Finite Group Databasebeta

← #14654612

Subgroups — #14654612

Order 2816.

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

normal subgroups only

This group has 734 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
1#13078612C211yesmaximal, characteristic, complemented
2#13071895C211yesmaximal, characteristic, complemented
3#13069449C211yesmaximal, characteristic, complemented
4#13067042C211yesmaximal, characteristic, complemented
5#13067041C211yesmaximal, characteristic, complemented
6#13066444C211yesmaximal, characteristic, complemented
7C11×#3100C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×C4×C22⋊D11—22no—
11C2×C4×D44C2211yescharacteristic
12C11×#480—21no—
13C11×#474—21no—
14C11×#459—21no—
15C11×#447—21no—
16C4×C11×D8—22no—
17C11×#431C2211yescharacteristic
18C2×#66901—22no—
19#10622836—21no—
20#10622700—21no—
21#10622685—21no—
22#10622649—21no—
23#10622646—21no—
24C4×#4323—22no—
25#10622605—21no—
26#10622573—21no—
27#10622562—21no—
28#10622545C2211yescharacteristic
29#10622538C2211yescharacteristic
30#10622537C2211yescharacteristic
31D4⋊(C11⋊C8)—22no—
32#10622097—22no—
33C2×C11×#41—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C22×C22⋊D11—22no—
37C22×D44D411yescharacteristic
38C22×C4×D11—21no—
39C2×C11×D8—22no—
40C11×C4⋊Q8D411yescharacteristic, complemented
41C11×#127D411yescharacteristic, complemented
42C11×#124—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—22no—
55C2×#4323—22no—
56C4×C22⋊D11—44no—
57C4×C22⋊D11—44no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11D412yes—
63C2×#4318—21no—
64C4×D44—21no—
65C4×D44—21no—
66C4×D44—21no—
67C4×D44—21no—
68C11×#107—22no—
69C11×C4⋊C8—21no—
70C11×#102—22no—
71C11×#102—22no—
72C11×C22⋊C8—21no—
73C4×C8×C11D412yescomplemented
74#66901—44no—
75#66896—22no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C22⋊(C11⋊C8)—21no—
79#66873—22no—
80#66871—22no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)—21no—
84C4×C11⋊C8D412yescomplemented
85#10012—111nomaximal, Sylow
86C24×C11—21no—
87C23×D11—21no—
88C11×#41—42no—
89C11×#41—42no—
90C2×Q8×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—42no—
97C2×D4×C11—41no—
98C22×C4×C11—21no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C2×C22⋊D11—44no—
108C2×C22⋊D11—44no—
109C2×C22⋊D11—44no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—42no—
115C2×C4×D11—41no—
116C2×C4×D11—41no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C11×D8—44no—
120C2×C8×C11—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C22⋊Dic11—44no—
134#4323—44no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140Dic11⋊C4—44no—
141C4×Dic11—22no—
142C4×Dic11D814yescomplemented
143#4318—42no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146#3100—111no—
147#3100D1111yescharacteristic, complemented
148#2397—111no—
149#1963—111no—
150#1486—111no—
151#1486—111no—
152#1274—111no—
153C23×C11—22no—
154C23×C11—42no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—42no—
158C23×C11—41no—
159C23×C11#12011yescharacteristic
160C22×D11—22no—
161C22×D11—41no—
162C22×D11—42no—
163C22×D11—41no—
164C22×D11—42no—
165Q8×C11—42no—
166D4×C11—22no—
167D4×C11—22no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—82no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—82no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12711yescharacteristic
190C2×C4×C11C2×D812yes—
191C2×C4×C11AGL(1,ℤ/8)12yes—
192C22⋊D11—416no—
193C2×Dic11—24no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—42no—
198D44—22no—
199D44—22no—
200D44—41no—
201D44—41no—
202C4×D11—82no—
203C4×D11—81no—
204C4×D11—81no—
205C8×C11—42no—
206C11⋊C8—42no—
207C11⋊C8—81no—
208#532C2×D1111yescharacteristic
209C2×C4×D4—111no—
210C2×C4×D4—222no—
211C2×C4×D4C2×D1111yescharacteristic
212#480—21no—
213#480—221no—
214#474—21no—
215#474—221no—
216#459—21no—
217#459—221no—
218#447—21no—
219#447—221no—
220C4×D8—22no—
221C4×D8—222no—
222#431—111no—
223#431C2×D1111yescharacteristic
224#423—111no—
225C2×#104—222no—
226#399—221no—
227#399—221no—
228#392—221no—
229#392—221no—
230#376—111no—
231D4⋊C8—222no—
232D4⋊C8—222no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—44no—
236C22×C11—42no—
237C22×C11—82no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11#39211yescharacteristic
244C22×C11#44712yes—
245C2×D11—44no—
246C2×D11—42no—
247C2×D11—82no—
248C2×D11—81no—
249C2×D11—81no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—81no—
