Finite Group Databasebeta

← #75995

Subgroups — #75995

Order 384.

604 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#896C211yesmaximal, characteristic, complemented
2C2×#896C211yesmaximal, characteristic, complemented
3C2×#893C211yesmaximal, characteristic
4C2×#872C211yesmaximal, characteristic, complemented
5C3×#389C211yesmaximal, characteristic, complemented
6#4992C211yesmaximal, characteristic, complemented
7#4991C211yesmaximal, characteristic
8#4990C211yesmaximal, characteristic, complemented
9#4976C211yesmaximal, characteristic, complemented
10#4976C211yesmaximal, characteristic, complemented
11#4940C211yesmaximal, characteristic, complemented
12#4675C211yesmaximal, characteristic, complemented
13#4672C211yesmaximal, characteristic
14#4667C211yesmaximal, characteristic, complemented
15#4646C211yesmaximal, characteristic, complemented
16#2415—31nomaximal, Sylow
17C22×D12C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×Dic6C2211yescharacteristic
21C2×C3×C4⋊C4C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C42C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×Dic3⋊C4C2211yescharacteristic
39C2×Dic3⋊C4C2211yescharacteristic
40C2×Dic3⋊C4C2211yescharacteristic
41C2×Dic3⋊C4C2211yescharacteristic
42C2×C4×Dic3C2211yescharacteristic
43C2×C4×Dic3C2211yescharacteristic
44#896—24no—
45#896—24no—
46#893—24no—
47#872—24no—
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×C22⋊Q8—31no—
57C2×C22⋊Q8—31no—
58C2×C4×D4—31no—
59C2×#117—31no—
60#397—31no—
61#397—31no—
62#394—31no—
63#394—31no—
64#391—31no—
65#389—31no—
66#389—31no—
67#389D311yescharacteristic, complemented
68#388—31no—
69#388—31no—
70#380—31no—
71C23×D3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C2×D12—22no—
87C2×D12—22no—
88C2×D12—22no—
89C2×C4×D3—22no—
90C2×C4×D3—22no—
91C2×C4×D3—22no—
92C2×C4×D3—22no—
93C2×C4×D3—22no—
94C2×C4×D3D414yes—
95C2×Dic6—22no—
96C2×Dic6—22no—
97C2×Dic6—22no—
98C3×C4⋊C4—22no—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—22no—
102C3×C42—22no—
103(C2×D3)⋊C4—22no—
104(C2×D3)⋊C4—22no—
105(C2×D3)⋊C4—22no—
106(C2×D3)⋊C4—22no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—22no—
109(C2×D3)⋊C4—22no—
110(C2×D3)⋊C4—22no—
111(C2×D3)⋊C4—22no—
112(C2×D3)⋊C4—22no—
113Dic3⋊C4—22no—
114Dic3⋊C4—22no—
115Dic3⋊C4—22no—
116Dic3⋊C4—22no—
117Dic3⋊C4—22no—
118Dic3⋊C4D414yescomplemented
119C4×Dic3—22no—
120C4×Dic3—22no—
121C22×Q8—31no—
122C22×D4—31no—
123C23×C4—31no—
124C23×C4—31no—
125C22⋊Q8—64no—
126C22⋊Q8—64no—
127C4×D4—64no—
128#117—64no—
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⋊C4C2×D311yescharacteristic
136C2×C4⋊C4C2×D311yescharacteristic
137C2×C4⋊C4C2×D311yescharacteristic
138C2×C4⋊C4C2×D311yescharacteristic
139C2×C22⋊C4—31no—
140C2×C22⋊C4—31no—
141C2×C22⋊C4—31no—
142C2×C22⋊C4—31no—
143C2×C22⋊C4—31no—
144C2×C22⋊C4—31no—
145C2×C22⋊C4—31no—
146C2×C22⋊C4—31no—
147C2×C22⋊C4—31no—
148C2×C22⋊C4—31no—
149C2×C42—31no—
150C2×C42—31no—
151C2×C42C2×D311yescharacteristic
152#95—31no—
153#95—31no—
154#95—31no—
155#95—31no—
156#95—31no—
157#95—31no—
158#95C2×D311yescharacteristic
159#95C2×D311yescharacteristic
160C23×C3C2411yescharacteristic
161C22×D3—21no—
162C22×D3—21no—
163C22×D3—21no—
164C22×D3—21no—
165C22×D3—21no—
166C22×D3—21no—
167C22×D3—21no—
168C22×D3—21no—
169C22×D3—21no—
170C22×D3—21no—
171C22×D3—21no—
172C22×D3—21no—
173C22×D3C2×D412yes—
174C22×D3#4112yes—
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—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4C2×D412yes—
194C2×C3×C4C2×D412yes—
195C2×C3×C4#4112yes—
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—21no—
210C2×Dic3C2×D412yes—
211C2×Dic3C2×D412yes—
212C2×Dic3C2×D412yes—
213C2×Dic3#4112yes—
214D12—28no—
215C4×D3—28no—
216C4×D3—44no—
217Dic6—44no—
218C24—31no—
219C24—31no—
220C2×Q8—62no—
221C2×Q8—62no—
222C2×Q8—62no—
223C2×D4—62no—
224C2×D4—62no—
