Finite Group Databasebeta

← #14672549

Subgroups — #14672549

Order 2816.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10622792C211yesmaximal, characteristic, complemented
2#13078225C211yesmaximal, characteristic
3C2×#10622126C211yesmaximal, characteristic, complemented
4#13070336C211yesmaximal, characteristic, complemented
5C2×#10622191C211yesmaximal, characteristic, complemented
6#13066723C211yesmaximal, characteristic, complemented
7C2×C11×#470C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×C22⋊Q8—21no—
11#10623322—21no—
12C2×#66957C2211yescharacteristic
13C11×#470—22no—
14C11×#470—22no—
15C2×C11×#106C2211yescharacteristic
16C2×C11×#103—21no—
17C2×#66893—21no—
18#10622792—22no—
19#10622792—22no—
20C2×#66892—21no—
21#10622750—21no—
22#10622748—21no—
23#10622747—22no—
24#10622726—21no—
25#10622719C2211yescharacteristic
26C2×#66876C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28#10622202—22no—
29#10622191—22no—
30#10622126—22no—
31C22×Q8×C11—21no—
32C23×C4×C11D411yescharacteristic
33C2×#4339—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16D412yescomplemented
40C2×C11×M16—21no—
41C2×C11×M16—21no—
42C2×C11×M16—21no—
43C2×C11×M16—21no—
44C2×C11×M16—21no—
45C2×C11×M16—21no—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—42no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—41no—
52C2×C11×C22⋊C4—41no—
53#67006—41no—
54#66983—22no—
55#66982—41no—
56C4×C22⋊D11—42no—
57#66979—21no—
58#66977—22no—
59C2×Dic44D411yescharacteristic
60#66957—21no—
61#66957—21no—
62#66957—21no—
63#66957—21no—
64C2×D88D411yescharacteristic
65C2×#4314—21no—
66C11×#106—21no—
67C11×#106D412yescomplemented
68C11×#103—24no—
69#66893—24no—
70#66892—24no—
71#66885—22no—
72#66882D412yes—
73#66881—21no—
74#66880—22no—
75#66876—21no—
76#66876—21no—
77#66876—21no—
78#66876D412yescomplemented
79C2×C11⋊C16—21no—
80C2×C11⋊C16—21no—
81#13317—111nomaximal, Sylow
82C24×C11D811yescharacteristic
83C2×Q8×C11—22no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11D811yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—42no—
100C2×C22⋊D11—41no—
101#4339—41no—
102#4339—41no—
103#4339—41no—
104#4339—41no—
105C2×D44—21no—
106C2×C4×D11—41no—
107C2×Dic22—21no—
108C11×Q16—22no—
109C11×Q16—22no—
110C11×Q16—41no—
111C11×Q16—41no—
112C11×M16—41no—
113C11×M16—41no—
114C11×M16—41no—
115C11×M16—41no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11#4111yescharacteristic
125C11×C4⋊C4—22no—
126C11×C4⋊C4—44no—
127C11×C4⋊C4—41no—
128C11×C22⋊C4—44no—
129C22⋊Dic11—42no—
130C22⋊Dic11—41no—
131(C2×D11)⋊C4—42no—
132C4⋊Dic11—22no—
133Dic11⋊C4—42no—
134C4×Dic11—41no—
135Dic44—21no—
136Dic44—21no—
137D88—21no—
138D88—21no—
139#4314—41no—
140#4314—41no—
141C11⋊C16—22no—
142C11⋊C16—41no—
143C2×#510—111no—
144#3054—111no—
145C2×#470D1111yescharacteristic, complemented
146C2×#360—111no—
147#2141—111no—
148C2×#349—111no—
149#1386—111no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—42no—
154C23×C11C2×D811yescharacteristic
155C22×D11—41no—
156Q8×C11—42no—
157Q8×C11—42no—
158Q8×C11—81no—
159Q8×C11—81no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—82no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C22⋊D11—84no—
179C22⋊D11—81no—
180C22⋊D11—81no—
181C2×Dic11—42no—
182C2×Dic11—41no—
183D44—41no—
184D44—41no—
185C4×D11—81no—
186C4×D11—81no—
187Dic22—41no—
188Dic22—41no—
189C8×C11—41no—
190C8×C11#12011yescharacteristic
191C8×C11#12111yescharacteristic
192C8×C11#12111yescharacteristic
193C8×C11#12711yescharacteristic
194C2×#135—111no—
195C22×Q16C2×D1111yescharacteristic
196C22×M16C2×D1111yescharacteristic
197#525—221no—
198C2×C22⋊Q8—21no—
199#510—222no—
200#510—222no—
201C2×Q32—221no—
202C2×SD32—221no—
203C2×M32—111no—
204C2×M32—111no—
205#470—22no—
206#470—22no—
207#470—221no—
208#469—221no—
209#468—222no—
210#427—111no—
211C2×#106C2×D1111yescharacteristic
212#416—221no—
213C2×#103—21no—
214#360—222no—
215#358—222no—
216#349—222no—
217C22×C11—22no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—41no—
221C22×C11—81no—
222C22×C11#44711yescharacteristic
223C22×C11#44711yescharacteristic
224C22×C11#46611yescharacteristic
