Finite Group Databasebeta

← #10595362

Subgroups — #10595362

Order 576.

658 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C2×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#3795C211yesmaximal, characteristic, complemented
3C3×#947C211yesmaximal, characteristic, complemented
4C3×#946C211yesmaximal, characteristic, complemented
5#63916C211yesmaximal, characteristic, complemented
6#63913C212yesmaximal, complemented
7#63912C212yesmaximal, complemented
8C4×#626C211yesmaximal, characteristic, complemented
9#63896C212yesmaximal, complemented
10#63881C212yesmaximal, complemented
11#63844C211yesmaximal, characteristic, complemented
12#5677—31nomaximal
13#5633—31nomaximal
14C2×C32×Q8C2211yescharacteristic
15Q8×C3⋊D3—24no—
16C2×C4×C3⋊D3C2212yes—
17C2×C4×C3⋊D3C2211yescharacteristic
18C2×#634C2212yes—
19C2×#634C2211yescharacteristic
20C2×C3×D12C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×#626C2212yes—
23C2×#626C2211yescharacteristic
24C2×#625C2212yes—
25C2×D3×Dic3C2212yes—
26#3795—24no—
27C3×(C2×D3)⋊C4C2212yes—
28C3×(C2×D3)⋊C4C2212yes—
29C3×(C2×D3)⋊C4C2212yes—
30C3×C4⋊Dic3C2211yescharacteristic
31C3×Dic3⋊C4C2212yes—
32C3×C4×Dic3C2211yescharacteristic
33#3724C2212yes—
34Dic3⋊Dic3C2211yescharacteristic
35#3722C2211yescharacteristic
36(C2×D3)⋊Dic3C2212yes—
37(C2×D3)⋊Dic3C2211yescharacteristic
38Dic32C2212yes—
39C2×D3×Q8—31no—
40C2×D3×Q8—31no—
41C2×D3×Q8—61no—
42C2×#237—31no—
43C2×#235—31no—
44C3×#124—31no—
45C3×C22⋊Q8—31no—
46#947D311yescharacteristic, complemented
47#946D311yescharacteristic, complemented
48#938—31no—
49C4×#67—31no—
50#896—32no—
51#895—31no—
52#893—32no—
53#887—31no—
54#885—32no—
55#885—32no—
56#884—32no—
57#884—32no—
58#67⋊C4—32no—
59#878—32no—
60C4×D12—31no—
61C4×Dic6—31no—
62C22×C3⋊D3C2311yescharacteristic
63C22×C3×D3C2312yes—
64C22×C3×D3C2311yescharacteristic
65C32×Q8—22no—
66C2×C32×C4C2312yes—
67C2×C32×C4C2311yescharacteristic
68C2×C3⋊Dic3C2311yescharacteristic
69C2×C3⋊Dic3C2312yes—
70C4×C3⋊D3—22no—
71C4×C3⋊D3—24no—
72#634—24no—
73#634D414yescomplemented
74C2×C3×Dic3C2311yescharacteristic
75C2×C3×Dic3C2312yes—
76C2×C3×Dic3C2311yescharacteristic
77C2×C3×Dic3C2311yescharacteristic
78C3×D12—22no—
79C3×C4×D3—22no—
80#626—24no—
81#626—22no—
82#625—24no—
83D3×Dic3—24no—
84#548—91noSylow
85C2×C3×Q8—21no—
86C2×C3×Q8C2×D311yescharacteristic
87C2×C3×Q8C2×D311yescharacteristic
88C2×C3×D4—31no—
89C22×C3×C4—31no—
90C2×#67—32no—
91C2×#67—32no—
92C2×#67—32no—
93C2×#67—31no—
94C22×Dic3—32no—
95D3×Q8—64no—
96D3×Q8—64no—
97D3×Q8—68no—
98#237—64no—
99#235—64no—
100C2×D12—31no—
101C2×D12—32no—
102C2×D12C2×D311yescharacteristic
103C2×C4×D3—32no—
104C2×C4×D3—31no—
105C2×C4×D3—32no—
106C2×C4×D3—32no—
