Finite Group Databasebeta

← #14655068

Subgroups — #14655068

Order 2816.

648 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10622699C211yesmaximal, characteristic, complemented
2#13076661C211yesmaximal, characteristic
3#13069590C211yesmaximal, characteristic, complemented
4C2×#10622178C211yesmaximal, characteristic, complemented
5C2×#10622102C211yesmaximal, characteristic, complemented
6#13066498C211yesmaximal, characteristic, complemented
7C2×C11×#489C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10C22×#4326—21no—
11C22×#4325—21no—
12C2×#66928C2211yescharacteristic
13C11×#489—22no—
14C11×#489—22no—
15C2×C11×#103—21no—
16C2×C11×#102—21no—
17C2×C11×#97C2211yescharacteristic
18#10622844—21no—
19#10622836—21no—
20#10622699—22no—
21#10622699—22no—
22#10622574—22no—
23#10622573—21no—
24#10622560—21no—
25#10622549C2211yescharacteristic
26C2×#66867C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622178—22no—
29#10622167—22no—
30#10622102—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×C22⋊D11—22no—
35C22×D44D411yescharacteristic
36C22×Dic22D411yescharacteristic
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D412yescomplemented
42C11×#124—21no—
43C11×#124—21no—
44C11×#124—21no—
45C11×#124—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11—22no—
52C2×#4326—24no—
53C2×#4326—44no—
54C2×#4325—24no—
55C2×#4325—44no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11D412yes—
60C22×C11⋊C8—21no—
61C22×C11⋊C8—21no—
62#66928—21no—
63#66928—21no—
64#66928—21no—
65#66928—21no—
66C11×#103—24no—
67C11×#102—24no—
68C11×#97—21no—
69C11×#97D412yescomplemented
70C11⋊#95—22no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73#66867—21no—
74#66867—21no—
75#66867—21no—
76#66867D412yescomplemented
77#10081—111nomaximal, Sylow
78C24×C11—21no—
79C23×D11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—21no—
83C2×Q8×C11—42no—
84C2×Q8×C11—42no—
85C2×Q8×C11—42no—
86C2×Q8×C11—41no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—42no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—82no—
96C2×C22⋊D11—82no—
97C2×C22⋊D11—82no—
98C22×Dic11—22no—
99C22×Dic11—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—42no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22—42no—
106C2×C8×C11—22no—
107C2×C8×C11—42no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C22⋊Dic11—82no—
121#4326—48no—
122#4325—48no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—82no—
128C4⋊Dic11—42no—
129C2×C11⋊C8—24no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×#497—111no—
135C2×#489D1111yescharacteristic, complemented
136#2819—111no—
137#1993—111no—
138C2×#329—111no—
139C2×#329—111no—
140#1295—111no—
141C23×C11—41no—
142C23×C11—42no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11#12011yescharacteristic
147C22×D11—41no—
148C22×D11—42no—
149C22×D11—42no—
150C22×D11—41no—
151C22×D11—41no—
152Q8×C11—42no—
153Q8×C11—42no—
154Q8×C11—42no—
155Q8×C11—81no—
156Q8×C11—82no—
157D4×C11—42no—
158D4×C11—81no—
159C2×C4×C11—22no—
160C2×C4×C11—21no—
161C2×C4×C11—22no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12711yescharacteristic
173C22⋊D11—88no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179D44—42no—
180D44—81no—
181Dic22—42no—
182Dic22—81no—
183C8×C11—42no—
184C11⋊C8—24no—
185C11⋊C8—42no—
186C22×Q16—221no—
187C22×SD16—221no—
188C2×C4⋊Q8C2×D1111yescharacteristic
189C2×#124—111no—
190C2×#124C2×D1111yescharacteristic
191#497—222no—
192#497—222no—
193#489—22no—
194#489—22no—
195C2×#103—21no—
196C2×#102—21no—
197C2×#97—111no—
198C2×#97—111no—
199C2×#97C2×D1111yescharacteristic
200#394—222no—
201#393—221no—
202#393—221no—
203#392—221no—
204#392—221no—
205#382—111no—
206#340—222no—
207#329—222no—
208#329—222no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11#39211yescharacteristic
215C22×C11#45312yes—
216C22×C11#45511yescharacteristic
217C22×C11#45512yes—
218C22×C11#45611yescharacteristic
219C2×D11—82no—
