Finite Group Databasebeta

← #14651431

Subgroups — #14651431

Order 2816.

568 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 91 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#13077644C211yesmaximal, characteristic, complemented
2#13073587C211yesmaximal, characteristic
3#13067239C211yesmaximal, characteristic, complemented
4#13067239C211yesmaximal, characteristic, complemented
5#13066956C211yesmaximal, characteristic, complemented
6#13066472C211yesmaximal, characteristic, complemented
7C11×#1285C211yesmaximal, characteristic, complemented
8C2×#66928C411yescharacteristic
9C2×#66928C2211yescharacteristic
10C2×#66927C411yescharacteristic
11C2×C4×D44C2211yescharacteristic
12C11×#432C2211yescharacteristic
13C11×#432C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15#10622604—21no—
16#10622604—21no—
17#10622552C411yescharacteristic
18#10622542C411yescharacteristic
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622449—22no—
22#10622339—21no—
23D11×C22⋊C8—21no—
24#10622319—22no—
25#10622278—21no—
26#10622278—21no—
27#10622106—21no—
28#10622106—21no—
29#10622102—22no—
30#10622102—22no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44C2×C411yescharacteristic
34C22×D44C2×C411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×C4×D11D411yescharacteristic
37C22×Dic22C2×C411yescharacteristic
38C2×C11×C4⋊C4—21no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4D411yescharacteristic
49C2×(C2×D11)⋊C4D411yescharacteristic
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×#4313—22no—
52C2×C8×D11—22no—
53#66928—21no—
54#66928—21no—
55#66928—21no—
56#66928—21no—
57#66928—42no—
58#66927—42no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×#97—21no—
68C11×#97D412yescomplemented
69C11×#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74(C2×D11)⋊C8—22no—
75(C2×D11)⋊C8—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78#66867—21no—
79#66867D412yescomplemented
80#9447—111nomaximal, Sylow
81C23×D11—21no—
82C23×D11C22⋊C411yescharacteristic
83C23×D11C22⋊C411yescharacteristic
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—21no—
90C22×Dic11C22⋊C411yescharacteristic
91C22×Dic11C22⋊C411yescharacteristic
92C2×D44—22no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—41no—
98C2×D44—42no—
99C2×D44—42no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—42no—
103C2×D44—42no—
104C2×D44—81no—
105C2×D44—81no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—81no—
111C2×C4×D11—81no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—41no—
115C2×Dic22—41no—
116C2×C8×C11—22no—
117C2×C8×C11—41no—
118C11×C4⋊C4—42no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11#4111yescharacteristic
125(C2×D11)⋊C4—21no—
126(C2×D11)⋊C4—21no—
127(C2×D11)⋊C4—21no—
128(C2×D11)⋊C4—21no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—81no—
136(C2×D11)⋊C4—81no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—41no—
141#4313—82no—
142C8×D11—82no—
143#2973—111no—
144#2544—111no—
145#1533—111no—
146#1533—111no—
147#1466—111no—
148#1285—111no—
149#1285D1111yescharacteristic, complemented
150C23×C11C2×C22⋊C411yescharacteristic
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11#10012yes—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11C4×D411yescharacteristic
179C2×C4×C11C4×D411yescharacteristic
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12311yescharacteristic
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191D44—42no—
192D44—42no—
193D44—81no—
194D44—81no—
195D44—84no—
196D44—84no—
197C4×D11—42no—
198C4×D11—42no—
199C4×D11—81no—
200C4×D11—81no—
201Dic22—81no—
202Dic22—81no—
203C8×C11—42no—
204C8×C11—81no—
205C11⋊C8—42no—
206C11⋊C8—81no—
207C2×#127—111no—
208C2×#124—111no—
209C2×#124—111no—
210C2×C4×D4—111no—
211#435—222no—
212#435—222no—
213#432—111no—
214#432—111no—
215#432C2×D1111yescharacteristic
216#432C2×D1111yescharacteristic
217#407—221no—
218C2×C22⋊C8—221no—
219#394—221no—
220#394—221no—
221#391—111no—
222#390—111no—
223#386—221no—
224#386—221no—
225C4×C4⋊C4C2×D1111yescharacteristic
226#329—222no—
227#329—222no—
228#323—221no—
229#323—221no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11#38611yescharacteristic
233C22×C11C2×#10011yescharacteristic
234C22×C11#41311yescharacteristic
