Finite Group Databasebeta

← #14765742

Subgroups — #14765742

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622292C211yesmaximal, characteristic, complemented
2C2×#10622303C211yesmaximal, characteristic
3#13071888C211yesmaximal, characteristic
4#13069555C211yesmaximal, characteristic, complemented
5#13069340C211yesmaximal, characteristic, complemented
6#13069339C212yesmaximal, complemented
7#13069230C212yesmaximal
8#13069229C212yesmaximal
9#13069181C212yesmaximal, complemented
10#13068597C211yesmaximal, characteristic
11C11×#1770C211yesmaximal, characteristic, complemented
12C2×#66925C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×#97C2212yes—
16C2×C4×C8×C11C2211yescharacteristic
17C4×C11×C4⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C8C2211yescharacteristic
19C2×(C2×D11)⋊C8C2211yescharacteristic
20C2×(C2×D11)⋊C8C2212yes—
21C2×#66879C2212yes—
22C2×Dic11⋊C8C2211yescharacteristic
23C2×Dic11⋊C8C2212yes—
24C2×Dic11⋊C8C2211yescharacteristic
25#10622607C412yes—
26#10622596C412yes—
27C4×(C2×D11)⋊C4C2212yes—
28C4×C4⋊Dic11C2212yes—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2212yes—
31C2×#66867C2211yescharacteristic
32#10622303—24no—
33#10622292—24no—
34#10622290C411yescharacteristic
35#10622286C411yescharacteristic
36#10622272C411yescharacteristic
37#10622269C411yescharacteristic
38C11×#336C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622162C2212yes—
43C22×C4×D11C2311yescharacteristic
44C22×Dic22C2×C411yescharacteristic
45C22×C8×C11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4C2×C412yes—
49C2×C42×C11C2312yes—
50C2×C42×C11C2311yescharacteristic
51C2×(C2×D11)⋊C4C2×C411yescharacteristic
52C2×(C2×D11)⋊C4C2×C411yescharacteristic
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×C4⋊Dic11C2×C411yescharacteristic
56C2×C4⋊Dic11C2×C412yes—
57C2×C4⋊Dic11C2×C412yes—
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2×C411yescharacteristic
60C2×Dic11⋊C4C2×C411yescharacteristic
61C2×C4×Dic11C2312yes—
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2311yescharacteristic
64C22×C11⋊C8C2311yescharacteristic
65C22×C11⋊C8C2312yes—
66#66925—22no—
67#66925—22no—
68C4×Dic22—22no—
69C4×Dic22—22no—
70C11×C4⋊C8—22no—
71C11×#97—42no—
72C4×C8×C11D414yes—
73C11×#95C2×C411yescharacteristic
74C11×#95C2×C411yescharacteristic
75C11⋊#95C2×C412yes—
76C11⋊#95C2×C412yes—
77C11⋊#95C2×C412yes—
78C11⋊#95C2×C412yes—
79(C2×D11)⋊C8—22no—
80(C2×D11)⋊C8—22no—
81(C2×D11)⋊C8—42no—
82#66879—24no—
83Dic11⋊C8—24no—
84Dic11⋊C8—22no—
85Dic11⋊C8—22no—
86C4⋊(C11⋊C8)—22no—
87C4⋊(C11⋊C8)—42no—
88#66867—22no—
89#22105—111nomaximal, Sylow
90C23×D11C22×C411yescharacteristic
91C22×C4×C11C22×C412yes—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C22×Dic11C22×C411yescharacteristic
97C22×Dic11C22×C412yes—
98C22×Dic11C22×C411yescharacteristic
99C22×Dic11C22×C411yescharacteristic
100C22×Dic11C22×C412yes—
101C2×C4×D11—21no—
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×Dic22—22no—
108C2×Dic22—42no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11—22no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—22no—
116C2×C8×C11C2×D412yes—
117C2×C8×C11C2×D412yes—
118C11×C4⋊C4—42no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11C2×D412yes—
122C42×C11#4112yes—
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127C4⋊Dic11—22no—
128C4⋊Dic11—42no—
129C4⋊Dic11—42no—
130Dic11⋊C4—24no—
131Dic11⋊C4—22no—
132Dic11⋊C4—22no—
133C4×Dic11—21no—
134C4×Dic11—22no—
135C4×Dic11—22no—
136C4×Dic11—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×#446—111no—
147C2×#433—111no—
148#2396—111no—
149#1985—111no—
150#1940—112no—
151#1940—111no—
152#1924—112no—
153#1924—112no—
154#1917—112no—
155#1798—111no—
156#1770D1111yescharacteristic, complemented
157C23×C11C23×C411yescharacteristic
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—22no—
162C22×D11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11C4×D412yes—
172C2×C4×C11C4×D412yes—
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11H(5,𝔽2)11yescharacteristic
176C2×C4×C112−1+411yescharacteristic
177C2×C4×C112−1+411yescharacteristic
178C2×C4×C112−1+411yescharacteristic
179C2×Dic11—22no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—22no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C4×D11—41no—
193C4×D11—41no—
194C4×D11—41no—
195C4×D11—41no—
196Dic22—44no—
197C8×C11—22no—
198C8×C11—22no—
199C8×C11—42no—
200C11⋊C8—41no—
201C11⋊C8—41no—
202C11⋊C8—42no—
203C2×C4×Q8—111no—
204C2×#117—111no—
205#446—224no—
206#433—224no—
207C2×C4⋊C8—111no—
208C2×C4⋊C8—111no—
209C2×C4⋊C8—112no—
210C2×C4⋊C8—111no—
211C2×C4⋊C8—112no—
212C2×C4⋊C8C2×D1111yescharacteristic
