Finite Group Databasebeta

← #14909727

Subgroups — #14909727

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2#13070875C212yesmaximal, complemented
3#13070847C212yesmaximal, complemented
4#13070663C211yesmaximal, characteristic, complemented
5#13070658C211yesmaximal, characteristic, complemented
6#13070653C211yesmaximal, characteristic, complemented
7#13070648C211yesmaximal, characteristic, complemented
8#13070556C212yesmaximal, complemented
9#13070539C212yesmaximal, complemented
10#13070415C211yesmaximal, characteristic, complemented
11C11×#3147C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C2×C11×#135C2212yes—
14C11×#532—21no—
15#10623010—21no—
16C11×#495—21no—
17C11×#495C2212yes—
18C11×#494C2211yescharacteristic
19C11×#493C2211yescharacteristic
20C11×#492—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66893C2212yes—
23C2×#66892C2212yes—
24C2×#66891C2212yes—
25C2×#66890C2212yes—
26#10622729C2211yescharacteristic
27#10622728C2211yescharacteristic
28#10622727—21no—
29C4×Dic44C2211yescharacteristic
30#10622310—21no—
31#10622309C2211yescharacteristic
32C4×D88C2211yescharacteristic
33C4×#4314—21no—
34#10622296C2211yescharacteristic
35#10622202C2212yes—
36#10622202C2212yes—
37#10622200C2212yes—
38#10622200C2212yes—
39C22⋊(C11⋊C16)C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4⋊(C11⋊C16)C2211yescharacteristic
42C4×C11⋊C16C2212yes—
43C2×C11×#41—22no—
44C11×#135—42no—
45C11×#135—42no—
46C11×#135—44no—
47C2×C11×Q16—21no—
48C2×C11×Q16C2312yes—
49C2×C11×SD16—22no—
50C2×C11×SD16—22no—
51C2×C11×D8—21no—
52C2×C11×D8C2312yes—
53C22×C8×C11D411yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—21no—
56C11×#127—21no—
57C11×#124—22no—
58C11×#121—41no—
59C11×#121—41no—
60C4×D4×C11—41no—
61C4×D4×C11—41no—
62C2×C42×C11D411yescharacteristic
63#66983—21no—
64#66982—41no—
65C4×C22⋊D11—41no—
66#66977—21no—
67C2×Dic44C2311yescharacteristic
68C2×D88C2311yescharacteristic
69C2×#4314—21no—
70#66929—41no—
71#66928—21no—
72C4×D44—21no—
73#66925—41no—
74#66923—21no—
75C4×Dic22—21no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80#66893—42no—
81#66892—42no—
82#66891—42no—
83#66890—42no—
84#66885—21no—
85#66885—21no—
86#66882C2311yescharacteristic
87#66882C2311yescharacteristic
88#66881—21no—
89#66880—21no—
90#66880—21no—
91C2×C11⋊C16C2312yes—
92C2×C11⋊C16C2312yes—
93#33778—111nomaximal, Sylow
94C11×#41—44no—
95C11×#41—44no—
96C2×Q8×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C22×C4×C11—42no—
102C22×C4×C11D811yescharacteristic
103C22×C4×C11D811yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—41no—
106C2×D44—21no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C11×Q16—22no—
110C11×Q16—22no—
111C11×Q16—42no—
112C11×SD16—44no—
113C11×SD16—44no—
114C11×D8—22no—
115C11×D8—22no—
116C11×D8—42no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2411yescharacteristic
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—42no—
128C42×C11D811yescharacteristic
129C42×C11D811yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C22⋊Dic11—41no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141Dic11⋊C4—41no—
142Dic11⋊C4—41no—
143C4×Dic11—41no—
144Dic44—21no—
145Dic44—21no—
146D88—21no—
147D88—21no—
148#4314—42no—
149C11⋊C16—22no—
150C11⋊C16—22no—
151#3168—111no—
152#3147D1111yescharacteristic, complemented
153#2249—112no—
154#2242—112no—
155#2209—111no—
156#2208—111no—
157#2207—111no—
158#2206—111no—
159#2189—112no—
160#2186—112no—
161#2162—111no—
162C23×C11—42no—
163C23×C11C2×D811yescharacteristic
164C22×D11—41no—
165Q8×C11—42no—
166Q8×C11—42no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—82no—
170D4×C11—84no—
171D4×C11—82no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—84no—
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C22⋊D11—82no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188D44—41no—
189D44—41no—
190C4×D11—82no—
191Dic22—41no—
192Dic22—41no—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11AGL(1,ℤ/8)12yes—
196C8×C11H(5,𝔽2)11yescharacteristic
197C8×C11H(5,𝔽2)11yescharacteristic
198C2×#135—21no—
199C2×#135C2×D1112yes—
200#532—21no—
201#529—221no—
202C2×Q32—112no—
203C2×SD32—112no—
204C2×SD32—112no—
205C2×D16—112no—
206#499—111no—
207#495—21no—
208#495—111no—
209#495C2×D1112yes—
210#494C2×D1111yescharacteristic
211#493C2×D1111yescharacteristic
212#492—21no—
213#488—221no—
214#467—111no—
