Finite Group Databasebeta

← #14771480

Subgroups — #14771480

Order 2816.

810 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
1C22×#66871C211yesmaximal, characteristic
2#13071491C211yesmaximal, characteristic
3#13069351C212yesmaximal, complemented
4#13069187C212yesmaximal, complemented
5#13069184C212yesmaximal, complemented
6#13068706C211yesmaximal, characteristic
7#13068704C211yesmaximal, characteristic
8#13068639C211yesmaximal, characteristic
9#13068514C212yesmaximal, complemented
10#13068394C211yesmaximal, characteristic
11C11×#2345C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C11×#389C2212yes—
16C11×#387—22no—
17C11×#380—21no—
18C11×#380C2211yescharacteristic
19C4×C11×C4⋊C4C2212yes—
20C4×C11×C22⋊C4—21no—
21C4×C11×C22⋊C4C2211yescharacteristic
22#10622825C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×#66872C2212yes—
25C2×#66871C418yescomplemented
26C2×#66871C2211yescharacteristic
27C2×#66871C2211yescharacteristic
28C2×#66871C2211yescharacteristic
29C2×#66871C2211yescharacteristic
30#10622555—21no—
31C22⋊C4×Dic11—21no—
32C4×C4⋊Dic11C2212yes—
33#10622541C2212yes—
34C2×#66867C2212yes—
35#10622267—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622162C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4D411yescharacteristic
54C2×C11×C22⋊C4D411yescharacteristic
55C2×C42×C11—22no—
56C2×C42×C11C2312yes—
57C2×C22⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11C2×C414yes—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C22×C11⋊C8—24no—
67C22×C11⋊C8C2×C414yes—
68C22×C11⋊C8C2312yes—
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C11×#95—22no—
72C11×#95—22no—
73C11×#95—21no—
74C11×#95D412yes—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C22⋊(C11⋊C8)—22no—
79#66872—24no—
80#66871C2×C414yes—
81#66871C2×C414yes—
82#66871C2×C414yes—
83#66871C2×C414yes—
84#66867—24no—
85#22618—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—24no—
92C22×C4×C11—22no—
93C22×C4×C11—82no—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4112yes—
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—24no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11—82no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—82no—
111C11×C4⋊C4C22×C412yes—
112C11×C4⋊C4C22×C412yes—
113C11×C22⋊C4—22no—
114C11×C22⋊C4—22no—
115C11×C22⋊C4—42no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11—82no—
119C22⋊Dic11—42no—
120C4⋊Dic11—24no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11C22×C412yes—
126C4⋊Dic11C22×C412yes—
127Dic11⋊C4—82no—
128C4×Dic11—82no—
129C2×C11⋊C8—28no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C22×C412yes—
135C2×C11⋊C8C22×C412yes—
136C2×C11⋊C8#4114yes—
137C22×#107—111no—
138#2345—111no—
139#2345D1111yescharacteristic
140#1943—112no—
141#1918—112no—
142#1918—112no—
143#1824—111no—
144#1824—111no—
145#1807—111no—
146#1776—112no—
147#1752—111no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11C4×D412yes—
151C23×C11#13712yes—
152C23×C11#13712yes—
153C23×C11C22×D411yescharacteristic
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—84no—
172C2×C4×C11C4×D412yes—
173C2×C4×C11C23×C411yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11C2×#4112yes—
176C2×C4×C112−1+412yes—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—84no—
185C11⋊C8—22no—
186C11⋊C8—42no—
187C11⋊C8#11714yes—
188C23×C8—111no—
189C22×C4⋊C4—111no—
190C22×C4⋊C4C2×D1111yescharacteristic
191C2×#107—111no—
192C2×#107—111no—
193C2×#107—111no—
194C2×#107—111no—
195C2×#107—118no—
196C2×#106—112no—
197C2×C22⋊C8—111no—
198C2×#97—112no—
199#389—112no—
200#389C2×D1112yes—
201#387—22no—
202#387—222no—
203#380—21no—
204#380—111no—
205#380—221no—
206#380C2×D1111yescharacteristic
207C4×C4⋊C4—112no—
208C4×C4⋊C4C2×D1112yes—
209C4×C22⋊C4—21no—
210C4×C22⋊C4—221no—
211C4×C22⋊C4C2×D1111yescharacteristic
212#340—112no—
213#340—112no—
214#340—112no—
215#340—112no—
216#340—112no—
217#336—112no—
218C22×C11—24no—
