Finite Group Databasebeta

← #14650315

Subgroups — #14650315

Order 2816.

560 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C211yesmaximal, characteristic
2#13077359C211yesmaximal, characteristic, complemented
3#13069457C211yesmaximal, characteristic, complemented
4#13067291C211yesmaximal, characteristic, complemented
5#13066513C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C2×#66954—21no—
10#10623008C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622830C414yes—
14C2×#66897—21no—
15C2×#66897—21no—
16#10622723—21no—
17#10622686—21no—
18#10622685—22no—
19#10622683—21no—
20#10622538C2211yescharacteristic
21#10622537C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23#10622451—21no—
24#10622449—22no—
25#10622447—21no—
26C11×#331—21no—
27C11×#331—21no—
28#10622124—21no—
29#10622123—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C412yes—
33C2×#4339—21no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4323—24no—
42#66983—21no—
43#66983C2×C412yes—
44C2×#4318—21no—
45C2×#4318D411yescharacteristic
46C2×#4318D411yescharacteristic
47#66954—42no—
48#66954—42no—
49C2×#4313—22no—
50C2×C8×D11—22no—
51#66928—21no—
52#66927D411yescharacteristic
53C4×D44—21no—
54C4×D44D412yes—
55#66922D411yescharacteristic
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D411yescharacteristic
60C11×C4⋊C8D411yescharacteristic
61#66897—42no—
62#66897—42no—
63#66896—24no—
64C22⋊(C11⋊C8)C2×C412yes—
65(C2×D11)⋊C8—22no—
66(C2×D11)⋊C8—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70#66867—21no—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—21no—
73#9273—111nomaximal, Sylow
74C24×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—81no—
86C2×D4×C11—81no—
87C2×D4×C11—82no—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—22no—
92#4339—41no—
93#4339—41no—
94#4339—41no—
95#4339—41no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44C22⋊C412yes—
99C2×C4×D11—22no—
100C2×Dic22—21no—
101C2×C8×C11—21no—
102C2×C8×C11—21no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—81no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111#4323—84no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114C4⋊Dic11—21no—
115C4⋊Dic11C22⋊C412yes—
116#4318—21no—
117#4318—21no—
118#4318—21no—
119#4318—41no—
120#4318—41no—
121#4318D812yescomplemented
122C2×C11⋊C8—22no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—41no—
126#4313—44no—
127C8×D11—44no—
128#3205—111no—
129#2935—111no—
130#1965—111no—
131#1547—111no—
132C2×#331D1111yescharacteristic, complemented
133#1301—111no—
134#1283—111no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—82no—
139C23×C11—82no—
140C23×C11C4×D411yescharacteristic
141C22×D11—22no—
142D4×C11—44no—
143D4×C11—82no—
144D4×C11—82no—
145D4×C11—81no—
146D4×C11—81no—
147D4×C11—81no—
148D4×C11—81no—
149D4×C11—81no—
150D4×C11—81no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11C2×C22⋊C411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12311yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C22⋊D11—42no—
165C22⋊D11—42no—
166C2×Dic11—22no—
167D44—42no—
168D44—41no—
169D44—41no—
170D44—41no—
171D44—41no—
172C4×D11—42no—
173C4×D11—42no—
174Dic22—41no—
175Dic22—41no—
176C8×C11—41no—
177C8×C11—41no—
178C8×C11—81no—
179C11⋊C8—22no—
180C11⋊C8—42no—
181C11⋊C8—41no—
182C11⋊C8—81no—
183C2×#131—221no—
184#532—111no—
185C2×#127C2×D1111yescharacteristic
186#493—221no—
187#486—221no—
188#459—222no—
189#447—114no—
190#436—221no—
191#435—222no—
192C8×D4—221no—
193#431—111no—
194#423—111no—
195C2×C4⋊C8C2×D1111yescharacteristic
196C2×C4⋊C8C2×D1111yescharacteristic
197C2×#100—221no—
198C2×#100—221no—
199#408—221no—
200C4×M16—111no—
201#332—221no—
202#331—21no—
203#331—21no—
204#331—221no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—162no—
211C22×C11—162no—
212C22×C11#38611yescharacteristic
213C22×C11C4×D811yescharacteristic
214C22×C11#44211yescharacteristic
215C2×D11—42no—
216C2×D11—42no—
217C2×D11—42no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11#44711yescharacteristic
