Finite Group Databasebeta

← #14738593

Subgroups — #14738593

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079983C212yesmaximal
2#13077591C211yesmaximal, characteristic
3#13068141C211yesmaximal, characteristic, complemented
4#13068136C211yesmaximal, characteristic, complemented
5#13068131C211yesmaximal, characteristic, complemented
6#13068126C211yesmaximal, characteristic, complemented
7#13067995C212yesmaximal, complemented
8#13067988C212yesmaximal, complemented
9#13067372C211yesmaximal, characteristic, complemented
10#13067346C212yesmaximal, complemented
11C11×#3160C211yesmaximal, characteristic, complemented
12C11×#533C2212yes—
13#10623010C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#500C2211yescharacteristic
16C11×#499—21no—
17C11×#499—21no—
18C11×#498C2212yes—
19C11×#427—21no—
20C11×#427—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23C8×C22⋊D11—21no—
24#10622704C2212yes—
25#10622703C2212yes—
26#10622697C2212yes—
27#10622696C2212yes—
28#10622665—22no—
29#10622662—22no—
30#10622641—22no—
31#10622635—22no—
32#10622539C2211yescharacteristic
33#10622537C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622184C2212yes—
43#10622184C2212yes—
44#10622095C2211yescharacteristic
45#10622095C2211yescharacteristic
46#10622095C2212yes—
47C22×C8×C11D411yescharacteristic
48C22×C8×C11D411yescharacteristic
49C11×C4⋊Q8C2312yes—
50C11×C4⋊Q8C2312yes—
51C11×#125—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C11×#117—22no—
57C2×C42×C11C2311yescharacteristic
58C2×#4326—22no—
59C2×#4325—22no—
60#66983D411yescharacteristic
61#66982—21no—
62C4×C22⋊D11—21no—
63#66977D411yescharacteristic
64C2×#4318—22no—
65C2×#4313—21no—
66C2×C8×D11—21no—
67#66929—21no—
68#66928D411yescharacteristic
69C4×D44C2311yescharacteristic
70#66925—21no—
71#66923D411yescharacteristic
72C4×Dic22C2311yescharacteristic
73C11×#107—21no—
74C11×#107—21no—
75C11×#107—21no—
76C11×#107—21no—
77C11×#106—22no—
78C11×#106—22no—
79C4×C8×C11D411yescharacteristic
80C4×C8×C11D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66899—22no—
84#66899—22no—
85C22⋊(C11⋊C8)—21no—
86(C2×D11)⋊C8—21no—
87(C2×D11)⋊C8—21no—
88#66879—21no—
89Dic11⋊C8—21no—
90Dic11⋊C8—21no—
91C8×Dic11—21no—
92#66874—22no—
93#66873—22no—
94#66872—22no—
95#66871—22no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101#66867—21no—
102#19360—111nomaximal, Sylow
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—21no—
109C2×D44C2×D411yescharacteristic
110C2×C4×D11—21no—
111C2×Dic22C2×D411yescharacteristic
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—42no—
124C11×C22⋊C4—42no—
125C42×C11—42no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C42×C11C2411yescharacteristic
130C22⋊Dic11—21no—
131#4326—82no—
132#4325—82no—
133(C2×D11)⋊C4—21no—
134(C2×D11)⋊C4—21no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—21no—
137C4⋊Dic11C2×D411yescharacteristic
138C4⋊Dic11C2×D411yescharacteristic
139Dic11⋊C4—21no—
140Dic11⋊C4—21no—
141Dic11⋊C4—21no—
142Dic11⋊C4—21no—
143C4×Dic11—21no—
144#4318—82no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149#4313—42no—
150C8×D11—42no—
151#3252—112no—
152#3160D1111yescharacteristic, complemented
153#2966—111no—
154#1696—111no—
155#1695—111no—
156#1694—111no—
157#1693—111no—
158#1672—112no—
159#1671—112no—
160#1566—111no—
161#1559—112no—
162C23×C11#12111yescharacteristic
163C22×D11—21no—
164Q8×C11—42no—
165Q8×C11—42no—
166Q8×C11—82no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C22⋊D11—42no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183D44—22no—
184C4×D11—41no—
185C4×D11—41no—
186Dic22—22no—
187C8×C11—21no—
188C8×C11—21no—
189C8×C11#13712yes—
190C8×C11#13712yes—
191C11⋊C8—41no—
192C11⋊C8—41no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195#533C2×D1112yes—
196#529—111no—
197#500C2×D1111yescharacteristic
198#500C2×D1111yescharacteristic
199#499—21no—
200#499—21no—
201#498C2×D1112yes—
202#479—222no—
203#477—112no—
204#476—112no—
205#470—222no—
206#468—222no—
207#464—222no—
208#462—112no—
209#461—112no—
210#446—111no—
211C8×Q8—111no—
212#436—111no—
213#435—221no—
214C8×D4—111no—
215C8×D4—221no—
216#433—221no—
217#432—111no—
218#427—21no—
219#427—21no—
220#423—112no—
221#405—221no—