219C22×C11—24no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11#44114yes—
223C22×C11C2×C4×D411yescharacteristic
224C22×C11#54712yes—
225C22×C11C2×#13711yescharacteristic
226C22×C11C2×#13711yescharacteristic
227C22×C11#57612yes—
228C4×C11—22no—
229C4×C11—42no—
230C4×C11—42no—
231C4×C11—42no—
232C4×C11—42no—
233C4×C11—82no—
234C4×C11C2×#11711yescharacteristic
235C4×C11#51911yescharacteristic
236C4×C11#55212yes—
237Dic11—42no—
238Dic11—42no—
239Dic11—82no—
240C23×C4—21no—
241C23×C4—221no—
242C23×C4C22×D1111yescharacteristic
243C22×C8—111no—
244C22×C8—114no—
245C22×C8—111no—
246C22×C8—112no—
247C22×C8—224no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—114no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—222no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4C4×D1114yes—
259C2×C4⋊C4C22×D1112yes—
260C2×C4⋊C4C22×D1111yescharacteristic
261C2×C4⋊C4C22×D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4C22⋊D1111yescharacteristic
265C2×C22⋊C4C22⋊D1111yescharacteristic
266C2×C42—22no—
267C2×C42—222no—
268C2×C42C22×D1112yes—
269#107—114no—
270#107—114no—
271#107—114no—
272#107—114no—
273#106—224no—
274C22⋊C8—222no—
275#97—224no—
276#95—22no—
277#95—22no—
278#95—21no—
279#95—222no—
280#95—222no—
281#95—221no—
282#95C22⋊D1112yes—
283C2×C11—24no—
284C2×C11#234411yescharacteristic
285C2×C11C2×#44111yescharacteristic
286C2×C11#294811yescharacteristic
287C2×C11#334612yes—
288C2×C11#334612yes—
289C24C2×C22⋊D1111yescharacteristic
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—82no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4—224no—
300C22×C4—222no—
301C22×C4—882no—
302C22×C4C2×C4×D1112yes—
303C22×C4#433912yes—
304C22×C4C2×C22⋊D1112yes—
305C22×C4C2×C22⋊D1112yes—
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C23×D1111yescharacteristic
308C2×C8—112no—
309C2×C8—114no—
310C2×C8—112no—
311C2×C8—228no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C4⋊C4—24no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—82no—
322C4⋊C4—112no—
323C4⋊C4—112no—
324C4⋊C4—224no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—882no—
330C4⋊C4C2×C4×D1112yes—
331C4⋊C4C2×C4×D1112yes—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—42no—
335C22⋊C4—442no—
336C42—22no—
337C42—22no—
338C42—82no—
339C42—882no—
340C11#2261811yescharacteristic, complemented, Sylow
341C23—22no—
342C23—22no—
343C23C4×C22⋊D1112yes—
344C23#6699512yes—
345C23#6700412yes—
346C23C22×C22⋊D1111yescharacteristic
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—24no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—84no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—884no—
373C2×C4C4×C22⋊D1112yes—
374C2×C4C22×C4×D1111yescharacteristic
375C2×C4C2×#433911yescharacteristic
376C2×C4#41×D1112yes—
377C2×C4#6704312yes—
378C8—114no—
379C8—222no—
380C8—442no—
381C22—24no—
382C22—24no—
383C22—22no—
384C22—22no—
385C22#1062264314yes—
386C22C2×C4×C22⋊D1111yescharacteristic
387C22C2×#6699511yescharacteristic
388C22C2×#6700411yescharacteristic
389C22#1062335512yes—
390C22#1062336612yes—
391C4—22no—
392C4—42no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—82no—
397C4—442no—
398C4—442no—
399C4—882no—
400C4#1062304711yescharacteristic
401C4D11×#11711yescharacteristic
402C4#1062306212yes—
403C2—24no—
404C2#1307148611yescharacteristic
405C2C2×#1062264311yescharacteristic
406C2#1307746611yescharacteristic
407C2#1308109512yes—
408C2#1308110112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2345C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2345D11
hypocenterC11#22618
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
3. #13069351C2semidirect
4. #13069187C2semidirect
5. #13069184C2semidirect
9. #13068514C2semidirect
25. C2×#66871C4semidirect
340. C11#22618semidirect

Maximal subgroups

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

subgroupindex
C22×#668712
#130714912
#130693512
#130691872
#130691842
#130687062
#130687042
#130686392
#130685142
#130683942
C11×#23452
#2261811