Finite Group Databasebeta

← #14651091

Subgroups — #14651091

Order 2816.

640 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 127 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#13077640C211yesmaximal, characteristic, complemented
2#13073572C211yesmaximal, characteristic
3#13067183C212yesmaximal, complemented
4#13066494C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66992—21no—
8C2×#66983C2211yescharacteristic
9C2×C11×#99—21no—
10C11×#380C2212yes—
11#10622826—21no—
12C2×C11⋊#95C2211yescharacteristic
13C2×C22⋊(C11⋊C8)—21no—
14C2×C22⋊(C11⋊C8)C2212yes—
15D4×C11⋊C8—24no—
16#10622604C411yescharacteristic, complemented
17#10622596C411yescharacteristic, complemented
18#10622573C411yescharacteristic, complemented
19#10622571—21no—
20#10622566C411yescharacteristic, complemented
21#10622553—21no—
22#10622538—21no—
23C11×#342—21no—
24#10622089—24no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C23×Dic11—21no—
31C22×D44C2×C411yescharacteristic
32C4×D4×C11—22no—
33C4×D4×C11—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C22⋊Dic11—21no—
41#66992—42no—
42#66992—42no—
43#66983—22no—
44#66983—22no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×Dic11⋊C4—21no—
51C22×C11⋊C8—22no—
52C22×C11⋊C8—22no—
53C11×#99—42no—
54C11×#95—22no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95C2×C411yescharacteristic
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)—22no—
62C22⋊(C11⋊C8)D414yescomplemented
63C4⋊(C11⋊C8)—22no—
64C4×C11⋊C8—22no—
65#9384—111nomaximal, Sylow
66C24×C11C22⋊C411yescharacteristic
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11D812yes—
72C2×D4×C11SD1612yes—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—42no—
76C22×C4×C11—81no—
77C22×C4×C11—81no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4112yes—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—42no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—42no—
91C2×C22⋊D11—81no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—42no—
96C22×Dic11—41no—
97C22×Dic11—41no—
98C22×Dic11—81no—
99C2×D44—22no—
100C2×D44—81no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—82no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C42×C11—21no—
108C42×C11—21no—
109C22⋊Dic11—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—81no—
115C4⋊Dic11—22no—
116Dic11⋊C4—42no—
117C2×C11⋊C8—24no—
118C2×C11⋊C8—82no—
119C2×C11⋊C8—82no—
120#2972—111no—
121#2543—111no—
122#1799D1111yescharacteristic, complemented
123#1519—112no—
124#1294—112no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11#10212yes—
132C23×C11C2×C22⋊C411yescharacteristic
133C23×C11#12112yes—
134C23×C11C2×D811yescharacteristic
135C23×C11C2×SD1611yescharacteristic
136C23×C11#13512yes—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144D4×C11—24no—
145D4×C11—24no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—81no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11—82no—
161C2×C4×C11#10212yes—
162C2×C4×C11C4×D412yes—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C22⋊D11—84no—
166C22⋊D11—82no—
167C22⋊D11—82no—
168C2×Dic11—22no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—82no—
178C2×Dic11—82no—
179D44—82no—
180C11⋊C8—44no—
181C2×#121—111no—
182C2×#121—221no—
183C2×C4×D4C2×D1111yescharacteristic
184C8×D4—224no—
185#431—221no—
186C2×#99—21no—
187C2×C22⋊C8—112no—
188C2×C22⋊C8—221no—
189#398—111no—
190#397—111no—
191#394—111no—
192#392—111no—
193#388—221no—
194#386—221no—
195#386—221no—
196#380C2×D1112yes—
197C2×#95—111no—
198#342—21no—
199#327—224no—
200C22×C11—21no—
201C22×C11—22no—
202C22×C11—21no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—81no—
212C22×C11#38611yescharacteristic
213C22×C11C2×#10211yescharacteristic
214C22×C11#41611yescharacteristic
215C22×C11#46512yes—
216C22×C11#46612yes—
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C4×C11—22no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—22no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—162no—