255C4×C11—81no—
256C4×C11#45912yes—
257C4×C11#49311yescharacteristic
258C4×C11#49611yescharacteristic
259Dic11—44no—
260Dic11—81no—
261C2×#41—21no—
262C22×D4—111no—
263C22×D4—222no—
264C22×D4C22⋊D1111yescharacteristic
265C23×C4—21no—
266C23×C4—221no—
267C2×D8—22no—
268C2×D8—222no—
269C2×M16—221no—
270C4⋊Q8C22⋊D1111yescharacteristic, complemented
271#127C22⋊D1111yescharacteristic, complemented
272#124—21no—
273#121—21no—
274#121—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—221no—
282C4×D4—221no—
283C4×D4—221no—
284C4×D4—221no—
285C4×D4—444no—
286C4×D4—444no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4C22⋊D1111yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—222no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—221no—
294C2×C42—112no—
295C2×C42C22×D1111yescharacteristic
296#107—22no—
297#107—222no—
298C4⋊C8—21no—
299C4⋊C8—221no—
300C4⋊C8—221no—
301C4⋊C8—221no—
302#104—444no—
303#102—22no—
304#102—22no—
305#102—222no—
306#102—222no—
307C22⋊C8—21no—
308C22⋊C8—221no—
309C4×C8—112no—
310C4×C8C22⋊D1112yescomplemented
311#95—221no—
312#95—221no—
313C2×C11—22no—
314C2×C11—82no—
315C2×C11—161no—
316C2×C11#201011yescharacteristic
317C2×C11#201011yescharacteristic
318C2×C11#201111yescharacteristic
319D11—82no—
320C24—21no—
321C24—221no—
322#41—42no—
323#41—42no—
324C2×Q8—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—221no—
333C2×D4—221no—
334C2×D4—442no—
335C2×D4—444no—
336C2×D4—444no—
337C2×D4—444no—
338C22×C4—21no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—222no—
345C22×C4—221no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4D4×D1111yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353D8—44no—
354D8—444no—
355M16—442no—
356C2×C8—22no—
357C2×C8—222no—
358C2×C8—441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—444no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—444no—
371C22⋊C4—444no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C42—114no—
375C42—222no—
376C42D4×D1111yescharacteristic
377C42#434111yescharacteristic
378C42C2×C22⋊D1111yescharacteristic
379C42C2×C22⋊D1111yescharacteristic
380C11#1001211yescharacteristic, complemented, Sylow
381C23—22no—
382C23—41no—
383C23—42no—
384C23—42no—
385C23—41no—
386C23—41no—
387C23—222no—
388C23—441no—
389C23—442no—
390C23—442no—
391C23—441no—
392C23#6699011yescharacteristic
393Q8—42no—
394D4—22no—
395D4—22no—
396D4—41no—
397D4—41no—
398D4—42no—
399D4—42no—
400D4—42no—
401D4—82no—
402D4—222no—
403D4—222no—
404D4—441no—
405D4—441no—
406D4—4416no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—82no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—224no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—441no—
422C2×C4—882no—
423C2×C4—881no—
424C2×C4—881no—
425C2×C4D8×D1112yes—
426C2×C4#6696412yes—
427C2×C4#6699011yescharacteristic
428C2×C4#6699111yescharacteristic
429C2×C4#6699211yescharacteristic
430C2×C4#6699211yescharacteristic
431C2×C4#6699311yescharacteristic
432C2×C4#6700611yescharacteristic
433C8—42no—
434C8—442no—
435C8—881no—
436C22—21no—
437C22—21no—
438C22—44no—
439C22—42no—
440C22—82no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—444no—
447C22—442no—
448C22—882no—
449C22—881no—
450C22—881no—
451C22#1062276912yes—
452C22#1062283611yescharacteristic
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—81no—
459C4—444no—
460C4—881no—
461C4#1062276312yes—
462C4#1062276411yescharacteristic
463C4#1062276711yescharacteristic
464C2—22no—
465C2—82no—
466C2—161no—
467C2—882no—
468C2#1306968011yescharacteristic
469C2#1306968111yescharacteristic
470C2#1306968511yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3100C2
socleC22×C11#392
hypercenter#3100D11
hypocenterC11#10012
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13078612C2semidirect
2. #13071895C2semidirect
3. #13069449C2semidirect
4. #13067042C2semidirect
5. #13067041C2semidirect
6. #13066444C2semidirect
7. C11×#3100C2semidirect
40. C11×C4⋊Q8D4semidirect
41. C11×#127D4semidirect
73. C4×C8×C11D4semidirect
84. C4×C11⋊C8D4semidirect
142. C4×Dic11D8semidirect
147. #3100D11semidirect
270. C4⋊Q8C22⋊D11semidirect
271. #127C22⋊D11semidirect
310. C4×C8C22⋊D11semidirect
380. C11#10012semidirect

Maximal subgroups

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

subgroupindex
#130786122
#130718952
#130694492
#130670422
#130670412
#130664442
C11×#31002
#1001211