Finite Group Databasebeta

← #14650301

Subgroups — #14650301

Order 2816.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic
2#13077359C211yesmaximal, characteristic
3#13069461C211yesmaximal, characteristic, complemented
4#13067291C211yesmaximal, characteristic
5#13066513C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66954—21no—
10#10623008C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×#66900—21no—
14C2×#66900—21no—
15#10622723—21no—
16#10622701—21no—
17#10622700—22no—
18#10622691—21no—
19#10622580C414yes—
20#10622538C2211yescharacteristic
21#10622537C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23#10622451—21no—
24#10622449—22no—
25#10622447—21no—
26C11×#332—21no—
27C11×#332—21no—
28#10622124—21no—
29#10622123—21no—
30C22×Q8×C11—21no—
31C2×#4339—21no—
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C412yes—
40C2×C42×C11C2311yescharacteristic
41#66983—21no—
42#66983C2×C412yes—
43C2×#4318—21no—
44C2×#4318D411yescharacteristic
45C2×#4318D411yescharacteristic
46#66954—42no—
47#66954—42no—
48C2×#4313—22no—
49C2×C8×D11—22no—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44D412yes—
54#66922D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D411yescharacteristic
59C11×C4⋊C8D411yescharacteristic
60#66900—42no—
61#66900—42no—
62C22⋊(C11⋊C8)C2×C412yes—
63(C2×D11)⋊C8—22no—
64(C2×D11)⋊C8—22no—
65#66873—24no—
66#66871—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70#66867—21no—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—21no—
73#9271—111nomaximal, Sylow
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C22×C4×C11—22no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C22⋊D11—22no—
85#4339—41no—
86#4339—41no—
87#4339—41no—
88#4339—41no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44C22⋊C412yes—
92C2×C4×D11—22no—
93C2×Dic22—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—81no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110C4⋊Dic11—21no—
111C4⋊Dic11C22⋊C412yes—
112#4318—21no—
113#4318—21no—
114#4318—21no—
115#4318—41no—
116#4318—41no—
117#4318D812yes—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—41no—
122#4313—44no—
123C8×D11—44no—
124#3226—111no—
125#2935—111no—
126#1966—111no—
127#1547—111no—
128C2×#332D1111yescharacteristic, complemented
129#1301—111no—
130#1283—111no—
131C23×C11C4×D411yescharacteristic
132C22×D11—22no—
133Q8×C11—81no—
134Q8×C11—81no—
135Q8×C11—81no—
136Q8×C11—81no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C22⋊D11—42no—
154C22⋊D11—42no—
155C2×Dic11—22no—
156D44—42no—
157D44—41no—
158D44—41no—
159D44—41no—
160D44—41no—
161C4×D11—42no—
162C4×D11—42no—
163Dic22—41no—
164Dic22—41no—
165C8×C11—41no—
166C8×C11—41no—
167C8×C11—81no—
168C11⋊C8—22no—
169C11⋊C8—42no—
170C11⋊C8—41no—
171C11⋊C8—81no—
172C2×#131—221no—
173#532—111no—
174C2×C4⋊Q8C2×D1111yescharacteristic
175#500—221no—
176#486—221no—
177#480—114no—
178#474—222no—
179#436—221no—
180#435—222no—
181C8×D4—221no—
182#431—111no—
183#423—111no—
184C2×C4⋊C8C2×D1111yescharacteristic
185C2×C4⋊C8C2×D1111yescharacteristic
186C2×#101—221no—
187C2×#101—221no—
188#408—221no—
189C4×M16—111no—
190#332—21no—
191#332—21no—
192#332—221no—
193#331—221no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11#38611yescharacteristic
197C22×C11C4×D811yescharacteristic
198C22×C11#44211yescharacteristic
199C2×D11—42no—
200C2×D11—42no—
201C2×D11—42no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—82no—
206C4×C11#44711yescharacteristic
207C4×C11#44911yescharacteristic
208C4×C11#45911yescharacteristic
209C4×C11#46311yescharacteristic
