Finite Group Databasebeta

← #14853520

Subgroups — #14853520

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076975C211yesmaximal, characteristic
2C4⋊Q8×Dic11C211yesmaximal, characteristic
3#13070175C211yesmaximal, characteristic
4#13070174C211yesmaximal, characteristic
5#13069859C211yesmaximal, characteristic
6#13069308C212yesmaximal
7#13069303C212yesmaximal
8#13068619C212yesmaximal
9#13068619C212yesmaximal
10#13068468C211yesmaximal, characteristic
11C11×#2043C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×Q8×Dic11C2212yes—
14C2×#66942—21no—
15C2×C11×#103C2212yes—
16C2×C11×#103C2212yes—
17C11×#389C2211yescharacteristic
18#10622843C2212yes—
19C2×#66899C2212yes—
20C2×#66899C2212yes—
21C2×#66879C2212yes—
22C2×Dic11⋊C8C2212yes—
23#10622598—21no—
24#10622598—21no—
25#10622598C2211yescharacteristic
26#10622589C2211yescharacteristic
27#10622589C2211yescharacteristic
28C4⋊C4×Dic11—21no—
29C4⋊C4×Dic11—21no—
30#10622586C2211yescharacteristic
31#10622585—21no—
32#10622548C2211yescharacteristic
33C42×Dic11C2211yescharacteristic
34#10622541C2211yescharacteristic
35#10622263—21no—
36#10622260—21no—
37C11×#336C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2211yescharacteristic
43C22×Q8×C11C2312yes—
44C22×C8×C11C2312yes—
45C11×C4⋊Q8—24no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C42×C11C2311yescharacteristic
52Q8×Dic11—24no—
53Q8×Dic11—24no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2312yes—
61C2×Dic11⋊C4—21no—
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×Dic11⋊C4—21no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75#66942—44no—
76C11×#103—24no—
77C11×#103—42no—
78C11×#95—21no—
79#66899—24no—
80#66899—42no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66879—42no—
87Dic11⋊C8—24no—
88#29132—111nomaximal, Sylow
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11#4114yes—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—42no—
117C42×C11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—42no—
124C4⋊Dic11—44no—
125C4⋊Dic11—42no—
126C4⋊Dic11—42no—
127Dic11⋊C4—42no—
128Dic11⋊C4—42no—
129Dic11⋊C4—42no—
130Dic11⋊C4—42no—
131Dic11⋊C4—42no—
132Dic11⋊C4—42no—
133C4×Dic11—22no—
134C4×Dic11—22no—
135C4×Dic11—22no—
136C4×Dic11—22no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139C4×Dic11—44no—
140C4×Dic11#4114yes—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144#2859—111no—
145C4×C4⋊Q8—111no—
146#2099—111no—
147#2099—111no—
148#2043—111no—
149#2043D1111yescharacteristic
150#1935—112no—
151#1935—112no—
152#1803—112no—
153#1803—112no—
154#1767—111no—
155C23×C11C22×D411yescharacteristic
156Q8×C11—24no—
157Q8×C11—24no—
158Q8×C11—42no—
159Q8×C11—42no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—24no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11AGL(1,ℤ/8)12yes—
174C2×C4×C11#13712yes—
175C2×C4×C11C2×#4112yes—
176C2×C4×C11C2×#4112yes—
177C2×C4×C11H(5,𝔽2)11yescharacteristic
178C2×C4×C112−1+411yescharacteristic
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—41no—
188C2×Dic11—42no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—42no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11#12412yes—
197C2×Dic11#12412yes—
198C2×Dic11#13712yes—
199C2×Dic11#13712yes—
200C8×C11—42no—
201C11⋊C8—42no—
202C2×C4⋊Q8C2×D1111yescharacteristic
203C2×#125—221no—
204C2×C4×Q8—112no—
205C2×C4⋊C8—112no—
206C2×#103—112no—
207C2×#103—112no—
208C2×#103C2×D1112yes—
209C2×#103C2×D1112yes—
210C2×#97—112no—
211#391—112no—
212#389—111no—
213#389—111no—
214#389—111no—
215#389—221no—
216#389—221no—
217#389—221no—
218#389—221no—
219#389C2×D1111yescharacteristic
220#384—111no—
221#384—111no—
222#384—111no—
223#382—221no—
224C4×C4⋊C4—221no—
225C4×C4⋊C4—221no—
226C43—111no—
227#340—112no—
228#340—112no—
229#340—112no—
