Finite Group Databasebeta

← #14908687

Subgroups — #14908687

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078274C211yesmaximal, characteristic
2#13077224C211yesmaximal, characteristic, complemented
3#13070834C214yesmaximal, complemented
4#13070829C214yesmaximal, complemented
5C2×#10622132C211yesmaximal, characteristic, complemented
6C2×#10622151C211yesmaximal, characteristic, complemented
7#13070365C211yesmaximal, characteristic, complemented
8#13070236C211yesmaximal, characteristic, complemented
9C11×#2148C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11#10623364—21no—
12#10623276—21no—
13C2×#66954C2211yescharacteristic
14C2×C11×M32C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16#10622845—21no—
17#10622802C2212yes—
18#10622784—22no—
19#10622772C2212yes—
20#10622737—21no—
21C2×#66883C2211yescharacteristic
22C2×#66881C2211yescharacteristic
23C2×#66876C2211yescharacteristic
24#10622506C2214yes—
25D11×#108—22no—
26C11×#362C2212yes—
27C11×#361C2212yes—
28#10622203C2212yes—
29#10622201C2212yes—
30#10622152C2214yes—
31#10622151C2214yes—
32#10622132C2214yes—
33C2×C11×#41—21no—
34C2×#4339D411yescharacteristic
35C11×#135—21no—
36C11×#135—21no—
37C11×#135—21no—
38C11×#135—21no—
39C2×C11×Q16C2311yescharacteristic
40C2×C11×SD16—21no—
41C2×C11×D8C2311yescharacteristic
42C2×C11×M16—21no—
43C22×C8×C11C2311yescharacteristic
44#66999—22no—
45#66992—42no—
46#66991—22no—
47#66983—41no—
48C2×C4⋊Dic11—21no—
49#66977—41no—
50C2×#4318—21no—
51C2×#4318D411yescharacteristic
52#66960—42no—
53M16×D11—24no—
54#66954—21no—
55#66954—21no—
56#66954—21no—
57#66954—21no—
58#66954—42no—
59C2×#4313C2312yes—
60C2×C8×D11D412yes—
61C11×M32—21no—
62C11×M32C2312yes—
63C2×C11×C16—21no—
64C11×#108—21no—
65C11×#108C2312yes—
66#66899—22no—
67#66896—22no—
68#66886—24no—
69#66883—21no—
70#66883C2312yes—
71#66881—21no—
72#66881C2312yes—
73#66876—21no—
74#66876C2312yes—
75C2×C11⋊C16—21no—
76#33659—111nomaximal, Sylow
77C11×#41—41no—
78C11×#41—41no—
79C11×#41—41no—
80C11×#41—41no—
81C2×Q8×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—42no—
87C2×C22⋊D11SD1612yes—
88C22×Dic11—41no—
89#4339—21no—
90#4339—21no—
91#4339—21no—
92#4339—21no—
93C2×D44SD1611yescharacteristic
94C2×C4×D11C2×D412yes—
95C2×Dic22SD1611yescharacteristic
96C11×Q16—21no—
97C11×Q16—21no—
98C11×SD16—41no—
99C11×SD16—41no—
100C11×D8—21no—
101C11×D8—21no—
102C11×M16—22no—
103C11×M16—41no—
104C2×C8×C11—41no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11#4111yescharacteristic
107C2×C8×C11#4111yescharacteristic
108C2×C8×C11#4111yescharacteristic
109C2×C8×C11#4111yescharacteristic
110C2×C8×C11C2411yescharacteristic
111C22⋊Dic11—42no—
112(C2×D11)⋊C4—42no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115Dic11⋊C4—42no—
116#4318—21no—
117#4318—21no—
118#4318—22no—
119#4318—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8C2×D412yes—
122#4313—22no—
123#4313—22no—
124#4313—44no—
125C8×D11—22no—
126C8×D11—22no—
127C8×D11—44no—
128C11×C16—22no—
129C11⋊C16—22no—
130#3060—111no—
131#2916—111no—
132#2239—114no—
133#2238—114no—
134C2×#365—111no—
135C2×#365—111no—
136#2148—111no—
137#2148D1111yescharacteristic, complemented
138#2115—111no—
139C23×C11—41no—
140C23×C11C2×SD1611yescharacteristic
141C22×D11C2×SD1612yes—
142Q8×C11—41no—
143Q8×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146D4×C11—81no—
147D4×C11—81no—
148C2×C4×C11—41no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C22⋊D11—22no—
158C22⋊D11—22no—
159C22⋊D11—162no—
160C2×Dic11—42no—
161C2×Dic11—161no—
162C2×Dic11C2×SD1612yes—
163D44—21no—
164D44—21no—
165C4×D11—22no—
166C4×D11—22no—
167Dic22—21no—
168Dic22—21no—
169C8×C11—42no—
170C8×C11#12311yescharacteristic
171C8×C11#12311yescharacteristic
172C8×C11C2×#4111yescharacteristic
173C8×C11C2×#4111yescharacteristic
174C11⋊C8—22no—
175C11⋊C8—42no—
176C2×#135C2×D1111yescharacteristic
177#568—221no—
178C2×#131—111no—
179#537—221no—
180C2×M32—111no—
181C2×M32C2×D1111yescharacteristic
182#470—112no—
183#469—112no—
184#465—222no—
185#430—114no—
186#430—221no—
187C2×#108—111no—
188C2×#108—222no—
189C2×#108C2×D1111yescharacteristic
190C2×#106—111no—
191#417—221no—
192#365—114no—
193#365—114no—
194#362—112no—
195#362C2×D1112yes—
196#361—112no—
197#361C2×D1112yes—
