Finite Group Databasebeta

← #14738599

Subgroups — #14738599

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#13079989C212yesmaximal
2#13079130C211yesmaximal, characteristic, complemented
3#13068144C211yesmaximal, characteristic, complemented
4#13068139C211yesmaximal, characteristic, complemented
5#13068134C211yesmaximal, characteristic, complemented
6#13068129C211yesmaximal, characteristic, complemented
7#13067998C212yesmaximal, complemented
8#13067991C212yesmaximal, complemented
9#13067372C211yesmaximal, characteristic, complemented
10#13067347C212yesmaximal, complemented
11C11×#2966C211yesmaximal, characteristic
12C11×#529C2211yescharacteristic
13#10623001C2212yes—
14C11×#446C2211yescharacteristic
15C8×Q8×C11C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#435—21no—
18C8×D4×C11—21no—
19C8×D4×C11C2211yescharacteristic
20C11×#433—21no—
21C11×#432C2211yescharacteristic
22C11×#405—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622719—21no—
25#10622719—21no—
26#10622676—22no—
27#10622667—22no—
28#10622665—22no—
29#10622655—22no—
30#10622644C2212yes—
31#10622634C2212yes—
32#10622632C2212yes—
33#10622621C2212yes—
34#10622537C2212yes—
35#10622296—21no—
36#10622296—21no—
37#10622295C2211yescharacteristic
38#10622295C2211yescharacteristic
39#10622293C2212yes—
40#10622124C2212yes—
41#10622124C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
44#10622095C2211yescharacteristic
45#10622095C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×M16—21no—
48C22×C8×C11—21no—
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C11×#126—21no—
52C11×#125D411yescharacteristic
53C11×#124D411yescharacteristic
54C11×#123—21no—
55C11×C22⋊Q8D411yescharacteristic
56C11×#121D411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63C2×#4324—22no—
64#66979—22no—
65#66977—22no—
66#66977—22no—
67C2×#4318—22no—
68#66923—22no—
69#66922C2312yes—
70#66922C2312yes—
71C4×Dic22—22no—
72C4×Dic22—22no—
73C11×C4⋊C8—21no—
74C11×C4⋊C8—21no—
75C11×C4⋊C8C2311yescharacteristic
76C11×C4⋊C8C2311yescharacteristic
77C11×C22⋊C8—21no—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—21no—
80C11×#97—21no—
81C11×#97—21no—
82C4×C8×C11—21no—
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2311yescharacteristic
86C4×C8×C11C2311yescharacteristic
87#66899—22no—
88#66896—22no—
89#66882—21no—
90#66882—21no—
91#66882—21no—
92#66882—21no—
93#66881—22no—
94#66881—22no—
95#66874—22no—
96#66874—22no—
97#66872—22no—
98#66871—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#19360—111nomaximal, Sylow
103C2×Q8×C11C2×D411yescharacteristic
104C2×D4×C11—21no—
105C2×D4×C11C2×D411yescharacteristic
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×Dic22—22no—
111C2×Dic22—22no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—42no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4C2×D411yescharacteristic
127C11×C4⋊C4C2×D411yescharacteristic
128C11×C22⋊C4—21no—
129C11×C22⋊C4—21no—
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C42×C11—21no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—42no—
139#4326—82no—
140#4324—82no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145Dic11⋊C4—42no—
146Dic11⋊C4—42no—
147C4×Dic11—42no—
148#4318—82no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151#3252—112no—
152#3160—111no—
153#2966D1111yescharacteristic
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—21no—
163C23×C11#12111yescharacteristic
164Q8×C11—22no—
165D4×C11—22no—
166D4×C11—42no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×Dic11—42no—
183C2×Dic11—42no—
184Dic22—42no—
185Dic22—42no—
186Dic22—82no—
187C8×C11—21no—
188C8×C11—21no—
189C8×C11—41no—
190C8×C11—41no—
191C8×C11#13712yes—
192C8×C11#13712yes—
193C11⋊C8—42no—
194C11⋊C8—42no—
195#533—112no—
196#529C2×D1111yescharacteristic
197#500—111no—
198#500—111no—
199#499—221no—
200#499—221no—
201#498—112no—
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#446C2×D1111yescharacteristic
211C8×Q8C2×D1111yescharacteristic
212#436C2×D1111yescharacteristic
213#435—21no—
214C8×D4—21no—
215C8×D4C2×D1111yescharacteristic
