Finite Group Databasebeta

← #14655826

Subgroups — #14655826

Order 2816.

496 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 103 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#13078409C211yesmaximal, characteristic
2C2×#10622700C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic, complemented
4#13067019C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic, complemented
7C11×#3230C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#500—21no—
12C11×#487—21no—
13C11×#484—22no—
14C11×#477—22no—
15C11×#431C2211yescharacteristic
16#10622700—22no—
17#10622700—21no—
18#10622700—22no—
19#10622697—21no—
20#10622679—22no—
21#10622614—21no—
22#10622608—21no—
23C2×#66873—21no—
24C2×#66871—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622184—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622106—22no—
31C22×Q8×C11—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×(C2×D11)⋊C4—21no—
50C2×C4⋊Dic11D411yescharacteristic
51C2×#4318—21no—
52C22×C11⋊C8—21no—
53C4×D44—21no—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C11×#107—24no—
58C11×C4⋊C8—21no—
59C11×#103—24no—
60C11×C22⋊C8D412yes—
61C4×C8×C11—21no—
62C22⋊(C11⋊C8)—21no—
63#66873—24no—
64#66873—22no—
65#66873—22no—
66#66872—22no—
67#66871—24no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75#10190—111nomaximal, Sylow
76C23×D11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×D44Q1612yes—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×C4×D11—82no—
96C2×C8×C11—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117#4318—41no—
118#4318—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124#3230D1111yescharacteristic, complemented
125#3077—111no—
126C2×#474—111no—
127#1548—111no—
128#1481—111no—
129#1460—111no—
130#1301—111no—
131C23×C11#12111yescharacteristic
132C22×D11—22no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—81no—
136C22×D11—81no—
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—82no—
140Q8×C11—82no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C2×C4×C11C2×Q1611yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—41no—
158C2×Dic11—81no—
159D44—22no—
160D44—22no—
161D44—41no—
162D44—41no—
163C4×D11—82no—
164C4×D11—82no—
165C8×C11—42no—
166C11⋊C8—42no—
167C11⋊C8—42no—
168C11⋊C8—81no—
169#533C2×D1111yescharacteristic
170C2×C4⋊Q8C2×D1111yescharacteristic
171C2×C4×D4—111no—
172#500—21no—
173#487—21no—
174#484—22no—
175#478—222no—
176#477—22no—
177#476—221no—
178#474—222no—
179#474—221no—
180#474—222no—
181#431—111no—
182#431C2×D1111yescharacteristic
183#428—221no—
184C2×#107—221no—
185#423—111no—
186C2×C4⋊C8—111no—
187#418—221no—
188C2×#102—221no—
189#333—222no—
190Q8⋊C8—222no—
191#323—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11#39211yescharacteristic
195C22×C11#46711yescharacteristic
196C22×C11#47011yescharacteristic
197C2×D11—42no—
198C2×D11—82no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—82no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—81no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11#45111yescharacteristic
209C4×C11#45111yescharacteristic
210C4×C11#45211yescharacteristic
211C4×C11#45211yescharacteristic
212C4×C11#47212yes—
213Dic11—81no—
214C22×Q8—21no—
215C22×D4—111no—
216C23×C4—221no—
217C2×M16—221no—
218C22×C8—221no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8C22⋊D1112yes—
223C4⋊Q8C22⋊D1111yescharacteristic
224C4⋊Q8C22⋊D1111yescharacteristic
225#125—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×D4—221no—
231C4×D4—221no—
232C4×D4—221no—
233C4×D4—221no—
234#117—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—111no—
238C2×C22⋊C4—221no—
239C2×C42C22×D1111yescharacteristic
240#107—24no—
241#107—224no—
242#107—222no—
243#106—222no—
244C4⋊C8—21no—
245C4⋊C8—112no—
246C4⋊C8—112no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250#103—24no—
251#102—224no—
252#102—222no—
253#102—222no—
254C22⋊C8—221no—
255C22⋊C8C22⋊D1112yes—
256C4×C8—21no—
257C4×C8—221no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11#200111yescharacteristic
261C2×C11#200911yescharacteristic
262C2×C11#201811yescharacteristic
263D11—82no—
264C24—221no—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—82no—
270C2×D4—112no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C22×C4—41no—
277C22×C4—221no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4—882no—
281C22×C4D4×D1111yescharacteristic
282C22×C4#434111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284M16—441no—
285M16—441no—
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—441no—
290C2×C8—441no—
291C2×C8—441no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C22⋊C4—41no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C42—41no—
308C42D4×D1111yescharacteristic
309C42D4×D1111yescharacteristic
310C42C2×C22⋊D1111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C11#1019011yescharacteristic, complemented, Sylow
313C23—222no—
314C23—441no—
315C23—441no—
316C23—881no—
317C23—881no—
318C23#6699111yescharacteristic
319Q8—42no—
320Q8—42no—
321Q8—82no—
322Q8—82no—
323D4—222no—
324D4—222no—
325D4—441no—
326D4—441no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—441no—
334C2×C4—882no—
335C2×C4—882no—
336C2×C4—881no—
337C2×C4Q16×D1111yescharacteristic
338C2×C4#6697111yescharacteristic
339C2×C4#6697111yescharacteristic
340C2×C4#6697211yescharacteristic
341C2×C4#6699011yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699211yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4#6699311yescharacteristic
346C2×C4#6700611yescharacteristic
347C8—42no—
348C8—442no—
349C8—442no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—442no—
354C22—882no—
355C22—882no—
356C22—881no—
357C22—881no—
358C22#1062280111yescharacteristic
359C22#1062280211yescharacteristic
360C22#1062283611yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—82no—
366C4—81no—
367C4—881no—
368C4#1062279911yescharacteristic
369C4#1062279911yescharacteristic
370C4#1062280011yescharacteristic
371C4#1062280011yescharacteristic
372C4#1062281212yes—
373C2—21no—
374C2—21no—
375C2—882no—
376C2#1306962311yescharacteristic
377C2#1306967611yescharacteristic
378C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3230C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#3230D11
hypocenterC11#10190
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
3. #13067297C2semidirect
4. #13067019C2semidirect
6. #13066512C2semidirect
7. C11×#3230C2semidirect
124. #3230D11semidirect
312. C11#10190semidirect

Maximal subgroups

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

subgroupindex
#130784092
C2×#106227002
#130672972
#130670192
#130669362
#130665122
C11×#32302
#1019011