198#349—114no—
199C22×C11—41no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#48111yescharacteristic
204C22×C11#48111yescharacteristic
205C22×C11C22×SD1611yescharacteristic
206C2×D11—22no—
207C2×D11—42no—
208C4×C11—81no—
209C4×C11#48111yescharacteristic
210C4×C11#48111yescharacteristic
211C4×C11C2×#12311yescharacteristic
212C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
213Dic11—22no—
214Dic11—82no—
215C2×#41—21no—
216C2×#41—111no—
217#135—21no—
218#135—21no—
219#135—21no—
220#135—21no—
221C2×Q16C22×D1111yescharacteristic
222C2×SD16—21no—
223C2×D8C22×D1111yescharacteristic
224#131—221no—
225#131—221no—
226#131—221no—
227#131—221no—
228#131—442no—
229#131—442no—
230C2×M16—21no—
231C2×M16—111no—
232C2×M16—112no—
233C2×M16—224no—
234C2×M16—221no—
235C22×C8—112no—
236C22×C8C22×D1111yescharacteristic
237C22⋊Q8—222no—
238C22⋊Q8—441no—
239#121—222no—
240#121—441no—
241#121—442no—
242C2×C4⋊C4—221no—
243M32—21no—
244M32—112no—
245M32—221no—
246M32C22×D1112yes—
247C2×C16—21no—
248C2×C16—221no—
249#108—21no—
250#108—112no—
251#108—224no—
252#108—221no—
253#108C22×D1112yes—
254#106—112no—
255#106—221no—
256#103—222no—
257#102—222no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—161no—
262C2×C11C2×#48111yescharacteristic
263D11—42no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268#41—221no—
269#41—221no—
270#41—221no—
271#41—221no—
272C2×Q8—21no—
273C2×Q8—111no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—112no—
277C2×D4—111no—
278C2×D4—442no—
279C22×C4—41no—
280C22×C4—112no—
281C22×C4—441no—
282C22×C4D4×D1111yescharacteristic
283Q16—21no—
284Q16—21no—
285SD16—41no—
286SD16—41no—
287D8—21no—
288D8—21no—
289M16—22no—
290M16—41no—
291M16—221no—
292M16—221no—
293M16—222no—
294M16—222no—
295M16—222no—
296M16—444no—
297M16—441no—
298C2×C8—41no—
299C2×C8—112no—
300C2×C8—222no—
301C2×C8—222no—
302C2×C8—444no—
303C2×C8—441no—
304C2×C8#433911yescharacteristic
305C2×C8#433911yescharacteristic
306C2×C8D4×D1111yescharacteristic
307C2×C8#434111yescharacteristic
308C2×C8#434111yescharacteristic
309C2×C8C23×D1111yescharacteristic
310C4⋊C4—222no—
311C4⋊C4—442no—
312C4⋊C4—441no—
313C22⋊C4—442no—
314C22⋊C4—442no—
315C16—22no—
316C16—222no—
317C11#3365911yescharacteristic, complemented, Sylow
318C23—41no—
319C23—112no—
320C23SD16×D1111yescharacteristic
321Q8—41no—
322Q8—41no—
323Q8—221no—
324Q8—221no—
325D4—41no—
326D4—41no—
327D4—81no—
328D4—81no—
329D4—222no—
330D4—222no—
331D4—221no—
332D4—221no—
333D4—1762no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—112no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—442no—
341C2×C4—1761no—
342C2×C4#6693611yescharacteristic
343C2×C4#6693611yescharacteristic
344C2×C4#6696411yescharacteristic
345C2×C4#6696411yescharacteristic
346C2×C4SD16×D1111yescharacteristic
347C2×C4C2×D4×D1111yescharacteristic
348C8—42no—
349C8—222no—
350C8—442no—
351C8#6693611yescharacteristic
352C8#6693611yescharacteristic
353C8C2×#433911yescharacteristic
354C8C2×#434111yescharacteristic
355C22—41no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—222no—
360C22—442no—
361C22#1062239011yescharacteristic
362C22#1062239011yescharacteristic
363C22C2×SD16×D1111yescharacteristic
364C4—81no—
365C4—222no—
366C4—882no—
367C4#1062239011yescharacteristic
368C4#1062239011yescharacteristic
369C4C2×#6693611yescharacteristic
370C4C2×#6696411yescharacteristic
371C2—21no—
372C2—21no—
373C2—21no—
374C2—161no—
375C2—442no—
376C2C2×#1062239011yescharacteristic
subgroupG/H
centerC2C2×#10622390
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2148C2
socleC2×C11C2×#481
prime radical#13078274C2
hypercenter#2148D11
hypocenterC11#33659
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #2148

Complements

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

NH ≅ G/Ntype
2. #13077224C2semidirect
3. #13070834C2semidirect
4. #13070829C2semidirect
5. C2×#10622132C2semidirect
6. C2×#10622151C2semidirect
7. #13070365C2semidirect
8. #13070236C2semidirect
9. C11×#2148C2semidirect
137. #2148D11semidirect
317. C11#33659semidirect

Maximal subgroups

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

subgroupindex
#130782742
#130772242
#130708342
#130708292
C2×#106221322
C2×#106221512
#130703652
#130702362
C11×#21482
#3365911