Finite Group Databasebeta

← #11775107

Subgroups — #11775107

Order 1152.

1002 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 133 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#10592425C211yesmaximal, characteristic, complemented
3C3⋊D3×#95C211yesmaximal, characteristic, complemented
4C32×#328C211yesmaximal, characteristic, complemented
5#10589404C211yesmaximal, characteristic, complemented
6#10589336C211yesmaximal, characteristic, complemented
7#10589317C211yesmaximal, characteristic, complemented
8#68334—34nomaximal
9C2×#3832C411yescharacteristic, complemented
10C22×C4×C3⋊D3—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C32×C22⋊Q8C2211yescharacteristic
13#64155C411yescharacteristic, complemented
14#64139C2211yescharacteristic
15C2×#3743—21no—
16#64104C411yescharacteristic, complemented
17#64103—21no—
18#64102—21no—
19#64101C411yescharacteristic, complemented
20#64091—21no—
21#64090—21no—
22C32×C22⋊C8C2211yescharacteristic
23C32×#95C2211yescharacteristic
24#63658—21no—
25#63658C2211yescharacteristic
26#63657C2211yescharacteristic
27#63647—21no—
28#5627—34no—
29#4726—34no—
30D3×#95—34no—
31C3×#328D314yescomplemented
32#4538—34no—
33#4470—34no—
34#4451—34no—
35C23×C3⋊D3D411yescharacteristic
36C2×C32×Q8C2×C411yescharacteristic, complemented
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C2×#638—21no—
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3D411yescharacteristic
42#3832—42no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
46C2×C4×C3⋊D3—24no—
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—42no—
49C2×C4×C3⋊D3—42no—
50C2×C4×C3⋊D3—42no—
51C2×C4×C3⋊D3C2×C411yescharacteristic
52C2×C4×C3⋊D3C2×C411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C32×C8—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4C2×C411yescharacteristic, complemented
58C32×C22⋊C4—21no—
59#3752—21no—
60#3752—21no—
61#3752—21no—
62#3752—21no—
63C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
64#3750—21no—
65C4×C3⋊Dic3—21no—
66C2×C3⋊(C3⋊C8)—21no—
67#3743—42no—
68#1504—91noSylow
69C2×#239—34no—
70C22×C4×D3—34no—
71C22×C4×D3—64no—
72C3×C22⋊Q8C2×D314yes—
73#946—34no—
74#930—34no—
75C2×ΓL(1,𝔽25)—64no—
76#895—34no—
77#894—64no—
78#893—64no—
79#892—34no—
80#882—64no—
81#67⋊C4—64no—
82C3×C22⋊C8C2×D314yes—
83C3×#95C2×D314yes—
84C3⋊#95—34no—
85C3⋊#95—64no—
86#830—34no—
87(C2×D3)⋊C8—64no—
88C23×C32C2×D411yescharacteristic
89C22×C3⋊D3—21no—
90C22×C3⋊D3—21no—
91C22×C3⋊D3—22no—
92C22×C3⋊D3—22no—
93C22×C3⋊D3—21no—
94C22×C3⋊D3C22⋊C411yescharacteristic
95C22×C3⋊D3C22⋊C411yescharacteristic
96C32×Q8—41no—
97C2×C32×C4—22no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105#638—41no—
106#638—41no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
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—
122C4×C3⋊D3—48no—
123C32×C8—41no—
124C3⋊(C3⋊C8)—41no—
125#525—91no—