222C4×C11#44911yescharacteristic
223C4×C11#45911yescharacteristic
224C4×C11#46311yescharacteristic
225C4×C11#47111yescharacteristic
226C4×C11#47211yescharacteristic
227Dic11—42no—
228C2×#41—221no—
229C22×D4—21no—
230C22×D4—21no—
231C22×D4C4×D1112yes—
232C2×D8—224no—
233#131—442no—
234#131—442no—
235C2×M16—111no—
236C2×M16—111no—
237C2×M16—222no—
238C2×M16—221no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—222no—
242C4⋊Q8—111no—
243#127—21no—
244#127—21no—
245#127—21no—
246#127—21no—
247#127—111no—
248#124—221no—
249#121—112no—
250#121—221no—
251C4×D4—112no—
252C4×D4—221no—
253C2×C42C22×D1111yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8C22⋊D1111yescharacteristic
261C4⋊C8C22⋊D1111yescharacteristic
262#102—224no—
263#100—442no—
264#100—442no—
265C22⋊C8—112no—
266C22⋊C8—222no—
267C22⋊C8—222no—
268#97—221no—
269C4×C8—221no—
270C4×C8—221no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—162no—
274C2×C11#187911yescharacteristic
275C2×C11#190711yescharacteristic
276C2×C11#191411yescharacteristic
277D11—82no—
278C24—22no—
279#41—441no—
280#41—441no—
281#41—441no—
282#41—441no—
283C2×Q8—221no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—81no—
295C2×D4—81no—
296C2×D4—82no—
297C2×D4—112no—
298C2×D4—222no—
299C2×D4—221no—
300C2×D4—221no—
301C22×C4—222no—
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4#434111yescharacteristic
305D8—884no—
306M16—112no—
307M16—221no—
308M16—221no—
309M16—221no—
310M16—444no—
311M16—441no—
312M16—441no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—81no—
319C2×C8—221no—
320C2×C8—222no—
321C2×C8—221no—
322C2×C8—444no—
323C2×C8—441no—
324C4⋊C4—112no—
325C4⋊C4—221no—
326C22⋊C4—222no—
327C22⋊C4—222no—
328C42#433911yescharacteristic
329C42D4×D1111yescharacteristic
330C42D4×D1111yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C11#927311yescharacteristic, complemented, Sylow
333C23—42no—
334C23—42no—
335C23—42no—
336C23—82no—
337C23—82no—
338C23—222no—
339C23(C22⋊D11)⋊C411yescharacteristic
340Q8—441no—
341Q8—441no—
342D4—44no—
343D4—82no—
344D4—82no—
345D4—81no—
346D4—81no—
347D4—81no—
348D4—81no—
349D4—81no—
350D4—81no—
351D4—442no—
352D4—442no—
353D4—442no—
354D4—441no—
355D4—441no—
356D4—441no—
357D4—441no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—222no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4C22⋊C4×D1111yescharacteristic
365C2×C4#6693611yescharacteristic
366C2×C4#6693711yescharacteristic
367C2×C4D8×D1111yescharacteristic
368C2×C4#6696411yescharacteristic
369C2×C4#6696711yescharacteristic
370C2×C4#6696911yescharacteristic
371C2×C4C4×C22⋊D1111yescharacteristic
372C2×C4#6699011yescharacteristic
373C2×C4#6699111yescharacteristic
374C8—41no—
375C8—41no—
376C8—81no—
377C8—222no—
378C8—442no—
379C8—441no—
380C8—881no—
381C22—21no—
382C22—21no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—162no—
387C22—162no—
388C22—442no—
389C22—442no—
390C22—442no—
391C22#1062236911yescharacteristic
392C22#1062239811yescharacteristic
393C22#1062256911yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—442no—
398C4#1062239911yescharacteristic
399C4#1062240011yescharacteristic
400C4#1062276911yescharacteristic
401C4#1062277311yescharacteristic
402C4#1062278511yescharacteristic
403C4#1062279011yescharacteristic
404C2—21no—
405C2—21no—
406C2—162no—
407C2—882no—
408C2#1306896111yescharacteristic
409C2#1306912711yescharacteristic
410C2#1306916011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC22×C11#386
prime radical#13079534C2
cosocleC2×C42×C11C23
hypercenterC2×#331D11
hypocenterC11#9273
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #13077359C2semidirect
3. #13069457C2semidirect
4. #13067291C2semidirect
5. #13066513C2semidirect
6. #13066466C2semidirect
7. C2×C11×#331C2semidirect
121. #4318D8semidirect
132. C2×#331D11semidirect
332. C11#9273semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130773592
#130694572
#130672912
#130665132
#130664662
C2×C11×#3312
#927311