Finite Group Databasebeta

← #14655075

Subgroups — #14655075

Order 2816.

590 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10622699C211yesmaximal, characteristic
2#13076666C211yesmaximal, characteristic
3#13069590C211yesmaximal, characteristic, complemented
4C2×#10622181C211yesmaximal, characteristic, complemented
5C2×#10622102C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic, complemented
7C2×C11×#501C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C22×#4326—21no—
11C22×#4325—21no—
12C2×#66928C2211yescharacteristic
13C11×#501—22no—
14C11×#501—22no—
15C2×C11×#107—21no—
16C2×C11×#106—21no—
17C2×C11×#97C2211yescharacteristic
18#10622699—22no—
19#10622699—22no—
20#10622607—22no—
21#10622606—21no—
22#10622605—21no—
23#10622604—21no—
24#10622592—21no—
25#10622549C2211yescharacteristic
26C2×#66867C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622181—22no—
29#10622167—22no—
30#10622102—22no—
31C22×Q8×C11—21no—
32C22×D44D411yescharacteristic
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C11×#125—21no—
40C11×#125—21no—
41C11×#125—21no—
42C11×#125—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×#4326—24no—
51C2×#4326—44no—
52C2×#4325—24no—
53C2×#4325—44no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11D412yes—
59C2×Dic11⋊C4—22no—
60C22×C11⋊C8—21no—
61C22×C11⋊C8—21no—
62#66928—21no—
63#66928—21no—
64#66928—21no—
65#66928—21no—
66C11×#107—24no—
67C11×#106—24no—
68C11×#97—21no—
69C11×#97D412yes—
70C11⋊#95—22no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73#66867—21no—
74#66867—21no—
75#66867—21no—
76#66867D412yes—
77#10082—111nomaximal, Sylow
78C23×D11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C2×Q8×C11—41no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—22no—
90C22×Dic11—21no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44—42no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—42no—
97C2×C8×C11—24no—
98C2×C8×C11—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115#4326—48no—
116#4325—48no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—82no—
122(C2×D11)⋊C4—82no—
123C4⋊Dic11—42no—
124Dic11⋊C4—82no—
125C2×C11⋊C8—24no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×#501D1111yescharacteristic, complemented
131C2×#497—111no—
132#2820—111no—
133#1993—111no—
134C2×#330—111no—
135C2×#329—111no—
136#1295—111no—
137C23×C11#12011yescharacteristic
138C22×D11—41no—
139C22×D11—42no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—42no—
143Q8×C11—42no—
144Q8×C11—42no—
145Q8×C11—82no—
146C2×C4×C11—22no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—82no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168D44—42no—
169D44—81no—
170Dic22—42no—
171Dic22—81no—
172C8×C11—24no—
173C11⋊C8—24no—
174C11⋊C8—42no—
175C22×Q16—221no—
176C22×SD16—221no—
177C2×C4⋊Q8C2×D1111yescharacteristic
178C2×#125C2×D1111yescharacteristic
179C2×#124—111no—
180#501—22no—
181#501—22no—
182#497—222no—
183#497—222no—
184C2×#107—21no—
185C2×#106—21no—
186C2×#97—111no—
187C2×#97—111no—
188C2×#97C2×D1111yescharacteristic
189#399—221no—
190#397—221no—
191#396—222no—
192#395—221no—
193#394—221no—
194#382—111no—
195#340—222no—
196#330—222no—
197#329—222no—
198C22×C11#39211yescharacteristic
199C22×C11#45312yes—
200C22×C11#45511yescharacteristic
201C22×C11#45611yescharacteristic
202C22×C11#45612yes—
203C2×D11—82no—
204C2×D11—82no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—81no—
215C4×C11—82no—
216C4×C11—81no—
217Dic11—82no—
218Dic11—81no—
219C22×Q8—21no—
220C22×Q8—111no—
221C22×D4—111no—
222C2×Q16—224no—
223C2×Q16—444no—
224C2×SD16—224no—
225C2×SD16—444no—
226C22×C8—21no—
227C22×C8—221no—
228C22×C8—221no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8C22⋊D1112yes—
233#125—21no—
234#125—21no—
235#125—21no—
236#125—21no—
237#124—221no—
238#124—221no—
239#124—221no—
240#124—221no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—112no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4C22⋊D1111yescharacteristic
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—222no—
252C2×C22⋊C4—222no—
253C2×C42C22×D1111yescharacteristic
254#107—24no—
255#106—24no—
256#97—21no—
257#97—112no—
258#97—221no—
259#97—221no—
260#97—221no—
261#97C22⋊D1112yes—
262#95—222no—
263#95—221no—
264#95—221no—
265C2×C11#166012yes—
266C2×C11#166112yes—
267C2×C11#200211yescharacteristic
268C2×C11#200511yescharacteristic
269C2×C11#200711yescharacteristic
270D11—161no—
271C24—221no—
272C2×Q8—22no—
273C2×Q8—42no—
274C2×Q8—42no—
275C2×Q8—41no—
276C2×Q8—221no—
277C2×Q8—221no—
278C2×Q8—442no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—442no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—222no—
286C22×C4—221no—
287C22×C4D4×D1111yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290Q16—448no—
291SD16—448no—
292C2×C8—24no—
293C2×C8—22no—
294C2×C8—224no—
295C2×C8—222no—
296C2×C8—222no—
297C2×C8—441no—
298C2×C8—441no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—442no—
312C4⋊C4—882no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—882no—
318C22⋊C4—882no—
319C42D4×D1111yescharacteristic
320C42#434111yescharacteristic
321C42C2×C22⋊D1111yescharacteristic
322C42C2×C22⋊D1111yescharacteristic
323C11#1008211yescharacteristic, complemented, Sylow
324C23—442no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—442no—
329C23#6699011yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—442no—
334Q8—881no—
335D4—442no—
336D4—881no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4#6699011yescharacteristic
354C2×C4#6699111yescharacteristic
355C2×C4#6699211yescharacteristic
356C2×C4#6699211yescharacteristic
357C2×C4#6699311yescharacteristic
358C2×C4#6700611yescharacteristic
359C8—24no—
360C8—224no—
361C8—442no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22—882no—
366C22—882no—
367C22#1062270812yes—
368C22#1062281112yes—
369C22#1062281511yescharacteristic
370C22#1062281811yescharacteristic
371C22#1062283611yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—81no—
379C4—82no—
380C4—81no—
381C4—881no—
382C4—882no—
383C2—1761no—
384C2#1306792612yes—
385C2#1306793112yes—
386C2#1306962811yescharacteristic
387C2#1306965211yescharacteristic
388C2#1306966111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#501C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#501D11
hypocenterC11#10082
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #13069590C2semidirect
4. C2×#10622181C2semidirect
6. #13066498C2semidirect
7. C2×C11×#501C2semidirect
130. C2×#501D11semidirect
323. C11#10082semidirect

Maximal subgroups

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

subgroupindex
C2×#106226992
#130766662
#130695902
C2×#106221812
C2×#106221022
#130664982
C2×C11×#5012
#1008211