Finite Group Databasebeta

← #13072437

Subgroups — #13072437

Order 1408.

584 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×#66999C211yesmaximal, characteristic, complemented
2C2×C4×D44C211yesmaximal, characteristic
3C11×#391C211yesmaximal, characteristic, complemented
4#10622844C211yesmaximal, characteristic, complemented
5#10622607C211yesmaximal, characteristic, complemented
6#10622602C211yesmaximal, characteristic, complemented
7#10622546C211yesmaximal, characteristic, complemented
8#10622281C211yesmaximal, characteristic, complemented
9#10622281C211yesmaximal, characteristic, complemented
10#10622280C211yesmaximal, characteristic, complemented
11#10622278C211yesmaximal, characteristic
12#10622278C211yesmaximal, characteristic
13D11×#95C211yesmaximal, characteristic, complemented
14#10622274C211yesmaximal, characteristic, complemented
15#10622273C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×C4×D11C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C42×C11C2211yescharacteristic
24#66999—24no—
25C2×(C2×D11)⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊Dic11C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C4×D44—24no—
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C23×D11C2311yescharacteristic
54C23×D11C2311yescharacteristic
55C2×Q8×C11—22no—
56C2×Q8×C11—22no—
57C2×Q8×C11—41no—
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C2×D44—22no—
72C2×D44—22no—
73C2×D44Q814yescomplemented
74C2×C4×D11—22no—
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C11×C4⋊C4—41no—
87C42×C11—22no—
88(C2×D11)⋊C4—22no—
89(C2×D11)⋊C4—22no—
90(C2×D11)⋊C4—22no—
91(C2×D11)⋊C4—22no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4D414yes—
96C4⋊Dic11—22no—
97C4⋊Dic11—22no—
98C4⋊Dic11—41no—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101Dic11⋊C4—22no—
102Dic11⋊C4—41no—
103#2450—111nomaximal, Sylow
104C23×C11C2411yescharacteristic
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11C2×D412yes—
116C22×D11C2×Q812yes—
117C22×D11C2×Q812yes—
118C22×D11#4112yes—
119Q8×C11—44no—
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×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11C2×D412yes—
138C2×C4×C11C2×Q812yes—
139C2×C4×C11#4112yes—
140C2×C4×C11#4112yes—
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×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11C2×D412yes—
159D44—28no—
160C4×D11—44no—
161C4×D11—44no—
162C4×D11—44no—
163C4×D11—44no—
164C2×C22⋊Q8—111no—
165C2×C4×D4—111no—
166#400—111no—
167#398—111no—
168#396—111no—
169#393—111no—
170#391D1111yescharacteristic, complemented
171#387—111no—
172#386—111no—
173#386—111no—
174#385—111no—
175#385—111no—
176#385—111no—
177#380—111no—
178C2×#95—111no—
179C22×C11C22×D411yescharacteristic
180C22×C11C22×Q811yescharacteristic
181C22×C11C2×#4111yescharacteristic
182C22×C11C2×#4111yescharacteristic
183C22×C11C2×#4111yescharacteristic
184C22×C11H(5,𝔽2)11yescharacteristic
185C22×C11H(5,𝔽2)11yescharacteristic
186C2×D11—22no—
187C2×D11—22no—
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—22no—
191C2×D11—22no—
192C2×D11—22no—
193C2×D11—22no—
194C2×D11—22no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11C22⋊Q814yes—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207Dic11—22no—
208Dic11—41no—
209Dic11—41no—
210Dic11—41no—
211Dic11—41no—
212Dic11—41no—
213C22×Q8C2×D1111yescharacteristic
214C22×D4—111no—
215C23×C4—111no—
216C23×C4—111no—
217C23×C4—111no—
218C23×C4—111no—
219C22⋊Q8—224no—
220C4×D4—224no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4C2×D1111yescharacteristic
229C2×C22⋊C4—111no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—111no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—111no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4—111no—
237C2×C42C2×D1111yescharacteristic
238#95—111no—
239#95—111no—
240#95—111no—
241#95—111no—
242#95—111no—
243#95—111no—
244#95—111no—
245#95—111no—
246#95C2×D1111yescharacteristic
247#95C2×D1111yescharacteristic
248#95C2×D1111yescharacteristic
249#95C2×D1111yescharacteristic
250C2×C11C2×C22⋊Q811yescharacteristic
251C2×C11#52911yescharacteristic
252C2×C11#53811yescharacteristic
253C2×C11#54611yescharacteristic
254C2×C11#54611yescharacteristic
255C2×C11#55411yescharacteristic
256C2×C11#55411yescharacteristic
257D11—24no—
258D11—42no—
259C24—111no—
260C24—111no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×D4—114no—
265C2×D4—222no—
266C2×D4—222no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—111no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—222no—
274C22×C4—222no—
275C22×C4—222no—
276C22×C4—222no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4—222no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4—441no—
285C22×C4C22×D1111yescharacteristic
286C22×C4C22×D1111yescharacteristic
287C22×C4C22×D1111yescharacteristic
288C22×C4C22×D1111yescharacteristic
289C22×C4C22×D1111yescharacteristic
290C22×C4C22×D1111yescharacteristic
291C22×C4C22×D1111yescharacteristic
292C4⋊C4—41no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C22⋊C4—114no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C22⋊C4—222no—
304C22⋊C4—222no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C42—22no—
309C11#245011yescharacteristic, complemented, Sylow
310C23—112no—
311C23—112no—
312C23—112no—
313C23—112no—
314C23—221no—
315C23—221no—
316C23—221no—
317C23—221no—
318C23—221no—
319C23—221no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—221no—
324C23C23×D1111yescharacteristic
325Q8—44no—
326D4—228no—
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—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—112no—
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—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—444no—
363C2×C4—444no—
364C2×C4—444no—
365C2×C4—444no—
366C2×C4#433912yes—
367C2×C4D4×D1112yes—
368C2×C4Q8×D1112yes—
369C2×C4#434312yes—
370C22—114no—
371C22—222no—
372C22—222no—
373C22—222no—
374C22—222no—
375C22—222no—
376C22—222no—
377C22—222no—
378C22—222no—
379C22—222no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22C2×#433911yescharacteristic
385C22C2×D4×D1111yescharacteristic
386C22#6703711yescharacteristic
387C22C2×Q8×D1111yescharacteristic
388C22C2×#434311yescharacteristic
389C22#41×D1111yescharacteristic
390C22#6704211yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—222no—
399C4—441no—
400C4—441no—
401C4—441no—
402C4—441no—
403C4—441no—
404C2—224no—
405C2—442no—
406C2#1062302111yescharacteristic
407C2#1062311011yescharacteristic
408C2#1062311111yescharacteristic
409C2D11×C22⋊Q811yescharacteristic
410C2#1062316111yescharacteristic
411C2#1062320911yescharacteristic
412C2#1062326111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC22×D44C22
hypercenter#391D11
hypocenterC11#2450
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#66999C2semidirect
3. C11×#391C2semidirect
4. #10622844C2semidirect
5. #10622607C2semidirect
6. #10622602C2semidirect
7. #10622546C2semidirect
8. #10622281C2semidirect
9. #10622281C2semidirect
10. #10622280C2semidirect
13. D11×#95C2semidirect
14. #10622274C2semidirect
15. #10622273C2semidirect
73. C2×D44Q8semidirect
170. #391D11semidirect
309. C11#2450semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×C4×D442
C11×#3912
#106228442
#106226072
#106226022
#106225462
#106222812
#106222802
#106222782
D11×#952
#106222742
#106222732
#245011