Finite Group Databasebeta

← #11722980

Subgroups — #11722980

Order 864.

430 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 80 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×#6293C211yesmaximal, characteristic, complemented
2C2×D3×C3⋊Dic3C211yesmaximal, characteristic
3#88815C211yesmaximal, characteristic, complemented
4#88806C211yesmaximal, characteristic, complemented
5C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
7C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
8#63982—31nomaximal
9#63899—31nomaximal
10#63896—31nomaximal
11C22×C32×D3C2211yescharacteristic
12C2×C3⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C3×C3⋊Dic3C2211yescharacteristic
14C2×C3×C3⋊Dic3C2211yescharacteristic
15C2×C3×C3⋊Dic3C2211yescharacteristic
16C2×C32×Dic3C2211yescharacteristic
17C2×C32×Dic3C2211yescharacteristic
18#6293—22no—
19D3×C3⋊Dic3—22no—
20C22×C3⋊Dic3—31no—
21C2×#634—31no—
22C2×#627—31no—
23C2×#627—31no—
24C2×#627—61no—
25C2×D3×Dic3—31no—
26C2×D3×Dic3—31no—
27C2×D3×Dic3—61no—
28#3750—31no—
29C3×#217—31no—
30C3×#217—31no—
31C3×(C2×D3)⋊C4—31no—
32C3×(C2×D3)⋊C4—31no—
33C3×C4⋊Dic3—31no—
34C3×Dic3⋊C4—31no—
35#3724—31no—
36#3724—31no—
37#3724—31no—
38#3724—61no—
39Dic3⋊Dic3—31no—
40Dic3⋊Dic3—31no—
41Dic3⋊Dic3D311yescharacteristic, complemented
42(C2×D3)⋊Dic3D311yescharacteristic
43(C2×D3)⋊Dic3D311yescharacteristic
44C22×C33C2311yescharacteristic
45C2×C32×D3—21no—
46C2×C32×D3—21no—
47C2×C32×D3Q812yescomplemented
48C3⋊(C3⋊Dic3)D412yes—
49C3×C3⋊Dic3—21no—
50C3×C3⋊Dic3—21no—
51C3×C3⋊Dic3—21no—
52C32×Dic3—21no—
53C32×Dic3—21no—
54#896—91no—
55#878—91no—
56#878—91no—
57C23×C32—31no—
58C22×C3×D3—21no—
59C22×C3×D3C2×D311yescharacteristic
60C22×C3×D3C2×D311yescharacteristic
61C2×C32×C4—31no—
62C2×C32×C4—31no—
63C2×C3⋊Dic3—31no—
64C2×C3⋊Dic3—31no—
65C2×C3⋊Dic3—31no—
66C2×C3⋊Dic3—61no—
67C2×C3⋊Dic3—61no—
68C2×C3⋊Dic3—61no—
69C2×C3⋊Dic3—62no—
70C2×C3⋊Dic3—121no—
71C2×C3⋊Dic3C2×D311yescharacteristic
72C2×C3⋊Dic3C2×D311yescharacteristic
73C2×C3⋊Dic3C2×D311yescharacteristic
74#634—62no—
75C2×C3×Dic3—21no—
76C2×C3×Dic3—21no—
77C2×C3×Dic3—31no—
78C2×C3×Dic3—31no—
79C2×C3×Dic3—31no—
80C2×C3×Dic3—31no—
81C2×C3×Dic3—31no—
82C2×C3×Dic3—31no—
83C2×C3×Dic3—61no—
84C2×C3×Dic3—61no—
85C2×C3×Dic3—61no—
86C2×C3×Dic3C2×D311yescharacteristic
87C2×C3×Dic3C2×D311yescharacteristic
88C2×C3×Dic3C2×D311yescharacteristic
89C2×C3×Dic3C2×D311yescharacteristic
90#627—62no—
91#627—62no—
92#627—64no—
93D3×Dic3—62no—
94D3×Dic3—62no—
95D3×Dic3—64no—
96C2×C33C2×D411yescharacteristic
97C2×C33C2×Q811yescharacteristic
98C2×C33#4111yescharacteristic
99C32×D3—22no—
100C22×Dic3—91no—
101C22×Dic3—91no—
102C22×Dic3—181no—
103C2×C4×D3—91no—
104C2×Dic6—91no—
105C2×Dic6—91no—
