Finite Group Databasebeta

← #77347

Subgroups — #77347

Order 384.

408 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#396C211yesmaximal, characteristic
2#4983C211yesmaximal, characteristic, complemented
3#4982C211yesmaximal, characteristic, complemented
4#4981C211yesmaximal, characteristic, complemented
5#4980C211yesmaximal, characteristic, complemented
6#4976C211yesmaximal, characteristic, complemented
7#4972C211yesmaximal, characteristic, complemented
8#4949C211yesmaximal, characteristic
9#4949C211yesmaximal, characteristic
10#4948C211yesmaximal, characteristic
11#4943C211yesmaximal, characteristic
12#4942C211yesmaximal, characteristic
13Dic3×C22⋊C4C211yesmaximal, characteristic
14#4657C211yesmaximal, characteristic, complemented
15#4653C211yesmaximal, characteristic, complemented
16#2667—31nomaximal, Sylow
17C23×Dic3C2211yescharacteristic
18C2×C3×C4⋊C4C2211yescharacteristic
19C2×C3×C4⋊C4C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21C2×C3×C22⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×#217C2211yescharacteristic
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×C4⋊Dic3C2211yescharacteristic
28C2×C4⋊Dic3C2211yescharacteristic
29C2×C4⋊Dic3C2211yescharacteristic
30C2×Dic3⋊C4C2211yescharacteristic
31C2×Dic3⋊C4C2211yescharacteristic
32C2×Dic3⋊C4C2211yescharacteristic
33C2×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊C4C2211yescharacteristic
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×C4×Dic3C2211yescharacteristic
39C2×C4×Dic3C2211yescharacteristic
40C3×#95C2211yescharacteristic
41C3⋊#95C2211yescharacteristic
42C3⋊#95C2211yescharacteristic
43C3⋊#95C2211yescharacteristic
44C3⋊#95C2211yescharacteristic
45C3⋊#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52#399—31no—
53#399—31no—
54#398—31no—
55#398—31no—
56#398—31no—
57#398—31no—
58#396—31no—
59#396D311yescharacteristic
60#389—31no—
61#389—31no—
62#387—31no—
63#387—31no—
64#381—31no—
65#380—31no—
66C4×C22⋊C4—31no—
67C24×C3C2311yescharacteristic
68C22×C3×C4C2311yescharacteristic
69C22×C3×C4C2311yescharacteristic
70C22×C3×C4C2311yescharacteristic
71C22×C3×C4C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×Dic3—41no—
75C22×Dic3—41no—
76C22×Dic3Q814yes—
77C22×Dic3C2311yescharacteristic
78C22×Dic3C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C3×C4⋊C4—22no—
86C3×C4⋊C4—41no—
87C3×C4⋊C4—41no—
88C3×C22⋊C4—22no—
89C3×C22⋊C4—41no—
90C3×C22⋊C4—41no—
91#217—22no—
92#217—41no—
93#217—41no—
94C4⋊Dic3—22no—
95C4⋊Dic3—22no—
96C4⋊Dic3—41no—
97Dic3⋊C4—22no—
98Dic3⋊C4—41no—
99Dic3⋊C4—41no—
100Dic3⋊C4—41no—
101Dic3⋊C4—41no—
102Dic3⋊C4—41no—
103Dic3⋊C4—41no—
104Dic3⋊C4—41no—
105C4×Dic3—41no—
106C4×Dic3—41no—
107C23×C4—31no—
108C2×C4⋊C4—31no—
109C2×C4⋊C4—31no—
110C2×C4⋊C4—31no—
111C2×C4⋊C4—31no—
112C2×C4⋊C4—31no—
113C2×C4⋊C4—31no—
114C2×C4⋊C4—31no—
115C2×C4⋊C4—31no—
116C2×C4⋊C4—31no—
117C2×C4⋊C4—31no—
118C2×C4⋊C4—31no—
119C2×C4⋊C4C2×D311yescharacteristic
120C2×C4⋊C4C2×D311yescharacteristic
121C2×C4⋊C4C2×D311yescharacteristic
122C2×C22⋊C4—31no—
123C2×C22⋊C4—31no—
124C2×C22⋊C4—31no—
125C2×C22⋊C4C2×D311yescharacteristic
126C2×C22⋊C4C2×D311yescharacteristic
127C2×C22⋊C4C2×D311yescharacteristic
128C2×C42—31no—
129C2×C42—31no—
130#95—31no—
131#95—31no—
132#95—31no—
133#95—31no—
134#95—31no—
135#95—31no—
136#95—31no—
137#95—31no—
138#95—31no—
139#95—31no—
140#95—31no—
141#95C2×D311yescharacteristic
142C23×C3—21no—
143C23×C3—21no—
144C23×C3—21no—
145C23×C3—21no—
146C23×C3—21no—
147C23×C3—21no—
148C23×C3C2×Q812yes—
149C23×C3C2411yescharacteristic
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4#4112yes—
