Finite Group Databasebeta

← #14773560

Subgroups — #14773560

Order 2816.

802 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×C4×#4314C211yesmaximal, characteristic
2#13071587C211yesmaximal, characteristic
3#13071579C211yesmaximal, characteristic, complemented
4#13069497C212yesmaximal
5#13069251C212yesmaximal, complemented
6#13069244C212yesmaximal
7#13068780C211yesmaximal, characteristic, complemented
8#13068632C211yesmaximal, characteristic, complemented
9#13068627C211yesmaximal, characteristic
10#13068513C212yesmaximal, complemented
11C11×#1770C211yesmaximal, characteristic, complemented
12C22×#4314C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#97C2212yes—
17C2×C4×C8×C11C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19C2×#66885C2212yes—
20C2×#66885C2211yescharacteristic
21C2×#66882C2212yes—
22C2×#66881C2212yes—
23C2×#66881C2211yescharacteristic
24C2×#66880C2212yes—
25C2×#66880C2211yescharacteristic
26#10622603—22no—
27#10622591—22no—
28#10622552C2212yes—
29#10622549C2211yescharacteristic
30#10622549C2211yescharacteristic
31C4×C4⋊Dic11C2212yes—
32C4×C4⋊Dic11C2212yes—
33#10622542C2212yes—
34C4×#4314C418yescomplemented
35#10622279—21no—
36#10622277—21no—
37#10622264—21no—
38#10622261—21no—
39C11×#336C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C22×Dic22C2311yescharacteristic
45C22×C8×C11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4D412yes—
49C2×C42×C11C2312yes—
50C2×C42×C11C2311yescharacteristic
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—22no—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2312yes—
56C2×C4⋊Dic11C2311yescharacteristic
57C2×C4⋊Dic11C2311yescharacteristic
58C2×Dic11⋊C4—21no—
59C2×C4×Dic11—21no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—22no—
62C2×#4314—22no—
63C2×#4314—22no—
64C2×#4314C2×C414yes—
65C4×D44—22no—
66C4×D44C2×C414yes—
67C4×Dic22—22no—
68C4×Dic22C2×C414yes—
69C11×C4⋊C8—22no—
70C11×#97—24no—
71C4×C8×C11C2×C414yes—
72C11×#95D411yescharacteristic
73C11×#95D411yescharacteristic
74C11⋊#95—21no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82#66885—42no—
83#66885C2×C414yes—
84#66882—24no—
85#66881—42no—
86#66881C2×C414yes—
87#66880—42no—
88#66880C2×C414yes—
89#22812—111nomaximal, Sylow
90C23×D11—21no—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44C22×C412yes—
107C2×C4×D11—24no—
108C2×C4×D11—82no—
109C2×Dic22—21no—
110C2×Dic22—21no—
111C2×Dic22—21no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22C22×C412yes—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—21no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11C22×C412yes—
121C2×C8×C11C22×C412yes—
122C2×C8×C11#4112yes—
123C2×C8×C11#4112yes—
124C11×C4⋊C4—42no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129(C2×D11)⋊C4—24no—
130(C2×D11)⋊C4—44no—
131(C2×D11)⋊C4—82no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11C22×C412yes—
139C4⋊Dic11C22×C412yes—
140Dic11⋊C4—24no—
141C4×Dic11—24no—
142C4×Dic11—44no—
143C4×Dic11—82no—
144#4314—28no—
145C2×C4×SD16—111no—
146#2357—111no—
147#2356—111no—
148#1973—112no—
149#1927—112no—
150#1926—112no—
151#1846—111no—
152#1805—111no—
153#1804—111no—
154#1776—112no—
155#1770D1111yescharacteristic, complemented
156C23×C11C22×D411yescharacteristic
157C22×D11—22no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—42no—
161C22×D11—42no—
162C2×C4×C11—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×C11C4×D412yes—
171C2×C4×C11C4×D412yes—
172C2×C4×C11C23×C411yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C11H(5,𝔽2)11yescharacteristic
177C2×C4×C112−1+411yescharacteristic
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191D44—22no—
192D44—22no—
193D44—41no—
194D44—41no—
195C4×D11—84no—
196Dic22—22no—
197Dic22—22no—
198Dic22—41no—
199Dic22—41no—
200C8×C11—22no—
201C8×C11—42no—
202C8×C11#11714yes—
203C22×SD16—111no—
204C2×C4×Q8—111no—
205C2×C4×D4—111no—
206C4×SD16—118no—
207C2×#107—112no—
208C2×#106—111no—
209C2×#106—112no—
210C2×C4⋊C8C2×D1111yescharacteristic
211C2×#103—111no—
212C2×#103—112no—
213C2×#102—111no—
214C2×#102—112no—
215C2×#97C2×D1112yes—
216C2×C4×C8C2×D1111yescharacteristic
217#391—112no—
218#390—112no—
219#388—222no—
220#387—222no—
221#383—221no—
222#382—111no—
223#382—111no—
224#381—221no—
225C4×C4⋊C4—112no—
226C4×C4⋊C4—112no—
227C4×C4⋊C4C2×D1111yescharacteristic
228C4×C22⋊C4—221no—
