Finite Group Databasebeta

← #14670653

Subgroups — #14670653

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622514C211yesmaximal, characteristic, complemented
2C2×#10622757C211yesmaximal, characteristic
3C2×#10622153C211yesmaximal, characteristic, complemented
4C2×#10622199C211yesmaximal, characteristic, complemented
5#13066697C211yesmaximal, characteristic, complemented
6#13066693C211yesmaximal, characteristic, complemented
7C11×#2113C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9C2×#67003C411yescharacteristic
10C2×#66954C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C2×#66901C411yescharacteristic
14#10622757—22no—
15#10622757—22no—
16C2×#66889C411yescharacteristic
17C2×#66886C411yescharacteristic
18C2×C8×Dic11C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622514—22no—
22#10622514—22no—
23C2×#66862—21no—
24C2×C16×D11—21no—
25C11×C22⋊C16—21no—
26C11×C22⋊C16—21no—
27#10622199—22no—
28#10622153—22no—
29C2×C11×#41C2×C411yescharacteristic
30C2×#4339C2×C411yescharacteristic
31C11×#131—21no—
32C11×#131—21no—
33C11×#131—21no—
34C11×#131—21no—
35C2×C11×M16—21no—
36C2×C11×M16C2×C411yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11C2311yescharacteristic
39#67003—22no—
40#67003—22no—
41C2×#4326C811yescharacteristic
42C2×#4325C811yescharacteristic
43C2×#4324C811yescharacteristic
44C2×#4323C811yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×#4318C2×C411yescharacteristic
47C22×C11⋊C8C2×C411yescharacteristic
48#66954—21no—
49#66954—21no—
50#66954D412yes—
51#66954D412yes—
52C2×#4313—21no—
53C2×C8×D11—21no—
54C11×M32—21no—
55C11×M32—21no—
56C2×C11×C16—21no—
57C2×C11×C16—21no—
58C2×C11×C16—21no—
59C2×C11×C16D411yescharacteristic
60C2×C11×C16D411yescharacteristic
61#66901—22no—
62#66889—22no—
63#66886—22no—
64C8×Dic11—21no—
65C8×Dic11—21no—
66#66876—21no—
67#66876D412yes—
68C2×C11⋊C16—21no—
69C2×C11⋊C16—21no—
70C2×C11⋊C16—21no—
71C2×C11⋊C16—21no—
72#66862—24no—
73C16×D11—24no—
74#12980—111nomaximal, Sylow
75C11×#41—21no—
76C11×#41—21no—
77C11×#41—21no—
78C11×#41—21no—
79C2×Q8×C11C2×C811yescharacteristic
80C2×D4×C11—21no—
81C2×D4×C11C2×C811yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11C22×C411yescharacteristic
84C2×C22⋊D11—21no—
85C22×Dic11—21no—
86#4339—21no—
87#4339—21no—
88#4339C22⋊C412yes—
89#4339M1612yes—
90C2×D44C2×C811yescharacteristic
91C2×C4×D11—21no—
92C2×Dic22C2×C811yescharacteristic
93C11×M16—21no—
94C11×M16—21no—
95C11×M16—41no—
96C11×M16—41no—
97C2×C8×C11—21no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11#4111yescharacteristic
105C2×C8×C11#4111yescharacteristic
106#4326—22no—
107#4325—22no—
108#4324—22no—
109#4323—22no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112#4318—21no—
113#4318C22⋊C412yes—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—21no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8C2×C811yescharacteristic
118C2×C11⋊C8C2×C811yescharacteristic
119#4313—22no—
120#4313—22no—
121C8×D11—22no—
122C8×D11—22no—
123C11×C16—21no—
124C11×C16—21no—
125C11×C16—41no—
126C11⋊C16—22no—
127C11⋊C16—41no—
128C2×#504—111no—
129C2×#443—111no—
130C2×#350—111no—
131C2×#350—111no—
132#2113D1111yescharacteristic, complemented
133#1376—111no—
134#1374—111no—
135C23×C11—21no—
136C23×C11#13111yescharacteristic
137C22×D11—21no—
138Q8×C11—21no—
139Q8×C11—21no—
140D4×C11—21no—
141D4×C11—21no—
142D4×C11—41no—
143D4×C11—41no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C22×C811yescharacteristic
151C2×C4×C11C2×M1611yescharacteristic
152C2×C4×C11#13111yescharacteristic
153C22⋊D11—22no—
154C22⋊D11—22no—
155C2×Dic11—21no—
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159D44—21no—
160D44C22⋊C812yes—
161C4×D11—22no—
162C4×D11—22no—
163Dic22—21no—
164Dic22C22⋊C812yes—
165C8×C11—41no—
166C8×C11#12011yescharacteristic
167C8×C11#12111yescharacteristic
168C8×C11#12111yescharacteristic
169C8×C11#12311yescharacteristic
170C11⋊C8—22no—
171C11⋊C8—21no—
172C11⋊C8—21no—
173C2×#135—111no—
174C2×#131—111no—
175C2×#131C2×D1111yescharacteristic
176#504—222no—
177#504—222no—
178C2×M32—111no—
179C2×M32—221no—
180C2×M32C2×D1111yescharacteristic
181C22×C16—111no—
182C22×C16—221no—
183C22×C16C2×D1111yescharacteristic
184#443—222no—
185#443—222no—
186C2×#108—111no—
187C2×#104—111no—
188C2×#104—111no—
189C2×C4×C8—111no—
190#350—222no—
191#350—222no—
192C22⋊C16—21no—
