Finite Group Databasebeta

← #14650288

Subgroups — #14650288

Order 2816.

480 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079741C211yesmaximal, characteristic
2#13077360C211yesmaximal, characteristic
3#13069604C211yesmaximal, characteristic, complemented
4C2×#10622120C211yesmaximal, characteristic, complemented
5#13066511C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C11×#1547C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67001—21no—
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622847—21no—
14#10622692—21no—
15#10622683—21no—
16#10622647C414yes—
17#10622625—21no—
18#10622624—22no—
19D4×C11⋊C8—21no—
20#10622621—22no—
21#10622538C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24C11×#332—21no—
25C11×#331—21no—
26#10622192—21no—
27#10622192—21no—
28#10622120—21no—
29#10622120—21no—
30C2×C11×#41—21no—
31C22×Dic22—21no—
32C2×C11×M16—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121C2×C412yes—
39C4×D4×C11—21no—
40C4×D4×C11D412yes—
41C2×C42×C11C2311yescharacteristic
42#67001—42no—
43#67001—42no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11C2×C412yes—
46C2×#4318—22no—
47C2×#4318D411yescharacteristic
48C2×#4318D411yescharacteristic
49C22×C11⋊C8—22no—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59#66896—24no—
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)—22no—
62C22⋊(C11⋊C8)C2×C412yes—
63#66872—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D411yescharacteristic
67C4⋊(C11⋊C8)D411yescharacteristic
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#9269—111nomaximal, Sylow
72C11×#41—41no—
73C11×#41—41no—
74C11×#41—41no—
75C11×#41—41no—
76C2×Q8×C11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11C22⋊C412yes—
81C22×C4×C11—22no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—22no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22—81no—
89C2×Dic22—81no—
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—81no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4C22⋊C412yes—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107#4318—21no—
108#4318—21no—
109#4318—21no—
110#4318—44no—
111#4318SD1612yes—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—21no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—44no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120#3227—111no—
121#2935—111no—
122#1997—111no—
123#1547D1111yescharacteristic
124C2×#332—111no—
125#1301—111no—
126#1283—111no—
127C23×C11—22no—
128C23×C11C4×D411yescharacteristic
129Q8×C11—41no—
130Q8×C11—41no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—41no—
137D4×C11—41no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11C2×SD1611yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×Dic11—42no—
155C2×Dic11—82no—
156Dic22—82no—
157Dic22—81no—
158Dic22—81no—
159C8×C11—81no—
160C8×C11—81no—
161C11⋊C8—22no—
162C11⋊C8—42no—
163C11⋊C8—41no—
164C11⋊C8—41no—
165C11⋊C8—41no—
166C2×#131—221no—
167#532C2×D1111yescharacteristic
168C2×C4⋊Q8—111no—
169#498—221no—
170#486—221no—
171#481—114no—
172#476—222no—
173#436—221no—
174#435—222no—
175C8×D4—221no—
176#431—111no—
177#423C2×D1111yescharacteristic
178C2×C4⋊C8—111no—
179C2×C4⋊C8C2×D1111yescharacteristic
180#408—221no—
181C4×M16—111no—
182#343—221no—
183#343—221no—
184#332—21no—
185#332—221no—
186#332—221no—
187#331—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11#38611yescharacteristic
194C22×C11C4×SD1611yescharacteristic
195C22×C11#44011yescharacteristic
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—42no—
200C4×C11#45011yescharacteristic
201C4×C11#45211yescharacteristic
202C4×C11#46111yescharacteristic
203C4×C11#46311yescharacteristic
204C4×C11#47111yescharacteristic
205C4×C11#47211yescharacteristic
206Dic11—82no—
207C2×#41—21no—
208C22×Q8—221no—
209#131—442no—
210#131—442no—
211C2×M16—21no—
212C2×M16—111no—
213C2×M16—111no—
214C2×M16—222no—
215C22×C8—21no—
216C22×C8—222no—
217C22×C8—221no—
218C4⋊Q8—221no—
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8C22⋊D1111yescharacteristic
223#127C22⋊D1111yescharacteristic
224#124—21no—
225#121—21no—
226#121C4×D1112yes—
227C4×D4—21no—
228C4×D4D4412yes—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—221no—
231C2×C42C22×D1111yescharacteristic
232#106—224no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—111no—
238C4⋊C8—111no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241#102—224no—
242C22⋊C8—112no—
243C22⋊C8—222no—
244C22⋊C8—222no—
245#97—221no—
246C4×C8—221no—
247C4×C8—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—82no—
251C2×C11#187711yescharacteristic
252C2×C11#190711yescharacteristic
253C2×C11#191511yescharacteristic
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×Q8—441no—
260C2×Q8—441no—
261C2×Q8—881no—
262C2×Q8—881no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4(C2×D11)⋊C412yes—
267C22×C4—22no—
268C22×C4—222no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4#434111yescharacteristic
272M16—41no—
273M16—41no—
274M16—112no—
275M16—221no—
276M16—221no—
277M16—221no—
278M16—444no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—81no—
282C2×C8—221no—
283C2×C8—221no—
284C2×C8—221no—
285C2×C8—221no—
286C2×C8—222no—
287C2×C8—444no—
288C2×C8—441no—
289C2×C8—441no—
290C4⋊C4—21no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4(C2×D11)⋊C412yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C42C2×D4411yescharacteristic
299C42D4×D1111yescharacteristic
300C42#434111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C11#926911yescharacteristic, complemented, Sylow
303C23—22no—
304C23(C22⋊D11)⋊C411yescharacteristic
305Q8—41no—
306Q8—41no—
307Q8—882no—
308Q8—881no—
309Q8—881no—
310D4—42no—
311D4—42no—
312D4—42no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—442no—
324C2×C4—882no—
325C2×C4(C22⋊D11)⋊C411yescharacteristic
326C2×C4#6693511yescharacteristic
327C2×C4#6693911yescharacteristic
328C2×C4#6696411yescharacteristic
329C2×C4#6696511yescharacteristic
330C2×C4SD16×D1111yescharacteristic
331C2×C4#6696811yescharacteristic
332C2×C4C2×(C2×D11)⋊C411yescharacteristic
333C2×C4#6699211yescharacteristic
334C2×C4#6699211yescharacteristic
335C8—81no—
336C8—81no—
337C8—222no—
338C8—442no—
339C8—441no—
340C8—441no—
341C8—441no—
342C22—21no—
343C22—21no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22#1062237011yescharacteristic
348C22#1062237111yescharacteristic
349C22#1062257111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—882no—
355C4#1062238911yescharacteristic
356C4#1062239611yescharacteristic
357C4#1062276611yescharacteristic
358C4#1062277511yescharacteristic
359C4#1062281211yescharacteristic
360C4#1062281611yescharacteristic
361C2—21no—
362C2—21no—
363C2—82no—
364C2#1306894811yescharacteristic
365C2#1306912211yescharacteristic
366C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1547C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1547D11
hypocenterC11#9269
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
3. #13069604C2semidirect
4. C2×#10622120C2semidirect
5. #13066511C2semidirect
6. #13066466C2semidirect
302. C11#9269semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130773602
#130696042
C2×#106221202
#130665112
#130664662
C11×#15472
#926911