Finite Group Databasebeta

← #14760517

Subgroups — #14760517

Order 2816.

954 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×#10622750C211yesmaximal, characteristic
2C2×#10622466C211yesmaximal, characteristic, complemented
3C2×#10622735C211yesmaximal, characteristic
4#13071294C212yesmaximal
5#13069475C211yesmaximal, characteristic, complemented
6#13069342C211yesmaximal, characteristic, complemented
7#13069304C212yesmaximal, complemented
8#13069037C212yesmaximal
9#13068515C211yesmaximal, characteristic, complemented
10#13068435C212yesmaximal, complemented
11C11×#1809C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66977C2212yes—
15C23×C11⋊C8C2211yescharacteristic
16C22×Dic44C2211yescharacteristic
17C2×#66940C2212yes—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C11×#380C2212yes—
21#10622750C418yescomplemented
22#10622735—24no—
23C2×#66881C2211yescharacteristic
24C2×#66880C2212yes—
25C2×#66879C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29C4⋊C4×Dic11C2212yes—
30#10622587C2212yes—
31#10622586C2212yes—
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34#10622558—22no—
35#10622557—22no—
36#10622466—24no—
37#10622268—22no—
38#10622260—22no—
39C11×#340C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×Dic22C2312yes—
44C2×C11×M16—22no—
45C2×C11×M16—22no—
46C2×C11×M16C2×C414yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C22⋊C4—22no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11D412yes—
54#66979—22no—
55#66979—22no—
56C2×C4⋊Dic11D412yes—
57C2×C4⋊Dic11C2312yes—
58#66977—24no—
59#66977C2×C418yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11C2311yescharacteristic
66C2×C4×Dic11C2311yescharacteristic
67C22×C11⋊C8—22no—
68C22×C11⋊C8—22no—
69C22×C11⋊C8—22no—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C2×Dic44—22no—
73C2×Dic44—22no—
74C2×Dic44C2×C414yes—
75#66940—24no—
76#66940—24no—
77C11×#107—22no—
78C11×#106—22no—
79C11×#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#66881C2×C414yes—
85#66880C2×C418yes—
86#66879—22no—
87#66879D414yes—
88C8×Dic11—22no—
89C8×Dic11—22no—
90#66874—24no—
91#66874—24no—
92#21542—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4112yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11C2×D412yes—
107C22×Dic11C2×D412yes—
108C2×Dic22—22no—
109C2×Dic22—22no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22C22×C414yes—
114C11×M16—28no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11C22×C412yes—
118C2×C8×C11C22×C412yes—
119C2×C8×C11C2×D412yes—
120C2×C8×C11#4112yes—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C22⋊C4—82no—
126C22⋊Dic11—24no—
127C22⋊Dic11—28no—
128C4⋊Dic11—24no—
129C4⋊Dic11—22no—
130C4⋊Dic11C22×C414yes—
131Dic11⋊C4—28no—
132Dic11⋊C4—44no—
133Dic11⋊C4—82no—
134C4×Dic11—21no—
135C4×Dic11—21no—
136C4×Dic11—44no—
137C4×Dic11—82no—
138C4×Dic11C2×D412yes—
139C4×Dic11#4112yes—
140C2×C11⋊C8—28no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8C2×D412yes—
146C2×C11⋊C8#4112yes—
147Dic44—28no—
148C2×#470—111no—
149C2×#441—111no—
150C2×#405—111no—
151#2323—112no—
152#1969—111no—
153#1941—111no—
154#1935—112no—
155#1892—112no—
156#1809D1111yescharacteristic
157#1776—111no—
158C4×#103—112no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11C4×D412yes—
164C23×C11C22×D411yescharacteristic
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C23×C411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—24no—
187C2×Dic11—24no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11#12114yes—
196Dic22—24no—
197Dic22—24no—
198Dic22—42no—
199Dic22—42no—
200C8×C11—22no—
201C8×C11C4×D414yes—
202C11⋊C8—22no—
203C11⋊C8—22no—
204C22×Q16—111no—
205C22×M16C2×D1111yescharacteristic
206C23×C8—111no—
207C2×C22⋊Q8—112no—
208C2×C4×Q8—112no—
209C2×#117—111no—
210#470—118no—
211#441—224no—
212C2×#107C2×D1111yescharacteristic
213C2×#106—111no—
214C2×#106C2×D1111yescharacteristic
215C2×#103—112no—
216C2×#103—112no—
217C2×#103—112no—
218#405—224no—
219C2×#97—111no—
220C2×#97—111no—
221C2×C4×C8—111no—
222C2×C4×C8—111no—
223#391—112no—
224#389—112no—
225#389—222no—
226#388—222no—
227#388—222no—
228#387—222no—
229#380C2×D1112yes—
230C4×C4⋊C4—112no—
231#340—112no—
232#340—112no—
233#340C2×D1112yes—
234C22×C11—24no—
