Finite Group Databasebeta

← #14669451

Subgroups — #14669451

Order 2816.

936 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#10623279C211yesmaximal, characteristic
2C2×#10622156C212yesmaximal, complemented
3#13070329C212yesmaximal, complemented
4#13068649C211yesmaximal, characteristic, complemented
5C2×C11×#349C211yesmaximal, characteristic, complemented
6C22×#4339—21no—
7C22×C11×M16C2211yescharacteristic
8#10623279—22no—
9#10623279—24no—
10#10623279C414yescomplemented
11C2×#66962—22no—
12C2×#66961—22no—
13C2×#66957—21no—
14C2×#66957C2212yes—
15C2×C11×M32C2212yescomplemented
16#10622825—21no—
17C2×#66882C2211yescharacteristic, complemented
18C2×#66881C2211yescharacteristic, complemented
19C11×#349—22no—
20#10622189—21no—
21#10622156—24no—
22#10622147—22no—
23#10622141—22no—
24C23×C4×C11D411yescharacteristic
25C22×C22⋊D11—41no—
26C2×#4339—22no—
27C2×#4339—24no—
28C2×#4339—24no—
29C2×#4339—22no—
30C2×#4339—42no—
31C2×#4339—41no—
32C2×#4339—41no—
33C2×#4339—42no—
34C22×D44—21no—
35C22×C4×D11—41no—
36C22×Dic22—21no—
37C2×C11×M16—22no—
38C2×C11×M16—22no—
39C2×C11×M16C2×C412yes—
40C2×C11×M16D412yes—
41C22×C8×C11D411yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C2×C22⋊Dic11—41no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46#66962—28no—
47#66962—28no—
48#66961—28no—
49#66961—28no—
50C2×Dic44—21no—
51C2×Dic44D412yes—
52#66957—24no—
53#66957—24no—
54#66957—22no—
55#66957—22no—
56#66957C2×C414yes—
57#66957D414yes—
58C2×D88—21no—
59C2×D88D412yes—
60C2×#4314—22no—
61C2×#4314—22no—
62C11×M32—22no—
63C11×M32—22no—
64C2×C11×C16—22no—
65C11⋊#95—41no—
66#66882—22no—
67#66881—22no—
68#12739—111nomaximal, Sylow
69C24×C11D811yescharacteristic
70C23×D11—41no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11C22⋊C412yes—
76C22×C4×C11D811yescharacteristic
77C22×C4×C11SD1612yes—
78C22×C4×C11C2×D411yescharacteristic
79C2×C22⋊D11—44no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—44no—
82C2×C22⋊D11—42no—
83C22×Dic11—41no—
84C22×Dic11—41no—
85C22×Dic11—41no—
86#4339—28no—
87#4339—24no—
88#4339—24no—
89#4339—44no—
90#4339—44no—
91#4339—44no—
92#4339—44no—
93#4339—44no—
94#4339—42no—
95#4339—42no—
96C2×D44—24no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44—42no—
100C2×C4×D11—42no—
101C2×C4×D11—44no—
102C2×C4×D11—44no—
103C2×C4×D11—42no—
104C2×Dic22—24no—
105C2×Dic22—22no—
106C2×Dic22—41no—
107C2×Dic22—42no—
108C11×M16—24no—
109C11×M16—24no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11C22⋊C412yes—
113C2×C8×C11C22×C411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D412yes—
116C2×C8×C11C2×D412yes—
117C22⋊Dic11—82no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122Dic44—24no—
123Dic44—22no—
124Dic44C22⋊C414yescomplemented
125D88—24no—
126D88—22no—
127D88C22⋊C414yescomplemented
128#4314—28no—
129#4314—24no—
130#4314—24no—
131C11×C16—42no—
132C2×#575—111no—
133C2×#360—112no—
134#2139—112no—
135C2×#349D1111yescharacteristic, complemented
136#1809—111no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11#10212yes—
142C23×C11C2×D811yescharacteristic
143C22×D11—44no—
144C22×D11—42no—
145C22×D11—82no—
146C22×D11—82no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11#10212yes—
154C2×C4×C11C2×C22⋊C411yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11C2×SD1611yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C22⋊D11—48no—
161C22⋊D11—44no—
162C22⋊D11—44no—
163C2×Dic11—44no—
164C2×Dic11—42no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171D44—24no—
172D44—44no—
173D44—42no—
174C4×D11—48no—
175C4×D11—44no—
176C4×D11—44no—
177Dic22—24no—
178Dic22—44no—
179Dic22—42no—
180C8×C11—22no—
181C8×C11C2×C22⋊C412yes—
182C8×C11#12012yes—
183C22×#41—221no—
184#575—114no—
185#575—224no—
186#575—222no—
187C2×#137—222no—
188C2×AGL(1,ℤ/8)—222no—
189C2×#135—112no—
190C2×#135—221no—
191C22×M16C2×D1111yescharacteristic
192C2×M32C2×D1112yescomplemented
193C2×#107—111no—
194C2×#106—111no—
195#380—221no—
196#360—224no—
197#358—222no—
198#357—222no—
199#349—22no—
200#340—221no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—22no—
204C22×C11—42no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—81no—
208C22×C11C2×#10211yescharacteristic
209C22×C11#44711yescharacteristic
210C22×C11#44711yescharacteristic
211C2×D11—44no—
212C2×D11—88no—
213C2×D11—82no—
214C2×D11—82no—
215C4×C11—22no—
216C4×C11#37911yescharacteristic