225C2×D4—62no—
226C22×C4—31no—
227C22×C4—31no—
228C22×C4—34no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—31no—
232C22×C4—31no—
233C22×C4—62no—
234C22×C4—62no—
235C22×C4—62no—
236C22×C4—62no—
237C22×C4—62no—
238C22×C4C22×D311yescharacteristic
239C22×C4C22×D311yescharacteristic
240C22×C4C22×D311yescharacteristic
241C22×C4C22×D311yescharacteristic
242C22×C4C22×D311yescharacteristic
243C22×C4C22×D311yescharacteristic
244C22×C4C22×D311yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—34no—
250C4⋊C4—62no—
251C4⋊C4—62no—
252C4⋊C4—62no—
253C4⋊C4—62no—
254C4⋊C4—62no—
255C22⋊C4—62no—
256C22⋊C4—62no—
257C22⋊C4—62no—
258C22⋊C4—62no—
259C22⋊C4—62no—
260C22⋊C4—62no—
261C22⋊C4—62no—
262C22⋊C4—62no—
263C22⋊C4—62no—
264C22⋊C4—62no—
265C42—22no—
266C42—62no—
267C42—62no—
268C22×C3C22×D411yescharacteristic
269C22×C3C22×D411yescharacteristic
270C22×C3C2×#4111yescharacteristic
271C22×C3C2×#4111yescharacteristic
272C22×C3C2×#4111yescharacteristic
273C22×C32−1+411yescharacteristic
274C22×C32−1+411yescharacteristic
275C2×D3—22no—
276C2×D3—22no—
277C2×D3—22no—
278C2×D3—22no—
279C2×D3—22no—
280C2×D3—22no—
281C2×D3—41no—
282C2×D3—41no—
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—41no—
287C2×D3—41no—
288C2×D3—41no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—22no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296Dic3—22no—
297Dic3—41no—
298Dic3—41no—
299Dic3—41no—
300Dic3—41no—
301Dic3#12114yes—
302C23—32no—
303C23—32no—
304C23—61no—
305C23—61no—
306C23—61no—
307C23—61no—
308C23—61no—
309C23—61no—
310C23—61no—
311C23—61no—
312C23—61no—
313C23—61no—
314C23—61no—
315C23—61no—
316C23C23×D311yescharacteristic
317Q8—124no—
318D4—68no—
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—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—32no—
338C2×C4—32no—
339C2×C4—32no—
340C2×C4—32no—
341C2×C4—68no—
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—61no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—124no—
357C2×C4#23512yes—
358C2×C4D3×D412yes—
359C2×C4D3×D412yes—
360C2×C3C2×#12111yescharacteristic
361C2×C3#52511yescharacteristic
362C2×C3#53611yescharacteristic
363C2×C3#54711yescharacteristic
364C2×C3#54811yescharacteristic
365C2×C3#55211yescharacteristic
366C2×C3#55611yescharacteristic
367D3—42no—
368D3—42no—
369C22—62no—
370C22—62no—
371C22—62no—
372C22—62no—
373C22—62no—
374C22—62no—
375C22—121no—
376C22—121no—
377C22—121no—
378C22—121no—
379C22—121no—
380C22—121no—
381C22—121no—
382C22—121no—
383C22C2×#23511yescharacteristic
384C22C2×D3×D411yescharacteristic
385C22C2×D3×D411yescharacteristic
386C22#100711yescharacteristic
387C22#100711yescharacteristic
388C22D3×#4111yescharacteristic
389C22D3×#4111yescharacteristic
390C4—22no—
391C4—22no—
392C4—22no—
393C4—34no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—62no—
399C4—121no—
400C4—121no—
401C4—121no—
402C4—121no—
403C3#241511yescharacteristic, complemented, Sylow
404C2—122no—
405C2—122no—
406C2#550711yescharacteristic
407C2#554711yescharacteristic
408C2#556811yescharacteristic
409C2D3×#12111yescharacteristic
410C2#563311yescharacteristic
411C2#569311yescharacteristic
412C2#572411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#389C2
prime radicalC22×D12C22
hypercenter#389D3
hypocenterC3#2415
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#896C2semidirect
2. C2×#896C2semidirect
4. C2×#872C2semidirect
5. C3×#389C2semidirect
6. #4992C2semidirect
8. #4990C2semidirect
9. #4976C2semidirect
10. #4976C2semidirect
11. #4940C2semidirect
12. #4675C2semidirect
14. #4667C2semidirect
15. #4646C2semidirect
67. #389D3semidirect
118. Dic3⋊C4D4semidirect
403. C3#2415semidirect

Maximal subgroups

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

subgroupindex
C2×#8962
C2×#8932
C2×#8722
C3×#3892
#49922
#49912
#49902
#49762
#49402
#46752
#46722
#46672
#46462
#24153