126#407—91no—
127C2×#95—91no—
128#328—91no—
129#328C3⋊D311yescharacteristic, complemented
130#327—91no—
131#327—91no—
132C23×D3—34no—
133C2×C3×Q8C4×D314yescomplemented
134C22×C3×C4—24no—
135C22×C3×C4C22×D314yes—
136C2×#67—64no—
137C22×Dic3—34no—
138C22×Dic3—64no—
139#239—128no—
140C2×D12—34no—
141C2×D12—64no—
142C2×D12—64no—
143C2×C4×D3—34no—
144C2×C4×D3—34no—
145C2×C4×D3—34no—
146C2×C4×D3—34no—
147C2×C4×D3—64no—
148C2×C4×D3—616no—
149C2×C4×D3—128no—
150C2×C4×D3—128no—
151C2×C4×D3—128no—
152C2×C3×C8—24no—
153C3×C4⋊C4—24no—
154C3×C4⋊C4C4×D314yescomplemented
155C3×C22⋊C4—24no—
156(C2×D3)⋊C4—64no—
157(C2×D3)⋊C4—64no—
158(C2×D3)⋊C4—64no—
159(C2×D3)⋊C4—64no—
160C4⋊Dic3—34no—
161Dic3⋊C4—64no—
162C4×Dic3—64no—
163C2×C3⋊C8—64no—
164ΓL(1,𝔽25)—128no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32C2×C22⋊C411yescharacteristic
168C22×C32AGL(1,ℤ/8)11yescharacteristic
169C22×C32#13711yescharacteristic
170C2×C3⋊D3—24no—
171C2×C3⋊D3—24no—
172C2×C3⋊D3—21no—
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3—21no—
176C2×C3⋊D3—41no—
177C2×C3⋊D3—41no—
178C2×C3⋊D3—41no—
179C2×C3⋊D3#9912yes—
180C2×C3⋊D3#10412yes—
181C32×C4—21no—
182C32×C4—21no—
183C32×C4—42no—
184C32×C4—41no—
185C32×C4—41no—
186C3⋊Dic3—21no—
187C3⋊Dic3—21no—
188C3⋊Dic3—42no—
189C3⋊Dic3—41no—
190C2×#41—91no—
191C23×C4—91no—
192C23×C4—181no—
193C2×M16—181no—
194#123—181no—
195C22⋊Q8—91no—
196C22⋊Q8C2×C3⋊D311yescharacteristic
197#121—91no—
198#121—91no—
199#120—181no—
200C4×D4—181no—
201C4×D4—181no—
202#117—91no—
203C22⋊C8—91no—
204C22⋊C8—181no—
205C22⋊C8C2×C3⋊D311yescharacteristic
206#95—91no—
207#95—181no—
208#95C2×C3⋊D311yescharacteristic
209C23×C3D3×D414yes—
210C22×D3—34no—
211C22×D3—34no—
212C22×D3—68no—
213C22×D3—68no—
214C22×D3—64no—
215C22×D3—64no—
216C22×D3—64no—
217C3×Q8—44no—
218C2×C3×C4—28no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—44no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4C2×C4×D314yes—
225C2×C3×C4D3×D414yes—
226#67—124no—
227#67—124no—
228C2×Dic3—34no—
229C2×Dic3—34no—
230C2×Dic3—68no—
231C2×Dic3—64no—
232C2×Dic3—124no—
233C2×Dic3—124no—
234C2×Dic3—124no—
235D12—124no—
236D12—128no—
237D12—128no—
238C4×D3—68no—
239C4×D3—68no—
240C4×D3—124no—
241C4×D3—124no—
242C4×D3—128no—
243C4×D3—1232no—
244C3×C8—44no—
245C3⋊C8—124no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32C2×#9911yescharacteristic
249C2×C32#41711yescharacteristic
250C2×C32C2×#10411yescharacteristic
251C3⋊D3—22no—
252C3⋊D3—22no—
253C3⋊D3—81no—
254C24—91no—
255#41—362no—
256C2×Q8C4×C3⋊D311yescharacteristic, complemented
257C2×D4—91no—
258C2×D4—181no—
259C2×D4—181no—
260C2×D4—181no—
261C22×C4—21no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—181no—
268C22×C4—184no—
269C22×C4—181no—
270C22×C4—362no—
271C22×C4—362no—
272C22×C4—362no—
273C22×C4C22×C3⋊D311yescharacteristic
274M16—362no—
275C2×C8—21no—
276C2×C8—181no—
277C4⋊C4—21no—
