Finite Group Databasebeta

← #14654542

Subgroups — #14654542

Order 2816.

548 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C211yesmaximal, characteristic
2#13073974C211yesmaximal, characteristic
3#13067180C211yesmaximal, characteristic, complemented
4#13067045C211yesmaximal, characteristic, complemented
5#13067008C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic, complemented
7C11×#3104C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#484—21no—
12C11×#477—21no—
13C11×#462—21no—
14C11×#451—21no—
15C4×C11×Q16—22no—
16C11×#431C2211yescharacteristic
17#10622844—21no—
18#10622700—21no—
19#10622697—21no—
20#10622679—22no—
21#10622614—21no—
22#10622608—21no—
23#10622605—21no—
24#10622602—22no—
25#10622552—21no—
26#10622549C2211yescharacteristic
27#10622541—21no—
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30#10622176—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622097—22no—
33C22×Q8×C11D411yescharacteristic
34C22×D44D411yescharacteristic
35C22×C4×D11—21no—
36C2×C11×Q16—22no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C11×#117—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×Dic11⋊C4—22no—
59C2×#4318—21no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44—21no—
64C11×#107—22no—
65C11×C4⋊C8—21no—
66C11×#103—22no—
67C11×#103—22no—
68C11×C22⋊C8—21no—
69C4×C8×C11D412yes—
70C11⋊#95—22no—
71C11⋊#95—21no—
72C11⋊#95D412yes—
73C22⋊(C11⋊C8)—21no—
74#66873—22no—
75#66873—22no—
76#66872—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4×C11⋊C8—21no—
82#10002—111nomaximal, Sylow
83C23×D11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—42no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—22no—
95C22×Dic11—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44Q1612yescomplemented
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—82no—
105C11×Q16—44no—
106C2×C8×C11—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125(C2×D11)⋊C4—44no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—82no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133Dic11⋊C4—82no—
134#4318—41no—
135#4318—41no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138#3104D1111yescharacteristic, complemented
139#3077—111no—
140#2580—111no—
141#1518—111no—
142#1487—111no—
143#1478—111no—
144#1286—111no—
145C23×C11#12011yescharacteristic
146C22×D11—22no—
147C22×D11—42no—
148C22×D11—42no—
149C22×D11—41no—
150C22×D11—41no—
151Q8×C11—22no—
152Q8×C11—22no—
153Q8×C11—41no—
154Q8×C11—41no—
155Q8×C11—42no—
156Q8×C11—81no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12711yescharacteristic
173C2×C4×C11C2×Q1611yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11#13711yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182D44—22no—
183D44—22no—
184D44—41no—
185D44—41no—
186C4×D11—82no—
187C4×D11—82no—
188C8×C11—42no—
189C11⋊C8—42no—
190C11⋊C8—81no—
191#533C2×D1111yescharacteristic
192C2×C4×Q8C2×D1111yescharacteristic
193C2×C4×D4—111no—
194#484—21no—
195#478—222no—
196#477—21no—
197#476—221no—
198#474—221no—
199#462—21no—
200#451—21no—
201C4×Q16—22no—
202#431—111no—
203#431C2×D1111yescharacteristic
204#428—221no—
205#423—111no—
206#418—221no—
207#399—221no—
208#393—221no—
209#390—221no—
210#389—221no—
211#385—222no—
212#382—111no—
213#328—222no—
214Q8⋊C8—222no—
215D4⋊C8—222no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11#39211yescharacteristic
219C22×C11#45111yescharacteristic
220C22×C11#45211yescharacteristic
221C2×D11—44no—
222C2×D11—42no—
223C2×D11—82no—
224C2×D11—81no—
225C2×D11—81no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—42no—
231C4×C11—81no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11#45111yescharacteristic