229#376—221no—
230#340—112no—
231#340—112no—
232#336C2×D1112yes—
233C22×C11C2×C4×D411yescharacteristic
234C22×C11#54711yescharacteristic
235C22×C11#55011yescharacteristic
236C22×C11#57512yes—
237C22×C11#57712yes—
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—42no—
241C2×D11—82no—
242C2×D11—82no—
243C4×C11—22no—
244C4×C11—22no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11C2×#11711yescharacteristic
248C4×C11#52011yescharacteristic
249C4×C11#55511yescharacteristic
250C4×C11#55611yescharacteristic
251Dic11—42no—
252Dic11—42no—
253Dic11—42no—
254Dic11—82no—
255Dic11—82no—
256C22×Q8—111no—
257C22×D4—111no—
258C23×C4—221no—
259C2×SD16—114no—
260C2×SD16—222no—
261C2×SD16—222no—
262C22×C8C22×D1112yes—
263C22×C8C22×D1111yescharacteristic
264C22×C8C22×D1111yescharacteristic
265C4×Q8—114no—
266C4×Q8—222no—
267C4×D4—114no—
268C4×D4—222no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4D4412yes—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—222no—
278C2×C42—221no—
279C2×C42—222no—
280C2×C42—222no—
281C2×C42C22×D1112yes—
282C2×C42C22×D1111yescharacteristic
283#107—224no—
284#106—114no—
285#106—442no—
286C4⋊C8—22no—
287#103—114no—
288#103—442no—
289#102—114no—
290#102—442no—
291#97—24no—
292C4×C8C4×D1114yes—
293#95—221no—
294#95—222no—
295#95—221no—
296#95—222no—
297#95—222no—
298#95—221no—
299#95—221no—
300#95—222no—
301#95D4411yescharacteristic
302#95D4411yescharacteristic
303C2×C11#235411yescharacteristic
304C2×C11#294311yescharacteristic
305C2×C11#294911yescharacteristic
306C2×C11#335112yes—
307C2×C11#340112yes—
308D11—82no—
309C24—221no—
310C2×Q8—112no—
311C2×Q8—221no—
312C2×Q8—221no—
313C2×Q8—221no—
314C2×Q8—221no—
315C2×Q8—221no—
316C2×D4—112no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—224no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4—882no—
329C22×C4C2×D4412yes—
330C22×C4C2×D4412yes—
331C22×C4C2×D4411yescharacteristic
332C22×C4C2×D4411yescharacteristic
333C22×C4C23×D1111yescharacteristic
334SD16—228no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8C2×C4×D1112yes—
341C2×C8C2×C4×D1112yes—
342C2×C8#434112yes—
343C2×C8#434312yes—
344C4⋊C4—42no—
345C4⋊C4—112no—
346C4⋊C4—112no—
347C4⋊C4—224no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C22⋊C4—224no—
355C22⋊C4—444no—
356C22⋊C4—882no—
357C42—22no—
358C42—22no—
359C42—224no—
360C42—444no—
361C42—882no—
362C42C2×C4×D1112yes—
363C42#433912yes—
364C11#2281211yescharacteristic, complemented, Sylow
365C23—222no—
366C23—442no—
367C23—442no—
368C23—441no—
369C23—441no—
370C23C22×D4411yescharacteristic
371Q8—222no—
372Q8—222no—
373Q8—441no—
374Q8—441no—
375D4—222no—
376D4—222no—
377D4—441no—
378D4—441no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—884no—
401C2×C4C4×D4412yes—
402C2×C4C4×D4412yes—
403C2×C4C22×C4×D1111yescharacteristic
404C2×C4C2×#433911yescharacteristic
405C2×C4C2×#434111yescharacteristic
406C2×C4C2×#434311yescharacteristic
407C2×C4#6704211yescharacteristic
408C2×C4#6704311yescharacteristic
409C8—22no—
410C8—42no—
411C8#6694514yes—
412C22—442no—
413C22—442no—
414C22—442no—
415C22—882no—
416C22—882no—
417C22C2×C4×D4411yescharacteristic
418C22#1062308611yescharacteristic
419C22#1062310811yescharacteristic
420C22#1062327912yes—
421C22#1062328212yes—
422C4—22no—
423C4—22no—
424C4—42no—
425C4—42no—
426C4—442no—
427C4—442no—
428C4—442no—
429C4—882no—
430C4—882no—
431C4C2×#6694511yescharacteristic
432C4#1062305411yescharacteristic
433C4#1062309411yescharacteristic
434C4#1062311511yescharacteristic
435C2—882no—
436C2#1307156311yescharacteristic
437C2#1307741811yescharacteristic
438C2#1307747711yescharacteristic
439C2#1308117812yes—
440C2#1308168412yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1770C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1770D11
hypocenterC11#22812
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1770

Complements

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

NH ≅ G/Ntype
3. #13071579C2semidirect
5. #13069251C2semidirect
7. #13068780C2semidirect
8. #13068632C2semidirect
10. #13068513C2semidirect
11. C11×#1770C2semidirect
34. C4×#4314C4semidirect
155. #1770D11semidirect
364. C11#22812semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43142
#130715872
#130715792
#130694972
#130692512
#130692442
#130687802
#130686322
#130686272
#130685132
C11×#17702
#2281211