Finite Group Databasebeta

← #14910195

Subgroups — #14910195

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079271C211yesmaximal, characteristic, complemented
2#13079263C211yesmaximal, characteristic
3#13070781C211yesmaximal, characteristic, complemented
4#13070780C211yesmaximal, characteristic, complemented
5#13070775C211yesmaximal, characteristic, complemented
6#13070771C211yesmaximal, characteristic, complemented
7#13070728C211yesmaximal, characteristic, complemented
8#13070726C211yesmaximal, characteristic, complemented
9#13070711C211yesmaximal, characteristic, complemented
10#13070709C211yesmaximal, characteristic, complemented
11#13070659C211yesmaximal, characteristic, complemented
12#13070659C211yesmaximal, characteristic, complemented
13#13070653C211yesmaximal, characteristic, complemented
14#13070373C211yesmaximal, characteristic, complemented
15C11×#2207C211yesmaximal, characteristic, complemented
16#10623250—21no—
17#10623114—21no—
18C2×C11×SD32C2211yescharacteristic
19C2×C11×SD32C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22#10622801C2211yescharacteristic
23#10622794C2211yescharacteristic
24#10622772—21no—
25#10622770C2211yescharacteristic
26#10622770C2211yescharacteristic
27#10622765—21no—
28D8×Dic11C2211yescharacteristic
29D8×Dic11C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31C2×#66891C2211yescharacteristic
32#10622684—21no—
33#10622643—21no—
34C2×#66862C2211yescharacteristic
35C2×C16×D11C2211yescharacteristic
36#10622500C2211yescharacteristic
37#10622491C2211yescharacteristic
38#10622429—21no—
39#10622410—21no—
40C4×Dic44C2211yescharacteristic
41#10622302C2211yescharacteristic
42#10622296C2211yescharacteristic
43C11×C4⋊C16C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622141C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55Dic11⋊C16C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8—21no—
61C2×C11×D8C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C11×#127—21no—
64C4×Q8×C11—21no—
65#66999—21no—
66#66997—21no—
67C2×#4326—21no—
68#66992—41no—
69#66992—41no—
70#66991—21no—
71#66991—21no—
72#66988—41no—
73#66988—41no—
74D4×Dic11—21no—
75D4×Dic11—21no—
76C2×Dic44C2311yescharacteristic
77C2×#4313D411yescharacteristic
78C2×C8×D11C2311yescharacteristic
79#66951—41no—
80#66950—21no—
81#66943—21no—
82#66942—41no—
83#66929—41no—
84#66925D411yescharacteristic
85#66923—21no—
86#66923—41no—
87C4×Dic22—21no—
88C11×SD32—41no—
89C11×SD32—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#103—21no—
94C4×C8×C11C2311yescharacteristic
95#66899—21no—
96#66896—21no—
97#66896—21no—
98#66896—21no—
99#66896—21no—
100#66891—41no—
101#66891—41no—
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106#66880—21no—
107#66879D411yescharacteristic
108C8×Dic11C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111#66874—21no—
112#66872—21no—
113#66867D411yescharacteristic
114#66862—41no—
115C16×D11—41no—
116#33826—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C2×C4×D11C2×D411yescharacteristic
127C2×Dic22—21no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×D8—21no—
131C11×D8—21no—
132C11×D8—21no—
133C11×D8—21no—
134C11×D8—42no—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2411yescharacteristic
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C42×C11—41no—
140C42×C11C2×D411yescharacteristic
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145#4326—42no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4D811yescharacteristic
149(C2×D11)⋊C4D811yescharacteristic
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—41no—
154C4⋊Dic11—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4D811yescharacteristic
163Dic11⋊C4D811yescharacteristic
164C4×Dic11—41no—
165C4×Dic11C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168Dic44—21no—
169Dic44—21no—
170#4313—41no—
171C8×D11—21no—
172C8×D11—21no—
173C11×C16—21no—
174C11×C16—21no—
175C11⋊C16—21no—
176C11⋊C16—21no—
177#3177—111no—
178#3176—111no—
179#2229—111no—
180#2229—111no—
181#2228—111no—
182#2228—111no—
183#2220—111no—
184#2220—111no—
185#2217—111no—
186#2217—111no—
187#2208—111no—
188#2208—111no—
189#2207—111no—
190#2207D1111yescharacteristic, complemented
191#2151—111no—
192C23×C11—41no—
193C23×C11—41no—
194C22×D11C2×D811yescharacteristic
195Q8×C11—41no—
196Q8×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—161no—
202D4×C11—161no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C22⋊D11—161no—
209C22⋊D11—161no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—161no—
215C2×Dic11—161no—
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218C2×Dic11C2×D811yescharacteristic
219C4×D11—21no—
220C4×D11—21no—
221Dic22—41no—
222Dic22—41no—
223C8×C11—21no—
224C8×C11H(5,𝔽2)11yescharacteristic
225C8×C112−1+411yescharacteristic
226C11⋊C8—21no—
227C11⋊C8—21no—
