Finite Group Databasebeta

← #14908298

Subgroups — #14908298

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622807C211yesmaximal, characteristic, complemented
2C2×#10622753C211yesmaximal, characteristic, complemented
3#13078286C211yesmaximal, characteristic, complemented
4#13070722C212yesmaximal, complemented
5#13070717C212yesmaximal, complemented
6#13070714C212yesmaximal, complemented
7#13070710C212yesmaximal, complemented
8C2×#10622128C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic, complemented
10#13070326C211yesmaximal, characteristic, complemented
11C11×#3061C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C2×C11×#131C2211yescharacteristic
14C11×#537—21no—
15#10623364—21no—
16C2×#66957C2211yescharacteristic
17C11×#468—22no—
18C11×#467C2212yes—
19C11×#466C2212yes—
20C2×C11×#107C2211yescharacteristic
21C11×#417—21no—
22#10622807—24no—
23C2×#66893C2211yescharacteristic
24C2×#66892C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27#10622753—24no—
28#10622747—22no—
29#10622746—21no—
30#10622729C2212yes—
31#10622728C2212yes—
32C2×#66882C2211yescharacteristic
33C2×#66876C2212yes—
34C2×#66876C2211yescharacteristic
35C22×C11⋊C16C2212yes—
36C22×C11⋊C16C2211yescharacteristic
37#10622202C2212yes—
38#10622200C2212yes—
39#10622130C2212yes—
40#10622129C2212yes—
41#10622128C2212yes—
42#10622128C2212yes—
43C2×C11×#41—21no—
44C2×C11×#41D411yescharacteristic
45C2×#4339—21no—
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C11×#131—22no—
52C11×#131—22no—
53C2×C11×M16D411yescharacteristic
54C2×C11×M16D412yes—
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—41no—
59C11×#121—22no—
60C11×#121—41no—
61C11×#121—42no—
62C2×C11×C4⋊C4—21no—
63#66999—41no—
64#66992—42no—
65#66991—41no—
66#66983—22no—
67C2×C4⋊Dic11—21no—
68#66977—22no—
69C2×Dic44C2311yescharacteristic
70#66957—22no—
71#66957—22no—
72C2×D88C2311yescharacteristic
73C2×#4314—21no—
74C11×#107—21no—
75C11×#107C2312yes—
76C11×#103—22no—
77C11×#102—22no—
78#66893—22no—
79#66892—22no—
80#66891—22no—
81#66890—22no—
82#66885—22no—
83#66882—21no—
84#66882C2312yes—
85#66880—22no—
86#66876—22no—
87#66876—24no—
88C2×C11⋊C16—24no—
89C2×C11⋊C16D414yescomplemented
90C2×C11⋊C16C2312yes—
91C2×C11⋊C16C2311yescharacteristic
92C2×C11⋊C16C2311yescharacteristic
93#33611—111nomaximal, Sylow
94C11×#41—22no—
95C11×#41—22no—
96C11×#41—42no—
97C11×#41—42no—
98C2×Q8×C11—21no—
99C2×Q8×C11D811yescharacteristic
100C2×D4×C11—21no—
101C2×D4×C11—41no—
102C2×D4×C11—42no—
103C2×D4×C11D811yescharacteristic
104C2×D4×C11D812yes—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C2×C22⋊D11—41no—
110C2×C22⋊D11—42no—
111C22×Dic11—41no—
112#4339—42no—
113#4339—42no—
114C2×D44—21no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C11×Q16—21no—
118C11×Q16—21no—
119C11×SD16—42no—
120C11×D8—21no—
121C11×D8—21no—
122C11×M16—24no—
123C11×M16—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11C2×D412yes—
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11#4112yes—
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—22no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—42no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C22⋊Dic11—42no—
