Finite Group Databasebeta

← #14853496

Subgroups — #14853496

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077001C211yesmaximal, characteristic
2C4×#66997C211yesmaximal, characteristic
3#13070181C212yesmaximal
4#13069860C212yesmaximal
5#13069308C212yesmaximal
6#13069307C212yesmaximal
7#13068632C211yesmaximal, characteristic
8#13068631C211yesmaximal, characteristic
9#13068628C211yesmaximal, characteristic
10#13068471C211yesmaximal, characteristic
11C11×#1805C211yesmaximal, characteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66997C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103C2212yes—
17C11×#382C2211yescharacteristic
18#10622843C2211yescharacteristic
19C2×#66899C2212yes—
20C2×#66880C2212yes—
21C2×#66879C2212yes—
22#10622598C2212yes—
23#10622589C2211yescharacteristic
24#10622587C2211yescharacteristic
25#10622586C2212yes—
26#10622585—22no—
27C2×#66874C2212yes—
28#10622549C2211yescharacteristic
29C4×Dic11⋊C4—22no—
30C42×Dic11C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622268—22no—
33#10622267—22no—
34C11×#340C2212yes—
35#10622189C2212yes—
36#10622188C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39C22×Q8×C11C2311yescharacteristic
40C22×Dic22C2311yescharacteristic
41C22×C8×C11C2312yes—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4C2311yescharacteristic
46C2×C11×C4⋊C4C2312yes—
47C2×C42×C11—21no—
48C2×C42×C11C2311yescharacteristic
49#66997—22no—
50#66997—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11C2311yescharacteristic
53C2×C4⋊Dic11C2312yes—
54C2×Dic11⋊C4—22no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—22no—
58C2×C4×Dic11—21no—
59C2×C4×Dic11D412yes—
60C2×C4×Dic11D412yes—
61C2×C4×Dic11C2311yescharacteristic
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2312yes—
64C4×Dic22—22no—
65C4×Dic22—22no—
66C11×C4⋊C8—22no—
67C11×#103—24no—
68C11×#95—21no—
69C11×#95—21no—
70#66899—42no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77#66880—42no—
78#66879—42no—
79#66874—24no—
80C4⋊(C11⋊C8)—22no—
81#29129—111nomaximal, Sylow
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11#4112yes—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—22no—
96C22×Dic11—21no—
97C22×Dic11C2×D412yes—
98C22×Dic11C2×D412yes—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—21no—
104C2×Dic22#4112yes—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—42no—
113C42×C11—42no—
114C42×C11#4112yes—
115C42×C11#4112yes—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—44no—
121Dic11⋊C4—28no—
122Dic11⋊C4—44no—
123Dic11⋊C4—44no—
124Dic11⋊C4—42no—
125C4×Dic11—24no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—42no—
131C4×Dic11—42no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135#2864—111no—
136C4×C4⋊Q8—111no—
137#2100—112no—
138#2043—112no—
139#1935—112no—
140#1935—112no—
141#1805—111no—
142#1805—111no—
143#1805—111no—
144#1805D1111yescharacteristic
145#1767—111no—
146C23×C11C22×D411yescharacteristic
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—41no—
150Q8×C11—41no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11#12412yes—
162C2×C4×C11#12412yes—
163C2×C4×C11C2×#4111yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×C4×C11H(5,𝔽2)11yescharacteristic
168C2×C4×C112−1+411yescharacteristic
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11#13714yes—
183Dic22—22no—
184Dic22—22no—
185Dic22—41no—
186Dic22—41no—
187C8×C11—42no—
188C11⋊C8—42no—
189C2×C4⋊Q8—111no—
190C2×C4×Q8—111no—
191C2×C4×Q8C2×D1111yescharacteristic
192C2×C4⋊C8—111no—
193C2×C4⋊C8C2×D1111yescharacteristic
194C2×#103—112no—
195C2×#103—112no—
196C2×#103—112no—
197C2×#103C2×D1112yes—
198C2×#97—112no—
199#391—111no—
200#391—111no—
201#389—112no—
202#389—112no—
203#389—222no—
204#387—222no—
205#387—222no—
206#384—111no—
207#382—111no—
208#382C2×D1111yescharacteristic
209C4×C4⋊C4—222no—
210C43—111no—
211#340—112no—
