Finite Group Databasebeta

← #13075341

Subgroups — #13075341

Order 1408.

568 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66948C211yesmaximal, characteristic
2C2×#66947C211yesmaximal, characteristic, complemented
3C11×#398C211yesmaximal, characteristic, complemented
4#10622606C211yesmaximal, characteristic, complemented
5#10622604C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622602C211yesmaximal, characteristic, complemented
8#10622600C211yesmaximal, characteristic, complemented
9#10622595C211yesmaximal, characteristic, complemented
10#10622288C211yesmaximal, characteristic, complemented
11#10622281C211yesmaximal, characteristic, complemented
12#10622281C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C22×D44C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×C4×D11C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊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×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×C4⋊Dic11C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41#66948—24no—
42#66947—24no—
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C23×D11C2311yescharacteristic
54C23×D11C2311yescharacteristic
55C23×D11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C2×D44—22no—
69C2×D44—22no—
70C2×D44—22no—
71C2×D44—22no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44D414yes—
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—41no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90(C2×D11)⋊C4—22no—
91(C2×D11)⋊C4—22no—
92(C2×D11)⋊C4—22no—
93(C2×D11)⋊C4—22no—
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102C4⋊Dic11—41no—
103Dic11⋊C4—22no—
104Dic11⋊C4—41no—
105#2708—111nomaximal, Sylow
106C23×C11C2411yescharacteristic
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×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11C2×D412yes—
126C22×D11C2×D412yes—
127C22×D11#4112yes—
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×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11C2×D412yes—
148C2×C4×C11#4112yes—
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×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164D44—44no—
165D44—44no—
166D44—44no—
167C4×D11—44no—
168C4×D11—44no—
169C4×D11—44no—
170C2×#123—111no—
171C2×#121—111no—
172#400—111no—
173#398D1111yescharacteristic, complemented
174#397—111no—
175#397—111no—
176#394—111no—
177#394—111no—
178#386—111no—
179#386—111no—
180#386—111no—
181#385—111no—
182#385—111no—
183#385—111no—
184#380—111no—
185C22×C11C22×D411yescharacteristic
186C22×C11C2×#4111yescharacteristic
187C22×C11C2×#4111yescharacteristic
188C22×C11H(5,𝔽2)11yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C22×C11H(5,𝔽2)11yescharacteristic
191C22×C112−1+411yescharacteristic
192C2×D11—22no—
193C2×D11—22no—
194C2×D11—22no—
195C2×D11—22no—
196C2×D11—22no—
197C2×D11—22no—
198C2×D11—22no—
199C2×D11—22no—
200C2×D11—22no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—41no—
218C4×C11—41no—
219C4×C11—41no—
220Dic11—41no—
221Dic11—41no—
222Dic11—41no—
223Dic11—41no—
224Dic11—41no—
225C22×D4—111no—
226C22×D4—111no—
227C22×D4—111no—
228C23×C4—111no—
229C23×C4—111no—
230C23×C4—111no—
231#123—224no—
232#121—224no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4C2×D1111yescharacteristic
237C2×C4⋊C4C2×D1111yescharacteristic
238C2×C4⋊C4C2×D1111yescharacteristic
239C2×C4⋊C4C2×D1111yescharacteristic
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—111no—
243C2×C22⋊C4—111no—
244C2×C22⋊C4—111no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4—111no—
249C2×C22⋊C4—111no—
250C2×C22⋊C4—111no—
251C2×C22⋊C4—111no—
252#95—111no—
253#95—111no—
254#95—111no—
255#95—111no—
256#95—111no—
257#95—111no—
258#95—111no—
259#95C2×D1111yescharacteristic
260#95C2×D1111yescharacteristic
261#95C2×D1111yescharacteristic
262C2×C11#53411yescharacteristic
263C2×C11#53811yescharacteristic
264C2×C11#53911yescharacteristic
265C2×C11#54611yescharacteristic
266C2×C11#54711yescharacteristic
267C2×C11#55311yescharacteristic
268C2×C11#56211yescharacteristic
269D11—42no—
270D11—42no—
271D11—42no—
272C24—111no—
273C24—111no—
274C24—111no—
275C2×D4—114no—
276C2×D4—222no—
277C2×D4—222no—
278C2×D4—222no—
279C2×D4—222no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—441no—
283C2×D4—441no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—222no—
290C22×C4—222no—
291C22×C4—222no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4C22×D1111yescharacteristic
299C22×C4C22×D1111yescharacteristic
300C22×C4C22×D1111yescharacteristic
301C22×C4C22×D1111yescharacteristic
302C22×C4C22×D1111yescharacteristic
303C22×C4C22×D1111yescharacteristic
304C22×C4C22×D1111yescharacteristic
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—222no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C22⋊C4—222no—
313C22⋊C4—222no—
314C22⋊C4—222no—
315C22⋊C4—222no—
316C22⋊C4—222no—
317C22⋊C4—222no—
318C22⋊C4—222no—
319C22⋊C4—222no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C22⋊C4—441no—
324C11#270811yescharacteristic, complemented, Sylow
325C23—112no—
326C23—112no—
327C23—112no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23—221no—
335C23—221no—
336C23—221no—
337C23—221no—
338C23—221no—
339C23—221no—
340C23—221no—
341C23—221no—
342C23—221no—
343C23—221no—
344C23—221no—
345C23—221no—
346C23C23×D1111yescharacteristic
347D4—444no—
348D4—444no—
349D4—444no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—444no—
385C2×C4—444no—
386C2×C4—444no—
387C2×C4D4×D1112yes—
388C2×C4#434312yes—
389C22—222no—
390C22—222no—
391C22—222no—
392C22—222no—
393C22—222no—
394C22—222no—
395C22—222no—
396C22—222no—
397C22—222no—
398C22—441no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22—441no—
403C22—441no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22—441no—
408C22—441no—
409C22—441no—
410C22C2×D4×D1111yescharacteristic
411C22#6703711yescharacteristic
412C22C2×#434311yescharacteristic
413C22#6704011yescharacteristic
414C22#41×D1111yescharacteristic
415C22#6704211yescharacteristic
416C22#6704211yescharacteristic
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—441no—
425C4—441no—
426C4—441no—
427C4—441no—
428C4—441no—
429C2—442no—
430C2—442no—
431C2—442no—
432C2#1062314311yescharacteristic
433C2#1062317511yescharacteristic
434C2#1062317811yescharacteristic
435C2#1062318411yescharacteristic
436C2#1062322311yescharacteristic
437C2#1062322611yescharacteristic
438C2#1062325711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#398C2
prime radicalC2×#66948C2
hypercenter#398D11
hypocenterC11#2708
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#66947C2semidirect
3. C11×#398C2semidirect
4. #10622606C2semidirect
5. #10622604C2semidirect
6. #10622604C2semidirect
7. #10622602C2semidirect
8. #10622600C2semidirect
9. #10622595C2semidirect
10. #10622288C2semidirect
11. #10622281C2semidirect
12. #10622281C2semidirect
13. #10622278C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
173. #398D11semidirect
324. C11#2708semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669472
C11×#3982
#106226062
#106226042
#106226022
#106226002
#106225952
#106222882
#106222812
#106222782
#270811