Finite Group Databasebeta

← #14655807

Subgroups — #14655807

Order 2816.

496 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079760C211yesmaximal, characteristic
2#13078423C211yesmaximal, characteristic
3C2×#10622703C211yesmaximal, characteristic
4#13067020C211yesmaximal, characteristic
5#13066939C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic
7C11×#1546C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4326—21no—
10#10623001C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14C2×#66899—21no—
15#10622734—21no—
16#10622733—21no—
17#10622707—22no—
18#10622706—21no—
19#10622703—22no—
20#10622703—22no—
21#10622692—21no—
22#10622584—22no—
23#10622538C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622464—21no—
26#10622463—21no—
27#10622442—22no—
28C11×#332—22no—
29#10622107—22no—
30#10622094—22no—
31C22×Q8×C11—21no—
32C22×Dic22D411yescharacteristic
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4326—24no—
42C2×#4326—42no—
43C2×#4326—42no—
44#66979—21no—
45C2×C4⋊Dic11D411yescharacteristic
46#66977—21no—
47#66977—21no—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C22×C11⋊C8—21no—
51#66923—21no—
52#66922D411yescharacteristic
53#66922D411yescharacteristic
54C4×Dic22—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22—21no—
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C22⋊C8—21no—
64C4×C8×C11—21no—
65#66899—24no—
66C22⋊(C11⋊C8)D412yes—
67#66882—22no—
68#66881—22no—
69#66880—22no—
70#66880—22no—
71#66874—24no—
72#66872—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77#10187—111nomaximal, Sylow
78C2×Q8×C11—22no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—21no—
89C22×Dic11—21no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C2×Dic22SD1612yes—
98C11×M16—41no—
99C11×M16—41no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C22⋊Dic11—41no—
111#4326—48no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122C4×Dic11—41no—
123C4×Dic11—41no—
124C4×Dic11—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129#3229—111no—
130#3078—111no—
131C2×#462—111no—
132#1546D1111yescharacteristic
133#1481—111no—
134#1461—111no—
135#1301—111no—
136C23×C11#12111yescharacteristic
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—81no—
140Q8×C11—81no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—81no—
163Dic22—22no—
164Dic22—22no—
165Dic22—41no—
166Dic22—41no—
167Dic22—42no—
168Dic22—42no—
169C8×C11—42no—
170C8×C11—81no—
171C11⋊C8—42no—
172C11⋊C8—42no—
173C22×Q16—221no—
174#533—111no—
175C2×C4⋊Q8C2×D1111yescharacteristic
176C2×C4×Q8—111no—
177#498—221no—
178#487—221no—
179#483—222no—
180#479—222no—
181#477—221no—
182#475—221no—
183#475—222no—
184#462—222no—
185#462—222no—
186#431—111no—
187#431C2×D1111yescharacteristic
188#428—221no—
189#423C2×D1111yescharacteristic
190C2×C4⋊C8—111no—
191#419—221no—
192C2×#103—221no—
193#332—22no—
194Q8⋊C8—222no—
195#324—222no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11#39211yescharacteristic
199C22×C11#46511yescharacteristic
200C22×C11#46811yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—82no—
205C4×C11#44811yescharacteristic
206C4×C11#44911yescharacteristic
207C4×C11#45011yescharacteristic
208C4×C11#45211yescharacteristic
209C4×C11#47312yes—
210Dic11—42no—
211Dic11—81no—
212Dic11—81no—
213Dic11—81no—
214C22×Q8—21no—
215C22×Q8—111no—
216C2×Q16—224no—
217C2×Q16—442no—
218C2×Q16—442no—
219C2×M16—21no—
220C22×C8—221no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—111no—
225C4⋊Q8—111no—
226C4⋊Q8D4412yes—
227#125—221no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230C4×Q8—221no—
231C4×Q8—221no—
232C4×Q8—221no—
233C4×Q8—221no—
234C4×Q8—221no—
235C4×Q8—221no—
236#117—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—221no—
241C2×C42—221no—
242C2×C42C22×D1111yescharacteristic
243#107—222no—
244#106—224no—
245#106—222no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—112no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251C4⋊C8C22⋊D1112yes—
252#103—224no—
253#103—222no—
254#103—222no—
255#103—224no—
256C22⋊C8—21no—
257C22⋊C8—112no—
258C4×C8—21no—
259C4×C8—221no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11#200011yescharacteristic
263C2×C11#200911yescharacteristic
264C2×C11#202011yescharacteristic
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—112no—
272C2×Q8—221no—
273C2×Q8—221no—
274C2×Q8—221no—
275C2×Q8—221no—
276C2×Q8—221no—
277C2×Q8—221no—
278C2×Q8—221no—
279C22×C4—41no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4#433911yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285Q16—448no—
286M16—41no—
287M16—41no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—441no—
309C42—441no—
310C42—441no—
311C42—441no—
312C42C2×D4411yescharacteristic
313C42D4×D1111yescharacteristic
314C42D4×D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C11#1018711yescharacteristic, complemented, Sylow
317C23#6693711yescharacteristic
318Q8—42no—
319Q8—42no—
320Q8—81no—
321Q8—81no—
322Q8—222no—
323Q8—222no—
324Q8—442no—
325Q8—441no—
326Q8—441no—
327Q8—442no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—222no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—881no—
340C2×C4#6693511yescharacteristic
341C2×C4#6693511yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4#6696411yescharacteristic
344C2×C4#6696511yescharacteristic
345C2×C4SD16×D1111yescharacteristic
346C2×C4#6696811yescharacteristic
347C2×C4#6698311yescharacteristic
348C2×C4#6699011yescharacteristic
349C2×C4#6699311yescharacteristic
350C8—42no—
351C8—81no—
352C8—442no—
353C8—442no—
354C22—21no—
355C22—21no—
356C22#1062239111yescharacteristic
357C22#1062239311yescharacteristic
358C22#1062257311yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—442no—
364C4—881no—
365C4—881no—
366C4—881no—
367C4#1062236812yes—
368C4#1062238911yescharacteristic
369C4#1062239611yescharacteristic
370C4#1062277111yescharacteristic
371C4#1062278311yescharacteristic
372C2—21no—
373C2—21no—
374C2#1306962011yescharacteristic
375C2#1306967811yescharacteristic
376C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1546D11
hypocenterC11#10187
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
316. C11#10187semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130784232
C2×#106227032
#130670202
#130669392
#130665112
C11×#15462
#1018711