228#541—221no—
229#540—221no—
230C2×SD32—111no—
231C2×SD32—111no—
232C2×SD32C2×D1111yescharacteristic
233C2×SD32C2×D1111yescharacteristic
234C2×M32—111no—
235C22×C16—111no—
236#499—111no—
237#499—111no—
238#494—111no—
239#493C2×D1111yescharacteristic
240#491—221no—
241#490—221no—
242#470—221no—
243#469—221no—
244#467—111no—
245#467—111no—
246#466—111no—
247#466—111no—
248#442—221no—
249#441—221no—
250C4×Q16—111no—
251C4×Q16C2×D1111yescharacteristic
252C4×D8—111no—
253C4×D8—111no—
254#405—111no—
255#367—111no—
256#367—111no—
257#366—111no—
258#366—111no—
259C4⋊C16—111no—
260C4⋊C16—111no—
261C4⋊C16—111no—
262C4⋊C16C2×D1111yescharacteristic
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357C2×D1111yescharacteristic
270#357C2×D1111yescharacteristic
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11C22×D811yescharacteristic
278C2×D11—21no—
279C2×D11—21no—
280C2×D11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#53711yescharacteristic
286C4×C11#57511yescharacteristic
287Dic11—21no—
288Dic11—21no—
289Dic11—21no—
290Dic11—81no—
291Dic11—81no—
292Dic11—81no—
293Dic11—81no—
294C2×Q16—111no—
295C2×Q16—221no—
296C2×Q16C22×D1111yescharacteristic
297C2×D8—21no—
298C2×D8C22×D1111yescharacteristic
299C2×D8C22×D1111yescharacteristic
300C2×M16—111no—
301C22×C8—111no—
302C4⋊Q8—221no—
303#127—21no—
304#126—441no—
305#126—441no—
306#125—221no—
307#125—221no—
308#125—441no—
309#125—441no—
310#123—441no—
311#123—441no—
312C22⋊Q8—221no—
313C22⋊Q8—221no—
314#121—221no—
315#121—221no—
316#121—441no—
317#121—441no—
318C4×Q8—21no—
319C4×Q8—221no—
320C4×D4—221no—
321C4×D4—221no—
322#117—111no—
323SD32—41no—
324SD32—41no—
325SD32—441no—
326SD32—441no—
327M32—441no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16—441no—
331C2×C16C22×D1111yescharacteristic
332C2×C16C22×D1111yescharacteristic
333#107—111no—
334#107—111no—
335#107—111no—
336#107C22×D1111yescharacteristic
337#106—221no—
338#106—221no—
339#103—21no—
340#103—221no—
341#103—221no—
342#103—221no—
343#102—221no—
344#102—221no—
345#102—221no—
346#102—221no—
347#97—111no—
348#97—111no—
349C4×C8—111no—
350C4×C8C22×D1111yescharacteristic
351C2×C11—161no—
352C2×C11—161no—
353C2×C11#324511yescharacteristic
354C2×C11#341611yescharacteristic
355C2×C11#341611yescharacteristic
356D11—41no—
357C2×Q8—21no—
358C2×Q8—221no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—441no—
364C2×D4—441no—
365C22×C4—111no—
366C22×C4—441no—
367C22×C4—441no—
368Q16—21no—
369Q16—21no—
370Q16—221no—
371Q16—221no—
372Q16—442no—
373D8—21no—
374D8—21no—
375D8—21no—
376D8—21no—
377D8—42no—
378M16—441no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8D4×D1111yescharacteristic
384C2×C8C23×D1111yescharacteristic
385C4⋊C4—21no—
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—111no—
402C22⋊C4—111no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C42—41no—
410C42—111no—
411C42—441no—
412C42D4×D1111yescharacteristic
413C16—21no—
414C16—21no—
415C16—221no—
416C16—221no—
417C11#3382611yescharacteristic, complemented, Sylow
418C23—41no—
419C23—41no—
420C23—111no—
421Q8—41no—
422Q8—41no—
423Q8—441no—
424Q8—441no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—161no—
430D4—161no—
431D4—1761no—
432D4—1761no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—111no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—1761no—
445C2×C4—1761no—
446C2×C4D8×D1111yescharacteristic
447C2×C4D8×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C8—21no—
450C8—221no—
451C8—221no—
452C8#6703711yescharacteristic
453C8#6704311yescharacteristic
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—221no—
461C22—221no—
462C22—221no—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—221no—
469C4—221no—
470C4—221no—
471C4—881no—
472C4—881no—
473C4—881no—
474C4—881no—
475C4#1062313911yescharacteristic
476C4#1062330411yescharacteristic
477C2—161no—
478C2—161no—
479C2—441no—
480C2#1307992411yescharacteristic
481C2#1308175811yescharacteristic
482C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
prime radical#13079263C2
hypercenter#2207D11
hypocenterC11#33826
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #13079271C2semidirect
3. #13070781C2semidirect
4. #13070780C2semidirect
5. #13070775C2semidirect
6. #13070771C2semidirect
7. #13070728C2semidirect
8. #13070726C2semidirect
9. #13070711C2semidirect
10. #13070709C2semidirect
11. #13070659C2semidirect
12. #13070659C2semidirect
13. #13070653C2semidirect
14. #13070373C2semidirect
15. C11×#2207C2semidirect
190. #2207D11semidirect
417. C11#33826semidirect

Maximal subgroups

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

subgroupindex
#130792712
#130792632
#130707812
#130707802
#130707752
#130707712
#130707282
#130707262
#130707112
#130707092
#130706592
#130706532
#130703732
C11×#22072
#3382611