107C2×C4×D3—31no—
108C2×C4×D3—62no—
109C2×C4×D3—61no—
110C2×C4×D3C2×D311yescharacteristic
111C2×Dic6—31no—
112C2×Dic6—31no—
113C2×Dic6—32no—
114C2×Dic6—32no—
115C2×Dic6—61no—
116C2×Dic6—62no—
117C3×C4⋊C4—31no—
118C3×C4⋊C4—32no—
119C3×C22⋊C4—32no—
120C3×C22⋊C4—32no—
121C3×C22⋊C4—32no—
122C3×C42—31no—
123#217—32no—
124#217—31no—
125(C2×D3)⋊C4—31no—
126(C2×D3)⋊C4—32no—
127(C2×D3)⋊C4—31no—
128(C2×D3)⋊C4—31no—
129(C2×D3)⋊C4C2×D312yes—
130(C2×D3)⋊C4C2×D312yes—
131(C2×D3)⋊C4C2×D312yes—
132C4⋊Dic3—31no—
133C4⋊Dic3C2×D311yescharacteristic
134Dic3⋊C4—32no—
135Dic3⋊C4—32no—
136Dic3⋊C4—31no—
137Dic3⋊C4C2×D312yes—
138C4×Dic3—32no—
139C4×Dic3—32no—
140C4×Dic3C2×D311yescharacteristic
141C22×C32C2411yescharacteristic
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3#4112yescomplemented
145C2×C3×D3—22no—
146C2×C3×D3—21no—
147C2×C3×D3—22no—
148C2×C3×D3—21no—
149C2×C3×D3—21no—
150C2×C3×D3—22no—
151C32×C4—22no—
152C32×C4C2×D412yes—
153C3⋊Dic3—21no—
154C3⋊Dic3C2×D414yes—
155C3×Dic3—21no—
156C3×Dic3—22no—
157C3×Dic3—21no—
158C3×Dic3—21no—
159C2×#41—91no—
160C22×Q8—91no—
161#124—31no—
162#124—92no—
163C22⋊Q8—31no—
164C22⋊Q8—92no—
165#121—92no—
166#121—91no—
167C4×Q8—91no—
168C4×D4—91no—
169C4×D4—92no—
170C23×C3—32no—
171C23×C3—31no—
172C22×D3—31no—
173C22×D3—31no—
174C22×D3—61no—
175C22×D3C22×D312yes—
176C22×D3C22×D311yescharacteristic
177C3×Q8—24no—
178C3×Q8—22no—
179C3×Q8—22no—
180C3×D4—62no—
181C2×C3×C4—22no—
182C2×C3×C4—21no—
183C2×C3×C4—31no—
184C2×C3×C4—32no—
185C2×C3×C4—31no—
186C2×C3×C4—31no—
187C2×C3×C4—62no—
188C2×C3×C4C22×D312yes—
189C2×C3×C4C22×D312yes—
190C2×C3×C4C22×D311yescharacteristic
191C2×C3×C4C22×D311yescharacteristic
192#67—62no—
193#67—64no—
194#67—64no—
195#67—64no—
196C2×Dic3—32no—
197C2×Dic3—32no—
198C2×Dic3—31no—
199C2×Dic3—31no—
200C2×Dic3—62no—
201C2×Dic3—61no—
202C2×Dic3—64no—
203C2×Dic3C22×D311yescharacteristic
204C2×Dic3C22×D312yes—
205C2×Dic3C22×D311yescharacteristic
206C2×Dic3C22×D311yescharacteristic
207D12—22no—
208D12—64no—
209D12—62no—
210C4×D3—22no—
211C4×D3—64no—
212C4×D3—64no—
213C4×D3—64no—
214C4×D3—68no—
215C4×D3—64no—
216C4×D3—62no—
217C4×D3—62no—
218Dic6—34no—
219Dic6—34no—
220Dic6—64no—
221Dic6—64no—
222Dic6—64no—
223Dic6—68no—
224C2×C32C22×D411yescharacteristic
225C2×C32C2×#4111yescharacteristic
226C2×C322−1+411yescharacteristic
227C3⋊D3—22no—
228C3×D3—41no—
229C3×D3—42no—
230#41—184no—
231C2×Q8—91no—
232C2×Q8—92no—
233C2×Q8—184no—
234C2×Q8D3211yescharacteristic
235C2×D4—31no—
236C2×D4—91no—
237C2×D4—92no—
238C2×D4—92no—
239C22×C4—31no—
240C22×C4—92no—
241C22×C4—92no—
242C22×C4—91no—
243C4⋊C4—32no—
244C4⋊C4—31no—
245C4⋊C4—91no—
246C4⋊C4—92no—
247C22⋊C4—32no—
248C22⋊C4—32no—
249C22⋊C4—32no—
