Finite Group Databasebeta

← #14908908

Subgroups — #14908908

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079272C211yesmaximal, characteristic, complemented
2#13077486C211yesmaximal, characteristic
3#13070817C211yesmaximal, characteristic, complemented
4#13070812C211yesmaximal, characteristic, complemented
5#13070781C211yesmaximal, characteristic, complemented
6#13070773C211yesmaximal, characteristic, complemented
7#13070663C211yesmaximal, characteristic, complemented
8#13070553C211yesmaximal, characteristic
9#13070553C211yesmaximal, characteristic
10#13070484C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12#13070472C211yesmaximal, characteristic, complemented
13SD32×Dic11C211yesmaximal, characteristic, complemented
14#13070422C211yesmaximal, characteristic, complemented
15C11×#2208C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17#10623262—21no—
18#10623077—21no—
19C2×C11×SD32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C11×#494C2211yescharacteristic
22C4×C11×D8C2211yescharacteristic
23#10622802—21no—
24#10622801C2211yescharacteristic
25#10622801C2211yescharacteristic
26#10622797—21no—
27Q16×Dic11C2211yescharacteristic
28Q16×Dic11C2211yescharacteristic
29C2×#66893C2211yescharacteristic
30C2×#66893C2211yescharacteristic
31D8×Dic11C2211yescharacteristic
32#10622695—21no—
33#10622631—21no—
34D11×#107C2211yescharacteristic
35#10622486C2211yescharacteristic
36#10622384—21no—
37#10622370—21no—
38C4×Dic44C2211yescharacteristic
39#10622302C2211yescharacteristic
40#10622296C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622140C2211yescharacteristic
55C16×Dic11C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×#4341—21no—
60C2×C11×Q16—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C11×C4⋊Q8—21no—
65C4×D4×C11—21no—
66#66999—21no—
67#66999—21no—
68Q8×Dic11—21no—
69Q8×Dic11—21no—
70D4×Dic11—21no—
71C2×#4324—21no—
72C4×C22⋊D11—41no—
73C2×Dic11⋊C4—41no—
74#66965—22no—
75#66965—22no—
76C2×Dic44C2311yescharacteristic
77C2×#4313D411yescharacteristic
78C2×C8×D11C2311yescharacteristic
79#66951—41no—
80#66951—41no—
81C4⋊C4×D11—21no—
82#66942—41no—
83#66942—41no—
84#66940—21no—
85(C22⋊D11)⋊C4—41no—
86#66930—41no—
87#66925D411yescharacteristic
88#66923—21no—
89C4×Dic22—21no—
90C11×SD32—22no—
91C11×SD32—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#102—21no—
96C4×C8×C11C2311yescharacteristic
97#66899—21no—
98#66899—21no—
99#66899—21no—
100#66899—21no—
101#66896—21no—
102#66893—22no—
103#66893—22no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108#66880—21no—
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66874—21no—
114#66871—21no—
115#66867D411yescharacteristic
116#33680—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×D4×C11—21no—
120C22×C4×C11—41no—
121C2×C22⋊D11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124#4341—24no—
125#4341—42no—
126C2×C4×D11—41no—
127C2×C4×D11C2×D411yescharacteristic
128C2×Dic22—21no—
129C11×Q16—21no—
130C11×Q16—21no—
131C11×Q16—21no—
132C11×Q16—21no—
133C11×Q16—42no—
134C11×D8—21no—
135C11×D8#4112yes—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C11×C4⋊C4—21no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11C2×D411yescharacteristic
143C22⋊Dic11—41no—
144#4324—24no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4D811yescharacteristic
148(C2×D11)⋊C4D811yescharacteristic
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4D811yescharacteristic
162Dic11⋊C4D811yescharacteristic
163C4×Dic11—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C4×Dic11C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170Dic44—21no—
171Dic44#4112yes—
172#4313—41no—
173C8×D11—21no—
174C8×D11—21no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3177—111no—
180#2951—111no—
181#2236—111no—
182#2235—111no—
183#2229—111no—
184#2228—111no—
185#2209—111no—
186#2208D1111yescharacteristic, complemented
187#2189—111no—
188#2189—111no—
189#2176—111no—
190#2175—111no—
191C4×Q32—111no—
192C4×SD32—111no—
193#2164—111no—
194C23×C11—41no—
195C22×D11C2×D811yescharacteristic
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—41no—
199Q8×C11—41no—
200D4×C11—22no—
201D4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—161no—
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C22⋊D11—44no—
210C2×Dic11—44no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—161no—
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218C2×Dic11C2×D811yescharacteristic
219C4×D11—21no—
220C4×D11—21no—
221C4×D11—161no—
222Dic22—22no—
223Dic22—41no—
224C8×C11—21no—
225C8×C11C2×#4111yescharacteristic
226C8×C11C2×#4111yescharacteristic
227C11⋊C8—21no—
228C11⋊C8—21no—
229C2×#135—111no—
230#541—221no—
231#520—221no—
232C2×Q32—111no—
233C2×Q32—111no—
234C2×SD32C2×D1111yescharacteristic
235C2×SD32C2×D1111yescharacteristic
236#499—111no—
237#494C2×D1111yescharacteristic
