Finite Group Databasebeta

← #14770972

Subgroups — #14770972

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66880C211yesmaximal, characteristic
2#13071491C211yesmaximal, characteristic
3C22⋊C4×Dic22C211yesmaximal, characteristic
4#13069292C212yesmaximal, complemented
5#13069258C212yesmaximal, complemented
6#13068873C212yesmaximal, complemented
7#13068707C211yesmaximal, characteristic
8#13068645C211yesmaximal, characteristic
9#13068552C211yesmaximal, characteristic
10C4×#66880C212yesmaximal, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C2×C4×Dic22C2212yes—
16C2×C11×C22⋊C8C2211yescharacteristic
17C2×C4×C8×C11C2212yes—
18C4×C11×C22⋊C4C2211yescharacteristic
19#10622825C2211yescharacteristic
20#10622825C2211yescharacteristic
21C2×#66882C2212yes—
22C2×#66880C418yescomplemented
23C2×#66880C2212yes—
24C2×#66880C2212yes—
25C2×#66880C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29#10622555—21no—
30#10622555—21no—
31C22⋊C4×Dic11—21no—
32C22⋊C4×Dic11—21no—
33C4×C4⋊Dic11C2212yes—
34#10622542C2212yes—
35#10622541C2212yes—
36#10622267—22no—
37#10622259—22no—
38C11×#336C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11—21no—
45C22×Dic22—24no—
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×Dic22—42no—
49C22×Dic22C2×C414yes—
50C22×Dic22C2311yescharacteristic
51C22×Dic22C2311yescharacteristic
52C22×C8×C11—42no—
53C22×C8×C11C2×C414yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C2×C11×C22⋊C4D411yescharacteristic
58C2×C11×C22⋊C4D411yescharacteristic
59C2×C42×C11C2312yes—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11C2×C414yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C4×Dic22—24no—
74C4×Dic22—42no—
75C11×C22⋊C8—22no—
76C4×C8×C11—42no—
77C11×#95D412yes—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#66882—42no—
85#66880—24no—
86#66880—42no—
87#66880C2×C414yes—
88#66880C2×C414yes—
89#66880C2×C414yes—
90#66880C2×C414yes—
91#22575—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11#4112yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—24no—
102C22×Dic11—24no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—44no—
110C22×Dic11—82no—
111C2×Dic22—28no—
112C2×Dic22—24no—
113C2×Dic22—21no—
114C2×Dic22—22no—
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—44no—
119C2×Dic22—48no—
120C2×Dic22—44no—
121C2×Dic22C22×C412yes—
122C2×Dic22C22×C412yes—
123C2×Dic22#4114yes—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—44no—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C22×C412yes—
132C11×C22⋊C4—22no—
133C11×C22⋊C4Q1614yes—
134C42×C11—22no—
135C42×C11—22no—
136C22⋊Dic11—42no—
137C22⋊Dic11—42no—
138C4⋊Dic11—24no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11C22×C412yes—
146C4⋊Dic11C22×C412yes—
147Dic11⋊C4—44no—
148Dic11⋊C4—82no—
149C4×Dic11—44no—
150C4×Dic11—82no—
151C22×#103—111no—
152#2345—111no—
153Q8×C22⋊C4—111no—
154#1933—112no—
155#1928—112no—
156#1863—112no—
157#1824—111no—
158#1808—111no—
159#1787—111no—
160C4×#103—112no—
161C8×C22⋊C4D1111yescharacteristic
162C23×C11—22no—
163C23×C11—22no—
164C23×C11C4×D412yes—
165C23×C11C2×Q1612yes—
166C23×C11#13512yes—
167C23×C11C22×D411yescharacteristic
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C2×Q1614yes—
179C2×C4×C11C23×C411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4112yes—
182C2×C4×C11H(5,𝔽2)12yes—
183C2×Dic11—22no—
184C2×Dic11—24no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—48no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—84no—
199Dic22—22no—
200Dic22—24no—
201Dic22—22no—
202Dic22—22no—
203Dic22—48no—
204Dic22—42no—
205Dic22#11714yes—
206C8×C11—22no—
207C8×C11—22no—
208C8×C11—42no—
209C23×Q8—111no—
210C23×C8C2×D1111yescharacteristic
211C2×C4×Q8—112no—
212C22×C4⋊C4—111no—
213C2×#107—112no—
214C2×#103—111no—
215C2×#103—111no—
216C2×#103—111no—
217C2×#103—111no—
218C2×#103—118no—
219C2×#103—112no—
220C2×#103—112no—
221C2×C22⋊C8C2×D1111yescharacteristic
222C2×C4×C8C2×D1112yes—
223#391—112no—
224#391—222no—
225#389—112no—
226#387—222no—
227#380—111no—
228#380—111no—
229#380—221no—
230#380—221no—
231C4×C4⋊C4—112no—
232C4×C22⋊C4—221no—
233C4×C22⋊C4—221no—
234C4×C22⋊C4C2×D1111yescharacteristic
235#340—112no—
236#340—112no—
237#340—112no—
238#336C2×D1112yes—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—24no—