235C22×C11—22no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—42no—
239C22×C11C2×C4×D411yescharacteristic
240C22×C11C2×#12111yescharacteristic
241C22×C11#53211yescharacteristic
242C22×C11#57712yes—
243C22×C11#57812yes—
244C4×C11—22no—
245C4×C11—82no—
246C4×C11—82no—
247C4×C11C2×C4×D411yescharacteristic
248C4×C11C4×#4111yescharacteristic
249C4×C11#52511yescharacteristic
250C4×C11#52911yescharacteristic
251Dic11—24no—
252Dic11—44no—
253Dic11—42no—
254Dic11—44no—
255C22×Q8—112no—
256C23×C4C22×D1111yescharacteristic
257C2×Q16—114no—
258C2×Q16—222no—
259C2×Q16—222no—
260C2×M16—22no—
261C2×M16—22no—
262C2×M16C4×D1114yes—
263C22×C8—111no—
264C22×C8—111no—
265C22×C8—222no—
266C22×C8—222no—
267C22×C8—222no—
268C22×C8C22×D1111yescharacteristic
269C22×C8C22×D1111yescharacteristic
270C22⋊Q8—118no—
271C22⋊Q8—224no—
272C4×Q8—224no—
273C4×Q8—224no—
274#117—222no—
275#117—222no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4C22×D1112yes—
282C2×C4⋊C4C22×D1112yes—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—112no—
285C2×C22⋊C4—222no—
286C2×C42—111no—
287C2×C42—111no—
288C2×C42—222no—
289C2×C42—222no—
290#107—22no—
291#106—22no—
292#106—114no—
293#103—118no—
294#103—224no—
295#103—224no—
296#97—114no—
297#97—222no—
298C4×C8—222no—
299C4×C8—222no—
300#95—22no—
301#95—222no—
302#95—222no—
303#95—222no—
304#95—222no—
305C2×C11—42no—
306C2×C11C4×#12111yescharacteristic
307C2×C11#294712yes—
308C2×C11#306312yes—
309C2×C11#317311yescharacteristic
310C2×C11#317711yescharacteristic
311C24D4×D1111yescharacteristic
312C2×Q8—114no—
313C2×Q8—222no—
314C2×Q8—222no—
315C2×Q8—222no—
316C2×Q8—222no—
317C2×Q8—222no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—112no—
325C22×C4—112no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4C2×C4×D1112yes—
329C22×C4D4×D1111yescharacteristic
330C22×C4#434312yes—
331C22×C4C23×D1111yescharacteristic
332Q16—228no—
333M16—28no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—112no—
337C2×C8—112no—
338C2×C8—228no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—221no—
343C2×C8C2×C4×D1112yes—
344C2×C8C2×C4×D1112yes—
345C2×C8D4×D1112yes—
346C2×C8#434112yes—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—114no—
352C4⋊C4—224no—
353C4⋊C4—228no—
354C4⋊C4—222no—
355C4⋊C4—444no—
356C4⋊C4—882no—
357C22⋊C4—82no—
358C22⋊C4—224no—
359C22⋊C4—228no—
360C42—112no—
361C42—112no—
362C42—221no—
363C42—221no—
364C42—444no—
365C42—882no—
366C11#2154211yescharacteristic, complemented, Sylow
367C23—22no—
368C23—22no—
369C23—21no—
370C23—21no—
371C23#6694612yes—
372C23C2×D4×D1111yescharacteristic
373Q8—224no—
374Q8—224no—
375Q8—442no—
376Q8—442no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—114no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—224no—
393C2×C4—224no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4#6694612yes—
402C2×C4C22×C4×D1111yescharacteristic
403C2×C4C2×D4×D1111yescharacteristic
404C2×C4C2×#434111yescharacteristic
405C2×C4C2×#434311yescharacteristic
406C2×C4#41×D1111yescharacteristic
407C2×C4#41×D1111yescharacteristic
408C8—22no—
409C8—222no—
410C8—222no—
411C8(C22⋊D11)⋊C414yes—
412C22—22no—
413C22—24no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22C2×#6694611yescharacteristic
418C22#1062312711yescharacteristic
419C22D11×#12111yescharacteristic
420C22#1062330612yes—
421C22#1062331012yes—
422C4—22no—
423C4—82no—
424C4—82no—
425C4—224no—
426C4—444no—
427C4—442no—
428C4—444no—
429C4C2×(C22⋊D11)⋊C411yescharacteristic
430C4#1062305311yescharacteristic
431C4#1062315511yescharacteristic
432C4#1062315811yescharacteristic
433C2—42no—
434C2#1307112211yescharacteristic
435C2#1307745712yes—
436C2#1307830212yes—
437C2#1307922811yescharacteristic
438C2#1307927011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#21542
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#10622466C2semidirect
5. #13069475C2semidirect
6. #13069342C2semidirect
7. #13069304C2semidirect
9. #13068515C2semidirect
10. #13068435C2semidirect
21. #10622750C4semidirect
366. C11#21542semidirect

Maximal subgroups

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

subgroupindex
C2×#106227502
C2×#106224662
C2×#106227352
#130712942
#130694752
#130693422
#130693042
#130690372
#130685152
#130684352
C11×#18092
#2154211