238#491—221no—
239#470—221no—
240#467—111no—
241#467—111no—
242#441—221no—
243#440—221no—
244#440—221no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×D8—111no—
250C4×D8C2×D1111yescharacteristic
251C2×#107—111no—
252#417—221no—
253#405—111no—
254#367—111no—
255#367—111no—
256#366—111no—
257#366—111no—
258C4⋊C16—111no—
259C4⋊C16C2×D1111yescharacteristic
260#358—111no—
261#358—111no—
262#358—111no—
263#358—111no—
264#358C2×D1111yescharacteristic
265#358C2×D1111yescharacteristic
266#357—111no—
267#357—111no—
268C22⋊C16—111no—
269C22⋊C16—111no—
270#346—111no—
271C4×C16—111no—
272C22×C11—42no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11C22×D811yescharacteristic
276C2×D11—21no—
277C2×D11—21no—
278C2×D11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11#52511yescharacteristic
285C4×C11#57511yescharacteristic
286Dic11—21no—
287Dic11—21no—
288Dic11—21no—
289Dic11—42no—
290Dic11—81no—
291Dic11—81no—
292Dic11—81no—
293C2×#41—221no—
294#135—222no—
295#135—222no—
296C2×Q16—21no—
297C2×Q16—111no—
298C2×Q16C22×D1111yescharacteristic
299C2×Q16C22×D1111yescharacteristic
300C2×SD16—221no—
301C2×D8C22×D1111yescharacteristic
302C2×M16—111no—
303C22×C8—111no—
304C4⋊Q8—21no—
305#126—441no—
306#126—441no—
307#125—221no—
308#125—441no—
309#125—441no—
310C22⋊Q8—221no—
311C22⋊Q8—221no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—21no—
317C4×D4—221no—
318C4×D4—441no—
319C4×D4—441no—
320#117—111no—
321#117—441no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—441no—
324Q32—222no—
325Q32—222no—
326SD32—22no—
327SD32—22no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16C22×D1111yescharacteristic
331C2×C16C22×D1111yescharacteristic
332#107—111no—
333#107—111no—
334#107—111no—
335#107—221no—
336#107C22×D1111yescharacteristic
337#106—221no—
338#103—221no—
339#103—221no—
340#103—221no—
341#103—221no—
342#103—221no—
343#103—221no—
344#102—21no—
345#102—221no—
346#97—111no—
347#97—111no—
348C4×C8—111no—
349C4×C8C22×D1111yescharacteristic
350C2×C11—82no—
351C2×C11#310011yescharacteristic
352C2×C11#341611yescharacteristic
353C2×C11#341711yescharacteristic
354D11—41no—
355#41—224no—
356#41—442no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—221no—
360C2×D4—21no—
361C2×D4—441no—
362C22×C4—41no—
363C22×C4—111no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367Q16—21no—
368Q16—21no—
369Q16—21no—
370Q16—21no—
371Q16—42no—
372Q16—112no—
373Q16—221no—
374SD16—224no—
375D8—21no—
376D8#434112yes—
377M16—441no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8D4×D1111yescharacteristic
383C2×C8C23×D1111yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—111no—
388C4⋊C4—111no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C22⋊C4—41no—
402C22⋊C4—111no—
403C22⋊C4—111no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C42—111no—
408C42—441no—
409C42—441no—
410C42—441no—
411C42—441no—
412C42D4×D1111yescharacteristic
413C16—21no—
414C16—21no—
415C16—221no—
416C16—221no—
417C11#3368011yescharacteristic, complemented, Sylow
418C23—41no—
419C23—111no—
420Q8—41no—
421Q8—41no—
422Q8—41no—
423Q8—41no—
424Q8—222no—
425Q8—441no—
426D4—22no—
427D4—41no—
428D4—444no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—111no—
433C2×C4—111no—
434C2×C4—111no—
435C2×C4—161no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—444no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—1761no—
444C2×C4—1761no—
445C2×C4D8×D1111yescharacteristic
446C2×C4D8×D1111yescharacteristic
447C2×C4C2×D4×D1111yescharacteristic
448C8—21no—
449C8—221no—
450C8—221no—
451C8C2×#434111yescharacteristic
452C8#41×D1111yescharacteristic
453C22—42no—
454C22—81no—
455C22—81no—
456C22—221no—
457C22—221no—
458C22—221no—
459C22C2×D8×D1111yescharacteristic
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—221no—
466C4—221no—
467C4—221no—
468C4—442no—
469C4—881no—
470C4—881no—
471C4—881no—
472C4#1062313711yescharacteristic
473C4#1062330411yescharacteristic
474C2—82no—
475C2—441no—
476C2#1307861511yescharacteristic
477C2#1308175811yescharacteristic
478C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2208C2
socleC22×C11C22×D8
prime radicalC2×#66965C22
hypercenter#2208D11
hypocenterC11#33680
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
1. #13079272C2semidirect
3. #13070817C2semidirect
4. #13070812C2semidirect
5. #13070781C2semidirect
6. #13070773C2semidirect
7. #13070663C2semidirect
10. #13070484C2semidirect
11. #13070481C2semidirect
12. #13070472C2semidirect
13. SD32×Dic11C2semidirect
14. #13070422C2semidirect
15. C11×#2208C2semidirect
186. #2208D11semidirect
417. C11#33680semidirect

Maximal subgroups

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

subgroupindex
#130792722
#130774862
#130708172
#130708122
#130707812
#130707732
#130706632
#130705532
#130704842
#130704812
#130704722
SD32×Dic112
#130704222
C11×#22082
#3368011