Finite Group Databasebeta

← #14657257

Subgroups — #14657257

Order 2816.

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

normal subgroups only

This group has 460 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#13069586C211yesmaximal, characteristic, complemented
2#13069433C211yesmaximal, characteristic
3#13068785C211yesmaximal, characteristic, complemented
4C2×#10622181C211yesmaximal, characteristic, complemented
5C2×#10622178C211yesmaximal, characteristic
6#13066497C211yesmaximal, characteristic, complemented
7C11×#2820C211yesmaximal, characteristic
8C2×C11×#125C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10C11×#399—21no—
11C11×#397—21no—
12C11×#396—21no—
13C11×#396—21no—
14C11×#395—21no—
15C11×#394—21no—
16C11×#382C2211yescharacteristic
17C2×#66899—21no—
18C2×#66896—21no—
19C2×#66872—21no—
20C2×#66871—21no—
21#10622548C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23C2×#66867C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25#10622181—22no—
26#10622178—22no—
27#10622167—21no—
28#10622167—21no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C11×#125—21no—
32C11×#125—21no—
33C11×#125—21no—
34C11×#125—21no—
35C11×#124—21no—
36C11×#124—21no—
37C11×#124—21no—
38C11×#124—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64#66899—42no—
65#66896—42no—
66#66872—42no—
67#66871—42no—
68#66867—21no—
69#66867—21no—
70#66867—21no—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74#10427—111nomaximal, Sylow
75C24×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×Dic11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—81no—
104C11×C4⋊C4—81no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—81no—
110C11×C22⋊C4—81no—
111C11×C22⋊C4—81no—
112C11×C22⋊C4—81no—
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11#4111yescharacteristic
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—42no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#2820D1111yescharacteristic
132#1992—111no—
133#1959—111no—
134#1847—111no—
135C2×#330—111no—
136C2×#329—111no—
137#1295—111no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11#12011yescharacteristic
146Q8×C11—42no—
147Q8×C11—81no—
148D4×C11—42no—
149D4×C11—81no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
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×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12311yescharacteristic
175C2×C4×C11#12311yescharacteristic
176C2×C4×C11#12411yescharacteristic
177C2×Dic11—81no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180C11⋊C8—24no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C2×#125C2×D1111yescharacteristic
184C2×#124C2×D1111yescharacteristic
185C2×#107—221no—
186C2×#106—221no—
187C2×#103—221no—
188C2×#102—221no—
189C2×#97—111no—
190C2×#97—111no—
191C2×#97—111no—
192#399—21no—
193#397—21no—
194#396—21no—
195#396—21no—
196#395—21no—
197#394—21no—
198#384—111no—
199#382C2×D1111yescharacteristic
200#340—221no—
201#340—221no—
202#330—222no—
203#329—222no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11#39411yescharacteristic
212C22×C11#45311yescharacteristic
213C22×C11#45311yescharacteristic
214C22×C11#45411yescharacteristic
215C22×C11#45511yescharacteristic
216C22×C11#45611yescharacteristic
217C22×C11#45611yescharacteristic
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11—81no—
229Dic11—161no—
230C22×Q8C22⋊D1111yescharacteristic
231C22×D4C22⋊D1111yescharacteristic
232C22×C8—221no—
233C22×C8—221no—
234C22×C8—221no—
235#125—21no—
236#125—21no—
237#125—21no—
238#125—21no—
239#124—21no—
240#124—21no—
241#124—21no—
242#124—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4C22⋊D1111yescharacteristic
251C2×C4⋊C4C22⋊D1111yescharacteristic
252C2×C4⋊C4C22⋊D1111yescharacteristic
253C2×C4⋊C4C22⋊D1111yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C42C22×D1111yescharacteristic
261#107—442no—
262#106—442no—
263#103—442no—
264#102—442no—
265#97—112no—
266#97—221no—
267#97—221no—
268#97—221no—
269#97—221no—
270#97—221no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275C2×C11—161no—
276C2×C11#165611yescharacteristic
277C2×C11#166011yescharacteristic
278C2×C11#166111yescharacteristic
279C2×C11#166411yescharacteristic
280C2×C11#203711yescharacteristic
281C2×C11#203811yescharacteristic
282C2×C11#203911yescharacteristic
283C24—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—441no—
298C22×C4C2×C22⋊D1111yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301C2×C8—222no—
302C2×C8—222no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8—441no—
307C2×C8—441no—
308C2×C8—441no—
309C2×C8—441no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C4⋊C4—81no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4—442no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C42D4×D1111yescharacteristic
336C42#434111yescharacteristic
337C42#434111yescharacteristic
338C42#434111yescharacteristic
339C11#1042711yescharacteristic, complemented, Sylow
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#6700611yescharacteristic
348Q8—42no—
349Q8—81no—
350D4—42no—
351D4—81no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4—881no—
376C2×C4#6698811yescharacteristic
377C2×C4#6698811yescharacteristic
378C2×C4#6698911yescharacteristic
379C2×C4#6699111yescharacteristic
380C2×C4#6699211yescharacteristic
381C2×C4#6699211yescharacteristic
382C8—224no—
383C8—442no—
384C8—442no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22#1062283511yescharacteristic
393C22#1062285411yescharacteristic
394C22#1062285411yescharacteristic
395C22#1062285511yescharacteristic
396C22#1062285811yescharacteristic
397C22#1062285911yescharacteristic
398C22#1062285911yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—1761no—
411C2—161no—
412C2#1306790911yescharacteristic
413C2#1306792711yescharacteristic
414C2#1306793311yescharacteristic
415C2#1306795011yescharacteristic
416C2#1306982311yescharacteristic
417C2#1306983011yescharacteristic
418C2#1306983711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2820C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2820D11
hypocenterC11#10427
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2820

Complements

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

NH ≅ G/Ntype
1. #13069586C2semidirect
3. #13068785C2semidirect
4. C2×#10622181C2semidirect
6. #13066497C2semidirect
339. C11#10427semidirect

Maximal subgroups

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

subgroupindex
#130695862
#130694332
#130687852
C2×#106221812
C2×#106221782
#130664972
C11×#28202
#1042711