235C4×C11#45211yescharacteristic
236C4×C11#46711yescharacteristic
237C4×C11#47011yescharacteristic
238Dic11—82no—
239Dic11—81no—
240C22×Q8C22⋊D1111yescharacteristic
241C22×D4—111no—
242C23×C4—221no—
243C2×Q16—22no—
244C2×M16—221no—
245C4⋊Q8C22⋊D1111yescharacteristic
246C4⋊Q8C22⋊D1111yescharacteristic
247#125—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—221no—
259C4×D4—221no—
260#117—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4C22⋊D1111yescharacteristic
266C2×C22⋊C4—222no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—222no—
269C2×C42—21no—
270C2×C42C22×D1111yescharacteristic
271#107—22no—
272#107—222no—
273#106—222no—
274C4⋊C8—21no—
275C4⋊C8—112no—
276C4⋊C8—221no—
277C4⋊C8—221no—
278#103—22no—
279#103—22no—
280#102—222no—
281#102—222no—
282C22⋊C8—21no—
283C22⋊C8—221no—
284C4×C8—221no—
285C4×C8C22⋊D1112yes—
286#95—112no—
287#95—222no—
288#95—221no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11#200111yescharacteristic
292C2×C11#200811yescharacteristic
293C2×C11#201011yescharacteristic
294D11—82no—
295C24—221no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—42no—
301C2×D4—112no—
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—221no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—222no—
310C22×C4—221no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4—882no—
314C22×C4D4×D1111yescharacteristic
315C22×C4D4×D1111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317Q16—44no—
318M16—441no—
319M16—441no—
320C2×C8—22no—
321C2×C8—222no—
322C2×C8—441no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C4⋊C4—882no—
338C22⋊C4—41no—
339C22⋊C4—444no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—882no—
343C42—41no—
344C42—41no—
345C42—41no—
346C42D4×D1111yescharacteristic
347C42#434111yescharacteristic
348C42C2×C22⋊D1111yescharacteristic
349C42C2×C22⋊D1111yescharacteristic
350C11#1000211yescharacteristic, complemented, Sylow
351C23—222no—
352C23—442no—
353C23—442no—
354C23—441no—
355C23—441no—
356C23#6699011yescharacteristic
357Q8—22no—
358Q8—22no—
359Q8—41no—
360Q8—41no—
361Q8—42no—
362Q8—81no—
363D4—222no—
364D4—222no—
365D4—441no—
366D4—441no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—441no—
382C2×C4—882no—
383C2×C4—882no—
384C2×C4Q16×D1111yescharacteristic
385C2×C4#6697111yescharacteristic
386C2×C4#6697111yescharacteristic
387C2×C4#6697211yescharacteristic
388C2×C4#6699011yescharacteristic
389C2×C4#6699111yescharacteristic
390C2×C4#6699211yescharacteristic
391C2×C4#6699211yescharacteristic
392C2×C4#6699311yescharacteristic
393C2×C4#6700611yescharacteristic
394C8—42no—
395C8—442no—
396C8—881no—
397C22—21no—
398C22—21no—
399C22—444no—
400C22—442no—
401C22—882no—
402C22—881no—
403C22—881no—
404C22#1062279911yescharacteristic
405C22#1062280011yescharacteristic
406C22#1062283611yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—42no—
412C4—81no—
413C4—81no—
414C4—81no—
415C4—882no—
416C4—881no—
417C4#1062279911yescharacteristic
418C4#1062280011yescharacteristic
419C4#1062280111yescharacteristic
420C4#1062280211yescharacteristic
421C2—21no—
422C2—21no—
423C2—882no—
424C2#1306962311yescharacteristic
425C2#1306966611yescharacteristic
426C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3104C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#3104D11
hypocenterC11#10002
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #13067180C2semidirect
4. #13067045C2semidirect
6. #13066475C2semidirect
7. C11×#3104C2semidirect
101. C2×D44Q16semidirect
138. #3104D11semidirect
350. C11#10002semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130739742
#130671802
#130670452
#130670082
#130664752
C11×#31042
#1000211