Finite Group Databasebeta

← #74830

Subgroups — #74830

Order 384.

528 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#924C211yesmaximal, characteristic, complemented
2C2×#878C211yesmaximal, characteristic, complemented
3C3×#386C211yesmaximal, characteristic
4#5221C211yesmaximal, characteristic
5#5220C211yesmaximal, characteristic
6#5210C211yesmaximal, characteristic, complemented
7#4949C211yesmaximal, characteristic, complemented
8#4949C211yesmaximal, characteristic, complemented
9#4948C211yesmaximal, characteristic, complemented
10#4948C211yesmaximal, characteristic, complemented
11#4946C211yesmaximal, characteristic, complemented
12#4661C211yesmaximal, characteristic, complemented
13#4657C211yesmaximal, characteristic, complemented
14#4647C211yesmaximal, characteristic, complemented
15#4646C211yesmaximal, characteristic, complemented
16#2732—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C23×Dic3C2211yescharacteristic
20C22×Dic6C2211yescharacteristic
21C2×C3×C22⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×#217C2211yescharacteristic
25C2×#217C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×C4⋊Dic3C2211yescharacteristic
32C2×C4⋊Dic3C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×C4⋊Dic3C2211yescharacteristic
35#924—24no—
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×Dic3⋊C4C2211yescharacteristic
39C2×Dic3⋊C4C2211yescharacteristic
40C2×Dic3⋊C4C2211yescharacteristic
41C2×Dic3⋊C4C2211yescharacteristic
42C2×Dic3⋊C4C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C2×C4×Dic3C2211yescharacteristic
45#878—24no—
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×C22⋊Q8—31no—
55C2×C22⋊Q8—31no—
56#399—31no—
57#399—31no—
58#398—31no—
59#398—31no—
60#396—31no—
61#396—31no—
62#391—31no—
63#390—31no—
64#389—31no—
65#386—31no—
66#386D311yescharacteristic
67#385—31no—
68#385—31no—
69C24×C3C2311yescharacteristic
70C24×C3C2311yescharacteristic
71C2×C3×D4—41no—
72C2×C3×D4—41no—
73C2×C3×D4Q814yescomplemented
74C22×C3×C4—22no—
75C22×C3×C4—41no—
76C22×C3×C4—41no—
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×Dic3—22no—
83C22×Dic3—41no—
84C22×Dic3—41no—
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C2×Dic6—41no—
94C2×Dic6—41no—
95C2×Dic6D414yescomplemented
96C3×C22⋊C4—22no—
97C3×C22⋊C4—41no—
98C3×C22⋊C4—41no—
99#217—22no—
100#217—22no—
101#217—22no—
102#217—22no—
103#217—22no—
104#217—41no—
105#217—41no—
106C4⋊Dic3—22no—
107C4⋊Dic3—22no—
108C4⋊Dic3—41no—
109C4⋊Dic3—41no—
110Dic3⋊C4—22no—
111Dic3⋊C4—22no—
112Dic3⋊C4—22no—
113Dic3⋊C4—22no—
114Dic3⋊C4—22no—
115Dic3⋊C4—41no—
116Dic3⋊C4—41no—
117Dic3⋊C4—41no—
118C4×Dic3—41no—
119C22×Q8—31no—
120C22×D4C2×D311yescharacteristic
121C23×C4—31no—
122C23×C4C2×D311yescharacteristic
123C22⋊Q8—64no—
124C22⋊Q8—64no—
125C2×C4⋊C4—31no—
126C2×C4⋊C4—31no—
127C2×C4⋊C4—31no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—31no—
132C2×C4⋊C4—31no—
133C2×C4⋊C4—31no—
134C2×C4⋊C4—31no—
135C2×C4⋊C4—31no—
136C2×C4⋊C4—31no—
137C2×C22⋊C4—31no—
138C2×C22⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C22⋊C4—31no—
141C2×C22⋊C4—31no—
142C2×C22⋊C4—31no—
143C2×C22⋊C4—31no—
144C2×C22⋊C4C2×D311yescharacteristic
145C2×C22⋊C4C2×D311yescharacteristic
146C2×C22⋊C4C2×D311yescharacteristic
147C2×C42—31no—
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95C2×D311yescharacteristic
155#95C2×D311yescharacteristic
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3C2×Q812yes—
169C23×C3C2×Q812yes—
170C23×C3C2411yescharacteristic
171C3×D4—44no—
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×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—44no—
186C2×C3×C4C2×D412yes—
187C2×C3×C4C2×Q812yes—
