Finite Group Databasebeta

← #14909723

Subgroups — #14909723

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#13079044C211yesmaximal, characteristic, complemented
2#13070875C212yesmaximal, complemented
3#13070850C212yesmaximal, complemented
4#13070666C211yesmaximal, characteristic, complemented
5#13070661C211yesmaximal, characteristic, complemented
6#13070656C211yesmaximal, characteristic, complemented
7#13070651C211yesmaximal, characteristic, complemented
8#13070554C212yesmaximal, complemented
9#13070537C212yesmaximal, complemented
10#13070415C211yesmaximal, characteristic, complemented
11C11×#3168C211yesmaximal, characteristic, complemented
12C11×#529—21no—
13C2×#66957—21no—
14C2×#66957C2212yes—
15#10623008—21no—
16C11×#499C2211yescharacteristic
17C11×#495C2211yescharacteristic
18C11×#488—21no—
19C11×#467C2211yescharacteristic
20C11×#466C2211yescharacteristic
21C11×#465—21no—
22C4×C11×Q16C2211yescharacteristic
23C4×C11×SD16—21no—
24C4×C11×D8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×#66893C2212yes—
27C2×#66892C2212yes—
28C2×#66891C2212yes—
29C2×#66890C2212yes—
30#10622312C2211yescharacteristic
31#10622309—21no—
32#10622309C2212yes—
33#10622308C2211yescharacteristic
34#10622306—21no—
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2212yes—
37#10622130C2212yes—
38#10622129C2212yes—
39#10622129C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C4⋊(C11⋊C16)C2211yescharacteristic
42C4×C11⋊C16C2212yes—
43C2×#4339—22no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8C2311yescharacteristic
47C22×C8×C11D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#126—41no—
50C11×#125—21no—
51C11×#124—21no—
52C11×#123—41no—
53C11×C22⋊Q8—21no—
54C11×#121—21no—
55C4×Q8×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—41no—
58C11×#117—41no—
59C2×C42×C11D411yescharacteristic
60#66983—41no—
61#66983—41no—
62C2×Dic44—21no—
63C2×Dic44C2312yes—
64#66957—42no—
65#66957—42no—
66#66957—44no—
67C2×D88—21no—
68C2×D88C2312yes—
69C2×#4314—22no—
70C2×#4314—22no—
71#66928—22no—
72#66927—21no—
73C4×D44—41no—
74C4×D44—41no—
75#66922—21no—
76C11×#107C2311yescharacteristic
77C11×#107C2311yescharacteristic
78C11×#106—21no—
79C11×#103—21no—
80C11×#103—21no—
81C11×#102—21no—
82C11×#102—21no—
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2311yescharacteristic
86C4×C8×C11C2311yescharacteristic
87#66893—42no—
88#66892—42no—
89#66891—42no—
90#66890—42no—
91C2×C11⋊C16C2312yes—
92C2×C11⋊C16C2312yes—
93#33778—111nomaximal, Sylow
94C2×Q8×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11D811yescharacteristic
99C22×C4×C11D811yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C2×C22⋊D11—42no—
102#4339—44no—
103#4339—44no—
104C2×D44—22no—
105C2×D44—41no—
106C2×D44—41no—
107C2×C4×D11—42no—
108C2×Dic22—22no—
109C11×Q16—21no—
110C11×Q16—21no—
111C11×SD16—42no—
112C11×D8—21no—
113C11×D8—21no—
114C2×C8×C11—22no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2411yescharacteristic
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C42×C11—41no—
133C42×C11D811yescharacteristic
134C42×C11D811yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139C4⋊Dic11—41no—
140C4⋊Dic11—41no—
141Dic44—22no—
142Dic44—22no—
143Dic44—42no—
144D88—22no—
145D88—22no—
146D88—42no—
147#4314—44no—
148#4314—44no—
149C11⋊C16—22no—
150C11⋊C16—22no—
151#3168D1111yescharacteristic, complemented
152#3147—111no—
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—41no—
163C23×C11C2×D811yescharacteristic
164C22×D11—42no—
165Q8×C11—41no—
166Q8×C11—41no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—82no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—82no—
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—84no—
185C2×Dic11—42no—
186D44—42no—
187D44—42no—
188D44—82no—
189D44—82no—
190C4×D11—84no—
191Dic22—42no—
192Dic22—42no—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11AGL(1,ℤ/8)12yes—
196C8×C11H(5,𝔽2)11yescharacteristic
197C8×C11H(5,𝔽2)11yescharacteristic
198C2×#135—112no—
199C2×#135—221no—
200#532—221no—
201#529—21no—
202C2×Q32—112no—
203C2×SD32—112no—
204C2×SD32—112no—
205C2×D16—112no—
206#499C2×D1111yescharacteristic
207#495—112no—
208#495—221no—
209#495C2×D1111yescharacteristic
210#494—111no—
211#493—111no—
212#492—221no—
213#488—21no—