231Dic11—42no—
232Dic11—81no—
233Dic11—81no—
234C22×D4—111no—
235C22×D4—221no—
236C22×D4—221no—
237C22×D4C22⋊D1111yescharacteristic
238C23×C4—221no—
239C23×C4D4411yescharacteristic
240C23×C4C22×D1111yescharacteristic
241C22×C8—222no—
242C22×C8—222no—
243#121—222no—
244#121—222no—
245#121—442no—
246#121—442no—
247C4×D4—22no—
248C4×D4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4C4×D1111yescharacteristic
253C2×C22⋊C4—22no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4C4×D1111yescharacteristic
260C2×C22⋊C4C22⋊D1111yescharacteristic
261C2×C42D4411yescharacteristic
262C4⋊C8—222no—
263#99—42no—
264C22⋊C8—114no—
265C22⋊C8—222no—
266C22⋊C8—222no—
267C4×C8—222no—
268#95—22no—
269#95—111no—
270#95—111no—
271#95—221no—
272#95—221no—
273#95—221no—
274C2×C11—21no—
275C2×C11—22no—
276C2×C11—21no—
277C2×C11—22no—
278C2×C11—42no—
279C2×C11#188411yescharacteristic
280C2×C11#189311yescharacteristic
281C2×C11#191311yescharacteristic
282D11—161no—
283C24—221no—
284C24(C2×D11)⋊C411yescharacteristic
285C24C2×C22⋊D1111yescharacteristic
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—222no—
289C2×D4—442no—
290C2×D4—442no—
291C2×D4—441no—
292C2×D4—442no—
293C2×D4—441no—
294C2×D4—442no—
295C2×D4—881no—
296C2×D4—881no—
297C2×D4#432312yes—
298C2×D4#432512yes—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—81no—
303C22×C4—81no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—442no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4—881no—
311C22×C4(C2×D11)⋊C411yescharacteristic
312C22×C4(C2×D11)⋊C411yescharacteristic
313C22×C4(C2×D11)⋊C411yescharacteristic
314C22×C4C2×C4×D1111yescharacteristic
315C22×C4C2×D4411yescharacteristic
316C22×C4D4×D1112yes—
317C22×C4#434112yes—
318C2×C8—224no—
319C2×C8—882no—
320C2×C8—882no—
321C4⋊C4—22no—
322C4⋊C4—82no—
323C4⋊C4—222no—
324C4⋊C4—442no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—442no—
330C22⋊C4—442no—
331C22⋊C4—442no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—881no—
335C42—21no—
336C42—21no—
337C11#938411yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23—441no—
348C23—441no—
349C23—441no—
350C23—441no—
351C23#6687312yes—
352C23C2×(C2×D11)⋊C411yescharacteristic
353C23C2×#432311yescharacteristic
354C23#6699212yes—
355C23C2×#432511yescharacteristic
356C23#6700312yes—
357D4—24no—
358D4—24no—
359D4—882no—
360D4—884no—
361D4—882no—
362D4—882no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—222no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—882no—
388C2×C4—882no—
389C2×C4#6687312yes—
390C2×C4(C22⋊D11)⋊C412yes—
391C2×C4#6693511yescharacteristic
392C2×C4#6693911yescharacteristic
393C8—444no—
394C22—21no—
395C22—22no—
396C22—21no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—881no—
407C22—881no—
408C22—881no—
409C22—881no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22#1062257111yescharacteristic
414C22C2×#6687311yescharacteristic
415C22#1062261511yescharacteristic
416C22#1062265112yes—
417C22#1062266112yes—
418C4—21no—
419C4—21no—
420C4—22no—
421C4—22no—
422C4—41no—
423C4—41no—
424C4—162no—
425C4—442no—
426C4—881no—
427C4—881no—
428C2—22no—
429C2—21no—
430C2—21no—
431C2—22no—
432C2—42no—
433C2—1761no—
434C2#1306899711yescharacteristic
435C2#1306904211yescharacteristic
436C2#1306915611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1799C2
socleC22×C11#386
prime radical#13073572C2
cosocleC23×C4×C11C23
hypercenter#1799D11
hypocenterC11#9384
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
1. #13077640C2semidirect
3. #13067183C2semidirect
4. #13066494C2semidirect
5. C11×#1799C2semidirect
16. #10622604C4semidirect
17. #10622596C4semidirect
18. #10622573C4semidirect
20. #10622566C4semidirect
62. C22⋊(C11⋊C8)D4semidirect
122. #1799D11semidirect
337. C11#9384semidirect

Maximal subgroups

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

subgroupindex
#130776402
#130735722
#130671832
#130664942
C11×#17992
#938411