Finite Group Databasebeta

← #13075539

Subgroups — #13075539

Order 1408.

498 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66931C211yesmaximal, characteristic, complemented
2C2×#66929C211yesmaximal, characteristic, complemented
3C11×#388C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic, complemented
5#10622592C211yesmaximal, characteristic, complemented
6#10622574C211yesmaximal, characteristic
7#10622571C211yesmaximal, characteristic
8#10622570C211yesmaximal, characteristic
9#10622565C211yesmaximal, characteristic, complemented
10#10622559C211yesmaximal, characteristic, complemented
11#10622541C211yesmaximal, characteristic, complemented
12#10622287C211yesmaximal, characteristic, complemented
13#10622286C211yesmaximal, characteristic, complemented
14#10622268C211yesmaximal, characteristic, complemented
15#10622263C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C42×C11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41#66931—24no—
42#66929—24no—
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C23×D11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—22no—
62C2×C22⋊D11—22no—
63C2×C22⋊D11—41no—
64C22×Dic11—22no—
65C22×Dic11—41no—
66C22×Dic11—41no—
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C2×Dic22—22no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—22no—
79C11×C22⋊C4—22no—
80C11×C22⋊C4—41no—
81C42×C11—22no—
82C22⋊Dic11—22no—
83C22⋊Dic11—22no—
84(C2×D11)⋊C4—22no—
85(C2×D11)⋊C4—22no—
86(C2×D11)⋊C4—22no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—41no—
90C4⋊Dic11—22no—
91C4⋊Dic11—22no—
92Dic11⋊C4—22no—
93Dic11⋊C4—22no—
94Dic11⋊C4—22no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4D414yescomplemented
98C4×Dic11—22no—
99#2723—111nomaximal, Sylow
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11#4112yes—
107C23×C11C2411yescharacteristic
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11C2×D412yes—
133C22⋊D11—44no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—44no—
153C2×Dic11C2×D412yes—
154C2×Dic11C2×D412yes—
155C2×Dic11#4112yes—
156Dic22—44no—
157C2×#126—111no—
158C2×C22⋊Q8—111no—
159#399—111no—
160#397—111no—
161#397—111no—
162#395—111no—
163#394—111no—
164#393—111no—
165#390—111no—
166#389—111no—
167#388D1111yescharacteristic, complemented
168#387—111no—
169#386—111no—
170#385—111no—
171#382—111no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11C22×D411yescharacteristic
180C22×C11C2×#4111yescharacteristic
181C22×C11C2×#4111yescharacteristic
182C22×C11H(5,𝔽2)11yescharacteristic
183C22×C11H(5,𝔽2)11yescharacteristic
184C22×C112−1+411yescharacteristic
185C22×C112−1+411yescharacteristic
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C4×C11—22no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199Dic11—22no—
200Dic11—22no—
201Dic11—22no—
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205Dic11—41no—
206C22×Q8—111no—
207C22×D4—111no—
208C23×C4—111no—
209#126—224no—
210C22⋊Q8—224no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4C2×D1111yescharacteristic
220C2×C22⋊C4—111no—
221C2×C22⋊C4—111no—
222C2×C22⋊C4—111no—
223C2×C22⋊C4—111no—
224C2×C22⋊C4—111no—
225C2×C22⋊C4—111no—
226C2×C22⋊C4—111no—
227C2×C22⋊C4—111no—
228C2×C22⋊C4C2×D1111yescharacteristic
229C2×C22⋊C4C2×D1111yescharacteristic
230C2×C22⋊C4C2×D1111yescharacteristic
231C2×C42—111no—
232C2×C42C2×D1111yescharacteristic
233#95—111no—
234#95—111no—
235#95—111no—
236#95—111no—
237#95—111no—
238#95—111no—
239#95—111no—
240#95—111no—
241#95C2×D1111yescharacteristic
242#95C2×D1111yescharacteristic
243C2×C11—42no—
244C2×C11#53511yescharacteristic
245C2×C11#53911yescharacteristic
246C2×C11#54211yescharacteristic
247C2×C11#54711yescharacteristic
248C2×C11#54811yescharacteristic
249C2×C11#55111yescharacteristic
250C2×C11#56311yescharacteristic
251D11—81no—
252C24—111no—
253C24C22×D1111yescharacteristic
254C2×Q8—222no—
255C2×Q8—441no—
256C2×Q8—441no—
257C2×D4—222no—
258C2×D4—222no—
259C2×D4—441no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—222no—
268C22×C4—441no—
269C22×C4—441no—
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C22×C4C22×D1111yescharacteristic
273C22×C4C22×D1111yescharacteristic
274C22×C4C22×D1111yescharacteristic
275C22×C4C22×D1111yescharacteristic
276C4⋊C4—41no—
277C4⋊C4—114no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—222no—
289C22⋊C4—222no—
290C22⋊C4—222no—
291C22⋊C4—222no—
292C22⋊C4—222no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C42—22no—
297C42—222no—
298C11#272311yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—221no—
306C23—221no—
307C23—221no—
308C23—221no—
309C23—221no—
310C23—221no—
311C23—221no—
312C23#433912yes—
313C23C23×D1111yescharacteristic
314Q8—444no—
315D4—444no—
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—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—112no—
334C2×C4—112no—
335C2×C4—112no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—444no—
355C2×C4D4×D1112yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22C2×#433911yescharacteristic
371C22C2×D4×D1111yescharacteristic
372C22#6703711yescharacteristic
373C22#41×D1111yescharacteristic
374C22#6704211yescharacteristic
375C22#6704311yescharacteristic
376C22#6704311yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—222no—
384C4—222no—
385C4—222no—
386C4—441no—
387C4—441no—
388C4—441no—
389C4—441no—
390C2—42no—
391C2—881no—
392C2#1062305811yescharacteristic
393C2#1062308311yescharacteristic
394C2#1062309511yescharacteristic
395C2#1062313811yescharacteristic
396C2#1062318611yescharacteristic
397C2#1062320011yescharacteristic
398C2#1062324311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC22×C22⋊D11C22
hypercenter#388D11
hypocenterC11#2723
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#66931C2semidirect
2. C2×#66929C2semidirect
3. C11×#388C2semidirect
4. #10622605C2semidirect
5. #10622592C2semidirect
9. #10622565C2semidirect
10. #10622559C2semidirect
11. #10622541C2semidirect
12. #10622287C2semidirect
13. #10622286C2semidirect
14. #10622268C2semidirect
15. #10622263C2semidirect
97. Dic11⋊C4D4semidirect
167. #388D11semidirect
298. C11#2723semidirect

Maximal subgroups

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

subgroupindex
C2×#669312
C2×#669292
C11×#3882
#106226052
#106225922
#106225742
#106225712
#106225702
#106225652
#106225592
#106225412
#106222872
#106222862
#106222682
#106222632
#272311