Finite Group Databasebeta

← #11775221

Subgroups — #11775221

Order 1152.

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

normal subgroups only

This group has 882 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
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
2#10592425C211yesmaximal, characteristic
3#10592365C211yesmaximal, characteristic
4C32×#328C211yesmaximal, characteristic, complemented
5#10589404C211yesmaximal, characteristic, complemented
6#10589333C211yesmaximal, characteristic, complemented
7#10589318C211yesmaximal, characteristic, complemented
8#68335—34nomaximal
9C2×Q8×C3⋊D3C411yescharacteristic, complemented
10C22×C4×C3⋊D3C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12#64155C411yescharacteristic, complemented
13C2×#3752—21no—
14#64133C2211yescharacteristic
15C2×C4×C3⋊Dic3—21no—
16C2×#3743—21no—
17#64106C411yescharacteristic, complemented
18#64105—21no—
19C4⋊C4×C3⋊D3—21no—
20C4⋊C4×C3⋊D3C411yescharacteristic, complemented
21C22⋊C4×C3⋊D3—21no—
22#64087—21no—
23C32×C22⋊C8C2211yescharacteristic
24C32×#95C2211yescharacteristic
25#63658C2211yescharacteristic
26#63657C2211yescharacteristic
27#63647—21no—
28D3×C22⋊Q8—34no—
29#4726—34no—
30#4666—34no—
31C3×#328D314yescomplemented
32#4538—34no—
33#4467—34no—
34#4452—34no—
35C23×C3⋊D3D411yescharacteristic
36C2×C32×Q8C2×C411yescharacteristic
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41Q8×C3⋊D3—42no—
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—42no—
45C2×C4×C3⋊D3C2×C411yescharacteristic
46C2×C4×C3⋊D3C2×C411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×#634—21no—
50C2×#634C2×C411yescharacteristic
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C22⋊C4—21no—
55#3757—21no—
56#3752—24no—
57#3752—21no—
58#3752—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)C2×C411yescharacteristic
61#3750—21no—
62#3750—21no—
63#3750—21no—
64C4×C3⋊Dic3—42no—
65C2×C3⋊(C3⋊C8)—21no—
66#3743—42no—
67#1508—91noSylow
68C2×D3×Q8—34no—
69C22×C4×D3—34no—
70C3×C22⋊Q8C2×D314yes—
71#946—34no—
72C2×(C2×D3)⋊C4—64no—
73#924—34no—
74C2×C4×Dic3—64no—
75C2×ΓL(1,𝔽25)—64no—
76#897—34no—
77#896—64no—
78D3×C4⋊C4—34no—
79D3×C4⋊C4—64no—
80D3×C22⋊C4—64no—
81#878—64no—
82C3×C22⋊C8C2×D314yes—
83C3×#95C2×D314yes—
84C3⋊#95—34no—
85#830—34no—
86(C2×D3)⋊C8—64no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—22no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3C22⋊C411yescharacteristic
93C22×C3⋊D3C22⋊C411yescharacteristic
94C32×Q8—41no—
95C2×C32×C4—22no—
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C4×C3⋊D3—22no—
112C4×C3⋊D3—22no—
113C4×C3⋊D3—41no—
114C4×C3⋊D3—41no—
115C4×C3⋊D3—42no—
116C4×C3⋊D3—42no—
117#634—42no—
118#634—41no—
119C32×C8—41no—
120C3⋊(C3⋊C8)—41no—
121C2×C22⋊Q8—91no—
122#407—91no—
123C4×C22⋊C4—91no—
124#328—91no—
125#328—91no—
126#328—91no—
127#328C3⋊D311yescharacteristic, complemented
128C23×D3—34no—
129C2×C3×Q8C4×D314yes—
130C22×C3×C4—24no—
131C22×C3×C4C22×D314yes—
132C22×Dic3—34no—
133C22×Dic3—64no—
134D3×Q8—128no—
135C2×C4×D3—34no—
136C2×C4×D3—34no—
137C2×C4×D3—34no—
138C2×C4×D3—34no—
139C2×C4×D3—64no—
140C2×C4×D3—64no—
141C2×C4×D3—128no—
142C2×Dic6—34no—
143C2×Dic6—64no—
144C2×C3×C8—24no—
145C3×C4⋊C4—24no—
146C3×C4⋊C4C4×D314yes—
147C3×C22⋊C4—24no—
148#217—64no—
149(C2×D3)⋊C4—64no—
150(C2×D3)⋊C4—64no—
151(C2×D3)⋊C4—616no—
152C4⋊Dic3—34no—
153C4⋊Dic3—64no—
154Dic3⋊C4—64no—
155Dic3⋊C4—64no—
156Dic3⋊C4—64no—
157C4×Dic3—128no—
158C2×C3⋊C8—64no—
159ΓL(1,𝔽25)—128no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32C2×C22⋊C411yescharacteristic
163C22×C32#13711yescharacteristic
164C22×C32#13711yescharacteristic
165C2×C3⋊D3—21no—
166C2×C3⋊D3—21no—
167C2×C3⋊D3—21no—
168C2×C3⋊D3—21no—
169C2×C3⋊D3—21no—
170C2×C3⋊D3—42no—
171C2×C3⋊D3—42no—
172C2×C3⋊D3#10412yes—
173C32×C4—21no—
174C32×C4—21no—
175C32×C4—42no—
176C32×C4—41no—
177C32×C4—41no—
178C3⋊Dic3—21no—
179C3⋊Dic3—42no—
180C3⋊Dic3—41no—
181C3⋊Dic3—41no—
182C3⋊Dic3#9912yes—
