—
89D3×C4⋊C4—62no—
90D3×C4⋊C4—62no—
91D3×C4⋊C4—62no—
92D3×C4⋊C4—62no—
93#890—32no—
94#890—32no—
95#889—62no—
96#889—62no—
97#888—34no—
98#888—62no—
99#888—62no—
100#888—62no—
101C42×D3—32no—
102C42×D3—61no—
103#870C2×D312yes—
104#869—32no—
105#869—61no—
106C3×#107—34no—
107C3×#106—34no—
108C3×#97—32no—
109#818—34no—
110#817—34no—
111#815—34no—
112#808—34no—
113#808C2×D314yes—
114#807—34no—
115#807C2×D314yes—
116#803C2×D312yes—
117C22×C3⋊D3C2×D411yescharacteristic
118C32×Q8—42no—
119C2×C32×C4—22no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2411yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3C2×D411yescharacteristic
125C2×C3⋊Dic3C2×D411yescharacteristic
126C2×C3⋊Dic3C2×D411yescharacteristic
127C4×C3⋊D3—22no—
128C4×C3⋊D3—22no—
129C4×C3⋊D3—44no—
130C4×C3⋊D3C2×Q814yes—
131#634—44no—
132#634—42no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135#624—42no—
136#624—42no—
137C3×C3⋊C8C2×Q818yescomplemented
138C2×C4⋊Q8—91no—
139C2×#125—91no—
140#501—32no—
141#501—92no—
142#501—94no—
143C2×#107—92no—
144C2×#106—92no—
145C2×#97—91no—
146C2×C3×Q8—22no—
147C2×C3×Q8—22no—
148D3×Q8—128no—
149D3×Q8—128no—
150C2×C4×D3—32no—
151C2×C4×D3—32no—
152C2×C4×D3—32no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×Dic6—64no—
161C2×Dic6—62no—
162C2×Dic6—64no—
163C2×Dic6—62no—
164C2×C3×C8—34no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—32no—
169C3×C4⋊C4—32no—
170C3×C4⋊C4—62no—
171C3×C4⋊C4—62no—
172C3×C4⋊C4C22×D314yes—
173C3×C42—21no—
174C3×C42C22×D312yes—
175C4⋊Dic3—34no—
176C4⋊Dic3—62no—
177C4⋊Dic3—62no—
178C4⋊Dic3—62no—
179C4⋊Dic3—62no—
180C4⋊Dic3—62no—
181C4⋊Dic3C22×D312yes—
182C4⋊Dic3C22×D312yes—
183Dic3⋊C4—22no—
184Dic3⋊C4—22no—
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191Dic3⋊C4—64no—
192Dic3⋊C4—64no—
193C4×Dic3—32no—
194C4×Dic3—32no—
195C4×Dic3—32no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199C2×C3⋊C8C22×D314yes—
200D3×C8—316no—
201C22×C32C22×D411yescharacteristic
202C2×C3⋊D3C4⋊Q812yes—
203C2×C3⋊D3AGL(1,ℤ/8)12yes—
204C2×C3⋊D3#13712yes—
205C32×C4—21no—
206C32×C4—21no—
207C32×C4—42no—
208C32×C4C22×Q812yes—
209C3⋊Dic3—21no—
210C3⋊Dic3—21no—
211C3⋊Dic3—42no—
212C3⋊Dic3C4⋊Q812yes—
213C3×Dic3—42no—
214C3×Dic3—42no—
215C22×Q8—181no—
216C22×C8—92no—
217C4⋊Q8—92no—
218C4⋊Q8—91no—
219C4⋊Q8—181no—
220C4⋊Q8—181no—
221C4⋊Q8D3211yescharacteristic
222#125—32no—
223#125—92no—
224#125—181no—
225#125—181no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—91no—
228C2×C4⋊C4—92no—
229C2×C4⋊C4—181no—
230C2×C4⋊C4—181no—
231C2×C4⋊C4—181no—
232C2×C42—91no—
233#107—34no—
234#107—94no—
235#106—34no—
236#106—94no—
237#97—32no—
238#97—92no—
239C22×D3—32no—
240C22×D3—61no—
241C3×Q8—44no—
242C3×Q8—44no—
243C2×C3×C4—24no—
244C2×C3×C4—24no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4D3×D412yes—
251C2×C3×C4D3×D412yes—
252C2×C3×C4C23×D312yes—
253C2×Dic3—22no—
