Finite Group Databasebeta

← #14648977

Subgroups — #14648977

Order 2816.

436 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078696C211yesmaximal, characteristic
2#13077757C211yesmaximal, characteristic
3#13069557C211yesmaximal, characteristic, complemented
4#13067205C211yesmaximal, characteristic
5#13066514C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#1491C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9#10623010C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12#10622841C411yescharacteristic
13#10622840C411yescharacteristic
14C4×#4326—21no—
15#10622641—21no—
16C4×#4325—21no—
17#10622635—21no—
18#10622584C411yescharacteristic
19#10622580C411yescharacteristic
20#10622538C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23#10622453—21no—
24#10622452—21no—
25#10622343—21no—
26(C22⋊D11)⋊C8—21no—
27#10622319—21no—
28#10622314—21no—
29C11×Q8⋊C8—21no—
30C11×Q8⋊C8—21no—
31#10622162—21no—
32#10622162—21no—
33#10622103—21no—
34#10622102—21no—
35C22×Q8×C11C2×C411yescharacteristic
36C2×C11×M16—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4326—21no—
46C2×#4325—21no—
47#66983C2×C411yescharacteristic
48#66982—21no—
49C4×C22⋊D11—21no—
50#66977C2×C411yescharacteristic
51C22×C11⋊C8—21no—
52C22×C11⋊C8D411yescharacteristic
53C22×C11⋊C8D411yescharacteristic
54C2×#4313—21no—
55C2×C8×D11—21no—
56#66929—21no—
57#66928D411yescharacteristic
58C4×D44D411yescharacteristic
59#66925—21no—
60#66923D411yescharacteristic
61C4×Dic22D411yescharacteristic
62C11×C4⋊C8D411yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C11×#97—21no—
67C4×C8×C11—21no—
68#66899—21no—
69#66899—21no—
70C22⋊(C11⋊C8)C2×C411yescharacteristic
71C22⋊(C11⋊C8)C2×C411yescharacteristic
72(C2×D11)⋊C8—21no—
73(C2×D11)⋊C8—21no—
74#66879—21no—
75Dic11⋊C8—21no—
76Dic11⋊C8—21no—
77C8×Dic11—21no—
78#66874—21no—
79#66873—21no—
80#66872—21no—
81#66871—21no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)—21no—
84C4⋊(C11⋊C8)—21no—
85#66867—21no—
86#66867—21no—
87C4×C11⋊C8—21no—
88#9051—111nomaximal, Sylow
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—42no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×C22⋊D11—21no—
98C2×D44C22⋊C411yescharacteristic
99C2×C4×D11—21no—
100C2×Dic22C22⋊C411yescharacteristic
101C11×M16—22no—
102C11×M16—41no—
103C2×C8×C11—21no—
104C2×C8×C11—21no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C22⋊Dic11—21no—
117#4326—42no—
118#4325—42no—
119(C2×D11)⋊C4—21no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122(C2×D11)⋊C4—21no—
123C4⋊Dic11C22⋊C411yescharacteristic
124C4⋊Dic11C22⋊C411yescharacteristic
125Dic11⋊C4—21no—
126Dic11⋊C4—21no—
127Dic11⋊C4—21no—
128Dic11⋊C4—21no—
129C4×Dic11—21no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139#4313—81no—
140C8×D11—81no—
141#3108—111no—
142#2992—111no—
143#1985—111no—
144#1524—111no—
145#1491D1111yescharacteristic, complemented
146#1302—111no—
147#1283—111no—
148C23×C11C4×D411yescharacteristic
149C22×D11—21no—
150Q8×C11—22no—
151Q8×C11—22no—
152Q8×C11—41no—
153Q8×C11—41no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11C2×C22⋊C411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C22⋊D11—41no—
172C22⋊D11—41no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176D44—41no—
177C4×D11—41no—
178C4×D11—41no—
179Dic22—41no—
180C8×C11—42no—
181C8×C11—41no—
182C8×C11—41no—
183C11⋊C8—42no—
184C11⋊C8—41no—
185C11⋊C8—41no—
186C11⋊C8—41no—
187C11⋊C8—41no—
188#529—111no—
189C2×C4×Q8C2×D1111yescharacteristic
190#483—111no—
191#480—111no—
192#479—221no—
193#464—221no—
194#451—111no—
195#448—111no—
196#446—221no—
197C4×Q16—221no—
198C4×SD16—221no—
199#435—221no—
200#435—221no—
201C8×D4—221no—
202#433—221no—
203#432C2×D1111yescharacteristic
204#431—111no—
205#424—221no—
206C2×C4⋊C8—111no—
207C4×M16C2×D1111yescharacteristic
208C2×#97—111no—
209#336—221no—
210#336—221no—
211#330—221no—
212#329—221no—
213Q8⋊C8—21no—
214Q8⋊C8—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11#38611yescharacteristic