137(C2×D11)⋊C4—42no—
138C4⋊Dic11—22no—
139C4⋊Dic11—41no—
140Dic11⋊C4—42no—
141Dic44—21no—
142Dic44—21no—
143D88—21no—
144D88—21no—
145#4314—42no—
146C11⋊C16—22no—
147C11⋊C16C2×D412yes—
148C11⋊C16C2×D412yes—
149C2×#508—111no—
150C2×#504—111no—
151#3061—111no—
152#3061D1111yescharacteristic, complemented
153#2219—112no—
154#2218—112no—
155#2217—112no—
156#2217—112no—
157C2×#367—111no—
158#2139—111no—
159#2139—111no—
160C23×C11—41no—
161C23×C11C2×D812yes—
162C23×C11C2×D811yescharacteristic
163C22×D11—41no—
164Q8×C11—22no—
165Q8×C11—41no—
166Q8×C11—41no—
167D4×C11—24no—
168D4×C11—22no—
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—82no—
172D4×C11—162no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—82no—
178C2×C4×C11—161no—
179C2×C4×C11#12112yes—
180C2×C4×C11C2×D812yes—
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11#13512yes—
183C2×C4×C11C22×D411yescharacteristic
184C22⋊D11—82no—
185C22⋊D11—162no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—161no—
189D44—41no—
190D44—41no—
191C4×D11—82no—
192Dic22—41no—
193Dic22—41no—
194C8×C11—22no—
195C8×C11#12112yes—
196C8×C11C22×D411yescharacteristic
197C8×C11C2×#4111yescharacteristic
198C2×#135—111no—
199C2×#135C2×D1111yescharacteristic
200C2×#131C2×D1111yescharacteristic
201#537—21no—
202#537—221no—
203#508—224no—
204C2×Q32—111no—
205C2×SD32—111no—
206C2×SD32—111no—
207C2×D16—111no—
208#504—224no—
209C2×M32—111no—
210C2×M32—112no—
211C22×C16—111no—
212C22×C16—112no—
213#468—22no—
214#468—222no—
215#467—112no—
216#467C2×D1112yes—
217#466—112no—
218#466C2×D1112yes—
219C2×#107—111no—
220C2×#107C2×D1111yescharacteristic
221#417—21no—
222#417—221no—
223#367—112no—
224#367—112no—
225#358—112no—
226#358—112no—
227#357—112no—
228#357—112no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11#46612yes—
238C22×C11C22×D811yescharacteristic
239C2×D11—81no—
240C2×D11—81no—
241C2×D11—81no—
242C4×C11—22no—
243C4×C11—82no—
244C4×C11—81no—
245C4×C11#46612yes—
246C4×C11C2×#12111yescharacteristic
247C4×C11C2×#13511yescharacteristic
248Dic11—82no—
249Dic11—81no—
250C2×#41—21no—
251C2×#41—221no—
252C2×#41C22⋊D1111yescharacteristic
253#135—22no—
254#135—22no—
255#135—222no—
256#135—222no—
257C2×Q16—111no—
258C2×Q16C22×D1111yescharacteristic
259C2×SD16—21no—
260C2×SD16—221no—
261C2×D8—111no—
262C2×D8C22×D1111yescharacteristic
263#131—22no—
264#131—22no—
265C2×M16C22⋊D1111yescharacteristic
266C2×M16C22⋊D1112yes—
267C22×C8C22×D1112yes—
268C22×C8C22×D1111yescharacteristic
269C22⋊Q8—22no—
270C22⋊Q8—41no—
271C22⋊Q8—222no—
272C22⋊Q8—441no—
273#121—22no—
274#121—41no—
275#121—42no—
276#121—222no—
277#121—441no—
278#121—442no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—221no—
281Q32—222no—
282SD32—222no—
283SD32—222no—
284D16—222no—
285M32—224no—
286M32—222no—
287C2×C16—114no—
288C2×C16—111no—
289C2×C16—111no—
290C2×C16—112no—
291C2×C16—224no—
292#107—21no—
293#107—112no—
294#107—221no—
295#107C22×D1112yes—
296#103—22no—
297#103—222no—
298#102—22no—
299#102—222no—
300C2×C11—22no—
301C2×C11—42no—
