Finite Group Databasebeta

← #14853493

Subgroups — #14853493

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077002C211yesmaximal, characteristic
2C4⋊Q8×Dic11C211yesmaximal, characteristic
3#13070180C211yesmaximal, characteristic
4#13070179C211yesmaximal, characteristic
5#13069859C211yesmaximal, characteristic
6#13069308C212yesmaximal
7#13069303C212yesmaximal
8#13068629C212yesmaximal
9#13068629C212yesmaximal
10#13068468C211yesmaximal, characteristic
11C11×#2043C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×Q8×Dic11C2212yes—
14C2×C11×#103C2212yes—
15C2×C11×#103C2212yes—
16C11×#389C2211yescharacteristic
17#10622843C2212yes—
18C2×#66899C2212yes—
19C2×#66899C2212yes—
20C2×#66879C2212yes—
21C2×Dic11⋊C8C2212yes—
22#10622598—21no—
23#10622598—21no—
24#10622598C2211yescharacteristic
25#10622594—21no—
26#10622591—21no—
27#10622590C2211yescharacteristic
28#10622590C2211yescharacteristic
29C4⋊C4×Dic11—21no—
30C4⋊C4×Dic11—21no—
31#10622586C2211yescharacteristic
32#10622548C2211yescharacteristic
33C42×Dic11C2211yescharacteristic
34#10622541C2211yescharacteristic
35#10622266—21no—
36#10622265—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×C4×Dic11—22no—
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71C11×#103—24no—
72C11×#103—42no—
73C11×#95—21no—
74#66899—24no—
75#66899—42no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C11⋊#95—21no—
79C11⋊#95—21no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66879—42no—
86Dic11⋊C8—24no—
87#29129—111nomaximal, Sylow
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11#4114yes—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—42no—
116C42×C11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—42no—
123C4⋊Dic11—42no—
124C4⋊Dic11—42no—
125C4⋊Dic11—44no—
126Dic11⋊C4—42no—
127Dic11⋊C4—42no—
128C4×Dic11—22no—
129C4×Dic11—22no—
130C4×Dic11—21no—
131C4×Dic11—21no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134C4×Dic11—44no—
135C4×Dic11#4114yes—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139#2864—111no—
140C4×C4⋊Q8—111no—
141#2100—111no—
142#2100—111no—
143#2043—111no—
144#2043D1111yescharacteristic
145#1935—112no—
146#1935—112no—
147#1805—112no—
148#1805—112no—
149#1767—111no—
150C23×C11C22×D411yescharacteristic
151Q8×C11—24no—
152Q8×C11—24no—
153Q8×C11—42no—
154Q8×C11—42no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—24no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11#13712yes—
169C2×C4×C11#13712yes—
170C2×C4×C11C2×#4112yes—
171C2×C4×C11C2×#4112yes—
172C2×C4×C11H(5,𝔽2)11yescharacteristic
173C2×C4×C112−1+411yescharacteristic
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11#12412yes—
194C2×Dic11#12412yes—
195C8×C11—42no—
196C11⋊C8—42no—
197C2×C4⋊Q8C2×D1111yescharacteristic
198C2×C4×Q8—112no—
199C2×C4⋊C8—112no—
200C2×#103—112no—
201C2×#103—112no—
202C2×#103C2×D1112yes—
203C2×#103C2×D1112yes—
204C2×#97—112no—
205#391—112no—
206#389—111no—
207#389—111no—
208#389—111no—
209#389—221no—
210#389—221no—
211#389C2×D1111yescharacteristic
212#387—221no—
213#387—221no—
214#387—221no—
215#387—221no—
216#384—111no—
217#382—111no—
218#382—111no—
219C4×C4⋊C4—221no—
220C4×C4⋊C4—221no—
221C43—111no—
222#340—112no—
223#340—112no—
224#340—112no—
225#340—112no—
226#336—111no—
227#336C2×D1111yescharacteristic
228C22×C11#52511yescharacteristic
229C22×C11C2×#12411yescharacteristic
230C22×C11#53711yescharacteristic
231C22×C11C2×#13711yescharacteristic
