Finite Group Databasebeta

← #13075630

Subgroups — #13075630

Order 1408.

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×#66949C211yesmaximal, characteristic, complemented
2C2×#66931C211yesmaximal, characteristic, complemented
3C11×#396C211yesmaximal, characteristic, complemented
4#10622607C211yesmaximal, characteristic, complemented
5#10622605C211yesmaximal, characteristic, complemented
6#10622597C211yesmaximal, characteristic, complemented
7#10622587C211yesmaximal, characteristic, complemented
8#10622585C211yesmaximal, characteristic, complemented
9#10622571C211yesmaximal, characteristic
10#10622570C211yesmaximal, characteristic
11#10622569C211yesmaximal, characteristic
12#10622562C211yesmaximal, characteristic, complemented
13#10622559C211yesmaximal, characteristic, complemented
14#10622281C211yesmaximal, characteristic, complemented
15#10622270C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×C4×Dic11C2211yescharacteristic
43#66949—24no—
44#66931—24no—
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—41no—
62C2×C22⋊D11—41no—
63C2×C22⋊D11Q814yescomplemented
64C22×Dic11—22no—
65C22×Dic11—41no—
66C22×Dic11—41no—
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C2×C4×D11—22no—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22D414yescomplemented
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C22⋊Dic11—22no—
87C22⋊Dic11—22no—
88(C2×D11)⋊C4—22no—
89(C2×D11)⋊C4—22no—
90(C2×D11)⋊C4—22no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93C4⋊Dic11—22no—
94C4⋊Dic11—41no—
95Dic11⋊C4—22no—
96Dic11⋊C4—22no—
97Dic11⋊C4—22no—
98Dic11⋊C4—22no—
99Dic11⋊C4—22no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102C4×Dic11—41no—
103#2732—111nomaximal, Sylow
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11C2×Q812yes—
111C23×C11C2411yescharacteristic
112C22×D11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11C2×Q812yes—
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×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11C2×D412yes—
137C22⋊D11—44no—
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×Dic11—21no—
155C2×Dic11—44no—
156C2×Dic11C2×D412yes—
157C2×Dic11C2×D412yes—
158C2×Dic11C2×Q812yes—
159C2×Dic11#4112yes—
160C4×D11—44no—
161Dic22—44no—
162C2×C22⋊Q8—111no—
163C2×C22⋊Q8—111no—
164#399—111no—
165#399—111no—
166#398—111no—
167#398—111no—
168#396—111no—
169#396D1111yescharacteristic, complemented
170#391—111no—
171#390—111no—
172#389—111no—
173#386—111no—
174#386—111no—
175#385—111no—
176#385—111no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11C22×D411yescharacteristic
185C22×C11C22×Q811yescharacteristic
186C22×C11C2×#4111yescharacteristic
187C22×C11H(5,𝔽2)11yescharacteristic
188C22×C11H(5,𝔽2)11yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C22×C112−1+411yescharacteristic
191C2×D11—22no—
192C2×D11—22no—
193C2×D11—22no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C4×C11—22no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204Dic11—22no—
205Dic11—22no—
206Dic11—22no—
207Dic11—22no—
208Dic11—41no—
209Dic11—41no—
210Dic11—41no—
211C22×Q8—111no—
212C22×D4—111no—
213C23×C4—111no—
214C23×C4—111no—
215C22⋊Q8—224no—
216C22⋊Q8—224no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4C2×D1111yescharacteristic
227C2×C4⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
237C2×C22⋊C4C2×D1111yescharacteristic
238C2×C22⋊C4C2×D1111yescharacteristic
239C2×C42—111no—
240#95—111no—
241#95—111no—
242#95—111no—
243#95—111no—
244#95—111no—
245#95—111no—
246#95—111no—
247#95C2×D1111yescharacteristic
248C2×C11—42no—
249C2×C11#53411yescharacteristic
250C2×C11#53911yescharacteristic
251C2×C11#54311yescharacteristic
252C2×C11D4×Q811yescharacteristic
253C2×C11#55011yescharacteristic
254C2×C11#55411yescharacteristic
255C2×C11#56211yescharacteristic
256D11—42no—
257C24—111no—
258C24C22×D1111yescharacteristic
259C2×Q8—114no—
260C2×Q8—441no—
261C2×Q8—441no—
262C2×D4—114no—
263C2×D4—441no—
264C2×D4—441no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—111no—
271C22×C4—111no—
272C22×C4—222no—
273C22×C4—222no—
274C22×C4—441no—
275C22×C4—441no—
276C22×C4—441no—
277C22×C4—441no—
278C22×C4C22×D1111yescharacteristic
279C22×C4C22×D1111yescharacteristic
280C22×C4C22×D1111yescharacteristic
281C22×C4C22×D1111yescharacteristic
282C22×C4C22×D1111yescharacteristic
283C22×C4C22×D1111yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—222no—
300C22⋊C4—222no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C22⋊C4—222no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C42—441no—
307C11#273211yescharacteristic, complemented, Sylow
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—112no—
315C23—221no—
316C23—221no—
317C23—221no—
318C23—221no—
319C23—221no—
320C23—221no—
321C23Q8×D1112yes—
322C23C23×D1111yescharacteristic
323Q8—444no—
324D4—444no—
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—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—112no—
343C2×C4—112no—
344C2×C4—112no—
345C2×C4—112no—
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—221no—
363C2×C4—444no—
364C2×C4—444no—
365C2×C4D4×D1112yes—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—222no—
374C22—222no—
375C22—222no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22C2×D4×D1111yescharacteristic
381C22#6703711yescharacteristic
382C22#6703711yescharacteristic
383C22C2×Q8×D1111yescharacteristic
384C22#41×D1111yescharacteristic
385C22#6704211yescharacteristic
386C22#6704311yescharacteristic
387C4—22no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—222no—
394C4—222no—
395C4—222no—
396C4—222no—
397C4—441no—
398C4—441no—
399C4—441no—
400C2—42no—
401C2—442no—
402C2#1062313011yescharacteristic
403C2#1062313611yescharacteristic
404C2#1062315211yescharacteristic
405C2#1062316311yescharacteristic
406C2#1062316511yescharacteristic
407C2#1062316711yescharacteristic
408C2#1062323811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#396C2
prime radicalC22×C22⋊D11C22
hypercenter#396D11
hypocenterC11#2732
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#66949C2semidirect
2. C2×#66931C2semidirect
3. C11×#396C2semidirect
4. #10622607C2semidirect
5. #10622605C2semidirect
6. #10622597C2semidirect
7. #10622587C2semidirect
8. #10622585C2semidirect
12. #10622562C2semidirect
13. #10622559C2semidirect
14. #10622281C2semidirect
15. #10622270C2semidirect
63. C2×C22⋊D11Q8semidirect
79. C2×Dic22D4semidirect
169. #396D11semidirect
307. C11#2732semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×#669312
C11×#3962
#106226072
#106226052
#106225972
#106225872
#106225852
#106225712
#106225702
#106225692
#106225622
#106225592
#106222812
#106222702
#273211