225C2×D11—82no—
226C2×D11—81no—
227C4×C11—41no—
228C4×C11—82no—
229C4×C11—82no—
230C4×C11#39211yescharacteristic
231C4×C11#44911yescharacteristic
232C4×C11#44911yescharacteristic
233C4×C11#46911yescharacteristic
234Dic11—82no—
235Dic11—81no—
236C2×#41—221no—
237C22×Q8—21no—
238C23×C4C22⋊D1111yescharacteristic
239#135—221no—
240#135—221no—
241#135—221no—
242#135—221no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—111no—
249C2×Q16C22⋊D1112yescomplemented
250C2×SD16—221no—
251C2×D8—111no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C22×C8C22⋊D1111yescharacteristic
259C22×C8C22×D1111yescharacteristic
260#123—441no—
261C22⋊Q8—24no—
262C22⋊Q8—42no—
263C22⋊Q8—222no—
264#121—222no—
265#120—441no—
266C4×D4—442no—
267#117—221no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—41no—
270C2×C22⋊C4—41no—
271Q32—224no—
272SD32—224no—
273M32—112no—
274M32—221no—
275M32—221no—
276M32—221no—
277C2×C16—221no—
278C2×C16—221no—
279#107—112no—
280#106—21no—
281#106—221no—
282#106C22⋊D1112yescomplemented
283#103—24no—
284#103—222no—
285#102—222no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—81no—
289C2×C11#199911yescharacteristic
290C2×C11#219112yes—
291D11—161no—
292C24#432311yescharacteristic
293#41—441no—
294#41—441no—
295#41—441no—
296#41—441no—
297C2×Q8—22no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—221no—
304C2×D4—221no—
305C2×D4—442no—
306C2×D4—441no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—441no—
316C22×C4#432311yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318Q16—22no—
319Q16—22no—
320Q16—41no—
321Q16—41no—
322Q16—221no—
323Q16—221no—
324SD16—441no—
325SD16—441no—
326D8—221no—
327D8—221no—
328M16—41no—
329M16—41no—
330M16—41no—
331M16—41no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8D4×D1111yescharacteristic
336C2×C8D4×D1111yescharacteristic
337C2×C8D4×D1111yescharacteristic
338C2×C8#434111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—44no—
343C4⋊C4—41no—
344C4⋊C4—222no—
345C4⋊C4—442no—
346C22⋊C4—44no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—441no—
350C42—441no—
351C16—222no—
352C16—441no—
353C11#1331711yescharacteristic, complemented, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—42no—
358C23—441no—
359C23C2×#432311yescharacteristic
360Q8—42no—
361Q8—42no—
362Q8—81no—
363Q8—81no—
364Q8—441no—
365Q8—441no—
366D4—441no—
367D4—441no—
368D4—884no—
369D4—881no—
370D4—881no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—82no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—442no—
384C2×C4—441no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4#6698511yescharacteristic
388C2×C4#6699011yescharacteristic
389C2×C4#6699211yescharacteristic
390C2×C4#6700211yescharacteristic
391C2×C4#6700311yescharacteristic
392C2×C4#6700611yescharacteristic
393C8—41no—
394C8#6699011yescharacteristic
395C8#6699111yescharacteristic
396C8#6699211yescharacteristic
397C8#6699311yescharacteristic
398C22—22no—
399C22—42no—
400C22—41no—
401C22—42no—
402C22—81no—
403C22—881no—
404C22—882no—
405C22#1062264911yescharacteristic
406C22#1062265111yescharacteristic
407C22#1062283011yescharacteristic
408C4—41no—
409C4—82no—
410C4—82no—
411C4—881no—
412C4—882no—
413C4#1062265011yescharacteristic
414C4#1062265211yescharacteristic
415C4#1062283611yescharacteristic
416C4#1062285111yescharacteristic
417C2—21no—
418C2—21no—
419C2—81no—
420C2—1761no—
421C2#1306961211yescharacteristic
422C2#1307056612yes—
subgroupG/H
centerC22#10622649
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#470C2
socleC22×C11#447
prime radical#13078225C2
hypercenterC2×#470D11
hypocenterC11#13317
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
3. C2×#10622126C2semidirect
4. #13070336C2semidirect
5. C2×#10622191C2semidirect
6. #13066723C2semidirect
7. C2×C11×#470C2semidirect
39. C2×C11×Q16D4semidirect
67. C11×#106D4semidirect
78. #66876D4semidirect
145. C2×#470D11semidirect
249. C2×Q16C22⋊D11semidirect
282. #106C22⋊D11semidirect
353. C11#13317semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
#130782252
C2×#106221262
#130703362
C2×#106221912
#130667232
C2×C11×#4702
#1331711