Finite Group Databasebeta

← #14657367

Subgroups — #14657367

Order 2816.

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

normal subgroups only

This group has 440 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×#10622632C211yesmaximal, characteristic
2#13067392C211yesmaximal, characteristic, complemented
3#13067289C211yesmaximal, characteristic, complemented
4#13067289C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic, complemented
7C11×#1800C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C22×#4324—21no—
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×#100—21no—
14#10622632—22no—
15#10622632—22no—
16C2×#66874—21no—
17#10622538C2211yescharacteristic
18#10622538C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#343—21no—
21D4⋊(C11⋊C8)—22no—
22#10622120—22no—
23#10622120—22no—
24#10622117—22no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11—21no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C2×C11×M16—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4324—24no—
38C2×#4324—42no—
39C2×#4324—42no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C22×C11⋊C8—21no—
43#66922—21no—
44#66922—21no—
45#66922—21no—
46#66922D412yes—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×#100—42no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54#66874—24no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)D412yes—
58C4⋊(C11⋊C8)D412yes—
59C4×C11⋊C8—21no—
60C4×C11⋊C8—21no—
61#10444—111nomaximal, Sylow
62C24×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11D812yes—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—82no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×Dic11—41no—
77C2×Dic22—22no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C11×M16—41no—
84C11×M16—41no—
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97#4324—48no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×#461—111no—
108#1800D1111yescharacteristic
109#1571—111no—
110#1546—111no—
111#1546—111no—
112#1478—111no—
113#1301—111no—
114C23×C11—22no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—81no—
118C23×C11—81no—
119C23×C11#12311yescharacteristic
120D4×C11—22no—
121D4×C11—22no—
122D4×C11—41no—
123D4×C11—41no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—82no—
128C2×C4×C11—82no—
129C2×C4×C11—81no—
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12311yescharacteristic
135C2×C4×C11#12411yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—42no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143Dic22—42no—
144Dic22—42no—
145Dic22—81no—
146Dic22—81no—
147C8×C11—81no—
148C8×C11—81no—
149C11⋊C8—42no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152C22×SD16—221no—
153C2×C4⋊Q8—111no—
154C2×C4×D4C2×D1111yescharacteristic
155#461—222no—
156#461—222no—
157#431—111no—
158#431—111no—
159#423C2×D1111yescharacteristic
160#423C2×D1111yescharacteristic
161C2×C4⋊C8—111no—
162C2×#103—221no—
163C2×#100—21no—
164#343—21no—
165#335—222no—
166#332—222no—
167#332—222no—
168D4⋊C8—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—42no—
172C22×C11—82no—
173C22×C11—82no—
174C22×C11—81no—
175C22×C11—81no—
176C22×C11#39411yescharacteristic
177C22×C11#48011yescharacteristic
178C22×C11#48211yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—81no—
183C4×C11#44711yescharacteristic
184C4×C11#45211yescharacteristic
185C4×C11#46611yescharacteristic
186C4×C11#46811yescharacteristic
187C4×C11#47112yes—
188Dic11—82no—
189C22×Q8—221no—
190C22×D4C22⋊D1111yescharacteristic
191C23×C4—21no—
192C2×SD16—224no—
193C2×SD16—442no—
194C2×SD16—442no—
195C2×M16—21no—
196C2×M16—21no—
197C22×C8—221no—
198C4⋊Q8—112no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4—21no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C22⋊D1111yescharacteristic
209C2×C22⋊C4—21no—
210C2×C42C22×D1111yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—112no—
216C4⋊C8—112no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219#103—224no—
220#100—42no—
221C22⋊C8—221no—
222C22⋊C8—221no—
223C4×C8—221no—
224C4×C8—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—82no—
228C2×C11#203311yescharacteristic
229C2×C11#204611yescharacteristic
230C2×C11#204911yescharacteristic
231C24—21no—
232C2×Q8—222no—
233C2×Q8—441no—
234C2×Q8—441no—
235C2×Q8—441no—
236C2×Q8—441no—
237C2×Q8—441no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4#432312yes—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—82no—
248C22×C4—441no—
249C22×C4#433911yescharacteristic
250C22×C4#433911yescharacteristic
251C22×C4C2×C22⋊D1111yescharacteristic
252SD16—448no—
253M16—41no—
254M16—41no—
255M16—41no—
256M16—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—222no—
260C2×C8—222no—
261C2×C8—441no—
262C2×C8—441no—
263C2×C8—441no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C42D4×D1111yescharacteristic
273C42D4×D1111yescharacteristic
274C42D4×D1111yescharacteristic
275C42#434111yescharacteristic
276C11#1044411yescharacteristic, complemented, Sylow
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23#6698211yescharacteristic
283Q8—442no—
284Q8—442no—
285Q8—881no—
286Q8—881no—
287D4—22no—
288D4—22no—
289D4—41no—
290D4—41no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—442no—
298C2×C4—881no—
299C2×C4—881no—
300C2×C4#6693611yescharacteristic
301C2×C4#6693711yescharacteristic
302C2×C4#6693711yescharacteristic
303C2×C4#6693811yescharacteristic
304C2×C4C2×#432311yescharacteristic
305C2×C4#6699011yescharacteristic
306C2×C4#6699211yescharacteristic
307C2×C4#6699511yescharacteristic
308C2×C4#6700211yescharacteristic
309C2×C4#6700311yescharacteristic
310C8—81no—
311C8—81no—
312C8—442no—
313C8—442no—
314C8—881no—
315C22—21no—
316C22—21no—
317C22—42no—
318C22—82no—
319C22—82no—
320C22—81no—
321C22—81no—
322C22#1062257211yescharacteristic
323C22#1062258011yescharacteristic
324C22#1062261611yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—882no—
330C4#1062236112yes—
331C4#1062264911yescharacteristic
332C4#1062265111yescharacteristic
333C4#1062266011yescharacteristic
334C4#1062266211yescharacteristic
335C2—21no—
336C2—21no—
337C2—82no—
338C2#1306979811yescharacteristic
339C2#1306987711yescharacteristic
340C2#1306989611yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#394
prime radicalC22×D4×C11D4
hypercenter#1800D11
hypocenterC11#10444
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. #13067392C2semidirect
3. #13067289C2semidirect
4. #13067289C2semidirect
6. #13066511C2semidirect
276. C11#10444semidirect

Maximal subgroups

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

subgroupindex
C2×#106226322
#130673922
#130672892
#130670072
#130665112
C11×#18002
#1044411