218C22×C11#44311yescharacteristic
219C22×C11#44411yescharacteristic
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—41no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—42no—
229C4×C11—81no—
230C4×C11#45511yescharacteristic
231C4×C11#45611yescharacteristic
232Dic11—41no—
233Dic11—41no—
234Dic11—41no—
235C22×Q8C4×D1111yescharacteristic
236C2×Q16—221no—
237C2×SD16—221no—
238C2×M16—21no—
239C2×M16—221no—
240C22×C8—111no—
241C22×C8—111no—
242C22×C8—221no—
243C22×C8—221no—
244#126—221no—
245#125—111no—
246#124—111no—
247#123—221no—
248C22⋊Q8—111no—
249#121—111no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—111no—
255C4×D4—111no—
256C4×D4—221no—
257#117—221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4C4×D1111yescharacteristic
260C2×C42—21no—
261C2×C42C22×D1111yescharacteristic
262#107—221no—
263#106—221no—
264C4⋊C8—221no—
265C4⋊C8—221no—
266C4⋊C8—221no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8C22⋊D1111yescharacteristic
270C4⋊C8C22⋊D1111yescharacteristic
271#103—221no—
272#103—221no—
273#103—221no—
274#102—221no—
275C22⋊C8—21no—
276C22⋊C8—111no—
277C22⋊C8—111no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280#97—21no—
281#97—21no—
282#97—221no—
283#97—221no—
284#97—221no—
285C4×C8—21no—
286C4×C8—221no—
287C4×C8—221no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11#187611yescharacteristic
291C2×C11#188211yescharacteristic
292C2×C11#189111yescharacteristic
293D11—81no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—42no—
297C2×Q8—111no—
298C2×D4—111no—
299C2×D4—221no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—221no—
303C22×C4C2×C4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4#434111yescharacteristic
306Q16—442no—
307SD16—442no—
308M16—22no—
309M16—41no—
310M16—881no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8—222no—
315C2×C8—221no—
316C2×C8—221no—
317C2×C8—221no—
318C2×C8—221no—
319C2×C8—441no—
320C2×C8—441no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8—881no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—111no—
329C4⋊C4—111no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C22⋊C4—221no—
335C22⋊C4—221no—
336C22⋊C4—221no—
337C22⋊C4—221no—
338C22⋊C4—221no—
339C42—41no—
340C42—41no—
341C42—221no—
342C42#433911yescharacteristic
343C42D4×D1111yescharacteristic
344C42D4×D1111yescharacteristic
345C42C2×C22⋊D1111yescharacteristic
346C11#905111yescharacteristic, complemented, Sylow
347C23—221no—
348C23(C22⋊D11)⋊C411yescharacteristic
349Q8—22no—
350Q8—22no—
351Q8—41no—
352Q8—41no—
353Q8—441no—
354D4—441no—
355D4—441no—
356D4—441no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4C22⋊C4×D1111yescharacteristic
374C2×C4#6693611yescharacteristic
375C2×C4#6693711yescharacteristic
376C2×C4C4×C22⋊D1111yescharacteristic
377C2×C4#6699011yescharacteristic
378C2×C4#6699111yescharacteristic
379C8—42no—
380C8—41no—
381C8—41no—
382C8—442no—
383C8—441no—
384C8—441no—
385C8—441no—
386C8—441no—
387C22—21no—
388C22—21no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22#1062243611yescharacteristic
393C22#1062243711yescharacteristic
394C22#1062256911yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—81no—
402C4—441no—
403C4—441no—
404C4—441no—
405C4#1062281511yescharacteristic
406C4#1062281811yescharacteristic
407C2—21no—
408C2—21no—
409C2—881no—
410C2#1306894011yescharacteristic
411C2#1306898211yescharacteristic
412C2#1306903111yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1491C2
socleC22×C11#386
prime radical#66983C2×C4
cosocleC2×C42×C11C23
hypercenter#1491D11
hypocenterC11#9051
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
3. #13069557C2semidirect
5. #13066514C2semidirect
6. #13066467C2semidirect
7. C11×#1491C2semidirect
145. #1491D11semidirect
346. C11#9051semidirect

Maximal subgroups

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

subgroupindex
#130786962
#130777572
#130695572
#130672052
#130665142
#130664672
C11×#14912
#905111