254C2×Dic3—22no—
255C2×Dic3—32no—
256C2×Dic3—32no—
257C2×Dic3—32no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C4×D3—38no—
264C4×D3—64no—
265C4×D3—64no—
266C4×D3—64no—
267C4×D3—64no—
268C4×D3—64no—
269C4×D3—124no—
270C4×D3—124no—
271C4×D3—128no—
272C4×D3—128no—
273Dic6—128no—
274Dic6—128no—
275Dic6—124no—
276Dic6—124no—
277C3×C8—38no—
278C3⋊C8D3×Q818yescomplemented
279C2×C32C2×C4⋊Q811yescharacteristic
280C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
281C2×C32C2×#13711yescharacteristic
282C3⋊D3#50114yescomplemented
283C2×Q8—21no—
284C2×Q8—182no—
285C2×Q8—181no—
286C2×Q8—364no—
287C22×C4—91no—
288C22×C4—91no—
289C22×C4—91no—
290C22×C4—182no—
291C22×C4—181no—
292C22×C4—181no—
293C2×C8—34no—
294C2×C8—98no—
295C4⋊C4—21no—
296C4⋊C4—32no—
297C4⋊C4—32no—
298C4⋊C4—62no—
299C4⋊C4—62no—
300C4⋊C4—92no—
301C4⋊C4—182no—
302C4⋊C4—182no—
303C4⋊C4—181no—
304C4⋊C4—181no—
305C4⋊C4—182no—
306C4⋊C4—182no—
307C4⋊C4—181no—
308C4⋊C4C2×D3212yes—
309C42—91no—
310C42—91no—
311C42—91no—
312C42C2×D3211yescharacteristic
313C22×C3—21no—
314C22×C3C2×D3×D412yes—
315C2×D3—34no—
316C2×D3—34no—
317C2×D3—34no—
318C2×D3—62no—
319C2×D3—62no—
320C2×D3—62no—
321C3×C4—22no—
322C3×C4—22no—
323C3×C4—22no—
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—44no—
327C3×C4—44no—
328C3×C4—122no—
329C3×C4—122no—
330C3×C4C2×D3×Q814yes—
331Dic3—34no—
332Dic3—42no—
333Dic3—42no—
334Dic3—62no—
335Dic3—62no—
336Dic3—62no—
337Dic3—62no—
338Dic3—62no—
339Dic3—124no—
340Dic3—124no—
341C32C2×#50111yescharacteristic, complemented, Sylow
342C23—91no—
343Q8—42no—
344Q8—362no—
345Q8—364no—
346C2×C4—22no—
347C2×C4—62no—
348C2×C4—62no—
349C2×C4—91no—
350C2×C4—94no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—364no—
357C2×C4—362no—
358C2×C4—362no—
359C2×C4#381111yescharacteristic
360C2×C4#381111yescharacteristic
361C2×C4C22×D3211yescharacteristic
362C8—38no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3D3×C4⋊Q812yes—
367C2×C3D3×AGL(1,ℤ/8)12yes—
368C2×C3D3×#13712yes—
369D3—38no—
370D3—64no—
371C22—92no—
372C22—92no—
373C22—92no—
374C22C2×#381111yescharacteristic
375C4—21no—
376C4—21no—
377C4—42no—
378C4—92no—
379C4—122no—
380C4—122no—
381C4—181no—
382C4—181no—
383C4—362no—
384C4D32×Q812yes—
385C3—21no—
386C3D3×#50112yescomplemented
387C2—94no—
388C2#1059510011yescharacteristic
389C2#1059532211yescharacteristic
390C2#1059536511yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32C2×#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5081C2semidirect
6. #10590546C2semidirect
8. #10590306C2semidirect
38. #5081D3semidirect
75. #3710Q8semidirect
137. C3×C3⋊C8C2×Q8semidirect
278. C3⋊C8D3×Q8semidirect
282. C3⋊D3#501semidirect
341. C32C2×#501semidirect
386. C3D3×#501semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105939482
C3×#50812
#105905752
#105905732
#105905462
#105903222
#105903062
D3×#5013