106C2×Dic6—91no—
107C2×Dic6—181no—
108C3×C4⋊C4—91no—
109C3×C22⋊C4—91no—
110C3×C22⋊C4—91no—
111#217—31no—
112#217—31no—
113(C2×D3)⋊C4—31no—
114(C2×D3)⋊C4—31no—
115C4⋊Dic3—31no—
116C4⋊Dic3—91no—
117Dic3⋊C4—31no—
118Dic3⋊C4—91no—
119Dic3⋊C4—91no—
120Dic3⋊C4—91no—
121Dic3⋊C4—91no—
122Dic3⋊C4—91no—
123Dic3⋊C4—181no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32—32no—
128C22×C32—41no—
129C22×C32—61no—
130C22×C32—61no—
131C22×C32C22×D311yescharacteristic
132C22×C32C22×D311yescharacteristic
133C22×C32C22×D311yescharacteristic
134C2×C3×D3—22no—
135C2×C3×D3—22no—
136C2×C3×D3—21no—
137C2×C3×D3—21no—
138C2×C3×D3—21no—
139C2×C3×D3—21no—
140C2×C3×D3—22no—
141C2×C3×D3Dic612yescomplemented
142C2×C3×D3Dic612yescomplemented
143C32×C4—61no—
144C32×C4—61no—
145C3⋊Dic3—21no—
146C3⋊Dic3—21no—
147C3⋊Dic3—21no—
148C3⋊Dic3—32no—
149C3⋊Dic3—32no—
150C3⋊Dic3—32no—
151C3⋊Dic3—62no—
152C3⋊Dic3—62no—
153C3⋊Dic3—62no—
154C3⋊Dic3—122no—
155C3×Dic3—22no—
156C3×Dic3—21no—
157C3×Dic3—21no—
158C3×Dic3—21no—
159C3×Dic3—21no—
160C3×Dic3—41no—
161C3×Dic3—62no—
162C3×Dic3—62no—
163C3×Dic3—61no—
164C3×Dic3—61no—
165C3×Dic3—61no—
166C3×Dic3—61no—
167C3×Dic3—61no—
168C3×Dic3—61no—
169C3×Dic3—121no—
170C22⋊Q8—271noSylow
171C33C22⋊Q811yescharacteristic, complemented, Sylow
172C23×C3—31no—
173C23×C3—31no—
174C23×C3—61no—
175C22×D3D3211yescharacteristic
176C2×C3×C4—31no—
177C2×C3×C4—31no—
178C2×C3×C4—31no—
179C2×C3×C4—31no—
180C2×C3×C4—61no—
181C2×C3×C4—61no—
182C2×C3×C4—91no—
183C2×C3×C4—91no—
184C2×C3×C4—91no—
185C2×Dic3—31no—
186C2×Dic3—31no—
187C2×Dic3—31no—
188C2×Dic3—31no—
189C2×Dic3—31no—
190C2×Dic3—31no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—91no—
195C2×Dic3—91no—
196C2×Dic3—91no—
197C2×Dic3—181no—
198C2×Dic3—181no—
199C2×Dic3—181no—
200C2×Dic3—182no—
201C2×Dic3—182no—
202C2×Dic3—184no—
203C2×Dic3—361no—
204C2×Dic3D3211yescharacteristic
205C2×Dic3D3211yescharacteristic
206C4×D3—182no—
207Dic6—182no—
208Dic6—182no—
209Dic6—182no—
210Dic6—184no—
211C2×C32—21no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32—21no—
215C2×C32—21no—
216C2×C32—21no—
217C2×C32—21no—
218C2×C32—21no—
219C2×C32—21no—
220C2×C32—41no—
221C2×C32—41no—
222C2×C32—41no—
223C2×C32—62no—
224C2×C32C2×Dic611yescharacteristic
225C2×C32C2×Dic611yescharacteristic
226C2×C32#23511yescharacteristic
227C2×C32D3×D411yescharacteristic
228C2×C32D3×D411yescharacteristic
229C2×C32D3×D411yescharacteristic
230C2×C32#23711yescharacteristic
231C2×C32#23711yescharacteristic
232C2×C32D3×Q811yescharacteristic
233C3×D3—24no—
234C3×D3—22no—
235C3×D3—22no—
236C2×Q8—271no—
237C22×C4—271no—
238C4⋊C4—91no—
239C4⋊C4—271no—
240C4⋊C4—271no—
241C22⋊C4—91no—
242C22⋊C4—91no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—32no—