250C22⋊C4—91no—
251C22⋊C4—91no—
252C22⋊C4—92no—
253C42—31no—
254C42—92no—
255C22×C3—21no—
256C22×C3—62no—
257C22×C3—61no—
258C22×C3—62no—
259C22×C3—62no—
260C22×C3—61no—
261C22×C3—61no—
262C22×C3C23×D311yescharacteristic
263C22×C3C23×D311yescharacteristic
264C2×D3—21no—
265C2×D3—22no—
266C2×D3—21no—
267C2×D3—21no—
268C2×D3—22no—
269C2×D3—22no—
270C2×D3—32no—
271C2×D3—32no—
272C2×D3—62no—
273C2×D3—62no—
274C2×D3—62no—
275C2×D3—61no—
276C2×D3—61no—
277C2×D3—61no—
278C2×D3—61no—
279C3×C4—24no—
280C3×C4—22no—
281C3×C4—22no—
282C3×C4—22no—
283C3×C4—61no—
284C3×C4—61no—
285C3×C4—61no—
286C3×C4—62no—
287C3×C4D3×D412yes—
288C3×C4D3×D412yes—
289Dic3—21no—
290Dic3—22no—
291Dic3—21no—
292Dic3—21no—
293Dic3—34no—
294Dic3—34no—
295Dic3—64no—
296Dic3—62no—
297Dic3—61no—
298Dic3—61no—
299C32#54811yescharacteristic, complemented, Sylow
300C23—31no—
301C23—32no—
302C23—91no—
303Q8—22no—
304Q8—94no—
305Q8—184no—
306D4—62no—
307D4—182no—
308D4—184no—
309D4—184no—
310C2×C4—31no—
311C2×C4—31no—
312C2×C4—32no—
313C2×C4—31no—
314C2×C4—62no—
315C2×C4—92no—
316C2×C4—91no—
317C2×C4—184no—
318C2×C4—184no—
319C2×C4—182no—
320C2×C4C2×D3212yes—
321C2×C4C2×D3211yescharacteristic
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—122no—
326C2×C3—121no—
327C2×C3C2×D3×D411yescharacteristic
328C2×C3C2×D3×D411yescharacteristic
329C2×C3#100711yescharacteristic
330C2×C3D3×#4111yescharacteristic
331C2×C3D3×#4111yescharacteristic
332C2×C3#101011yescharacteristic
333D3—41no—
334D3—42no—
335D3—64no—
336D3—62no—
337D3—62no—
338C22—61no—
339C22—62no—
340C22—61no—
341C22—62no—
342C22—61no—
343C22—62no—
344C22—92no—
345C22—181no—
346C22—181no—
347C22C22×D3211yescharacteristic
348C4—22no—
349C4—61no—
350C4—61no—
351C4—62no—
352C4—61no—
353C4—94no—
354C4—181no—
355C4#381112yes—
356C3—21no—
357C3#563311yescharacteristic, complemented
358C3#567711yescharacteristic, complemented
359C2—121no—
360C2—122no—
361C2—182no—
362C2#6431511yescharacteristic
363C2#6431911yescharacteristic
364C2C2×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×Q8C22
hypercenterC2×Q8D32
hypocenterC32#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊D3C2semidirect
2. C2×#3795C2semidirect
3. C3×#947C2semidirect
4. C3×#946C2semidirect
5. #63916C2semidirect
6. #63913C2semidirect
7. #63912C2semidirect
8. C4×#626C2semidirect
9. #63896C2semidirect
10. #63881C2semidirect
11. #63844C2semidirect
46. #947D3semidirect
47. #946D3semidirect
73. #634D4semidirect
144. C2×C3⋊D3#41semidirect
299. C32#548semidirect
357. C3#5633semidirect
358. C3#5677semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊D32
C2×#37952
C3×#9472
C3×#9462
#639162
#639132
#639122
C4×#6262
#638962
#638812
#638442
#56773
#56333