230#340—112no—
231#336—111no—
232#336C2×D1111yescharacteristic
233C22×C11#52511yescharacteristic
234C22×C11C2×#12411yescharacteristic
235C22×C11#53711yescharacteristic
236C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
237C22×C11C2×#13711yescharacteristic
238C22×C11C2×#13711yescharacteristic
239C22×C11C2×#13711yescharacteristic
240C4×C11—22no—
241C4×C11—22no—
242C4×C11—44no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11#55212yes—
246C4×C11#55312yes—
247Dic11—22no—
248Dic11—41no—
249Dic11—41no—
250Dic11—81no—
251Dic11—82no—
252Dic11—81no—
253Dic11#49114yes—
254C22×Q8C22×D1112yes—
255C22×C8—112no—
256C22×C8C22×D1112yes—
257C4⋊Q8—24no—
258#125—444no—
259C4×Q8—224no—
260C4×Q8—224no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4C22×D1111yescharacteristic
278C2×C4⋊C4C22×D1111yescharacteristic
279C2×C42—111no—
280C2×C42—111no—
281C2×C42—111no—
282C2×C42—111no—
283C2×C42—111no—
284C2×C42—111no—
285C2×C42—222no—
286C2×C42C22×D1111yescharacteristic
287C4⋊C8—224no—
288#103—24no—
289#103—42no—
290#103—224no—
291#103—442no—
292#97—442no—
293#95—21no—
294#95—222no—
295#95—222no—
296#95—221no—
297#95—221no—
298#95—221no—
299C2×C11#256211yescharacteristic
300C2×C11#311211yescharacteristic
301C2×C11#311311yescharacteristic
302C2×C11C2×#49111yescharacteristic
303C2×C11#314111yescharacteristic
304C2×C11#325411yescharacteristic
305C2×C11#325511yescharacteristic
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8#434114yes—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—111no—
319C22×C4—222no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4D4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C22×C4C23×D1111yescharacteristic
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—42no—
337C4⋊C4—222no—
338C4⋊C4—221no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—221no—
342C4⋊C4—444no—
343C4⋊C4—442no—
344C4⋊C4—442no—
345C4⋊C4—442no—
346C4⋊C4—442no—
347C4⋊C4—442no—
348C4⋊C4—442no—
349C4⋊C4—442no—
350C4⋊C4—442no—
351C4⋊C4—442no—
352C42—22no—
353C42—114no—
354C42—222no—
355C42—222no—
356C42—222no—
357C42—222no—
358C42—221no—
359C42—221no—
360C42—444no—
361C11#2913211yescharacteristic, complemented, Sylow
362C23C2×D4×D1111yescharacteristic
363Q8—24no—
364Q8—24no—
365Q8—42no—
366Q8—42no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—24no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—112no—
381C2×C4—112no—
382C2×C4—112no—
383C2×C4—112no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—442no—
401C2×C4#6696712yes—
402C2×C4#6697112yes—
403C2×C4C2×#434112yes—
404C2×C4#6703711yescharacteristic
405C2×C4#41×D1112yes—
406C2×C4#6704311yescharacteristic
407C8—42no—
408C8—442no—
409C22#1062311711yescharacteristic
410C22#1062313911yescharacteristic
411C22D11×#12411yescharacteristic
412C22C2×#6696711yescharacteristic
413C22C2×#6697111yescharacteristic
414C22D11×#13711yescharacteristic
415C22D11×#13711yescharacteristic
416C4—22no—
417C4—22no—
418C4—44no—
419C4—81no—
420C4—81no—
421C4—114no—
422C4—222no—
423C4—441no—
424C4—441no—
425C4—881no—
426C4—881no—
427C4—882no—
428C4#1062313212yes—
429C4#1062318112yes—
430C2#1307377611yescharacteristic
431C2#1307873311yescharacteristic
432C2#1307874111yescharacteristic
433C2D11×#49111yescharacteristic
434C2#1307901111yescharacteristic
435C2#1308000011yescharacteristic
436C2#1308000811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2043C2
socle, prime radicalC23×C11C22×D4
hypercenter#2043D11
hypocenterC11#29132
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
361. C11#29132semidirect

Maximal subgroups

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

subgroupindex
#130769752
C4⋊Q8×Dic112
#130701752
#130701742
#130698592
#130693082
#130693032
#130686192
#130684682
C11×#20432
#2913211