212#340—112no—
213#340—112no—
214#340C2×D1112yes—
215#336—112no—
216C22×C11#52511yescharacteristic
217C22×C11C2×#12411yescharacteristic
218C22×C11#53711yescharacteristic
219C22×C11C2×#13712yes—
220C22×C11#57512yes—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11—42no—
224C4×C11—82no—
225C4×C11—81no—
226C4×C11#55211yescharacteristic
227C4×C11#55211yescharacteristic
228C4×C11#55311yescharacteristic
229C4×C11#55311yescharacteristic
230Dic11—24no—
231Dic11—42no—
232Dic11—42no—
233Dic11—81no—
234Dic11—82no—
235C22×Q8—111no—
236C22×Q8C22×D1111yescharacteristic
237C22×C8—112no—
238C22×C8C22×D1112yes—
239C4⋊Q8—222no—
240C4⋊Q8—222no—
241C4×Q8—22no—
242C4×Q8—22no—
243C4×Q8—222no—
244C4×Q8—222no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—111no—
247C2×C4⋊C4—112no—
248C2×C4⋊C4—222no—
249C2×C4⋊C4—222no—
250C2×C4⋊C4—222no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4C22×D1111yescharacteristic
254C2×C4⋊C4C22×D1112yes—
255C2×C42—21no—
256C2×C42—112no—
257C2×C42—111no—
258C2×C42—111no—
259C2×C42—112no—
260C2×C42—221no—
261C2×C42C22×D1111yescharacteristic
262C4⋊C8—22no—
263C4⋊C8—222no—
264#103—24no—
265#103—224no—
266#103—442no—
267#103—442no—
268#97—442no—
269#95—21no—
270#95—21no—
271#95—222no—
272#95—222no—
273#95—222no—
274#95—222no—
275#95—221no—
276#95—221no—
277C2×C11#256211yescharacteristic
278C2×C11#311712yes—
279C2×C11#313511yescharacteristic
280C2×C11#313911yescharacteristic
281C2×C11#325212yes—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—112no—
288C2×Q8—221no—
289C2×Q8—221no—
290C2×Q8—221no—
291C2×Q8—221no—
292C2×Q8—221no—
293C2×Q8#434112yes—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—112no—
298C22×C4—112no—
299C22×C4—221no—
300C22×C4—222no—
301C22×C4—221no—
302C22×C4D4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4C23×D1111yescharacteristic
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—222no—
309C2×C8—222no—
310C2×C8—222no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—42no—
316C4⋊C4—228no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—222no—
320C4⋊C4—222no—
321C4⋊C4—444no—
322C4⋊C4—444no—
323C4⋊C4—444no—
324C4⋊C4—442no—
325C42—42no—
326C42—224no—
327C42—221no—
328C42—221no—
329C42—221no—
330C42—221no—
331C42—442no—
332C42—442no—
333C42#433912yes—
334C42#434112yes—
335C11#2912911yescharacteristic, complemented, Sylow
336C23C2×D4×D1111yescharacteristic
337Q8—22no—
338Q8—22no—
339Q8—41no—
340Q8—41no—
341Q8—222no—
342Q8—222no—
343Q8—441no—
344Q8—441no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—114no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4#6693812yes—
370C2×C4#6693812yes—
371C2×C4C2×#433911yescharacteristic
372C2×C4C2×#434111yescharacteristic
373C2×C4C2×#434111yescharacteristic
374C2×C4#6704011yescharacteristic
375C2×C4#41×D1111yescharacteristic
376C2×C4#6704211yescharacteristic
377C8—42no—
378C8—442no—
379C22C2×#6693811yescharacteristic
380C22#1062313711yescharacteristic
381C22#1062316011yescharacteristic
382C22#1062329912yes—
383C22D11×#13712yes—
384C4—22no—
385C4—22no—
386C4—42no—
387C4—82no—
388C4—81no—
389C4—224no—
390C4—442no—
391C4—442no—
392C4—881no—
393C4—882no—
394C4#1062304411yescharacteristic
395C4#1062306111yescharacteristic
396C4#1062314911yescharacteristic
397C4#1062317011yescharacteristic
398C2#1307377911yescharacteristic
399C2#1307878612yes—
400C2#1307895911yescharacteristic
401C2#1307899411yescharacteristic
402C2#1307998812yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1805C2
socle, prime radicalC23×C11C22×D4
hypercenter#1805D11
hypocenterC11#29129
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
335. C11#29129semidirect

Maximal subgroups

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

subgroupindex
#130770012
C4×#669972
#130701812
#130698602
#130693082
#130693072
#130686322
#130686312
#130686282
#130684712
C11×#18052
#2912911