213C2×C22⋊C8—111no—
214C2×C22⋊C8—111no—
215C2×C22⋊C8—112no—
216C2×#97—112no—
217C2×#97—111no—
218C2×#97C2×D1112yes—
219C2×C4×C8C2×D1111yescharacteristic
220#400—111no—
221#399—111no—
222#398—112no—
223#396—112no—
224#395—111no—
225#393—111no—
226C4×C4⋊C4—112no—
227C4×C4⋊C4C2×D1111yescharacteristic
228C4×C22⋊C4—112no—
229#336—112no—
230#336—112no—
231#336—112no—
232#336—112no—
233#336C2×D1112yes—
234C22×C11C2×C4×D411yescharacteristic
235C22×C11#51911yescharacteristic
236C22×C11#52011yescharacteristic
237C22×C11#56812yes—
238C22×C11#56812yes—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—42no—
243C2×D11—42no—
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11#53611yescharacteristic
249C4×C11#53711yescharacteristic
250C4×C11#54111yescharacteristic
251C4×C11#54211yescharacteristic
252Dic11—41no—
253Dic11—42no—
254Dic11—41no—
255Dic11—42no—
256Dic11—41no—
257C22×Q8—111no—
258C23×C4—111no—
259C22×C8—111no—
260C22×C8—111no—
261C22×C8—112no—
262C22×C8C22×D1112yes—
263C22×C8C22×D1111yescharacteristic
264C22×C8C22×D1111yescharacteristic
265C4×Q8—222no—
266C4×Q8—222no—
267#117—222no—
268#117—222no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—112no—
275C2×C4⋊C4C4×D1112yes—
276C2×C22⋊C4—111no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4—112no—
279C2×C22⋊C4—112no—
280C2×C42—111no—
281C2×C42—112no—
282C2×C42C22×D1112yes—
283C2×C42C22×D1111yescharacteristic
284C4⋊C8—22no—
285C4⋊C8—222no—
286C4⋊C8—222no—
287C4⋊C8—224no—
288C4⋊C8—222no—
289C4⋊C8—442no—
290C22⋊C8—222no—
291C22⋊C8—222no—
292C22⋊C8—442no—
293#97—42no—
294#97—224no—
295#97—222no—
296C4×C8D4414yes—
297#95—112no—
298#95—112no—
299#95—112no—
300#95—112no—
301#95C4×D1111yescharacteristic
302#95C4×D1111yescharacteristic
303C2×C11#232311yescharacteristic
304C2×C11#293011yescharacteristic
305C2×C11#293211yescharacteristic
306C2×C11#298712yes—
307C2×C11#299512yes—
308D11—81no—
309C24—111no—
310C2×Q8—222no—
311C2×Q8—442no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—112no—
316C22×C4—112no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4C2×C4×D1112yes—
324C22×C4C2×C4×D1112yes—
325C22×C4C2×C4×D1111yescharacteristic
326C22×C4C2×C4×D1111yescharacteristic
327C22×C4C23×D1111yescharacteristic
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—222no—
342C2×C8—221no—
343C2×C8—221no—
344C2×C8C2×D4412yes—
345C2×C8C2×D4412yes—
346C4⋊C4—42no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—224no—
350C4⋊C4—222no—
351C4⋊C4—442no—
352C4⋊C4—442no—
353C22⋊C4—222no—
354C22⋊C4—222no—
355C22⋊C4—442no—
356C22⋊C4—442no—
357C42—22no—
358C42—22no—
359C42—222no—
360C42—221no—
361C42—221no—
362C42—222no—
363C42C2×D4412yes—
364C42#433912yes—
365C11#2210511yescharacteristic, complemented, Sylow
366C23—221no—
367C23—222no—
368C23—222no—
369C23—221no—
370C23—221no—
371C23C22×C4×D1111yescharacteristic
372Q8—444no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—221no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4C4×D4412yes—
399C2×C4C4×D4412yes—
400C2×C4C22×D4411yescharacteristic
401C2×C4C2×#433911yescharacteristic
402C2×C4#6703711yescharacteristic
403C2×C4#6704011yescharacteristic
404C2×C4#6704311yescharacteristic
405C2×C4#6704311yescharacteristic
406C8—22no—
407C8—22no—
408C8—42no—
409C8—441no—
410C8—442no—
411C8—441no—
412C22—442no—
413C22—441no—
414C22—441no—
415C22—441no—
416C22—442no—
417C22C2×C4×D4411yescharacteristic
418C22#1062307711yescharacteristic
419C22#1062310311yescharacteristic
420C22#1062327612yes—
421C22#1062328112yes—
422C4—22no—
423C4—22no—
424C4—42no—
425C4—42no—
426C4—442no—
427C4—441no—
428C4—441no—
429C4—442no—
430C4—441no—
431C4#1062304111yescharacteristic
432C4#1062305711yescharacteristic
433C4#1062309211yescharacteristic
434C4#1062311411yescharacteristic
435C2—881no—
436C2#1307129911yescharacteristic
437C2#1307732111yescharacteristic
438C2#1307733511yescharacteristic
439C2#1307771912yes—
440C2#1307778012yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1770C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1770D11
hypocenterC11#22105
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1770

Complements

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

NH ≅ G/Ntype
1. C2×#10622292C2semidirect
4. #13069555C2semidirect
5. #13069340C2semidirect
6. #13069339C2semidirect
9. #13069181C2semidirect
11. C11×#1770C2semidirect
156. #1770D11semidirect
365. C11#22105semidirect

Maximal subgroups

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

subgroupindex
C2×#106222922
C2×#106223032
#130718882
#130695552
#130693402
#130693392
#130692302
#130692292
#130691812
#130685972
C11×#17702
#2210511