Finite Group Databasebeta

← #74945

Subgroups — #74945

Order 384.

568 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#893C211yesmaximal, characteristic
2C3×#387C211yesmaximal, characteristic, complemented
3#4989C211yesmaximal, characteristic, complemented
4#4987C211yesmaximal, characteristic, complemented
5#4980C211yesmaximal, characteristic, complemented
6#4940C211yesmaximal, characteristic, complemented
7C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8#4669C211yesmaximal, characteristic, complemented
9#4668C211yesmaximal, characteristic, complemented
10#4665C211yesmaximal, characteristic
11#4665C211yesmaximal, characteristic
12#4664C211yesmaximal, characteristic, complemented
13D3×#95C211yesmaximal, characteristic, complemented
14#4651C211yesmaximal, characteristic, complemented
15#4650C211yesmaximal, characteristic, complemented
16#2318—31nomaximal, Sylow
17C22×D12C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×C4×D3C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C42C2211yescharacteristic
25C2×(C2×D3)⋊C4C2211yescharacteristic
26C2×(C2×D3)⋊C4C2211yescharacteristic
27C2×(C2×D3)⋊C4C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊C4C2211yescharacteristic
36C2×C4×Dic3C2211yescharacteristic
37C2×C4×Dic3C2211yescharacteristic
38#893C418yescomplemented
39C3×#95C2211yescharacteristic
40C3×#95C2211yescharacteristic
41C3×#95C2211yescharacteristic
42C3×#95C2211yescharacteristic
43C3⋊#95C2211yescharacteristic
44C3⋊#95C2211yescharacteristic
45C3⋊#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C2×C4×D4—31no—
54#388—31no—
55#388—31no—
56#387—31no—
57#387D311yescharacteristic, complemented
58#386—31no—
59#386—31no—
60#385—31no—
61#385—31no—
62#383—31no—
63#382—31no—
64#381—31no—
65#380—31no—
66C4×C22⋊C4—31no—
67C2×#95—31no—
68C23×D3C2311yescharacteristic
69C23×D3C2311yescharacteristic
70C22×C3×C4C2311yescharacteristic
71C22×C3×C4C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×Dic3C2311yescharacteristic
78C22×Dic3C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C2×D12—22no—
84C2×D12—22no—
85C2×D12C2×C414yes—
86C2×C4×D3—22no—
87C2×C4×D3—22no—
88C2×C4×D3—41no—
89C2×C4×D3—41no—
90C2×C4×D3—41no—
91C2×C4×D3—41no—
92C2×C4×D3—41no—
93C2×C4×D3—41no—
94C2×C4×D3—41no—
95C2×C4×D3—41no—
96C2×C4×D3C2×C414yes—
97C2×C4×D3C2×C414yescomplemented
98C3×C4⋊C4—41no—
99C3×C4⋊C4C2×C414yescomplemented
100C3×C42—41no—
101(C2×D3)⋊C4—22no—
102(C2×D3)⋊C4—22no—
103(C2×D3)⋊C4—41no—
104(C2×D3)⋊C4—41no—
105(C2×D3)⋊C4—41no—
106(C2×D3)⋊C4—41no—
107(C2×D3)⋊C4C2×C414yes—
108(C2×D3)⋊C4C2×C414yescomplemented
109C4⋊Dic3—41no—
110Dic3⋊C4—41no—
111Dic3⋊C4—41no—
112C4×Dic3—41no—
113C4×Dic3C2×C414yescomplemented
114C22×D4—31no—
115C23×C4—31no—
116C23×C4—31no—
117C23×C4—31no—
118C23×C4—31no—
119C4×D4—38no—
120C2×C4⋊C4—31no—
121C2×C4⋊C4—31no—
122C2×C4⋊C4—31no—
123C2×C4⋊C4C2×D311yescharacteristic
124C2×C4⋊C4C2×D311yescharacteristic
125C2×C22⋊C4—31no—
126C2×C22⋊C4—31no—
127C2×C22⋊C4—31no—
128C2×C22⋊C4—31no—
129C2×C22⋊C4—31no—
130C2×C22⋊C4—31no—
131C2×C22⋊C4—31no—
132C2×C22⋊C4—31no—
133C2×C42—31no—
134C2×C42—31no—
135C2×C42C2×D311yescharacteristic
136#95—31no—
137#95—31no—
138#95—31no—
139#95—31no—
140#95—31no—
141#95—31no—
142#95—31no—
143#95—31no—
144#95—31no—
145#95—31no—
146#95C2×D311yescharacteristic
147#95C2×D311yescharacteristic
148#95C2×D311yescharacteristic
149#95C2×D311yescharacteristic
150C23×C3C2411yescharacteristic
151C22×D3—21no—
152C22×D3—21no—
153C22×D3—21no—
154C22×D3—21no—
155C22×D3—21no—
156C22×D3—21no—
157C22×D3—21no—
158C22×D3—21no—
159C22×D3—21no—
160C22×D3—21no—
161C22×D3C22×C412yes—
162C22×D3C22×C412yes—
163C22×D3#4112yes—
164C22×D3#4112yes—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4C22×C412yes—
184C2×C3×C4C22×C412yes—
185C2×C3×C4C22×C412yes—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3C22×C412yes—
203C2×Dic3C22×C412yes—
204D12—28no—
205C4×D3—44no—
206C4×D3—44no—
207C4×D3—44no—
208C4×D3—44no—
209C24—31no—
210C24—31no—
211C2×D4—34no—