278C4⋊C4—91no—
279C4⋊C4—181no—
280C4⋊C4C4×C3⋊D311yescharacteristic, complemented
281C22⋊C4—21no—
282C22⋊C4—181no—
283C22⋊C4—181no—
284C22⋊C4—181no—
285C22⋊C4—181no—
286C42—181no—
287C22×C3—24no—
288C22×C3—24no—
289C22×C3D3×C22⋊C414yes—
290C22×C3#91414yes—
291C22×C3#91814yes—
292C2×D3—38no—
293C2×D3—38no—
294C2×D3—616no—
295C2×D3—616no—
296C2×D3—64no—
297C2×D3—64no—
298C2×D3—64no—
299C2×D3—64no—
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—124no—
303C3×C4—24no—
304C3×C4—24no—
305C3×C4—48no—
306C3×C4—44no—
307C3×C4—44no—
308Dic3—64no—
309Dic3—64no—
310Dic3—128no—
311Dic3—124no—
312C32#150411yescharacteristic, complemented, Sylow
313C23—91no—
314C23—91no—
315C23—182no—
316C23—182no—
317C23—181no—
318C23—181no—
319C23—181no—
320C23D4×C3⋊D311yescharacteristic
321Q8—41no—
322D4—361no—
323D4—362no—
324D4—362no—
325D4—361no—
326D4—361no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—91no—
334C2×C4—91no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—181no—
339C2×C4—361no—
340C2×C4—361no—
341C2×C4—362no—
342C2×C4—368no—
343C2×C4—361no—
344C2×C4—361no—
345C2×C4—361no—
346C2×C4C2×C4×C3⋊D311yescharacteristic
347C2×C4D4×C3⋊D311yescharacteristic
348C8—41no—
349C8—361no—
350C2×C3—24no—
351C2×C3—24no—
352C2×C3D3×#9914yes—
353C2×C3#480314yes—
354C2×C3D3×#10414yes—
355D3—68no—
356D3—68no—
357D3—244no—
358C22—21no—
359C22—21no—
360C22—92no—
361C22—92no—
362C22—184no—
363C22—184no—
364C22—181no—
365C22—181no—
366C22—181no—
367C22—181no—
368C22—361no—
369C22—361no—
370C22—361no—
371C22C22⋊C4×C3⋊D311yescharacteristic
372C22#6412311yescharacteristic
373C22#6412711yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—41no—
378C4—41no—
379C4—181no—
380C4—181no—
381C4—362no—
382C4—361no—
383C3#6833414yescomplemented
384C2—21no—
385C2—21no—
386C2—182no—
387C2—182no—
388C2—721no—
389C2C3⋊D3×#9911yescharacteristic
390C2#1059250211yescharacteristic
391C2C3⋊D3×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#328C2
socleC22×C32C2×C22⋊C4
prime radical#10596098C2
cosocleC22×C32×C4C23
hypercenter#328C3⋊D3
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #10592425C2semidirect
3. C3⋊D3×#95C2semidirect
4. C32×#328C2semidirect
5. #10589404C2semidirect
6. #10589336C2semidirect
7. #10589317C2semidirect
9. C2×#3832C4semidirect
13. #64155C4semidirect
16. #64104C4semidirect
19. #64101C4semidirect
31. C3×#328D3semidirect
36. C2×C32×Q8C2×C4semidirect
45. C2×C4⋊(C3⋊D3)C2×C4semidirect
57. C32×C4⋊C4C2×C4semidirect
63. C4⋊(C3⋊Dic3)C2×C4semidirect
129. #328C3⋊D3semidirect
133. C2×C3×Q8C4×D3semidirect
154. C3×C4⋊C4C4×D3semidirect
256. C2×Q8C4×C3⋊D3semidirect
280. C4⋊C4C4×C3⋊D3semidirect
312. C32#1504semidirect
383. C3#68334semidirect

Maximal subgroups

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

subgroupindex
#105960982
#105924252
C3⋊D3×#952
C32×#3282
#105894042
#105893362
#105893172
#683343