Finite Group Databasebeta

← #14737635

Subgroups — #14737635

Order 2816.

628 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
1#13079176C211yesmaximal, characteristic
2#13078738C211yesmaximal, characteristic
3C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068072C212yesmaximal, complemented
5#13068062C212yesmaximal, complemented
6#13067996C212yesmaximal, complemented
7#13067966C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067316C211yesmaximal, characteristic, complemented
10#13067312C211yesmaximal, characteristic
11C11×#3113C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#483—21no—
16C11×#475C2212yes—
17C11×#462C2212yes—
18C11×#451—21no—
19C11×#441—22no—
20C11×#432C2211yescharacteristic
21#10622840—21no—
22#10622701C2211yescharacteristic
23#10622698C2211yescharacteristic
24#10622694C2211yescharacteristic
25#10622692C2211yescharacteristic
26#10622661—21no—
27#10622661—21no—
28#10622640C2212yes—
29#10622639—22no—
30C4×#4325—21no—
31C4×#4325—21no—
32Q8×C11⋊C8—21no—
33Q8×C11⋊C8—21no—
34Q8×C11⋊C8C2212yes—
35Q8×C11⋊C8C2212yes—
36#10622634C2212yes—
37#10622580—21no—
38#10622539C2211yescharacteristic
39C2×C4⋊(C11⋊C8)—21no—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8—21no—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yes—
44#10622185C2212yes—
45#10622123C2212yes—
46#10622119C2212yes—
47#10622118C2212yes—
48#10622117C2212yes—
49C22×Q8×C11D411yescharacteristic
50C2×#4339—21no—
51C2×C11×Q16—22no—
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11D412yes—
62C4×Q8×C11C2312yes—
63C11×#117—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4325—22no—
69C2×#4325—21no—
70C2×#4325—21no—
71#66983—21no—
72#66983—21no—
73C22×C11⋊C8—21no—
74C22×C11⋊C8D411yescharacteristic
75C22×C11⋊C8D411yescharacteristic
76#66928—21no—
77#66927C2311yescharacteristic
78C4×D44—21no—
79C4×D44—21no—
80#66922C2311yescharacteristic
81C11×#106—22no—
82C11×C4⋊C8C2312yes—
83C11×#103—22no—
84C11×#103—22no—
85C11×C22⋊C8—21no—
86C11×#97—21no—
87#66899—22no—
88#66899—21no—
89#66899—21no—
90C22⋊(C11⋊C8)—21no—
91#66873—22no—
92#66873—21no—
93#66873—21no—
94#66872—21no—
95#66872—21no—
96#66871—22no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#66867—21no—
103C4×C11⋊C8—22no—
104C4×C11⋊C8—22no—
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#19263—111nomaximal, Sylow
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11C2×D412yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—41no—
121#4339—82no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×C4×D11—41no—
126C2×Dic22—21no—
127C11×Q16—44no—
128C2×C8×C11—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4C2×D412yes—
139C11×C22⋊C4—41no—
140C42×C11—22no—
141C42×C11—22no—
142C42×C11—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147#4325—42no—
148#4325—42no—
149#4325—44no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—41no—
158C2×C11⋊C8—42no—
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163#3167—111no—
164#3113D1111yescharacteristic, complemented
165#3112—111no—
166C2×C8×Q8—111no—
167#1684—112no—
168#1682—112no—
169#1672—112no—
170#1666—112no—
171#1568—111no—
172#1552—111no—
173#1551—111no—
174C23×C11#12111yescharacteristic
175C22×D11—41no—
176Q8×C11—24no—
177Q8×C11—22no—
178Q8×C11—42no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11#13514yes—
182C2×C4×C11—24no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C22⋊D11—82no—
199C2×Dic11—41no—
200D44—42no—
201D44—41no—
202D44—41no—
203D44—81no—
204C4×D11—82no—
205Dic22—81no—
206C8×C11—42no—
207C11⋊C8—21no—
208C11⋊C8—21no—
209C11⋊C8—21no—
210C11⋊C8—42no—
211C11⋊C8—42no—
212C11⋊C8#13712yes—
213#533C2×D1111yescharacteristic
214#532—111no—
215C2×C4×Q8C2×D1111yescharacteristic
216#498—111no—
217#492—111no—
218#487—111no—
219#486—111no—
220#483—21no—
221#480—221no—
222#477—112no—
223#475C2×D1112yes—
224#465—221no—
225#465—221no—
226#462C2×D1112yes—
227#460—112no—
228#451—21no—
229#448—221no—
230C8×Q8—112no—
231C8×Q8—112no—
232C8×Q8—221no—
233C8×Q8—221no—
234#441—22no—
235#440—222no—
236C4×SD16—221no—
237C4×SD16—221no—
238#432—111no—
239#432C2×D1111yescharacteristic
240C2×C4⋊C8—111no—
241C2×C4⋊C8—221no—
242C2×C4×C8—111no—
243C2×C4×C8—221no—
244#335—112no—