217C4×C11#41811yescharacteristic
218C4×C11#45011yescharacteristic
219C4×C11#45011yescharacteristic
220Dic11—44no—
221Dic11—161no—
222Dic11—161no—
223C2×#41—222no—
224C2×#41—224no—
225C2×#41—224no—
226C2×#41—222no—
227C2×#41—441no—
228C2×#41—442no—
229C2×#41—442no—
230C2×#41—441no—
231C22×Q8—221no—
232C22×D4—221no—
233C22×D4—441no—
234C23×C4—441no—
235C23×C4D4411yescharacteristic
236#137—228no—
237#137—228no—
238AGL(1,ℤ/8)—228no—
239AGL(1,ℤ/8)—228no—
240#135—114no—
241#135—114no—
242#135—224no—
243#135—224no—
244#135—222no—
245#135—222no—
246C2×Q16—112no—
247C2×Q16—221no—
248C2×SD16—222no—
249C2×SD16—222no—
250C2×D8—112no—
251C2×D8—221no—
252C2×M16—22no—
253C2×M16—22no—
254C2×M16C4×D1112yes—
255C2×M16C22⋊D1112yes—
256C22×C8D4411yescharacteristic
257C22×C8C22×D1111yescharacteristic
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C22⋊C4—441no—
261M32—22no—
262M32—22no—
263C2×C16—22no—
264#107—222no—
265#106—222no—
266#95—441no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—42no—
270C2×C11#178611yescharacteristic
271C2×C11#219011yescharacteristic
272C2×C11#219111yescharacteristic
273D11—84no—
274C24—441no—
275C24D8811yescharacteristic
276#41—228no—
277#41—224no—
278#41—224no—
279#41—444no—
280#41—444no—
281#41—444no—
282#41—444no—
283#41—444no—
284#41—442no—
285#41—442no—
286C2×Q8—224no—
287C2×Q8—222no—
288C2×Q8—441no—
289C2×Q8—442no—
290C2×D4—224no—
291C2×D4—222no—
292C2×D4—441no—
293C2×D4—442no—
294C2×D4—444no—
295C2×D4—442no—
296C2×D4—444no—
297C2×D4—442no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—442no—
303C22×C4—444no—
304C22×C4—444no—
305C22×C4—441no—
306C22×C4—442no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4#431412yes—
310C22×C4D8811yescharacteristic
311C22×C4(C2×D11)⋊C412yes—
312C22×C4C2×D4411yescharacteristic
313Q16—114no—
314Q16—224no—
315Q16—222no—
316SD16—228no—
317SD16—224no—
318SD16—224no—
319D8—114no—
320D8—224no—
321D8—222no—
322M16—24no—
323M16—24no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8(C2×D11)⋊C412yes—
327C2×C8C2×C4×D1111yescharacteristic
328C2×C8D4×D1112yes—
329C2×C8D4×D1112yes—
330C2×C8C2×C22⋊D1111yescharacteristic
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—882no—
336C16—42no—
337C11#1273911yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—444no—
343C23—442no—
344C23—882no—
345C23—882no—
346C23#6688512yes—
347C23C2×D8811yescharacteristic
348Q8—224no—
349Q8—444no—
350Q8—442no—
351D4—224no—
352D4—444no—
353D4—448no—
354D4—444no—
355D4—444no—
356D4—442no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—448no—
364C2×C4—444no—
365C2×C4—442no—
366C2×C4—444no—
367C2×C4—444no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4—881no—
374C2×C4#6688512yes—
375C2×C4#6693511yescharacteristic
376C2×C4#6693511yescharacteristic
377C2×C4C2×#431411yescharacteristic
378C2×C4#6696111yescharacteristic
379C2×C4#6696111yescharacteristic
380C2×C4C2×(C2×D11)⋊C411yescharacteristic
381C8—22no—
382C8C22⋊C4×D1112yes—
383C8#6699012yes—
384C22—21no—
385C22—21no—
386C22—22no—
387C22—42no—
388C22—41no—
389C22—41no—
390C22—81no—
391C22—444no—
392C22—888no—
393C22—882no—
394C22—882no—
395C22#1062234511yescharacteristic
396C22#1062234511yescharacteristic
397C22C2×#6688511yescharacteristic
398C4—22no—
399C4—444no—
400C4—1761no—
401C4—1761no—
402C4#1062234411yescharacteristic
403C4#1062234411yescharacteristic
404C4#1062256811yescharacteristic
405C4#1062274411yescharacteristic
406C2—21no—
407C2—21no—
408C2—42no—
409C2—884no—
410C2#1306854811yescharacteristic
411C2#1307056411yescharacteristic
412C2#1307056911yescharacteristic
subgroupG/H
centerC22#10622345
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#349C2
socleC22×C11#447
prime radicalC2×#10623279C2
cosocleC22×C8×C11C23
hypercenterC2×#349D11
hypocenterC11#12739
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. C2×#10622156C2semidirect
3. #13070329C2semidirect
4. #13068649C2semidirect
5. C2×C11×#349C2semidirect
10. #10623279C4semidirect
15. C2×C11×M32C22semidirect
17. C2×#66882C22semidirect
18. C2×#66881C22semidirect
124. Dic44C22⋊C4semidirect
127. D88C22⋊C4semidirect
135. C2×#349D11semidirect
192. C2×M32C2×D11semidirect
337. C11#12739semidirect

Maximal subgroups

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

subgroupindex
C2×#106232792
C2×#106221562
#130703292
#130686492
C2×C11×#3492
#1273911