Finite Group Databasebeta

← #13075422

Subgroups — #13075422

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×#66989C211yesmaximal, characteristic
2C2×#66932C211yesmaximal, characteristic, complemented
3C11×#386C211yesmaximal, characteristic
4#10622835C211yesmaximal, characteristic
5#10622825C211yesmaximal, characteristic, complemented
6#10622823C211yesmaximal, characteristic, complemented
7#10622565C211yesmaximal, characteristic, complemented
8#10622565C211yesmaximal, characteristic, complemented
9#10622564C211yesmaximal, characteristic, complemented
10#10622561C211yesmaximal, characteristic, complemented
11#10622561C211yesmaximal, characteristic, complemented
12#10622269C211yesmaximal, characteristic, complemented
13#10622265C211yesmaximal, characteristic, complemented
14#10622260C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30#66989—24no—
31C2×C4⋊Dic11C2211yescharacteristic
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
41C2×C4×Dic11C2211yescharacteristic
42#66932—24no—
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11—41no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C2×Dic22—22no—
75C2×Dic22—22no—
76C2×Dic22—41no—
77C11×C22⋊C4—22no—
78C11×C22⋊C4—22no—
79C11×C22⋊C4—41no—
80C22⋊Dic11—22no—
81C22⋊Dic11—22no—
82C22⋊Dic11—22no—
83C22⋊Dic11—22no—
84C22⋊Dic11—41no—
85C22⋊Dic11—41no—
86C22⋊Dic11—41no—
87C22⋊Dic11D414yes—
88C4⋊Dic11—22no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91Dic11⋊C4—22no—
92Dic11⋊C4—22no—
93Dic11⋊C4—22no—
94Dic11⋊C4—22no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97C4×Dic11—22no—
98C4×Dic11—22no—
99#2715—111nomaximal, Sylow
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11C2×D412yes—
114C23×C11C2411yescharacteristic
115D4×C11—44no—
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—44no—
130C2×C4×C11#4112yes—
131C2×C4×C11#4112yes—
132C2×Dic11—21no—
133C2×Dic11—21no—
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—21no—
153C2×Dic11—21no—
154C2×Dic11C2×D412yes—
155C2×Dic11C2×D412yes—
156Dic22—44no—
157C2×#126—111no—
158C2×#124—111no—
159#397—111no—
160#397—111no—
161#396—111no—
162#396—111no—
163#395—111no—
164#394—111no—
165#391—111no—
166#389—111no—
167#388—111no—
168#387—111no—
169#386D1111yescharacteristic
170#385—111no—
171#380—111no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11C22×D411yescharacteristic
187C22×C11C2×#4111yescharacteristic
188C22×C11C2×#4111yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C22×C11H(5,𝔽2)11yescharacteristic
191C22×C112−1+411yescharacteristic
192C22×C112−1+411yescharacteristic
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198Dic11—22no—
199Dic11—22no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205Dic11—41no—
206C22×Q8—111no—
207C22×D4C2×D1111yescharacteristic
208C23×C4C2×D1111yescharacteristic
209#126—224no—
210#124—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⋊C4—111no—
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×C42—111no—
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—81no—
245C2×C11#53711yescharacteristic
246C2×C11#53811yescharacteristic
247C2×C11#54211yescharacteristic
248C2×C11#54611yescharacteristic
249C2×C11#54711yescharacteristic
250C2×C11#55611yescharacteristic
251C2×C11#56311yescharacteristic
252C24C22×D1111yescharacteristic
253C24C22×D1111yescharacteristic
254C2×Q8—222no—
255C2×Q8—222no—
256C2×Q8—441no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—41no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—111no—
271C22×C4C22×D1111yescharacteristic
272C22×C4C22×D1111yescharacteristic
273C22×C4C22×D1111yescharacteristic
274C22×C4C22×D1111yescharacteristic
275C22×C4C22×D1111yescharacteristic
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—114no—
289C22⋊C4—222no—
290C22⋊C4—222no—
291C22⋊C4—222no—
292C22⋊C4—222no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C42—222no—
297C42—222no—
298C11#271511yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23D4×D1112yes—
313C23C23×D1111yescharacteristic
314Q8—444no—
315D4—44no—
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—44no—
330C2×C4—112no—
331C2×C4—112no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
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#433912yes—
355C2×C4#434112yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C2×#433911yescharacteristic
371C22C2×D4×D1111yescharacteristic
372C22C2×#434111yescharacteristic
373C22#6703711yescharacteristic
374C22#6703711yescharacteristic
375C22#6704311yescharacteristic
376C22#6704311yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—222no—
383C4—222no—
384C4—441no—
385C4—441no—
386C4—441no—
387C4—441no—
388C4—441no—
389C4—441no—
390C2—42no—
391C2—81no—
392C2#1062302111yescharacteristic
393C2#1062307311yescharacteristic
394C2#1062309211yescharacteristic
395C2#1062312411yescharacteristic
396C2#1062312811yescharacteristic
397C2#1062314211yescharacteristic
398C2#1062318211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC22×D4×C11C22
hypercenter#386D11
hypocenterC11#2715
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#66932C2semidirect
5. #10622825C2semidirect
6. #10622823C2semidirect
7. #10622565C2semidirect
8. #10622565C2semidirect
9. #10622564C2semidirect
10. #10622561C2semidirect
11. #10622561C2semidirect
12. #10622269C2semidirect
13. #10622265C2semidirect
14. #10622260C2semidirect
15. #10622259C2semidirect
298. C11#2715semidirect

Maximal subgroups

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

subgroupindex
C2×#669892
C2×#669322
C11×#3862
#106228352
#106228252
#106228232
#106225652
#106225642
#106225612
#106222692
#106222652
#106222602
#106222592
#271511