216#433—21no—
217#432C2×D1111yescharacteristic
218#427—221no—
219#427—221no—
220#423—112no—
221#405—21no—
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×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11C2×#12111yescharacteristic
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—41no—
242C4×C11—41no—
243C4×C11—41no—
244C4×C11C2×#13711yescharacteristic
245C4×C11C2×#13711yescharacteristic
246C4×C11#57712yes—
247Dic11—82no—
248Dic11—82no—
249C2×Q16—222no—
250C2×SD16—222no—
251C2×M16—21no—
252C2×M16—222no—
253C22×C8—21no—
254C22×C8C22⋊D1111yescharacteristic
255C22×C8C22⋊D1111yescharacteristic
256C4⋊Q8—112no—
257C4⋊Q8—112no—
258#126—21no—
259#125—222no—
260#125D4411yescharacteristic
261#124D4411yescharacteristic
262#123—21no—
263C22⋊Q8—222no—
264C22⋊Q8—222no—
265C22⋊Q8D4411yescharacteristic
266#121D4411yescharacteristic
267C4×Q8—222no—
268C4×Q8—222no—
269C4×Q8C22×D1111yescharacteristic
270C4×D4—21no—
271C4×D4C22×D1111yescharacteristic
272#117—21no—
273#117—222no—
274C2×C42C22×D1111yescharacteristic
275#107—221no—
276#107—221no—
277#107—221no—
278#107—221no—
279#107—222no—
280#106—222no—
281#106—222no—
282#106—222no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—112no—
286C4⋊C8—112no—
287C4⋊C8—222no—
288C4⋊C8C22×D1111yescharacteristic
289C4⋊C8C22×D1111yescharacteristic
290#103—222no—
291#103—222no—
292#103—222no—
293#102—222no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297#97—21no—
298#97—21no—
299C4×C8—21no—
300C4×C8C22⋊D1111yescharacteristic
301C4×C8C22⋊D1111yescharacteristic
302C4×C8C22×D1111yescharacteristic
303C4×C8C22×D1111yescharacteristic
304C2×C11—41no—
305C2×C11—81no—
306C2×C11#303911yescharacteristic
307C2×C11#306011yescharacteristic
308C2×C11#306711yescharacteristic
309C2×Q8—222no—
310C2×Q8—222no—
311C2×Q8C2×D4411yescharacteristic
312C2×D4—21no—
313C2×D4C2×D4411yescharacteristic
314C22×C4—21no—
315C22×C4C2×D4411yescharacteristic
316C22×C4#433911yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318Q16—882no—
319SD16—882no—
320M16—42no—
321M16—882no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—42no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8C2×C22⋊D1111yescharacteristic
330C2×C8C2×C22⋊D1111yescharacteristic
331C2×C8C2×C22⋊D1111yescharacteristic
332C2×C8C2×C22⋊D1111yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—442no—
342C4⋊C4—442no—
343C4⋊C4C2×D4411yescharacteristic
344C4⋊C4C2×D4411yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—442no—
351C42—21no—
352C42—442no—
353C42C2×D4411yescharacteristic
354C42#433911yescharacteristic
355C42C2×C22⋊D1111yescharacteristic
356C42C23×D1111yescharacteristic
357C11#1936011yescharacteristic, complemented, Sylow
358C23—21no—
359C23#6698311yescharacteristic
360Q8—22no—
361Q8—442no—
362Q8—442no—
363Q8—882no—
364D4—22no—
365D4—42no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4#6698311yescharacteristic
378C2×C4#6698311yescharacteristic
379C2×C4#6698311yescharacteristic
380C2×C4C22×D4411yescharacteristic
381C2×C4C2×#433911yescharacteristic
382C2×C4C22×C22⋊D1111yescharacteristic
383C8—21no—
384C8—21no—
385C8—41no—
386C8—41no—
387C8—442no—
388C8—442no—
389C8#6700412yes—
390C8#6700412yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22C2×#6698311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—882no—
406C4—882no—
407C4#1062328212yes—
408C4C2×#6700411yescharacteristic
409C4C2×#6700411yescharacteristic
410C2—41no—
411C2—81no—
412C2#1307810311yescharacteristic
413C2#1307827811yescharacteristic
414C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#2966D11
hypocenterC11#19360
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #13079130C2semidirect
3. #13068144C2semidirect
4. #13068139C2semidirect
5. #13068134C2semidirect
6. #13068129C2semidirect
7. #13067998C2semidirect
8. #13067991C2semidirect
9. #13067372C2semidirect
10. #13067347C2semidirect
357. C11#19360semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130791302
#130681442
#130681392
#130681342
#130681292
#130679982
#130679912
#130673722
#130673472
C11×#29662
#1936011