Finite Group Databasebeta

← #14664443

Subgroups — #14664443

Order 2816.

574 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068690C211yesmaximal, characteristic, complemented
2#13066943C211yesmaximal, characteristic, complemented
3#13066616C212yesmaximal, complemented
4#13066613C212yesmaximal, complemented
5C11×#2617C211yesmaximal, characteristic
6C2×C11×#121C411yescharacteristic, complemented
7C2×C11×#120—21no—
8C22×C11×C22⋊C4C2211yescharacteristic
9C11×#397C411yescharacteristic, complemented
10C11×#397C2211yescharacteristic
11C11×#394—21no—
12C11×#394—21no—
13C11×#392C411yescharacteristic, complemented
14C11×#392C2211yescharacteristic
15C11×#386—21no—
16C11×#380C411yescharacteristic, complemented
17#10622860—21no—
18#10622820—21no—
19#10622164—21no—
20#10622164C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C25×C11D411yescharacteristic
24C22×D4×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C11×#121—41no—
31C11×#121—41no—
32C11×#120—44no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—41no—
42C2×C11×C22⋊C4—41no—
43C2×C11×C22⋊C4C2×C411yescharacteristic
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C11×C22⋊C4C2311yescharacteristic
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—41no—
49C2×C22⋊Dic11—41no—
50C2×#4318—41no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95C2×C411yescharacteristic
54C11×#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—41no—
57#11799—111nomaximal, Sylow
58C24×C11—21no—
59C24×C11—21no—
60C24×C11—22no—
61C24×C11—21no—
62C24×C11—41no—
63C24×C11—81no—
64C24×C11—81no—
65C24×C11C22⋊C411yescharacteristic
66C24×C11C22⋊C411yescharacteristic
67C24×C11C2×D411yescharacteristic
68C2×D4×C11—41no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—42no—
75C2×D4×C11—81no—
76C2×D4×C11—81no—
77C2×D4×C11—81no—
78C2×D4×C11—81no—
79C2×D4×C11—81no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—81no—
88C22×C4×C11—81no—
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—42no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—81no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—81no—
105C11×C22⋊C4—81no—
106C22⋊Dic11—42no—
107C22⋊Dic11—42no—
108C22⋊Dic11—82no—
109C22⋊Dic11—82no—
110#4318—82no—
111C2×C11⋊C8—42no—
112#2617D1111yescharacteristic
113#1819—111no—
114#1462—111no—
115#1344—112no—
116#1343—112no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—81no—
142C23×C11—81no—
143C23×C11—84no—
144C23×C11—84no—
145C23×C11#9911yescharacteristic
146C23×C11#9911yescharacteristic
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11AGL(1,ℤ/8)12yes—
149D4×C11—82no—
150D4×C11—82no—
151D4×C11—82no—
152D4×C11—84no—
153D4×C11—84no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
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—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×Dic11—82no—
176C2×Dic11—82no—
177C2×Dic11—82no—
178C11⋊C8—82no—
179C2×#121Dic1111yescharacteristic, complemented
180C2×#120—21no—
181C22×C22⋊C4C2×D1111yescharacteristic
182#407—221no—
183#397Dic1111yescharacteristic, complemented
184#397C2×D1111yescharacteristic
185#394—21no—
186#394—21no—
187#392Dic1111yescharacteristic, complemented
188#392C2×D1111yescharacteristic
189#386—21no—
190#380Dic1111yescharacteristic, complemented
191#379—221no—
192#342—112no—
193#342—221no—
194#323—112no—
195#323—221no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—22no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—84no—
221C22×C11—84no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11C2×#9911yescharacteristic
226C22×C11#41811yescharacteristic
227C22×C11#42111yescharacteristic
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—41no—
231C4×C11—41no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—81no—
235Dic11—162no—
236C25C22⋊D1111yescharacteristic
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4C2×Dic1111yescharacteristic
241C23×C4C2×Dic1111yescharacteristic
242C23×C4C22⋊D1111yescharacteristic
243C2×M16—441no—
244#121—41no—
245#121—41no—
246#120—44no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C2×Dic1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—41no—
256C2×C22⋊C4—41no—
257C2×C22⋊C4—222no—
258C2×C22⋊C4—441no—
259C2×C22⋊C4—441no—
260C2×C22⋊C4C2×Dic1111yescharacteristic
261C2×C22⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4C22⋊D1111yescharacteristic
263C2×C22⋊C4C22×D1111yescharacteristic
264C22⋊C8—222no—
265C22⋊C8—441no—
266#95—21no—
267#95—21no—
268#95C2×Dic1111yescharacteristic
269#95C2×Dic1111yescharacteristic
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—42no—
273C2×C11—41no—
274C2×C11—41no—
275C2×C11—81no—
276C2×C11—161no—
277C2×C11#151011yescharacteristic
278C2×C11#212111yescharacteristic
279C2×C11#212711yescharacteristic
280C24—21no—
281C24—21no—
282C24—22no—
283C24—21no—
284C24—41no—
285C24—81no—
286C24—81no—
287C24C22⋊Dic1111yescharacteristic
288C24C22⋊Dic1111yescharacteristic
289C24C2×C22⋊D1111yescharacteristic
290C2×D4—41no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—81no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4—81no—
301C2×D4—81no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—81no—
310C22×C4—81no—
311C22×C4—442no—
312C22×C4C22⋊Dic1111yescharacteristic
313C22×C4C22⋊Dic1111yescharacteristic
314C22×C4C22×Dic1111yescharacteristic
315C22×C4C2×C22⋊D1111yescharacteristic
316M16—882no—
317C2×C8—442no—
318C4⋊C4—41no—
319C4⋊C4—81no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—81no—
329C22⋊C4—81no—
330C22⋊C4—442no—
331C22⋊C4—442no—
332C22⋊C4—882no—
333C22⋊C4—882no—
334C11#1179911yescharacteristic, complemented, Sylow
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—42no—
345C23—42no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—81no—
360C23—81no—
361C23—84no—
362C23—84no—
363C23#6689811yescharacteristic
364C23#6689811yescharacteristic
365C23#6698512yes—
366C23C2×C22⋊Dic1111yescharacteristic
367D4—82no—
368D4—82no—
369D4—82no—
370D4—84no—
371D4—84no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—882no—
394C2×C4—882no—
395C2×C4—882no—
396C8—882no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—42no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—84no—
422C22—84no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1062282811yescharacteristic
427C22C2×#6689811yescharacteristic
428C22#1062284911yescharacteristic
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—1762no—
437C2—21no—
438C2—21no—
439C2—42no—
440C2—41no—
441C2—41no—
442C2—81no—
443C2—161no—
444C2#1306714511yescharacteristic
445C2#1307026211yescharacteristic
446C2#1307028511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2617C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#2617D11
hypocenterC11#11799
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. #13068690C2semidirect
2. #13066943C2semidirect
3. #13066616C2semidirect
4. #13066613C2semidirect
6. C2×C11×#121C4semidirect
9. C11×#397C4semidirect
13. C11×#392C4semidirect
16. C11×#380C4semidirect
179. C2×#121Dic11semidirect
183. #397Dic11semidirect
187. #392Dic11semidirect
190. #380Dic11semidirect
334. C11#11799semidirect

Maximal subgroups

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

subgroupindex
#130686902
#130669432
#130666162
#130666132
C11×#26172
#1179911