168C2×Dic3—21no—
169C2×Dic3—21no—
170C2×Dic3—21no—
171C2×Dic3—21no—
172C2×Dic3—21no—
173C2×Dic3—21no—
174C2×Dic3—21no—
175C2×Dic3—21no—
176C2×Dic3—21no—
177C2×Dic3—21no—
178C2×Dic3—21no—
179C2×Dic3—21no—
180C2×Dic3—21no—
181C2×Dic3—21no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—44no—
190C2×Dic3C2×Q812yes—
191C2×Dic3C2×Q812yes—
192C2×Dic3#4112yes—
193C24C22×D311yescharacteristic
194C22×C4—31no—
195C22×C4—31no—
196C22×C4—31no—
197C22×C4—34no—
198C22×C4—31no—
199C22×C4—31no—
200C22×C4—31no—
201C22×C4—31no—
202C22×C4—31no—
203C22×C4—121no—
204C22×C4—121no—
205C22×C4C22×D311yescharacteristic
206C22×C4C22×D311yescharacteristic
207C22×C4C22×D311yescharacteristic
208C22×C4C22×D311yescharacteristic
209C22×C4C22×D311yescharacteristic
210C22×C4C22×D311yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—62no—
215C4⋊C4—62no—
216C4⋊C4—62no—
217C4⋊C4—121no—
218C4⋊C4—121no—
219C4⋊C4—121no—
220C4⋊C4—121no—
221C4⋊C4—121no—
222C4⋊C4—121no—
223C4⋊C4—121no—
224C4⋊C4—121no—
225C22⋊C4—22no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—62no—
229C22⋊C4—121no—
230C22⋊C4—121no—
231C42—121no—
232C42—121no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—22no—
236C22×C3—41no—
237C22×C3—41no—
238C22×C3—41no—
239C22×C3—41no—
240C22×C3C22×Q811yescharacteristic
241C22×C3C2×#4111yescharacteristic
242C22×C3C2×#4111yescharacteristic
243C22×C3H(5,𝔽2)11yescharacteristic
244C22×C3H(5,𝔽2)11yescharacteristic
245C22×C3H(5,𝔽2)11yescharacteristic
246C22×C32−1+411yescharacteristic
247C3×C4—22no—
248C3×C4—41no—
249C3×C4—41no—
250C3×C4—41no—
251C3×C4—41no—
252C3×C4—41no—
253Dic3—22no—
254Dic3—22no—
255Dic3—22no—
256Dic3—41no—
257Dic3—41no—
258Dic3—41no—
259Dic3—41no—
260Dic3—41no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23D3×Q812yes—
268C23C23×D311yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—32no—
287C2×C4—32no—
288C2×C4—32no—
289C2×C4—61no—
290C2×C4—61no—
291C2×C4—61no—
292C2×C4—61no—
293C2×C4—61no—
294C2×C4—61no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—124no—
311C2×C4#23712yes—
312C2×C3—42no—
313C2×C3#53311yescharacteristic
314C2×C3#53911yescharacteristic
315C2×C3#53911yescharacteristic
316C2×C3#54011yescharacteristic
317C2×C3#54011yescharacteristic
318C2×C3#54311yescharacteristic
319C2×C3#54411yescharacteristic
320C22—22no—
321C22—22no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22C2×#23711yescharacteristic
328C22#100411yescharacteristic
329C22#100411yescharacteristic
330C22C2×D3×Q811yescharacteristic
331C22D3×#4111yescharacteristic
332C22#100911yescharacteristic
333C22#101011yescharacteristic
334C4—22no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—62no—
341C4—62no—
342C4—62no—
343C4—121no—
344C4—121no—
345C4—121no—
346C4—121no—
347C4—121no—
348C3#266711yescharacteristic, complemented, Sylow
349C2—42no—
350C2#560211yescharacteristic
351C2#561511yescharacteristic
352C2#561911yescharacteristic
353C2#562211yescharacteristic
354C2#562311yescharacteristic
355C2#563411yescharacteristic
356C2#570711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#396C2
prime radicalC24×C3C23
hypercenter#396D3
hypocenterC3#2667
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
2. #4983C2semidirect
3. #4982C2semidirect
4. #4981C2semidirect
5. #4980C2semidirect
6. #4976C2semidirect
7. #4972C2semidirect
14. #4657C2semidirect
15. #4653C2semidirect
348. C3#2667semidirect

Maximal subgroups

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

subgroupindex
C3×#3962
#49832
#49822
#49812
#49802
#49762
#49722
#49492
#49482
#49432
#49422
Dic3×C22⋊C42
#46572
#46532
#26673