235C2×D11—22no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—81no—
244C2×D11—81no—
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—81no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—42no—
259C4×C11—81no—
260Dic11—41no—
261Dic11—41no—
262Dic11—81no—
263C22×Q8—111no—
264C22×D4—111no—
265C22×D4—111no—
266C22×D4—221no—
267C22×D4—221no—
268C23×C4—111no—
269C23×C4—111no—
270C2×M16—222no—
271C22×C8—222no—
272#127—442no—
273#124—221no—
274#124—221no—
275#124—221no—
276#124—221no—
277#124—442no—
278C4×D4—221no—
279C4×D4—221no—
280C4×D4—221no—
281C4×D4—221no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—111no—
284C2×C22⋊C4—111no—
285C2×C22⋊C4—111no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—221no—
289C2×C22⋊C4—221no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—221no—
292C2×C42C4×D1111yescharacteristic
293C2×C42C4×D1111yescharacteristic
294C2×C42C22×D1111yescharacteristic
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8—221no—
298C4⋊C8—221no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—222no—
302C22⋊C8—222no—
303C22⋊C8—221no—
304C22⋊C8—221no—
305#97—21no—
306#97—112no—
307#97—221no—
308#97D4412yescomplemented
309#95—21no—
310#95—221no—
311#95—221no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11#188411yescharacteristic
315C2×C11#190011yescharacteristic
316C2×C11#191111yescharacteristic
317D11—42no—
318D11—81no—
319D11—161no—
320C24—111no—
321C24—111no—
322C24—221no—
323C2×Q8—221no—
324C2×Q8—221no—
325C2×Q8—441no—
326C2×Q8—441no—
327C2×D4—222no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—441no—
335C2×D4—442no—
336C2×D4—442no—
337C2×D4—442no—
338C2×D4—442no—
339C2×D4—881no—
340C2×D4—881no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—881no—
351C22×C4—881no—
352C22×C4C2×C4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4D4×D1111yescharacteristic
355M16—882no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—222no—
359C2×C8—441no—
360C2×C8—882no—
361C4⋊C4—42no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C22⋊C4—221no—
365C22⋊C4—221no—
366C22⋊C4—221no—
367C22⋊C4—221no—
368C22⋊C4—442no—
369C22⋊C4—442no—
370C22⋊C4—441no—
371C22⋊C4—441no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C22⋊C4—881no—
375C22⋊C4—881no—
376C42—41no—
377C42—41no—
378C42C2×D4411yescharacteristic
379C42#433911yescharacteristic
380C42D4×D1111yescharacteristic
381C42#434311yescharacteristic
382C11#944711yescharacteristic, complemented, Sylow
383C23—112no—
384C23—221no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—441no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23C22⋊C4×D1111yescharacteristic
401Q8—881no—
402Q8—881no—
403D4—442no—
404D4—442no—
405D4—881no—
406D4—881no—
407D4—884no—
408D4—884no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—881no—
429C2×C4—881no—
430C2×C4C4×D4411yescharacteristic
431C2×C4#6693511yescharacteristic
432C2×C4#6693711yescharacteristic
433C2×C4#6694611yescharacteristic
434C2×C4#6694711yescharacteristic
435C2×C4#6694811yescharacteristic
436C8—42no—
437C8—81no—
438C8—442no—
439C8—881no—
440C22—21no—
441C22—21no—
442C22—222no—
443C22—442no—
444C22—442no—
445C22—441no—
446C22—441no—
447C22—441no—
448C22—441no—
449C22—441no—
450C22—881no—
451C22—881no—
452C22—881no—
453C22—881no—
454C22—881no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22—881no—
459C22#1062227811yescharacteristic
460C22D11×#10011yescharacteristic
461C22#1062236411yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—81no—
470C4—441no—
471C4—441no—
472C4—881no—
473C2—21no—
474C2—21no—
475C2—442no—
476C2—881no—
477C2—1761no—
478C2#1306899811yescharacteristic
479C2#1306907811yescharacteristic
480C2#1306914711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11#386
prime radicalC2×#66927C4
cosocleC2×C42×C11C23
hypercenter#1285D11
hypocenterC11#9447
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
1. #13077644C2semidirect
3. #13067239C2semidirect
4. #13067239C2semidirect
5. #13066956C2semidirect
6. #13066472C2semidirect
7. C11×#1285C2semidirect
68. C11×#97D4semidirect
79. #66867D4semidirect
149. #1285D11semidirect
308. #97D44semidirect
382. C11#9447semidirect

Maximal subgroups

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

subgroupindex
#130776442
#130735872
#130672392
#130669562
#130664722
C11×#12852
#944711