215#466—111no—
216#465—221no—
217C4×Q16—111no—
218C4×SD16—221no—
219C4×D8—111no—
220C2×C4×C8C2×D1111yescharacteristic
221C4⋊C16—111no—
222C4⋊C16—111no—
223#358—112no—
224#358—112no—
225#357—112no—
226#357—112no—
227C22⋊C16—112no—
228C4×C16—112no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—82no—
233C22×C11—82no—
234C22×C11—82no—
235C22×C11C22×D811yescharacteristic
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—82no—
244C4×C11#50812yes—
245C4×C11#53511yescharacteristic
246C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
247Dic11—81no—
248Dic11—81no—
249Dic11—81no—
250C2×#41—22no—
251#135—42no—
252#135—42no—
253#135—44no—
254C2×Q16—21no—
255C2×Q16—111no—
256C2×Q16C22×D1112yes—
257C2×SD16—22no—
258C2×SD16—22no—
259C2×SD16—221no—
260C2×D8—21no—
261C2×D8—111no—
262C2×D8C22×D1112yes—
263C22×C8C22⋊D1111yescharacteristic
264C22×C8C22×D1111yescharacteristic
265C4⋊Q8—21no—
266#127—21no—
267#126—441no—
268#125—221no—
269#124—22no—
270#124—221no—
271#123—441no—
272C22⋊Q8—221no—
273#121—41no—
274#121—41no—
275#121—221no—
276C4×Q8—221no—
277C4×D4—41no—
278C4×D4—41no—
279C4×D4—221no—
280C4×D4—441no—
281#117—441no—
282C2×C42C22⋊D1111yescharacteristic
283Q32—442no—
284SD32—442no—
285SD32—442no—
286D16—442no—
287C2×C16—112no—
288C2×C16—112no—
289#107—111no—
290#107—111no—
291#106—221no—
292#103—221no—
293#103—221no—
294#102—221no—
295#102—221no—
296C4×C8C22⋊D1111yescharacteristic
297C4×C8C22⋊D1111yescharacteristic
298C4×C8C22×D1111yescharacteristic
299C4×C8C22×D1111yescharacteristic
300C2×C11—41no—
301C2×C11—162no—
302C2×C11#320511yescharacteristic
303C2×C11C2×#50811yescharacteristic
304C2×C11#341411yescharacteristic
305D11—161no—
306#41—44no—
307#41—44no—
308C2×Q8—22no—
309C2×Q8—221no—
310C2×D4—22no—
311C2×D4—42no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—221no—
315C2×D4—441no—
316C22×C4—42no—
317C22×C4—441no—
318C22×C4#432311yescharacteristic
319C22×C4#432311yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321Q16—22no—
322Q16—22no—
323Q16—42no—
324Q16—221no—
325Q16—221no—
326SD16—44no—
327SD16—44no—
328SD16—442no—
329D8—22no—
330D8—22no—
331D8—42no—
332D8—221no—
333D8—221no—
334C2×C8—22no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8C2×C22⋊D1111yescharacteristic
338C2×C8C2×C22⋊D1111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—221no—
344C4⋊C4—221no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C42—441no—
357C42#432311yescharacteristic
358C42#432311yescharacteristic
359C42C2×C22⋊D1111yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C16—222no—
362C16—222no—
363C11#3377811yescharacteristic, complemented, Sylow
364C23—42no—
365C23—441no—
366C23C2×#432311yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—441no—
370Q8—441no—
371D4—42no—
372D4—42no—
373D4—82no—
374D4—84no—
375D4—82no—
376D4—441no—
377D4—441no—
378D4—882no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—84no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—882no—
389C2×C4C2×#432311yescharacteristic
390C2×C4C2×#432311yescharacteristic
391C2×C4C2×#432311yescharacteristic
392C2×C4C2×#432311yescharacteristic
393C2×C4C2×#432311yescharacteristic
394C2×C4C22×C22⋊D1111yescharacteristic
395C8—21no—
396C8—21no—
397C8#6698512yes—
398C8#6703711yescharacteristic
399C8#6703711yescharacteristic
400C22—21no—
401C22—21no—
402C22—21no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22—881no—
407C22—881no—
408C22—881no—
409C22C22×#432311yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—82no—
415C4—881no—
416C4—881no—
417C4—881no—
418C4#1062280712yes—
419C4C2×#6698511yescharacteristic
420C4#1062333611yescharacteristic
421C2—41no—
422C2—162no—
423C2—1761no—
424C2#1307953411yescharacteristic
425C2C2×#1062280711yescharacteristic
426C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3147C2
socleC22×C11C22×D8
hypercenter#3147D11
hypocenterC11#33778
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13070875C2semidirect
3. #13070847C2semidirect
4. #13070663C2semidirect
5. #13070658C2semidirect
6. #13070653C2semidirect
7. #13070648C2semidirect
8. #13070556C2semidirect
9. #13070539C2semidirect
10. #13070415C2semidirect
11. C11×#3147C2semidirect
152. #3147D11semidirect
363. C11#33778semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708752
#130708472
#130706632
#130706582
#130706532
#130706482
#130705562
#130705392
#130704152
C11×#31472
#3377811