Finite Group Databasebeta

← #14649391

Subgroups — #14649391

Order 2816.

600 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#10622539C211yesmaximal, characteristic, complemented
2#13076917C211yesmaximal, characteristic
3C2×#10622102C212yesmaximal, complemented
4#13066498C212yesmaximal, complemented
5C11×#1749C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C2×#66977C411yescharacteristic
9C2×#66928C2211yescharacteristic
10C2×C11×C22⋊C8—21no—
11C2×C11×#97C2212yes—
12#10622826—21no—
13#10622826—21no—
14C2×C22⋊(C11⋊C8)—21no—
15#10622553—21no—
16#10622553—21no—
17#10622552C411yescharacteristic
18#10622549C2211yescharacteristic
19#10622542C411yescharacteristic
20#10622539—24no—
21C2×C4⋊(C11⋊C8)—21no—
22C2×#66867C2212yes—
23C11×#336—21no—
24#10622102—24no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C22×D44C2×C411yescharacteristic
30C22×Dic22C2×C411yescharacteristic
31C22×C8×C11—22no—
32C2×C42×C11—22no—
33C2×C42×C11—22no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39#66983—42no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×C4⋊Dic11C2×C411yescharacteristic
47#66977—42no—
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8—22no—
50#66928—22no—
51#66928—22no—
52C11×C22⋊C8—24no—
53C11×#97—22no—
54C11×#97—22no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—24no—
60C4⋊(C11⋊C8)—24no—
61#66867—22no—
62#66867D414yescomplemented
63#9124—111nomaximal, Sylow
64C24×C11C22⋊C411yescharacteristic
65C23×D11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—42no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C2×D44—22no—
89C2×D44—41no—
90C2×D44—41no—
91C2×Dic22—22no—
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×C8×C11—24no—
95C2×C8×C11—42no—
96C2×C8×C11—42no—
97C42×C11—22no—
98C42×C11—21no—
99C42×C11—22no—
100C42×C11—21no—
101C42×C11C2×D412yes—
102C42×C11#4112yes—
103C22⋊Dic11—42no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112Dic11⋊C4—42no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C2×#432—111no—
117#2850—111no—
118#1749D1111yescharacteristic, complemented
119C2×#329—112no—
120#1295—112no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11#10012yes—
128C23×C11C2×C22⋊C411yescharacteristic
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11#10412yes—
155C2×C4×C11C4×D412yes—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12112yes—
158C2×C4×C11#12311yescharacteristic
159C22⋊D11—84no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169D44—82no—
170Dic22—82no—
171C8×C11—44no—
172C11⋊C8—44no—
173C2×#124—111no—
174C2×C22⋊Q8—111no—
175C2×#121—111no—
176C22×C42C2×D1111yescharacteristic
177#432—224no—
178C2×C4⋊C8—221no—
179C2×C22⋊C8—21no—
180C2×C22⋊C8—221no—
181C2×#97—112no—
182C2×#97C2×D1112yes—
183#391—111no—
184#390—111no—
185#388—221no—
186#388—221no—
187#386—221no—
188#386—221no—
189#382—111no—
190#336—21no—
191#329—224no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11#38611yescharacteristic
200C22×C11C2×#10011yescharacteristic
201C22×C11#41311yescharacteristic
202C22×C11C2×#10411yescharacteristic
203C22×C11#42111yescharacteristic
204C22×C11#42111yescharacteristic
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—22no—
214C4×C11—22no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—22no—
218C4×C11—41no—
219C4×C11—41no—
220Dic11—81no—
221Dic11—81no—
222Dic11—81no—
223C22×Q8—111no—
224C22×D4—111no—
225C22×D4—221no—
226C23×C4C4×D1111yescharacteristic
227C23×C4D4411yescharacteristic
228C23×C4C22⋊D1111yescharacteristic
229C22×C8—22no—
230C22×C8—222no—
231#124—222no—
232#124—222no—
233C22⋊Q8—442no—
234#121—442no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—111no—
237C2×C4⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42C4×D1111yescharacteristic
247C2×C42D4411yescharacteristic
248C2×C42C22⋊D1111yescharacteristic
249C2×C42C22×D1111yescharacteristic
250C4⋊C8—224no—
251C22⋊C8—24no—
252C22⋊C8—224no—
253#97—22no—
254#97—22no—
255#97—114no—
256#97—222no—
257#95—221no—
258#95—221no—
259#95—221no—
260#95—221no—
261C2×C11—42no—
262C2×C11#152911yescharacteristic
263C2×C11#153011yescharacteristic
264C2×C11#153311yescharacteristic
265C2×C11#153511yescharacteristic
266C2×C11#187111yescharacteristic
267C2×C11#189711yescharacteristic
268C2×C11#190011yescharacteristic
269D11—161no—
270C24—221no—
271C24(C2×D11)⋊C411yescharacteristic
272C2×Q8—222no—
273C2×Q8—441no—
274C2×Q8—441no—
275C2×D4—222no—
276C2×D4—441no—
277C2×D4—441no—
278C2×D4—442no—
279C2×D4—442no—
280C2×D4—442no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4(C2×D11)⋊C411yescharacteristic
295C22×C4(C2×D11)⋊C411yescharacteristic
296C22×C4(C2×D11)⋊C411yescharacteristic
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4C2×D4411yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300C2×C8—24no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—224no—
304C2×C8—442no—
305C2×C8—442no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C4⋊C4—442no—
309C22⋊C4—442no—
310C22⋊C4—442no—
311C22⋊C4—442no—
312C22⋊C4—442no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—442no—
316C42—22no—
317C42—21no—
318C42—21no—
319C42—22no—
320C42D4×D1112yes—
321C42#434112yes—
322C11#912411yescharacteristic, complemented, Sylow
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—441no—
330C23—441no—
331C23—441no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23#6688712yes—
337C23C2×(C2×D11)⋊C411yescharacteristic
338Q8—882no—
339D4—882no—
340D4—884no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4#6686912yes—
369C2×C4(C22⋊D11)⋊C412yes—
370C2×C4#6693511yescharacteristic
371C2×C4#6693911yescharacteristic
372C2×C4#6699212yes—
373C8—44no—
374C8—444no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22—881no—
389C22C2×#6686911yescharacteristic
390C22#1062257111yescharacteristic
391C22#1062261811yescharacteristic
392C22C2×#6688711yescharacteristic
393C22#1062274511yescharacteristic
394C22#1062275211yescharacteristic
395C22#1062275211yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—881no—
404C4—881no—
405C4—881no—
406C2—42no—
407C2—1761no—
408C2#1306722111yescharacteristic
409C2#1306722611yescharacteristic
410C2#1306723911yescharacteristic
411C2#1306724811yescharacteristic
412C2#1306891611yescharacteristic
413C2#1306906211yescharacteristic
414C2#1306907711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C4
cosocleC2×C42×C11C23
hypercenter#1749D11
hypocenterC11#9124
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C2×#10622539C2semidirect
3. C2×#10622102C2semidirect
4. #13066498C2semidirect
5. C11×#1749C2semidirect
62. #66867D4semidirect
118. #1749D11semidirect
322. C11#9124semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130769172
C2×#106221022
#130664982
C11×#17492
#912411