Finite Group Databasebeta

← #14651609

Subgroups — #14651609

Order 2816.

542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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#13077639C211yesmaximal, characteristic
2#13073974C211yesmaximal, characteristic
3#13068605C211yesmaximal, characteristic
4#13067045C211yesmaximal, characteristic, complemented
5#13066476C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1487C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622844C412yes—
13C2×#66887—21no—
14#10622605C412yes—
15#10622602—22no—
16#10622552—21no—
17#10622549C2211yescharacteristic
18#10622541—21no—
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21#10622447—22no—
22D11×C22⋊C8—22no—
23C8×D44—22no—
24C11×Q8⋊C8—22no—
25#10622192—21no—
26Q8⋊(C11⋊C8)—22no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11D412yes—
30C2×C11×M16—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4C2×C412yes—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—22no—
45C2×#4318—21no—
46C2×C8×D11—24no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C4×C8×C11D412yes—
56C11⋊#95—21no—
57C11⋊#95—22no—
58C11⋊#95C2×C412yes—
59C22⋊(C11⋊C8)—21no—
60#66887—42no—
61(C2×D11)⋊C8—24no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8D412yes—
66#9483—111nomaximal, Sylow
67C23×D11C22⋊C412yes—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—42no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—22no—
77C22×Dic11C22⋊C412yes—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44SD1612yes—
83C2×D44Q1612yes—
84C2×C4×D11—22no—
85C2×C4×D11—22no—
86C2×C4×D11—82no—
87C11×M16—41no—
88C11×M16—41no—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—44no—
104(C2×D11)⋊C4—82no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109Dic11⋊C4—82no—
110#4318—41no—
111#4318—41no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—41no—
114C8×D11—84no—
115#2972—111no—
116#2580—111no—
117#1800—111no—
118#1487—111no—
119#1487D1111yescharacteristic, complemented
120#1286—111no—
121#1286—111no—
122C23×C11C2×C22⋊C411yescharacteristic
123C22×D11—22no—
124C22×D11—22no—
125C22×D11—42no—
126C22×D11—42no—
127C22×D11#10314yes—
128Q8×C11—22no—
129Q8×C11—22no—
130Q8×C11—41no—
131Q8×C11—41no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11C2×SD1611yescharacteristic
147C2×C4×C11C2×Q1611yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×Dic11—22no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155D44—22no—
156D44—22no—
157D44—22no—
158D44—22no—
159C4×D11—44no—
160C4×D11—82no—
161C8×C11—42no—
162C8×C11—81no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165C2×C4×Q8C2×D1111yescharacteristic
166C2×C4×D4—111no—
167C8×D4—222no—
168C8×D4—222no—
169#431—111no—
170#431C2×D1111yescharacteristic
171#423—111no—
172#423C2×D1111yescharacteristic
173C2×#100—221no—
174C2×C22⋊C8—222no—
175#399—112no—
176#393—112no—
177#390—221no—
178#389—221no—
179#385—222no—
180#382—111no—
181#343—221no—
182Q8⋊C8—22no—
183Q8⋊C8—222no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11#38611yescharacteristic
187C22×C11C2×#10311yescharacteristic
188C22×C11#41611yescharacteristic
189C2×D11—24no—
190C2×D11—42no—
191C2×D11—42no—
192C2×D11—44no—
193C2×D11—82no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—42no—
199C4×C11—81no—
200C4×C11#46511yescharacteristic
201C4×C11#46511yescharacteristic
202C4×C11#46711yescharacteristic
203C4×C11#46711yescharacteristic
204Dic11—42no—
205Dic11—82no—
206C22×Q8C4×D1111yescharacteristic
207C22×D4—111no—
208C23×C4—112no—
209C2×M16—21no—
210C2×M16—221no—
211C22×C8—224no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×D4—221no—
217C4×D4—221no—
218C4×D4—221no—
219C4×D4—221no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—222no—
224C2×C4⋊C4C4×D1111yescharacteristic
225C2×C22⋊C4—112no—
226C2×C22⋊C4—222no—
227C2×C22⋊C4—222no—
228C2×C42—21no—
229C2×C42C22×D1111yescharacteristic
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236#100—442no—
237C22⋊C8—21no—
238C22⋊C8—224no—
239C22⋊C8—221no—
240C4×C8—112no—
241C4×C8C22⋊D1112yes—
242#95—112no—
243#95—222no—
244#95—221no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11#189111yescharacteristic
248C2×C11#189211yescharacteristic
249C2×C11#191111yescharacteristic
250D11—44no—
251C24—112no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—42no—
255C2×D4—112no—
256C2×D4—112no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—112no—
264C22×C4—222no—
265C22×C4—222no—
266C22×C4—222no—
267C22×C4—882no—
268C22×C4C2×C4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271M16—41no—
272M16—41no—
273M16—441no—
274M16—441no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—222no—
278C2×C8—441no—
279C2×C8—884no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—882no—
289C22⋊C4—222no—
290C22⋊C4—222no—
291C22⋊C4—444no—
292C22⋊C4—882no—
293C42—41no—
294C42—41no—
295C42#433911yescharacteristic
296C42D4×D1111yescharacteristic
297C42#434111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C11#948311yescharacteristic, complemented, Sylow
300C23—114no—
301C23—222no—
302C23—222no—
303C23—442no—
304C23—442no—
305C23C22⋊C4×D1111yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—41no—
309Q8—41no—
310D4—222no—
311D4—222no—
312D4—222no—
313D4—222no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—222no—
323C2×C4—444no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—882no—
329C2×C4(C22⋊D11)⋊C411yescharacteristic
330C2×C4#6693611yescharacteristic
331C2×C4#6693711yescharacteristic
332C2×C4SD16×D1111yescharacteristic
333C2×C4#6696911yescharacteristic
334C2×C4Q16×D1111yescharacteristic
335C2×C4#6697211yescharacteristic
336C2×C4C4×C22⋊D1111yescharacteristic
337C2×C4#6699011yescharacteristic
338C2×C4#6699111yescharacteristic
339C8—42no—
340C8—81no—
341C8—442no—
342C8—881no—
343C22—21no—
344C22—21no—
345C22—224no—
346C22—444no—
347C22—442no—
348C22—442no—
349C22—882no—
350C22D11×#10311yescharacteristic
351C22#1062241711yescharacteristic
352C22#1062256911yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—42no—
358C4—81no—
359C4—442no—
360C4—882no—
361C4#1062242011yescharacteristic
362C4#1062242611yescharacteristic
363C4#1062278411yescharacteristic
364C4#1062280111yescharacteristic
365C2—21no—
366C2—21no—
367C2—444no—
368C2#1306903111yescharacteristic
369C2#1306903611yescharacteristic
370C2#1306914511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1487C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1487D11
hypocenterC11#9483
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
4. #13067045C2semidirect
5. #13066476C2semidirect
6. #13066475C2semidirect
7. C11×#1487C2semidirect
119. #1487D11semidirect
299. C11#9483semidirect

Maximal subgroups

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

subgroupindex
#130776392
#130739742
#130686052
#130670452
#130664762
#130664752
C11×#14872
#948311