245#334—112no—
246#333—112no—
247#332—112no—
248#332—112no—
249#331—112no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11#47112yes—
253C22×C11C2×#12111yescharacteristic
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C4×C11—21no—
258C4×C11—24no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11C2×#13512yes—
266C4×C11C2×#13711yescharacteristic
267C4×C11#57511yescharacteristic
268Dic11—81no—
269C2×#41—221no—
270C22×Q8C22⋊D1111yescharacteristic
271C2×Q16—22no—
272C2×SD16—221no—
273C2×SD16—221no—
274C2×SD16—222no—
275C22×C8—111no—
276C22×C8—111no—
277C22×C8—221no—
278C4⋊Q8—111no—
279C4⋊Q8C22×D1111yescharacteristic
280C4⋊Q8C22×D1111yescharacteristic
281#127—111no—
282#125—21no—
283#124—221no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286#121—221no—
287#121—221no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8C22⋊D1112yes—
293C4×Q8C22×D1112yes—
294C4×D4—221no—
295C4×D4—221no—
296#117—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4C22⋊D1111yescharacteristic
299C2×C42—21no—
300C2×C42C22×D1111yescharacteristic
301#107—222no—
302#106—22no—
303#106—221no—
304#106—221no—
305C4⋊C8—112no—
306C4⋊C8—112no—
307C4⋊C8—222no—
308C4⋊C8—222no—
309C4⋊C8—221no—
310C4⋊C8C22×D1112yes—
311#103—22no—
312#103—22no—
313#103—221no—
314#103—221no—
315#103—222no—
316#102—221no—
317#102—221no—
318#102—222no—
319C22⋊C8—21no—
320C22⋊C8—221no—
321#97—21no—
322#97—221no—
323C4×C8—111no—
324C4×C8—111no—
325C4×C8—111no—
326C4×C8—111no—
327C4×C8—222no—
328C4×C8—222no—
329C2×C11—22no—
330C2×C11#303711yescharacteristic
331C2×C11#305011yescharacteristic
332C2×C11C2×#47111yescharacteristic
333D11—161no—
334#41—882no—
335C2×Q8—24no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—221no—
340C2×Q8C2×C22⋊D1112yes—
341C2×D4—221no—
342C2×D4—221no—
343C2×D4—221no—
344C2×D4—441no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—441no—
348C22×C4D4×D1111yescharacteristic
349C22×C4#434111yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351Q16—44no—
352SD16—442no—
353SD16—442no—
354SD16—444no—
355C2×C8—22no—
356C2×C8—111no—
357C2×C8—111no—
358C2×C8—111no—
359C2×C8—111no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—441no—
364C2×C8—442no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4C2×C22⋊D1112yes—
377C22⋊C4—41no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C42—22no—
381C42—22no—
382C42—41no—
383C42D4×D1111yescharacteristic
384C42#434111yescharacteristic
385C42C2×C22⋊D1111yescharacteristic
386C42C23×D1111yescharacteristic
387C11#1926311yescharacteristic, complemented, Sylow
388C23—441no—
389C23#6699211yescharacteristic
390Q8—24no—
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—42no—
395Q8—881no—
396Q8#6700314yes—
397D4—441no—
398D4—441no—
399D4—442no—
400D4—881no—
401D4—882no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—441no—
413C2×C4—882no—
414C2×C4#6699211yescharacteristic
415C2×C4#6699211yescharacteristic
416C2×C4#6699211yescharacteristic
417C2×C4C2×D4×D1111yescharacteristic
418C2×C4C2×#434111yescharacteristic
419C2×C4C22×C22⋊D1111yescharacteristic
420C8—42no—
421C8—112no—
422C8—221no—
423C8—221no—
424C8—221no—
425C8—442no—
426C8—442no—
427C22—21no—
428C22—21no—
429C22—881no—
430C22—881no—
431C22—881no—
432C22#1062281612yes—
433C22C2×#6699211yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—24no—
438C4—21no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—881no—
443C4D11×#13711yescharacteristic
444C4#1062330811yescharacteristic
445C4C2×#6700312yes—
446C2—22no—
447C2—1761no—
448C2#1307808511yescharacteristic
449C2#1307819411yescharacteristic
450C2C2×#1062281611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3113C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3113D11
hypocenterC11#19263
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
3. C2×Q8×C11⋊C8C2semidirect
4. #13068072C2semidirect
5. #13068062C2semidirect
6. #13067996C2semidirect
7. #13067966C2semidirect
8. #13067377C2semidirect
9. #13067316C2semidirect
11. C11×#3113C2semidirect
164. #3113D11semidirect
387. C11#19263semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130787382
C2×Q8×C11⋊C82
#130680722
#130680622
#130679962
#130679662
#130673772
#130673162
#130673122
C11×#31132
#1926311