247C22×C3—32no—
248C22×C3—41no—
249C22×C3—62no—
250C22×C3—62no—
251C22×C3—62no—
252C22×C3—61no—
253C22×C3—61no—
254C22×C3—61no—
255C22×C3—61no—
256C22×C3C2×D3211yescharacteristic
257C22×C3C2×D3211yescharacteristic
258C22×C3C2×D3211yescharacteristic
259C2×D3—21no—
260C2×D3—21no—
261C2×D3#62712yescomplemented
262C3×C4—62no—
263C3×C4—61no—
264C3×C4—61no—
265C3×C4—61no—
266C3×C4—61no—
267C3×C4—121no—
268C3×C4—181no—
269C3×C4—181no—
270C3×C4—181no—
271Dic3—21no—
272Dic3—21no—
273Dic3—62no—
274Dic3—62no—
275Dic3—61no—
276Dic3—61no—
277Dic3—61no—
278Dic3—61no—
279Dic3—61no—
280Dic3—61no—
281Dic3—92no—
282Dic3—92no—
283Dic3—92no—
284Dic3—121no—
285Dic3—182no—
286Dic3—182no—
287Dic3—182no—
288Dic3—362no—
289C32—21no—
290C32—21no—
291C32—21no—
292C32—41no—
293C32#87811yescharacteristic, complemented
294C32#87811yescharacteristic, complemented
295C32#89611yescharacteristic, complemented
296C23—31no—
297Q8—542no—
298C2×C4—31no—
299C2×C4—31no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—91no—
303C2×C4—271no—
304C2×C4—542no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—41no—
315C2×C3—41no—
316C2×C3—41no—
317C2×C3—64no—
318C2×C3—62no—
319C2×C3—62no—
320C2×C3D3×Dic611yescharacteristic
321C2×C3D3×Dic611yescharacteristic
322C2×C3#379511yescharacteristic
323C2×C3#380211yescharacteristic
324C2×C3#380411yescharacteristic
325C2×C3#380511yescharacteristic
326C2×C3C2×#62711yescharacteristic
327C2×C3#381111yescharacteristic
328C2×C3#381111yescharacteristic
329D3—22no—
330C22—32no—
331C22—61no—
332C22—61no—
333C22D3311yescharacteristic
334C4—61no—
335C4—61no—
336C4—181no—
337C4—181no—
338C4—181no—
339C4—272no—
340C3—21no—
341C3—21no—
342C3—21no—
343C3—41no—
344C3#6389611yescharacteristic, complemented
345C3#6389911yescharacteristic, complemented
346C3#6398211yescharacteristic, complemented
347C2—62no—
348C2#8895411yescharacteristic
349C2D3×#62711yescharacteristic
350C2#8896111yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D33
commutator, Fitting, socle, cosocleC22×C33C23
prime radicalC22×C32×D3C22
hypocenterC33C22⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#6293C2semidirect
3. #88815C2semidirect
4. #88806C2semidirect
5. C3×Dic3⋊Dic3C2semidirect
41. Dic3⋊Dic3D3semidirect
47. C2×C32×D3Q8semidirect
141. C2×C3×D3Dic6semidirect
142. C2×C3×D3Dic6semidirect
171. C33C22⋊Q8semidirect
261. C2×D3#627semidirect
293. C32#878semidirect
294. C32#878semidirect
295. C32#896semidirect
344. C3#63896semidirect
345. C3#63899semidirect
346. C3#63982semidirect

Maximal subgroups

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

subgroupindex
C2×#62932
C2×D3×C3⋊Dic32
#888152
#888062
C3×Dic3⋊Dic32
C3×(C2×D3)⋊Dic32
#639823
#638993
#638963