210C4×C11#47111yescharacteristic
211C4×C11#47311yescharacteristic
212Dic11—42no—
213C2×#41—221no—
214C22×Q8—21no—
215#131—442no—
216#131—442no—
217C2×M16—111no—
218C2×M16—111no—
219C2×M16—222no—
220C2×M16—221no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—222no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—111no—
229#127—111no—
230#124—221no—
231#121—112no—
232#121—221no—
233C4×D4—112no—
234C4×D4—221no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C4×D1112yes—
237C2×C42C22×D1111yescharacteristic
238#107—224no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—221no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8C22⋊D1111yescharacteristic
246C4⋊C8C22⋊D1111yescharacteristic
247#102—224no—
248#101—442no—
249#101—442no—
250C22⋊C8—112no—
251C22⋊C8—222no—
252C22⋊C8—222no—
253#97—221no—
254C4×C8—221no—
255C4×C8—221no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11#187911yescharacteristic
259C2×C11#190811yescharacteristic
260C2×C11#191511yescharacteristic
261D11—82no—
262#41—441no—
263#41—441no—
264#41—441no—
265#41—441no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—221no—
273C2×D4—112no—
274C2×D4—222no—
275C2×D4—221no—
276C2×D4—221no—
277C22×C4—22no—
278C22×C4—222no—
279C22×C4C2×C4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4#434111yescharacteristic
282M16—112no—
283M16—221no—
284M16—221no—
285M16—221no—
286M16—444no—
287M16—441no—
288M16—441no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—81no—
295C2×C8—221no—
296C2×C8—222no—
297C2×C8—221no—
298C2×C8—444no—
299C2×C8—441no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—112no—
305C4⋊C4—221no—
306C22⋊C4—222no—
307C22⋊C4—222no—
308C42#433911yescharacteristic
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C11#927111yescharacteristic, complemented, Sylow
313C23—222no—
314C23(C22⋊D11)⋊C411yescharacteristic
315Q8—81no—
316Q8—81no—
317Q8—81no—
318Q8—81no—
319Q8—441no—
320Q8—441no—
321D4—442no—
322D4—442no—
323D4—442no—
324D4—441no—
325D4—441no—
326D4—441no—
327D4—441no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—222no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4C22⋊C4×D1111yescharacteristic
338C2×C4#6693611yescharacteristic
339C2×C4#6693711yescharacteristic
340C2×C4D8×D1111yescharacteristic
341C2×C4#6696411yescharacteristic
342C2×C4#6696711yescharacteristic
343C2×C4#6696911yescharacteristic
344C2×C4C4×C22⋊D1111yescharacteristic
345C2×C4#6699011yescharacteristic
346C2×C4#6699111yescharacteristic
347C8—41no—
348C8—41no—
349C8—81no—
350C8—222no—
351C8—442no—
352C8—441no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22—442no—
357C22—442no—
358C22—442no—
359C22#1062236911yescharacteristic
360C22#1062239811yescharacteristic
361C22#1062256911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—442no—
367C4#1062239911yescharacteristic
368C4#1062240011yescharacteristic
369C4#1062276911yescharacteristic
370C4#1062278511yescharacteristic
371C4#1062279011yescharacteristic
372C4#1062280511yescharacteristic
373C2—21no—
374C2—21no—
375C2—882no—
376C2#1306896111yescharacteristic
377C2#1306913411yescharacteristic
378C2#1306916511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenterC2×#332D11
hypocenterC11#9271
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #13069461C2semidirect
5. #13066513C2semidirect
6. #13066466C2semidirect
7. C2×C11×#332C2semidirect
128. C2×#332D11semidirect
312. C11#9271semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130773592
#130694612
#130672912
#130665132
#130664662
C2×C11×#3322
#927111