193C22⋊C16—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11#40811yescharacteristic
200C22×C11C8×D411yescharacteristic
201C22×C11#43511yescharacteristic
202C2×D11—22no—
203C2×D11—41no—
204C2×D11—41no—
205C4×C11—41no—
206C4×C11#38611yescharacteristic
207C4×C11C2×C22⋊C811yescharacteristic
208C4×C11C8×D411yescharacteristic
209C4×C11#43511yescharacteristic
210Dic11—22no—
211Dic11—42no—
212C2×#41—111no—
213C2×#41C4×D1111yescharacteristic
214#135—222no—
215#135—222no—
216C2×Q16—111no—
217C2×SD16—111no—
218C2×SD16—111no—
219C2×D8—111no—
220#131—21no—
221#131—21no—
222#131—21no—
223#131—21no—
224#131—112no—
225#131—112no—
226#131—221no—
227#131—221no—
228C2×M16—21no—
229C2×M16—111no—
230C2×M16—221no—
231C2×M16C4×D1111yescharacteristic
232C22×C8—21no—
233C22×C8—111no—
234C22×C8—221no—
235C22×C8C22×D1111yescharacteristic
236C2×C42—111no—
237M32—21no—
238M32—21no—
239M32—112no—
240M32—224no—
241M32—221no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—224no—
246C2×C16—221no—
247C2×C16—221no—
248C2×C16—221no—
249C2×C16—221no—
250C2×C16C22⋊D1111yescharacteristic
251C2×C16C22⋊D1111yescharacteristic
252#108—222no—
253#104—222no—
254#104—222no—
255C4×C8—221no—
256C4×C8—221no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—81no—
260C2×C11#186911yescharacteristic
261C2×C11#217011yescharacteristic
262C2×C11#217111yescharacteristic
263D11—42no—
264#41—21no—
265#41—21no—
266#41—21no—
267#41—21no—
268#41—112no—
269#41—112no—
270#41—221no—
271#41—221no—
272C2×Q8—111no—
273C2×Q8C8×D1111yescharacteristic
274C2×D4—21no—
275C2×D4—111no—
276C2×D4—221no—
277C2×D4C8×D1111yescharacteristic
278C22×C4—21no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4C2×C4×D1111yescharacteristic
282Q16—222no—
283SD16—222no—
284SD16—222no—
285D8—222no—
286M16—21no—
287M16—21no—
288M16—41no—
289M16—41no—
290M16—112no—
291M16—221no—
292M16—222no—
293M16—222no—
294C2×C8—21no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—111no—
298C2×C8—111no—
299C2×C8—221no—
300C2×C8—221no—
301C2×C8—221no—
302C2×C8—222no—
303C2×C8—222no—
304C2×C8#433911yescharacteristic
305C2×C8D4×D1111yescharacteristic
306C2×C8D4×D1111yescharacteristic
307C2×C8D4×D1111yescharacteristic
308C2×C8#434111yescharacteristic
309C2×C8C2×C22⋊D1111yescharacteristic
310C42—221no—
311C42—221no—
312C16—21no—
313C16—21no—
314C16—41no—
315C16—222no—
316C16—441no—
317C11#1298011yescharacteristic, complemented, Sylow
318C23—21no—
319C23—221no—
320C23#6695411yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—112no—
324Q8—221no—
325D4—21no—
326D4—21no—
327D4—41no—
328D4—41no—
329D4—112no—
330D4—222no—
331D4—222no—
332D4—221no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—221no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4C22⋊C4×D1111yescharacteristic
343C2×C4(C22⋊D11)⋊C411yescharacteristic
344C2×C4C2×C8×D1111yescharacteristic
345C2×C4M16×D1111yescharacteristic
346C2×C4#6696011yescharacteristic
347C2×C4C4×C22⋊D1111yescharacteristic
348C8—41no—
349C8—222no—
350C8—221no—
351C8—221no—
352C8#6693611yescharacteristic
353C8#6693711yescharacteristic
354C8#6699011yescharacteristic
355C8#6699111yescharacteristic
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—222no—
362C22—441no—
363C22—441no—
364C22#1062234011yescharacteristic
365C22#1062234111yescharacteristic
366C22C8×C22⋊D1111yescharacteristic
367C4—41no—
368C4—222no—
369C4—442no—
370C4D11×C22⋊C811yescharacteristic
371C4(C22⋊D11)⋊C811yescharacteristic
372C4#1062256911yescharacteristic
373C4#1062274011yescharacteristic
374C2—21no—
375C2—21no—
376C2—81no—
377C2—442no—
378C2#1306890511yescharacteristic
379C2#1307045111yescharacteristic
380C2#1307045611yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D11
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#2113C2
socleC22×C11C8×D4
prime radicalC2×#67003C4
cosocleC22×C8×C11C23
hypercenter#2113D11
hypocenterC11#12980
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ #2113

Complements

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

NH ≅ G/Ntype
1. C2×#10622514C2semidirect
3. C2×#10622153C2semidirect
4. C2×#10622199C2semidirect
5. #13066697C2semidirect
6. #13066693C2semidirect
7. C11×#2113C2semidirect
132. #2113D11semidirect
317. C11#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#106225142
C2×#106227572
C2×#106221532
C2×#106221992
#130666972
#130666932
C11×#21132
#1298011