Finite Group Databasebeta

← #14908914

Subgroups — #14908914

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#13079268C211yesmaximal, characteristic, complemented
2#13077490C211yesmaximal, characteristic
3#13070818C211yesmaximal, characteristic, complemented
4#13070783C211yesmaximal, characteristic, complemented
5#13070772C211yesmaximal, characteristic, complemented
6#13070665C211yesmaximal, characteristic, complemented
7#13070660C211yesmaximal, characteristic, complemented
8#13070558C211yesmaximal, characteristic
9#13070554C211yesmaximal, characteristic
10#13070486C211yesmaximal, characteristic, complemented
11#13070483C211yesmaximal, characteristic, complemented
12#13070472C211yesmaximal, characteristic, complemented
13#13070467C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2235C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17#10623156—21no—
18#10623035—21no—
19C11×#467C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22#10622794C2211yescharacteristic
23C2×#66893C2211yescharacteristic
24C2×#66892C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622714C2211yescharacteristic
27#10622665—21no—
28#10622579—21no—
29C2×Dic88C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31#10622502—21no—
32#10622502—21no—
33#10622491C2211yescharacteristic
34#10622486C2211yescharacteristic
35#10622486C2211yescharacteristic
36#10622486C2211yescharacteristic
37#10622485C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622410—21no—
40#10622402—21no—
41C11×#367C2211yescharacteristic
42C11×#367C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×C22⋊C16C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622140C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4339—21no—
60C2×C11×Q16C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C2×C11×C4⋊C4—21no—
64Q8×Dic11—21no—
65#66997—21no—
66C2×#4326—21no—
67C4×C22⋊D11—41no—
68C4×C22⋊D11—41no—
69#66979D411yescharacteristic
70#66977—21no—
71C2×#4318D411yescharacteristic
72C2×Dic44C2311yescharacteristic
73C2×Dic44C2311yescharacteristic
74#66957—22no—
75#66957—22no—
76C2×D88C2311yescharacteristic
77C2×#4314—21no—
78#66946—21no—
79#66946—21no—
80#66945—41no—
81C4⋊C4×D11—41no—
82#66943—21no—
83#66943—41no—
84#66942—41no—
85#66940—21no—
86#66940—21no—
87#66940—21no—
88#66932—41no—
89#66932—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107—21no—
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#103—21no—
97#66899—21no—
98#66893—22no—
99#66892—22no—
100#66882C2311yescharacteristic
101#66880—21no—
102#66879D411yescharacteristic
103#66879D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66874—21no—
110#66874—21no—
111#66873—21no—
112#66873—21no—
113#66872—21no—
114Dic88—22no—
115#66864—22no—
116#33680—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C2×C22⋊D11—41no—
121#4339—24no—
122#4339—42no—
123C2×D44—21no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C11×Q16—21no—
130C11×Q16—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2411yescharacteristic
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C22⋊C4—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11D811yescharacteristic
143C22⋊Dic11D811yescharacteristic
144#4326—42no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147C4⋊Dic11—21no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11D811yescharacteristic
151C4⋊Dic11D811yescharacteristic
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11C2×D411yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165#4318—41no—
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168Dic44—21no—
169Dic44—21no—
170Dic44—21no—
171Dic44#4112yes—
172D88—21no—
173D88#4112yes—
174#4314—24no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3177—111no—
180#2951—111no—
181#2236—111no—
182#2235D1111yescharacteristic, complemented
183#2229—111no—
184#2228—111no—
185#2209—111no—
186#2208—111no—
187#2189—111no—
188#2189—111no—
189#2176—111no—
190#2175—111no—
191C4×Q32—111no—
192C4×SD32—111no—
193#2164—111no—
194C23×C11C2×D811yescharacteristic
195C22×D11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—161no—
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C22⋊D11—44no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11C2×D811yescharacteristic
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215D44—22no—
216D44—41no—
217C4×D11—44no—
218C4×D11—161no—
219C4×D11—161no—
220Dic22—22no—
221Dic22—41no—
222Dic22—41no—
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×SD32—111no—
235C2×SD32—111no—
236#499—111no—
237#494—111no—