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×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—44no—
210C2×Dic3C2×D412yes—
211C2×Dic3C2×D412yes—
212C2×Dic3#4112yes—
213Dic6—44no—
214C24C22×D311yescharacteristic
215C24C22×D311yescharacteristic
216C2×Q8—34no—
217C2×Q8—121no—
218C2×Q8—121no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4Dic614yescomplemented
222C22×C4—22no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—31no—
227C22×C4—31no—
228C22×C4—31no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—62no—
234C22×C4—121no—
235C22×C4—121no—
236C22×C4C22×D311yescharacteristic
237C22×C4C22×D311yescharacteristic
238C22×C4C22×D311yescharacteristic
239C22×C4C22×D311yescharacteristic
240C22×C4C22×D311yescharacteristic
241C4⋊C4—62no—
242C4⋊C4—62no—
243C4⋊C4—62no—
244C4⋊C4—62no—
245C4⋊C4—62no—
246C4⋊C4—62no—
247C4⋊C4—62no—
248C4⋊C4—121no—
249C4⋊C4—121no—
250C4⋊C4—121no—
251C4⋊C4—121no—
252C4⋊C4—121no—
253C22⋊C4—22no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—62no—
257C22⋊C4—62no—
258C22⋊C4—62no—
259C22⋊C4—62no—
260C22⋊C4—62no—
261C22⋊C4—121no—
262C22⋊C4—121no—
263C42—121no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3C22×D411yescharacteristic
279C22×C3C22×Q811yescharacteristic
280C22×C3C2×#4111yescharacteristic
281C22×C3H(5,𝔽2)11yescharacteristic
282C22×C3H(5,𝔽2)11yescharacteristic
283C22×C3H(5,𝔽2)11yescharacteristic
284C22×C32−1+411yescharacteristic
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290Dic3—22no—
291Dic3—22no—
292Dic3—22no—
293Dic3—41no—
294Dic3—41no—
295Dic3—41no—
296Dic3—41no—
297Dic3—41no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23C2×Dic612yes—
311C23C2×Dic612yes—
312C23C23×D311yescharacteristic
313Q8—124no—
314D4—44no—
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—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—32no—
329C2×C4—32no—
330C2×C4—32no—
331C2×C4—44no—
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—61no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—124no—
354C2×C4C2×Dic612yes—
355C2×C4D3×D412yes—
356C2×C3—42no—
357C2×C3—42no—
358C2×C3#53411yescharacteristic
359C2×C3#53911yescharacteristic
360C2×C3#54311yescharacteristic
361C2×C3D4×Q811yescharacteristic
362C2×C3#55011yescharacteristic
363C2×C3#55411yescharacteristic
364C2×C3#56211yescharacteristic
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22C22×Dic611yescharacteristic
380C22C2×D3×D411yescharacteristic
381C22#100411yescharacteristic
382C22#100411yescharacteristic
383C22#100411yescharacteristic
384C22D3×#4111yescharacteristic
385C22#101011yescharacteristic
386C4—22no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—62no—
392C4—62no—
393C4—62no—
394C4—121no—
395C4—121no—
396C4—121no—
397C4—121no—
398C4—121no—
399C3#273211yescharacteristic, complemented, Sylow
400C2—42no—
401C2—42no—
402C2#548311yescharacteristic
403C2D4×Dic611yescharacteristic
404C2#553911yescharacteristic
405C2#558911yescharacteristic
406C2#559911yescharacteristic
407C2#562111yescharacteristic
408C2#566011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
prime radicalC22×C3×D4C22
hypercenter#386D3
hypocenterC3#2732
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#924C2semidirect
2. C2×#878C2semidirect
6. #5210C2semidirect
7. #4949C2semidirect
8. #4949C2semidirect
9. #4948C2semidirect
10. #4948C2semidirect
11. #4946C2semidirect
12. #4661C2semidirect
13. #4657C2semidirect
14. #4647C2semidirect
15. #4646C2semidirect
73. C2×C3×D4Q8semidirect
95. C2×Dic6D4semidirect
221. C2×D4Dic6semidirect
399. C3#2732semidirect

Maximal subgroups

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

subgroupindex
C2×#9242
C2×#8782
C3×#3862
#52212
#52202
#52102
#49492
#49482
#49462
#46612
#46572
#46472
#46462
#27323