222C2×C4×C8C2×D1111yescharacteristic
223#334—112no—
224#334—111no—
225#334—111no—
226#333—112no—
227#333—112no—
228#332—112no—
229#332—112no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11C2×#12111yescharacteristic
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—82no—
242C4×C11—82no—
243C4×C11C2×#13711yescharacteristic
244C4×C11C2×#13711yescharacteristic
245C4×C11#57712yes—
246Dic11—41no—
247Dic11—41no—
248Dic11—41no—
249C2×Q16—222no—
250C2×SD16—222no—
251C2×M16—222no—
252C2×M16—221no—
253C22×C8—221no—
254C22×C8C22⋊D1111yescharacteristic
255C22×C8C22⋊D1111yescharacteristic
256C4⋊Q8C22×D1112yes—
257C4⋊Q8C22×D1112yes—
258#126—221no—
259#125—22no—
260#125—111no—
261#124—111no—
262#123—221no—
263C22⋊Q8—22no—
264C22⋊Q8—22no—
265C22⋊Q8—111no—
266#121—111no—
267C4×Q8—22no—
268C4×Q8—22no—
269C4×Q8—111no—
270C4×D4—111no—
271C4×D4—221no—
272#117—22no—
273#117—221no—
274C2×C42C22×D1111yescharacteristic
275#107—21no—
276#107—21no—
277#107—21no—
278#107—21no—
279#107—222no—
280#106—22no—
281#106—22no—
282#106—222no—
283C4⋊C8—111no—
284C4⋊C8—111no—
285C4⋊C8—112no—
286C4⋊C8—112no—
287C4⋊C8—221no—
288C4⋊C8—221no—
289C4⋊C8—222no—
290#103—222no—
291#103—222no—
292#103—222no—
293#102—222no—
294C22⋊C8—221no—
295C22⋊C8—221no—
296C22⋊C8—221no—
297#97—221no—
298#97—221no—
299C4×C8—221no—
300C4×C8C22⋊D1111yescharacteristic
301C4×C8C22⋊D1111yescharacteristic
302C4×C8C22×D1111yescharacteristic
303C4×C8C22×D1111yescharacteristic
304C2×C11—41no—
305C2×C11#303911yescharacteristic
306C2×C11#306011yescharacteristic
307C2×C11#306711yescharacteristic
308D11—81no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—111no—
312C2×D4—111no—
313C2×D4—221no—
314C22×C4—221no—
315C22×C4D4×D1111yescharacteristic
316C22×C4#434111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318Q16—882no—
319SD16—882no—
320M16—442no—
321M16—882no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—221no—
327C2×C8—221no—
328C2×C8—442no—
329C2×C8C2×C22⋊D1111yescharacteristic
330C2×C8C2×C22⋊D1111yescharacteristic
331C2×C8C2×C22⋊D1111yescharacteristic
332C2×C8C2×C22⋊D1111yescharacteristic
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—111no—
340C4⋊C4—111no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—221no—
344C4⋊C4—221no—
345C22⋊C4—42no—
346C22⋊C4—221no—
347C22⋊C4—221no—
348C22⋊C4—221no—
349C22⋊C4—221no—
350C22⋊C4—221no—
351C42—42no—
352C42—221no—
353C42D4×D1111yescharacteristic
354C42#434111yescharacteristic
355C42C2×C22⋊D1111yescharacteristic
356C42C23×D1111yescharacteristic
357C11#1936011yescharacteristic, complemented, Sylow
358C23—221no—
359C23#6699111yescharacteristic
360Q8—42no—
361Q8—42no—
362Q8—82no—
363Q8—222no—
364D4—222no—
365D4—442no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4#6699111yescharacteristic
378C2×C4#6699111yescharacteristic
379C2×C4#6699111yescharacteristic
380C2×C4C2×D4×D1111yescharacteristic
381C2×C4C2×#434111yescharacteristic
382C2×C4C22×C22⋊D1111yescharacteristic
383C8—21no—
384C8—21no—
385C8—442no—
386C8—442no—
387C8—441no—
388C8—441no—
389C8#6699512yes—
390C8#6699512yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—441no—
395C22—441no—
396C22—441no—
397C22C2×#6699111yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—441no—
405C4—441no—
406C4—441no—
407C4#1062330112yes—
408C4C2×#6699511yescharacteristic
409C4C2×#6699511yescharacteristic
410C2—41no—
411C2—881no—
412C2#1307809911yescharacteristic
413C2#1307827411yescharacteristic
414C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3160C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#3160D11
hypocenterC11#19360
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3160

Complements

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

NH ≅ G/Ntype
3. #13068141C2semidirect
4. #13068136C2semidirect
5. #13068131C2semidirect
6. #13068126C2semidirect
7. #13067995C2semidirect
8. #13067988C2semidirect
9. #13067372C2semidirect
10. #13067346C2semidirect
11. C11×#3160C2semidirect
152. #3160D11semidirect
357. C11#19360semidirect

Maximal subgroups

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

subgroupindex
#130799832
#130775912
#130681412
#130681362
#130681312
#130681262
#130679952
#130679882
#130673722
#130673462
C11×#31602
#1936011