238#491—221no—
239#470—221no—
240#467—111no—
241#467C2×D1111yescharacteristic
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×D8—111no—
251C2×#107C2×D1111yescharacteristic
252#417—221no—
253#405—111no—
254#367C2×D1111yescharacteristic
255#367C2×D1111yescharacteristic
256#366—111no—
257#366—111no—
258C4⋊C16—111no—
259C4⋊C16—111no—
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⋊C16C2×D1111yescharacteristic
270#346—111no—
271C4×C16—111no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11C22×D811yescharacteristic
276C2×D11—42no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11#52511yescharacteristic
285C4×C11#57511yescharacteristic
286Dic11—21no—
287Dic11—21no—
288Dic11—21no—
289Dic11—21no—
290Dic11—42no—
291Dic11—81no—
292Dic11—81no—
293C2×#41—221no—
294#135—222no—
295#135—222no—
296C2×Q16—111no—
297C2×Q16—111no—
298C2×Q16—221no—
299C2×Q16C22×D1111yescharacteristic
300C2×SD16—221no—
301C2×D8—111no—
302C2×M16—111no—
303C22×C8C22×D1111yescharacteristic
304C4⋊Q8—221no—
305#126—441no—
306#126—441no—
307#125—221no—
308#125—441no—
309#125—441no—
310C22⋊Q8—21no—
311C22⋊Q8—221no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—221no—
317C4×D4—221no—
318C4×D4—441no—
319C4×D4—441no—
320#117—111no—
321#117—441no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—441no—
324Q32—222no—
325Q32—222no—
326SD32—222no—
327SD32—222no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16C22×D1111yescharacteristic
331C2×C16C22×D1111yescharacteristic
332#107—21no—
333#107—111no—
334#107C22×D1111yescharacteristic
335#107C22×D1111yescharacteristic
336#107C22×D1111yescharacteristic
337#106—221no—
338#103—21no—
339#103—221no—
340#103—221no—
341#103—221no—
342#103—221no—
343#103—221no—
344#102—221no—
345#102—221no—
346#97—111no—
347#97—111no—
348C4×C8—111no—
349C4×C8—111no—
350C2×C11—41no—
351C2×C11#310011yescharacteristic
352C2×C11#341611yescharacteristic
353C2×C11#341711yescharacteristic
354D11—82no—
355#41—224no—
356#41—442no—
357C2×Q8—21no—
358C2×Q8—221no—
359C2×Q8—221no—
360C2×D4—221no—
361C2×D4—441no—
362C22×C4—41no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4D4×D1111yescharacteristic
367Q16—21no—
368Q16—21no—
369Q16—112no—
370Q16—221no—
371Q16—221no—
372Q16—221no—
373Q16—442no—
374SD16—224no—
375D8—112no—
376D8—221no—
377M16—441no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—111no—
381C2×C8—111no—
382C2×C8D4×D1111yescharacteristic
383C2×C8C23×D1111yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—111no—
390C4⋊C4—111no—
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—111no—
409C42—441no—
410C42—441no—
411C42—441no—
412C42—441no—
413C16—21no—
414C16—21no—
415C16—221no—
416C16—221no—
417C11#3368011yescharacteristic, complemented, Sylow
418C23—441no—
419C23D8×D1111yescharacteristic
420Q8—41no—
421Q8—41no—
422Q8—222no—
423Q8—441no—
424Q8—441no—
425Q8—441no—
426D4—222no—
427D4—444no—
428D4—441no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—111no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—111no—
439C2×C4—161no—
440C2×C4—444no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—1761no—
445C2×C4—1761no—
446C2×C4D8×D1111yescharacteristic
447C2×C4C2×D4×D1111yescharacteristic
448C8—21no—
449C8—221no—
450C8—221no—
451C8#41×D1111yescharacteristic
452C8#41×D1111yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—442no—
457C22—881no—
458C22—881no—
459C22C2×D8×D1111yescharacteristic
460C4—21no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—221no—
466C4—221no—
467C4—221no—
468C4—221no—
469C4—442no—
470C4—881no—
471C4—881no—
472C4#1062318711yescharacteristic
473C4#1062330811yescharacteristic
474C2—41no—
475C2—882no—
476C2#1307861311yescharacteristic
477C2#1308175811yescharacteristic
478C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2235C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2235D11
hypocenterC11#33680
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
1. #13079268C2semidirect
3. #13070818C2semidirect
4. #13070783C2semidirect
5. #13070772C2semidirect
6. #13070665C2semidirect
7. #13070660C2semidirect
10. #13070486C2semidirect
11. #13070483C2semidirect
12. #13070472C2semidirect
13. #13070467C2semidirect
14. #13070420C2semidirect
15. C11×#2235C2semidirect
182. #2235D11semidirect
417. C11#33680semidirect

Maximal subgroups

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

subgroupindex
#130792682
#130774902
#130708182
#130707832
#130707722
#130706652
#130706602
#130705582
#130705542
#130704862
#130704832
#130704722
#130704672
#130704202
C11×#22352
#3368011