Finite Group Databasebeta

← #14648709

Subgroups — #14648709

Order 2816.

578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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
2#13071787C211yesmaximal, characteristic
3#13069590C211yesmaximal, characteristic, complemented
4C2×#10622102C211yesmaximal, characteristic
5#13066498C211yesmaximal, characteristic, complemented
6#13066497C211yesmaximal, characteristic, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4326—21no—
10C22×#4325—21no—
11C2×#66928C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13C11×#382C2211yescharacteristic
14#10622699—22no—
15#10622699C414yescomplemented
16#10622603—21no—
17#10622602—21no—
18#10622549C2211yescharacteristic
19C2×#66867C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622283—21no—
22#10622281—21no—
23#10622278—21no—
24#10622259—21no—
25C11×#340—21no—
26C11×#340—21no—
27#10622167—21no—
28#10622167—21no—
29#10622102—22no—
30C22×Q8×C11—21no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8C2×C412yescomplemented
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×#4326—24no—
45C2×#4326—42no—
46C2×#4326—42no—
47C2×#4325—24no—
48C2×#4325—42no—
49C2×#4325—42no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×C4⋊Dic11D411yescharacteristic
56C2×C4⋊Dic11D411yescharacteristic
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11—21no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8—21no—
61#66928—21no—
62#66928—21no—
63#66928C2×C412yes—
64#66928D412yes—
65C11×#97—21no—
66C11×#97—21no—
67C11×#95—21no—
68C11×#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73#66867—21no—
74#66867—21no—
75#66867—21no—
76#66867C2×C412yescomplemented
77#9003—111nomaximal, Sylow
78C23×D11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C2×D44—21no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44C22⋊C412yes—
98C2×C4×D11—81no—
99C2×C4×D11—81no—
100C2×C4×D11—81no—
101C2×Dic22—21no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C2×Dic22C22⋊C412yes—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C42×C11C22×C411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11#4111yescharacteristic
118#4326—48no—
119#4325—48no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4—81no—
125(C2×D11)⋊C4—81no—
126(C2×D11)⋊C4—81no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129Dic11⋊C4—81no—
130C4×Dic11—81no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×#497—111no—
138#2379—111no—
139#1993—111no—
140#1993D1111yescharacteristic, complemented
141C2×#329—111no—
142#1295—111no—
143#1295—111no—
144C23×C11#12011yescharacteristic
145C22×D11—22no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152Q8×C11—42no—
153Q8×C11—42no—
154Q8×C11—81no—
155Q8×C11—81no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—42no—
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—81no—
170C2×C4×C11—81no—
171C2×C4×C11C2×C22⋊C411yescharacteristic
172C2×C4×C11C4×D411yescharacteristic
173C2×C4×C11C4×D411yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12311yescharacteristic
177C2×Dic11—22no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186D44—42no—
187D44—81no—
188C4×D11—84no—
189Dic22—42no—
190Dic22—81no—
191C8×C11—42no—
192C11⋊C8—24no—
193C11⋊C8—42no—
194C22×Q16—221no—
195C22×SD16—221no—
196C2×C4⋊Q8C2×D1111yescharacteristic
197C2×#124—111no—
198#497—114no—
199#497—222no—
200C2×#97—111no—
201C2×#97—111no—
202C2×#97C2×D1111yescharacteristic
203#391—221no—
204#388—221no—
205#388—221no—
206#386—221no—
207#385—221no—
208#385—221no—
209#382—111no—
210#382C2×D1111yescharacteristic
211#340—21no—
212#340—21no—
213#340—221no—
214#340—221no—
215#329—222no—
216C22×C11#38611yescharacteristic
217C22×C11#45311yescharacteristic
218C22×C11#45311yescharacteristic
219C22×C11#45511yescharacteristic
220C22×C11#45511yescharacteristic
221C22×C11#45611yescharacteristic
222C22×C11#45611yescharacteristic
223C2×D11—42no—
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—82no—