232C22×C11C2×#13711yescharacteristic
233C22×C11#57511yescharacteristic
234C22×C11#57511yescharacteristic
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—44no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11#55212yes—
241C4×C11#55312yes—
242Dic11—22no—
243Dic11—22no—
244Dic11—41no—
245Dic11—41no—
246Dic11—81no—
247Dic11—82no—
248Dic11—81no—
249C22×Q8C22×D1112yes—
250C22×C8—112no—
251C22×C8C22×D1112yes—
252C4⋊Q8—24no—
253C4×Q8—224no—
254C4×Q8—224no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4C22×D1111yescharacteristic
268C2×C4⋊C4C22×D1111yescharacteristic
269C2×C42—111no—
270C2×C42—111no—
271C2×C42—111no—
272C2×C42—111no—
273C2×C42—111no—
274C2×C42—111no—
275C2×C42—222no—
276C2×C42C22×D1111yescharacteristic
277C4⋊C8—224no—
278#103—24no—
279#103—42no—
280#103—224no—
281#103—442no—
282#97—442no—
283#95—21no—
284#95—222no—
285#95—222no—
286#95—221no—
287#95—221no—
288#95—221no—
289#95—221no—
290#95—221no—
291#95—221no—
292#95—221no—
293C2×C11#256211yescharacteristic
294C2×C11#311711yescharacteristic
295C2×C11#311711yescharacteristic
296C2×C11#313511yescharacteristic
297C2×C11#313911yescharacteristic
298C2×C11#325211yescharacteristic
299C2×C11#325211yescharacteristic
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8#434114yes—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—222no—
316C22×C4D4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4C23×D1111yescharacteristic
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—222no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—42no—
331C4⋊C4—222no—
332C4⋊C4—221no—
333C4⋊C4—222no—
334C4⋊C4—222no—
335C4⋊C4—221no—
336C4⋊C4—442no—
337C4⋊C4—442no—
338C4⋊C4—444no—
339C4⋊C4—442no—
340C4⋊C4—442no—
341C4⋊C4—442no—
342C42—22no—
343C42—114no—
344C42—222no—
345C42—222no—
346C42—221no—
347C42—221no—
348C42—441no—
349C42—441no—
350C42—444no—
351C11#2912911yescharacteristic, complemented, Sylow
352C23C2×D4×D1111yescharacteristic
353Q8—24no—
354Q8—24no—
355Q8—42no—
356Q8—42no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—24no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—112no—
371C2×C4—112no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—442no—
391C2×C4#6696812yes—
392C2×C4#6697112yes—
393C2×C4C2×#434112yes—
394C2×C4#6703711yescharacteristic
395C2×C4#41×D1112yes—
396C2×C4#6704311yescharacteristic
397C8—42no—
398C8—442no—
399C22#1062311711yescharacteristic
400C22#1062313911yescharacteristic
401C22D11×#12411yescharacteristic
402C22C2×#6696811yescharacteristic
403C22C2×#6697111yescharacteristic
404C22#1062330811yescharacteristic
405C22#1062330811yescharacteristic
406C4—22no—
407C4—22no—
408C4—44no—
409C4—81no—
410C4—81no—
411C4—222no—
412C4—222no—
413C4—441no—
414C4—441no—
415C4—881no—
416C4—882no—
417C4—881no—
418C4#1062313212yes—
419C4#1062318112yes—
420C2#1307377611yescharacteristic
421C2#1307878211yescharacteristic
422C2#1307878811yescharacteristic
423C2#1307896311yescharacteristic
424C2#1307899311yescharacteristic
425C2#1307998511yescharacteristic
426C2#1307998711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2043C2
socle, prime radicalC23×C11C22×D4
hypercenter#2043D11
hypocenterC11#29129
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
351. C11#29129semidirect

Maximal subgroups

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

subgroupindex
#130770022
C4⋊Q8×Dic112
#130701802
#130701792
#130698592
#130693082
#130693032
#130686292
#130684682
C11×#20432
#2912911