243C22×C11C4×Q1614yes—
244C22×C11C2×C4×D411yescharacteristic
245C22×C11#54612yes—
246C22×C11C22×Q1611yescharacteristic
247C22×C11C2×#13511yescharacteristic
248C22×C11#57712yes—
249C4×C11—22no—
250C4×C11—24no—
251C4×C11—42no—
252C4×C11C2×#11711yescharacteristic
253C4×C11#51811yescharacteristic
254C4×C11#55112yes—
255Dic11—24no—
256Dic11—42no—
257Dic11—42no—
258Dic11—42no—
259Dic11—82no—
260Dic11—82no—
261C22×Q8—114no—
262C22×Q8—111no—
263C22×Q8—111no—
264C22×Q8—224no—
265C22×Q8—221no—
266C22×Q8—222no—
267C22×Q8—442no—
268C23×C4—221no—
269C23×C4—221no—
270C23×C4C22×D1111yescharacteristic
271C22×C8—42no—
272C22×C8C4×D1114yes—
273C22×C8C22×D1112yes—
274C22×C8C22×D1111yescharacteristic
275C22×C8C22×D1111yescharacteristic
276C4×Q8—224no—
277C4×Q8—442no—
278C2×C4⋊C4—114no—
279C2×C4⋊C4—111no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4—222no—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—221no—
289C2×C22⋊C4D4411yescharacteristic
290C2×C22⋊C4D4411yescharacteristic
291C2×C42—222no—
292C2×C42—222no—
293C2×C42C22×D1112yes—
294#107—442no—
295#103—114no—
296#103—114no—
297#103—114no—
298#103—114no—
299#103—224no—
300#103—442no—
301C22⋊C8—22no—
302C4×C8—42no—
303#95—222no—
304#95—222no—
305#95—222no—
306#95—221no—
307#95—221no—
308#95—222no—
309#95D4412yes—
310C2×C11—24no—
311C2×C11#234211yescharacteristic
312C2×C11C2×C4×Q1611yescharacteristic
313C2×C11#294911yescharacteristic
314C2×C11#329912yes—
315C2×C11#330112yes—
316C24C2×D4411yescharacteristic
317C2×Q8—112no—
318C2×Q8—112no—
319C2×Q8—114no—
320C2×Q8—228no—
321C2×Q8—224no—
322C2×Q8—221no—
323C2×Q8—221no—
324C2×Q8—222no—
325C2×Q8—222no—
326C2×Q8—222no—
327C2×Q8—444no—
328C2×Q8—444no—
329C2×Q8—448no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—221no—
333C22×C4—224no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—221no—
337C22×C4—224no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—444no—
341C22×C4—882no—
342C22×C4C2×C4×D1112yes—
343C22×C4C2×D4412yes—
344C22×C4C2×D4411yescharacteristic
345C22×C4C2×D4412yes—
346C22×C4#433912yes—
347C22×C4C23×D1111yescharacteristic
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—44no—
354C2×C8C2×C4×D1112yes—
355C2×C8C2×C4×D1112yes—
356C4⋊C4—112no—
357C4⋊C4—112no—
358C4⋊C4—224no—
359C4⋊C4—221no—
360C4⋊C4—221no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—444no—
366C4⋊C4—882no—
367C22⋊C4—22no—
368C22⋊C4—442no—
369C22⋊C4—442no—
370C22⋊C4Dic4414yes—
371C42—22no—
372C42—22no—
373C42—444no—
374C42—882no—
375C11#2257511yescharacteristic, complemented, Sylow
376C23—22no—
377C23—22no—
378C23C4×D4412yes—
379C23#6695712yes—
380C23C2×Dic4412yes—
381C23C22×D4411yescharacteristic
382Q8—114no—
383Q8—222no—
384Q8—224no—
385Q8—222no—
386Q8—222no—
387Q8—448no—
388Q8—442no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—222no—
399C2×C4—224no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4—448no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—884no—
414C2×C4C4×D4412yes—
415C2×C4C2×Dic4414yes—
416C2×C4C22×C4×D1111yescharacteristic
417C2×C4C2×#433911yescharacteristic
418C2×C4#6703712yes—
419C2×C4#41×D1112yes—
420C8—22no—
421C8—22no—
422C8—42no—
423C22—22no—
424C22—24no—
425C22—24no—
426C22—22no—
427C22C4×Dic4414yes—
428C22C2×C4×D4411yescharacteristic
429C22#1062308512yes—
430C22C2×#6695711yescharacteristic
431C22C22×Dic4411yescharacteristic
432C22#1062328212yes—
433C4—22no—
434C4—24no—
435C4—42no—
436C4—224no—
437C4—442no—
438C4—442no—
439C4—442no—
440C4—882no—
441C4—882no—
442C4#1062301711yescharacteristic
443C4D11×#11711yescharacteristic
444C4#1062308712yes—
445C2—24no—
446C2#1307146811yescharacteristic
447C2C2×C4×Dic4411yescharacteristic
448C2#1307747711yescharacteristic
449C2#1308049312yes—
450C2#1308052012yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11#22575
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #13069292C2semidirect
5. #13069258C2semidirect
6. #13068873C2semidirect
10. C4×#66880C2semidirect
22. C2×#66880C4semidirect
375. C11#22575semidirect

Maximal subgroups

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

subgroupindex
C22×#668802
#130714912
C22⋊C4×Dic222
#130692922
#130692582
#130688732
#130687072
#130686452
#130685522
C4×#668802
C8×C11×C22⋊C42
#2257511