Finite Group Databasebeta

← #14664800

Subgroups — #14664800

Order 2816.

522 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 95 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#13073572C211yesmaximal, characteristic
2#13066937C211yesmaximal, characteristic, complemented
3#13066615C212yesmaximal, complemented
4#13066612C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66992—21no—
8C2×#66983C411yescharacteristic, complemented
9C2×C11×#99—21no—
10C11×#380—21no—
11#10622826—21no—
12C2×C11⋊#95C411yescharacteristic, complemented
13#10622604C411yescharacteristic, complemented
14#10622596C411yescharacteristic, complemented
15#10622573C2211yescharacteristic
16#10622571—21no—
17#10622566C2211yescharacteristic
18#10622553—21no—
19#10622538—21no—
20C11×#342C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C23×Dic11—21no—
29C22×D44C2×C411yescharacteristic
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—21no—
39#66992—42no—
40#66992—42no—
41#66983—41no—
42#66983—41no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×Dic11⋊C4—21no—
49C11×#99—42no—
50C11×#95—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—41no—
58C4×C11⋊C8—41no—
59#11876—111nomaximal, Sylow
60C24×C11C22⋊C411yescharacteristic
61C24×C11C2×D411yescharacteristic
62C23×D11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11D812yes—
66C2×D4×C11SD1612yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—42no—
72C22×C4×C11—81no—
73C22×C4×C11—81no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—81no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—42no—
90C22×Dic11—42no—
91C22×Dic11—81no—
92C2×D44—41no—
93C2×D44—81no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—82no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C42×C11—21no—
101C42×C11—21no—
102C22⋊Dic11—41no—
103C22⋊Dic11—41no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—81no—
109C4⋊Dic11—41no—
110Dic11⋊C4—42no—
111C2×C11⋊C8—42no—
112#2543—111no—
113#1799D1111yescharacteristic, complemented
114#1460—111no—
115#1344—112no—
116#1343—112no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11#10212yes—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11C2×D811yescharacteristic
128C23×C11C2×SD1611yescharacteristic
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136D4×C11—42no—
137D4×C11—42no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11—82no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11#9911yescharacteristic
155C2×C4×C11#9911yescharacteristic
156C2×C4×C11#10212yes—
157C22⋊D11—82no—
158C22⋊D11—82no—
159C22⋊D11—84no—
160C2×Dic11—22no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—84no—
170D44—82no—
171C11⋊C8—82no—
172C2×#121—111no—
173C2×#121—221no—
174C2×C4×D4C2×D1111yescharacteristic
175#431—221no—
176C2×#99—21no—
177#398—111no—
178#397—111no—
179#394—111no—
180#392—111no—
181#388—221no—
182#386—221no—
183#386—221no—
184#380—21no—
185C2×#95—111no—
186#342C2×D1112yes—
187#323—112no—
188#323—221no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—22no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—42no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—81no—
203C22×C11C2×#9911yescharacteristic
204C22×C11C2×#10211yescharacteristic
205C22×C11#42111yescharacteristic
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—22no—
216C4×C11—41no—
217C4×C11—41no—
218C4×C11—41no—
219C4×C11—162no—
220Dic11—42no—
221Dic11—81no—
222Dic11—81no—
223C22×D4—111no—
224C22×D4—221no—
225C22×D4—221no—
226C22×D4C22⋊D1111yescharacteristic
227C23×C4—221no—
228C23×C4C4×D1111yescharacteristic
229C23×C4C22⋊D1111yescharacteristic
230#121—442no—
231#121—442no—
232#121—441no—
233#121—441no—
234C4×D4—41no—
235C4×D4—41no—
236C2×C4⋊C4—41no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4C4×D1111yescharacteristic
240C2×C22⋊C4—22no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4D4411yescharacteristic
247C2×C22⋊C4C22×D1111yescharacteristic
248C2×C42D4411yescharacteristic
249C4⋊C8—441no—
250#99—42no—
251C22⋊C8—222no—
252C4×C8—441no—
253#95—41no—
254#95—111no—
255#95—111no—
256#95—221no—
257#95—221no—
258#95—221no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—41no—
262C2×C11—42no—
263C2×C11—41no—
264C2×C11#151911yescharacteristic
265C2×C11#212111yescharacteristic
266C2×C11#212611yescharacteristic
267D11—161no—
268C24—221no—
269C24(C2×D11)⋊C411yescharacteristic
270C24C2×C22⋊D1111yescharacteristic
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—441no—
274C2×D4—442no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—881no—
281C2×D4—881no—
282C2×D4#432312yes—
283C2×D4#432512yes—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—42no—
289C22×C4—81no—
290C22×C4—81no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—442no—
295C22×C4—442no—
296C22×C4—881no—
297C22×C4(C2×D11)⋊C411yescharacteristic
298C22×C4(C2×D11)⋊C411yescharacteristic
299C22×C4(C2×D11)⋊C411yescharacteristic
300C22×C4C2×C4×D1111yescharacteristic
301C22×C4C2×D4411yescharacteristic
302C2×C8—442no—
303C4⋊C4—41no—
304C4⋊C4—82no—
305C4⋊C4—441no—
306C4⋊C4—442no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—442no—
312C22⋊C4—441no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C22⋊C4—442no—
317C22⋊C4—881no—
318C42—21no—
319C42—21no—
320C11#1187611yescharacteristic, complemented, Sylow
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—441no—
330C23—441no—
331C23—441no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23#6687312yes—
337C23C2×(C2×D11)⋊C411yescharacteristic
338C23C2×#432311yescharacteristic
339C23C2×#432511yescharacteristic
340D4—42no—
341D4—42no—
342D4—882no—
343D4—882no—
344D4—882no—
345D4—884no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—222no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—884no—
372C2×C4#6687011yescharacteristic
373C2×C4#6687011yescharacteristic
374C2×C4#6687312yes—
375C8—882no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—81no—
390C22—881no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22—881no—
395C22—881no—
396C22—881no—
397C22C2×#6687011yescharacteristic
398C22C2×#6687311yescharacteristic
399C22#1062261811yescharacteristic
400C4—22no—
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—162no—
407C4—442no—
408C4—881no—
409C4—881no—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—42no—
414C2—41no—
415C2—1761no—
416C2#1306718311yescharacteristic
417C2#1307026011yescharacteristic
418C2#1307027911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1799C2
socleC22×C11C2×#99
prime radical#13073572C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1799D11
hypocenterC11#11876
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #13066937C2semidirect
3. #13066615C2semidirect
4. #13066612C2semidirect
5. C11×#1799C2semidirect
8. C2×#66983C4semidirect
12. C2×C11⋊#95C4semidirect
13. #10622604C4semidirect
14. #10622596C4semidirect
113. #1799D11semidirect
320. C11#11876semidirect

Maximal subgroups

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

subgroupindex
#130735722
#130669372
#130666152
#130666122
C11×#17992
#1187611