183C22×Q8—91no—
184C23×C4—91no—
185C2×M16—181no—
186C22⋊Q8—91no—
187C22⋊Q8—91no—
188C22⋊Q8—91no—
189C22⋊Q8—181no—
190C22⋊Q8—181no—
191C22⋊Q8C2×C3⋊D311yescharacteristic
192C2×C4⋊C4—91no—
193C2×C4⋊C4—181no—
194C2×C22⋊C4—181no—
195C2×C22⋊C4—181no—
196C2×C42—181no—
197C22⋊C8—91no—
198C22⋊C8—181no—
199C22⋊C8C2×C3⋊D311yescharacteristic
200#95—91no—
201#95C2×C3⋊D311yescharacteristic
202C23×C3D3×D414yes—
203C22×D3—34no—
204C22×D3—34no—
205C22×D3—68no—
206C22×D3—64no—
207C22×D3—64no—
208C22×D3—124no—
209C3×Q8—44no—
210C2×C3×C4—28no—
211C2×C3×C4—24no—
212C2×C3×C4—24no—
213C2×C3×C4—44no—
214C2×C3×C4—44no—
215C2×C3×C4—44no—
216C2×C3×C4C2×C4×D314yes—
217C2×C3×C4D3×D414yes—
218C2×Dic3—34no—
219C2×Dic3—34no—
220C2×Dic3—68no—
221C2×Dic3—68no—
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—124no—
225C2×Dic3—124no—
226C4×D3—68no—
227C4×D3—68no—
228C4×D3—124no—
229C4×D3—124no—
230C4×D3—128no—
231C4×D3—128no—
232Dic6—128no—
233Dic6—124no—
234C3×C8—44no—
235C3⋊C8—124no—
236C2×C32—21no—
237C2×C32—21no—
238C2×C32C2×#9911yescharacteristic
239C2×C32#41911yescharacteristic
240C2×C32C2×#10411yescharacteristic
241C3⋊D3—22no—
242C3⋊D3—41no—
243C24—91no—
244C2×Q8—91no—
245C2×Q8—181no—
246C2×Q8—362no—
247C2×Q8C4×C3⋊D311yescharacteristic
248C22×C4—21no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—181no—
255C22×C4—181no—
256C22×C4—181no—
257C22×C4—362no—
258C22×C4C22×C3⋊D311yescharacteristic
259M16—362no—
260C2×C8—21no—
261C2×C8—181no—
262C4⋊C4—21no—
263C4⋊C4—91no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4—181no—
267C4⋊C4—181no—
268C4⋊C4C4×C3⋊D311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—181no—
271C22⋊C4—181no—
272C22⋊C4—184no—
273C22⋊C4—181no—
274C42—362no—
275C22×C3—24no—
276C22×C3—24no—
277C22×C3D3×C22⋊C414yes—
278C22×C3#91514yes—
279C22×C3#91814yes—
280C2×D3—38no—
281C2×D3—64no—
282C2×D3—64no—
283C2×D3—64no—
284C2×D3—64no—
285C2×D3—64no—
286C2×D3—128no—
287C2×D3—128no—
288C3×C4—24no—
289C3×C4—24no—
290C3×C4—48no—
291C3×C4—44no—
292C3×C4—44no—
293Dic3—38no—
294Dic3—64no—
295Dic3—128no—
296Dic3—124no—
297Dic3—124no—
298C32#150811yescharacteristic, complemented, Sylow
299C23—91no—
300C23—91no—
301C23—182no—
302C23—181no—
303C23—181no—
304C23—361no—
305C23D4×C3⋊D311yescharacteristic
306Q8—41no—
307Q8—361no—
308Q8—362no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—91no—
316C2×C4—91no—
317C2×C4—182no—
318C2×C4—182no—
319C2×C4—182no—
320C2×C4—182no—
321C2×C4—181no—
322C2×C4—181no—
323C2×C4—361no—
324C2×C4—361no—
325C2×C4—362no—
326C2×C4—362no—
327C2×C4—361no—
328C2×C4—361no—
329C2×C4C2×C4×C3⋊D311yescharacteristic
330C2×C4D4×C3⋊D311yescharacteristic
331C8—41no—
332C8—361no—
333C2×C3—24no—
334C2×C3—24no—
335C2×C3D3×#9914yes—
336C2×C3#480214yes—
337C2×C3D3×#10414yes—
338D3—68no—
339D3—124no—
340C22—21no—
341C22—21no—
342C22—92no—
343C22—181no—
344C22—181no—
345C22—181no—
346C22—181no—
347C22—181no—
348C22—362no—
349C22—362no—
350C22C22⋊C4×C3⋊D311yescharacteristic
351C22#6412411yescharacteristic
352C22#6412711yescharacteristic
353C4—21no—
354C4—21no—
355C4—42no—
356C4—41no—
357C4—41no—
358C4—92no—
359C4—181no—
360C4—362no—
361C4—361no—
362C4—361no—
363C3#6833514yescomplemented
364C2—21no—
365C2—21no—
366C2—182no—
367C2—361no—
368C2C3⋊D3×#9911yescharacteristic
369C2#1059250111yescharacteristic
370C2C3⋊D3×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#328C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenter#328C3⋊D3
hypocenterC32#1508
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
4. C32×#328C2semidirect
5. #10589404C2semidirect
6. #10589333C2semidirect
7. #10589318C2semidirect
9. C2×Q8×C3⋊D3C4semidirect
12. #64155C4semidirect
17. #64106C4semidirect
20. C4⋊C4×C3⋊D3C4semidirect
31. C3×#328D3semidirect
127. #328C3⋊D3semidirect
298. C32#1508semidirect
363. C3#68335semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
#105924252
#105923652
C32×#3282
#105894042
#105893332
#105893182
#683353