237C4×C11—81no—
238C4×C11—81no—
239Dic11—42no—
240Dic11—81no—
241Dic11—81no—
242C22×Q8—21no—
243C22×Q8—111no—
244C22×D4—111no—
245C23×C4—221no—
246C2×Q16—224no—
247C2×Q16—442no—
248C2×Q16—442no—
249C2×SD16—224no—
250C2×SD16—442no—
251C2×SD16—442no—
252C22×C8—21no—
253C22×C8—221no—
254C22×C8—221no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8C4×D1112yescomplemented
259#124—112no—
260#124—112no—
261#124—221no—
262#124—221no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4C22⋊D1111yescharacteristic
269C2×C4⋊C4C22⋊D1111yescharacteristic
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—221no—
274C2×C22⋊C4—221no—
275C2×C42—221no—
276C2×C42C22×D1111yescharacteristic
277#97—21no—
278#97—21no—
279#97—112no—
280#97—221no—
281#97—221no—
282#97—221no—
283#95—21no—
284#95—21no—
285#95—221no—
286#95—221no—
287#95—221no—
288#95—221no—
289C2×C11#165911yescharacteristic
290C2×C11#166011yescharacteristic
291C2×C11#166111yescharacteristic
292C2×C11#166111yescharacteristic
293C2×C11#188211yescharacteristic
294C2×C11#188211yescharacteristic
295C2×C11#188711yescharacteristic
296D11—82no—
297C24—221no—
298C2×Q8—22no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—112no—
305C2×Q8—221no—
306C2×Q8—441no—
307C2×Q8—441no—
308C2×D4—112no—
309C2×D4—221no—
310C2×D4—441no—
311C2×D4—441no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—881no—
319C22×C4—881no—
320C22×C4—881no—
321C22×C4D4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4C2×C22⋊D1111yescharacteristic
324Q16—448no—
325SD16—448no—
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—441no—
334C2×C8—441no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4—881no—
344C22⋊C4—222no—
345C22⋊C4—222no—
346C22⋊C4—222no—
347C22⋊C4—222no—
348C22⋊C4—881no—
349C22⋊C4—881no—
350C22⋊C4—881no—
351C42—881no—
352C42C2×C4×D1111yescharacteristic
353C42#433911yescharacteristic
354C42D4×D1111yescharacteristic
355C42#434111yescharacteristic
356C11#900311yescharacteristic, complemented, Sylow
357C23—222no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23#6699011yescharacteristic
365Q8—42no—
366Q8—42no—
367Q8—81no—
368Q8—81no—
369Q8—442no—
370Q8—881no—
371D4—442no—
372D4—881no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—222no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—884no—
398C2×C4C22⋊C4×D1111yescharacteristic
399C2×C4(C22⋊D11)⋊C411yescharacteristic
400C2×C4#6693611yescharacteristic
401C2×C4#6693711yescharacteristic
402C2×C4C4×C22⋊D1111yescharacteristic
403C2×C4#6699111yescharacteristic
404C8—42no—
405C8—224no—
406C8—442no—
407C22—442no—
408C22—442no—
409C22—442no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22—881no—
414C22#1062256911yescharacteristic
415C22#1062267411yescharacteristic
416C22#1062270811yescharacteristic
417C22#1062281111yescharacteristic
418C22#1062281111yescharacteristic
419C22#1062281511yescharacteristic
420C22#1062281811yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—81no—
428C4—81no—
429C4—82no—
430C4—442no—
431C4—881no—
432C4—881no—
433C2—882no—
434C2#1306792111yescharacteristic
435C2#1306792611yescharacteristic
436C2#1306793111yescharacteristic
437C2#1306793211yescharacteristic
438C2#1306898211yescharacteristic
439C2#1306898811yescharacteristic
440C2#1306901111yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1993C2
socleC23×C11#120
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1993D11
hypocenterC11#9003
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
3. #13069590C2semidirect
5. #13066498C2semidirect
6. #13066497C2semidirect
7. C11×#1993C2semidirect
15. #10622699C4semidirect
38. C11×C4⋊Q8C2×C4semidirect
76. #66867C2×C4semidirect
140. #1993D11semidirect
258. C4⋊Q8C4×D11semidirect
356. C11#9003semidirect

Maximal subgroups

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

subgroupindex
C2×#106226992
#130717872
#130695902
C2×#106221022
#130664982
#130664972
C11×#19932
#900311