302C2×C11—161no—
303C2×C11C2×#46611yescharacteristic
304C2×C11#341611yescharacteristic
305C2×C11#341611yescharacteristic
306D11—161no—
307#41—22no—
308#41—22no—
309#41—42no—
310#41—42no—
311#41—442no—
312#41—442no—
313C2×Q8—21no—
314C2×Q8—221no—
315C2×Q8#432311yescharacteristic
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—42no—
319C2×D4—221no—
320C2×D4—441no—
321C2×D4—442no—
322C2×D4#432312yes—
323C2×D4#432311yescharacteristic
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—441no—
327C22×C4—441no—
328C22×C4C2×C22⋊D1112yes—
329C22×C4C2×C22⋊D1111yescharacteristic
330Q16—21no—
331Q16—21no—
332Q16—221no—
333Q16—221no—
334SD16—42no—
335SD16—442no—
336D8—21no—
337D8—21no—
338D8—221no—
339D8—221no—
340M16—22no—
341M16—24no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8D4×D1112yes—
345C2×C8#434112yes—
346C2×C8C2×C22⋊D1112yes—
347C2×C8C2×C22⋊D1111yescharacteristic
348C2×C8C23×D1111yescharacteristic
349C4⋊C4—22no—
350C4⋊C4—41no—
351C4⋊C4—42no—
352C4⋊C4—222no—
353C4⋊C4—441no—
354C4⋊C4—442no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—442no—
358C22⋊C4—442no—
359C16—112no—
360C16—112no—
361C16—222no—
362C11#3361111yescharacteristic, complemented, Sylow
363C23—41no—
364C23—441no—
365C23C2×#432312yes—
366C23C2×#432311yescharacteristic
367Q8—22no—
368Q8—41no—
369Q8—41no—
370Q8—441no—
371Q8—441no—
372D4—24no—
373D4—22no—
374D4—41no—
375D4—41no—
376D4—82no—
377D4—162no—
378D4—441no—
379D4—441no—
380D4—882no—
381D4—1762no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—82no—
387C2×C4—161no—
388C2×C4—442no—
389C2×C4—441no—
390C2×C4—882no—
391C2×C4—1761no—
392C2×C4C2×#432312yes—
393C2×C4C2×#432311yescharacteristic
394C2×C4#6699212yes—
395C2×C4#6700312yes—
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—22no—
398C8#6699212yes—
399C8C2×D4×D1111yescharacteristic
400C8C2×#434111yescharacteristic
401C22—21no—
402C22—21no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—881no—
410C22—881no—
411C22—881no—
412C22#1062265112yes—
413C22C22×#432311yescharacteristic
414C4—22no—
415C4—82no—
416C4—81no—
417C4—882no—
418C4—881no—
419C4#1062265112yes—
420C4C2×#6699211yescharacteristic
421C4C2×#6700311yescharacteristic
422C2—22no—
423C2—42no—
424C2—161no—
425C2—1761no—
426C2C2×#1062265111yescharacteristic
427C2#1308176011yescharacteristic
428C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3061C2
socleC22×C11C22×D8
hypercenter#3061D11
hypocenterC11#33611
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3061

Complements

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

NH ≅ G/Ntype
1. C2×#10622807C2semidirect
2. C2×#10622753C2semidirect
3. #13078286C2semidirect
4. #13070722C2semidirect
5. #13070717C2semidirect
6. #13070714C2semidirect
7. #13070710C2semidirect
8. C2×#10622128C2semidirect
9. #13070328C2semidirect
10. #13070326C2semidirect
11. C11×#3061C2semidirect
89. C2×C11⋊C16D4semidirect
152. #3061D11semidirect
362. C11#33611semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
C2×#106227532
#130782862
#130707222
#130707172
#130707142
#130707102
C2×#106221282
#130703282
#130703262
C11×#30612
#3361111