212C2×D4—62no—
213C2×D4—62no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—34no—
217C22×C4—34no—
218C22×C4—31no—
219C22×C4—31no—
220C22×C4—31no—
221C22×C4—31no—
222C22×C4—62no—
223C22×C4—62no—
224C22×C4—121no—
225C22×C4—121no—
226C22×C4—121no—
227C22×C4—121no—
228C22×C4—121no—
229C22×C4—121no—
230C22×C4—121no—
231C22×C4—121no—
232C22×C4C22×D311yescharacteristic
233C22×C4C22×D311yescharacteristic
234C22×C4C22×D311yescharacteristic
235C22×C4C22×D311yescharacteristic
236C22×C4C22×D311yescharacteristic
237C22×C4C22×D311yescharacteristic
238C22×C4C22×D311yescharacteristic
239C4⋊C4—41no—
240C4⋊C4—121no—
241C4⋊C4—121no—
242C4⋊C4—121no—
243C4⋊C4C4×D314yescomplemented
244C22⋊C4—34no—
245C22⋊C4—34no—
246C22⋊C4—62no—
247C22⋊C4—62no—
248C22⋊C4—121no—
249C22⋊C4—121no—
250C22⋊C4—121no—
251C22⋊C4—121no—
252C42—34no—
253C42—41no—
254C42—121no—
255C22×C3C23×C411yescharacteristic
256C22×C3C2×#4111yescharacteristic
257C22×C3C2×#4111yescharacteristic
258C22×C3H(5,𝔽2)11yescharacteristic
259C22×C3H(5,𝔽2)11yescharacteristic
260C22×C3H(5,𝔽2)11yescharacteristic
261C22×C32−1+411yescharacteristic
262C2×D3—22no—
263C2×D3—22no—
264C2×D3—22no—
265C2×D3—22no—
266C2×D3—22no—
267C2×D3—22no—
268C2×D3—22no—
269C2×D3—22no—
270C2×D3—22no—
271C2×D3—41no—
272C2×D3—41no—
273C2×D3—41no—
274C2×D3—41no—
275C2×D3#11714yes—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—41no—
283Dic3—22no—
284Dic3—22no—
285Dic3—41no—
286Dic3—41no—
287Dic3—41no—
288Dic3—41no—
289C23—32no—
290C23—32no—
291C23—32no—
292C23—32no—
293C23—61no—
294C23—61no—
295C23—61no—
296C23—61no—
297C23—61no—
298C23—61no—
299C23—61no—
300C23—61no—
301C23—61no—
302C23—61no—
303C23C23×D311yescharacteristic
304D4—68no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—32no—
324C2×C4—32no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—61no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—61no—
341C2×C4—124no—
342C2×C4—124no—
343C2×C4—124no—
344C2×C4—124no—
345C2×C4C2×C4×D312yes—
346C2×C4C2×C4×D312yes—
347C2×C4C2×C4×D312yes—
348C2×C3C2×#11711yescharacteristic
349C2×C3#51811yescharacteristic
350C2×C3#52011yescharacteristic
351C2×C3#53811yescharacteristic
352C2×C3#53811yescharacteristic
353C2×C3#53911yescharacteristic
354C2×C3#53911yescharacteristic
355D3—24no—
356D3—42no—
357C22—34no—
358C22—62no—
359C22—62no—
360C22—62no—
361C22—62no—
362C22—62no—
363C22—62no—
364C22—62no—
365C22—62no—
366C22—62no—
367C22—121no—
368C22—121no—
369C22—121no—
370C22—121no—
371C22C22×C4×D311yescharacteristic
372C22#100411yescharacteristic
373C22#100711yescharacteristic
374C22D3×#4111yescharacteristic
375C22D3×#4111yescharacteristic
376C22#100911yescharacteristic
377C22#100911yescharacteristic
378C4—22no—
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—62no—
386C4—62no—
387C4—121no—
388C4—121no—
389C4—121no—
390C4—121no—
391C3#231811yescharacteristic, complemented, Sylow
392C2—64no—
393C2—122no—
394C2D3×#11711yescharacteristic
395C2#554511yescharacteristic
396C2#557411yescharacteristic
397C2#563811yescharacteristic
398C2#565711yescharacteristic
399C2#569211yescharacteristic
400C2#570411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#387C2
socle, cosocleC23×C3C24
prime radicalC22×D12C22
hypercenter#387D3
hypocenterC3#2318
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C3×#387C2semidirect
3. #4989C2semidirect
4. #4987C2semidirect
5. #4980C2semidirect
6. #4940C2semidirect
7. C4×(C2×D3)⋊C4C2semidirect
8. #4669C2semidirect
9. #4668C2semidirect
12. #4664C2semidirect
13. D3×#95C2semidirect
14. #4651C2semidirect
15. #4650C2semidirect
38. #893C4semidirect
57. #387D3semidirect
97. C2×C4×D3C2×C4semidirect
99. C3×C4⋊C4C2×C4semidirect
108. (C2×D3)⋊C4C2×C4semidirect
113. C4×Dic3C2×C4semidirect
243. C4⋊C4C4×D3semidirect
391. C3#2318semidirect

Maximal subgroups

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

subgroupindex
C2×#8932
C3×#3872
#49892
#49872
#49802
#49402
C4×(C2×D3)⋊C42
#46692
#46682
#46652
#46642
D3×#952
#46512
#46502
#23183