220C2×D11—82no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—82no—
231C4×C11—81no—
232Dic11—82no—
233Dic11—81no—
234C22×Q8—21no—
235C22×Q8—111no—
236C22×Q8C22⋊D1111yescharacteristic
237C22×D4—111no—
238C22×D4—222no—
239C22×D4C22⋊D1111yescharacteristic
240C2×Q16—224no—
241C2×Q16—444no—
242C2×SD16—224no—
243C2×SD16—444no—
244C22×C8—21no—
245C22×C8—221no—
246C22×C8—221no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C22⋊D1112yescomplemented
251#124—21no—
252#124—21no—
253#124—21no—
254#124—21no—
255#124—221no—
256#124—221no—
257#124—221no—
258#124—221no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—112no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—222no—
267C2×C22⋊C4—222no—
268C2×C42C22×D1111yescharacteristic
269#103—24no—
270#102—24no—
271#97—21no—
272#97—112no—
273#97—221no—
274#97—221no—
275#97—221no—
276#97C22⋊D1112yescomplemented
277#95—222no—
278#95—221no—
279#95—221no—
280C2×C11—161no—
281C2×C11#165912yes—
282C2×C11#166112yes—
283C2×C11#200211yescharacteristic
284C2×C11#200411yescharacteristic
285C2×C11#200711yescharacteristic
286D11—161no—
287C24—21no—
288C24—221no—
289C2×Q8—22no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—42no—
293C2×Q8—42no—
294C2×Q8—42no—
295C2×Q8—41no—
296C2×Q8—221no—
297C2×Q8—221no—
298C2×Q8—442no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—42no—
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—442no—
305C2×D4—882no—
306C2×D4—882no—
307C2×D4—882no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—222no—
311C22×C4—221no—
312C22×C4D4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315Q16—448no—
316SD16—448no—
317C2×C8—22no—
318C2×C8—42no—
319C2×C8—224no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—441no—
323C2×C8—441no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—442no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—882no—
338C22⋊C4—882no—
339C42D4×D1111yescharacteristic
340C42#434111yescharacteristic
341C42C2×C22⋊D1111yescharacteristic
342C42C2×C22⋊D1111yescharacteristic
343C11#1008111yescharacteristic, complemented, Sylow
344C23—42no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—42no—
349C23—442no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—442no—
354C23#6699011yescharacteristic
355Q8—42no—
356Q8—42no—
357Q8—42no—
358Q8—81no—
359Q8—82no—
360Q8—442no—
361Q8—881no—
362D4—42no—
363D4—81no—
364D4—442no—
365D4—881no—
366D4—888no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—442no—
380C2×C4#6699011yescharacteristic
381C2×C4#6699111yescharacteristic
382C2×C4#6699211yescharacteristic
383C2×C4#6699211yescharacteristic
384C2×C4#6699311yescharacteristic
385C2×C4#6700611yescharacteristic
386C8—42no—
387C8—224no—
388C8—442no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—82no—
393C22—82no—
394C22—881no—
395C22—881no—
396C22—881no—
397C22—882no—
398C22—882no—
399C22#1062267412yes—
400C22#1062281112yes—
401C22#1062281511yescharacteristic
402C22#1062281811yescharacteristic
403C22#1062283611yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—82no—
411C4—81no—
412C4—881no—
413C4—882no—
414C2—161no—
415C2—1761no—
416C2#1306792112yes—
417C2#1306793212yes—
418C2#1306962811yescharacteristic
419C2#1306964511yescharacteristic
420C2#1306966111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#489C2
socleC23×C11#120
prime radical#13076661C2
hypercenterC2×#489D11
hypocenterC11#10081
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10622699C2semidirect
3. #13069590C2semidirect
4. C2×#10622178C2semidirect
5. C2×#10622102C2semidirect
6. #13066498C2semidirect
7. C2×C11×#489C2semidirect
41. C11×C4⋊Q8D4semidirect
69. C11×#97D4semidirect
76. #66867D4semidirect
135. C2×#489D11semidirect
250. C4⋊Q8C22⋊D11semidirect
276. #97C22⋊D11semidirect
343. C11#10081semidirect

Maximal subgroups

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

subgroupindex
C2×#106226992
#130766612
#130695902
C2×#106221782
C2×#106221022
#130664982
C2×C11×#4892
#1008111