214#467C2×D1111yescharacteristic
215#466C2×D1111yescharacteristic
216#465—21no—
217C4×Q16C2×D1111yescharacteristic
218C4×SD16—21no—
219C4×D8C2×D1111yescharacteristic
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—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11C22×D811yescharacteristic
236C2×D11—82no—
237C2×D11—82no—
238C2×D11—82no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11—81no—
246C4×C11#50812yes—
247C4×C11#53511yescharacteristic
248C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
249Dic11—82no—
250C2×#41—222no—
251#135—442no—
252#135—442no—
253#135—444no—
254C2×Q16—112no—
255C2×Q16—221no—
256C2×Q16C22×D1111yescharacteristic
257C2×SD16—21no—
258C2×SD16—222no—
259C2×SD16—222no—
260C2×D8—112no—
261C2×D8—221no—
262C2×D8C22×D1111yescharacteristic
263C22×C8C22⋊D1111yescharacteristic
264C22×C8C22×D1111yescharacteristic
265C4⋊Q8—221no—
266#127—221no—
267#126—41no—
268#125—21no—
269#124—21no—
270#124—222no—
271#123—41no—
272C22⋊Q8—21no—
273#121—21no—
274#121—441no—
275#121—441no—
276C4×Q8—21no—
277C4×D4—21no—
278C4×D4—41no—
279C4×D4—441no—
280C4×D4—441no—
281#117—41no—
282C2×C42C22⋊D1111yescharacteristic
283Q32—442no—
284SD32—442no—
285SD32—442no—
286D16—442no—
287C2×C16—112no—
288C2×C16—112no—
289#107C22×D1111yescharacteristic
290#107C22×D1111yescharacteristic
291#106—21no—
292#103—21no—
293#103—21no—
294#102—21no—
295#102—21no—
296C4×C8C22⋊D1111yescharacteristic
297C4×C8C22⋊D1111yescharacteristic
298C4×C8C22×D1111yescharacteristic
299C4×C8C22×D1111yescharacteristic
300C2×C11—41no—
301C2×C11—161no—
302C2×C11#320511yescharacteristic
303C2×C11C2×#50811yescharacteristic
304C2×C11#341411yescharacteristic
305D11—162no—
306#41—444no—
307#41—444no—
308C2×Q8—21no—
309C2×Q8—222no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—222no—
313C2×D4—442no—
314C2×D4—441no—
315C2×D4—441no—
316C22×C4—41no—
317C22×C4—442no—
318C22×C4#432311yescharacteristic
319C22×C4#432311yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321Q16—21no—
322Q16—21no—
323Q16—222no—
324Q16—222no—
325Q16—442no—
326SD16—42no—
327SD16—444no—
328SD16—444no—
329D8—21no—
330D8—21no—
331D8—222no—
332D8—222no—
333D8—442no—
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—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—442no—
355C22⋊C4—442no—
356C42—41no—
357C42#432311yescharacteristic
358C42#432311yescharacteristic
359C42C2×C22⋊D1111yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C16—222no—
362C16—222no—
363C11#3377811yescharacteristic, complemented, Sylow
364C23—41no—
365C23—442no—
366C23C2×#432311yescharacteristic
367Q8—41no—
368Q8—41no—
369Q8—442no—
370Q8—442no—
371D4—41no—
372D4—41no—
373D4—82no—
374D4—442no—
375D4—442no—
376D4—882no—
377D4—884no—
378D4—882no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—82no—
387C2×C4—442no—
388C2×C4—884no—
389C2×C4C2×#432311yescharacteristic
390C2×C4C2×#432311yescharacteristic
391C2×C4C2×#432311yescharacteristic
392C2×C4C2×#432311yescharacteristic
393C2×C4C2×#432311yescharacteristic
394C2×C4C22×C22⋊D1111yescharacteristic
395C8—21no—
396C8—21no—
397C8#6700212yes—
398C8#6704211yescharacteristic
399C8#6704211yescharacteristic
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—882no—
407C22—882no—
408C22—882no—
409C22C22×#432311yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4—882no—
418C4#1062280712yes—
419C4C2×#6700211yescharacteristic
420C4#1062336111yescharacteristic
421C2—41no—
422C2—161no—
423C2—1762no—
424C2#1307953111yescharacteristic
425C2C2×#1062280711yescharacteristic
426C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3168C2
socleC22×C11C22×D8
hypercenter#3168D11
hypocenterC11#33778
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13079044C2semidirect
2. #13070875C2semidirect
3. #13070850C2semidirect
4. #13070666C2semidirect
5. #13070661C2semidirect
6. #13070656C2semidirect
7. #13070651C2semidirect
8. #13070554C2semidirect
9. #13070537C2semidirect
10. #13070415C2semidirect
11. C11×#3168C2semidirect
151. #3168D11semidirect
363. C11#33778semidirect

Maximal subgroups

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

subgroupindex
#130790442
#130708752
#130708502
#130706662
#130706612
#130706562
#130706512
#130705542
#130705372
#130704152
C11×#31682
#3377811