Finite Group Databasebeta

← #14651621

Subgroups — #14651621

Order 2816.

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

normal subgroups only

This group has 626 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, complemented
2#13073518C211yesmaximal, characteristic
3#13068605C211yesmaximal, characteristic, complemented
4#13067042C211yesmaximal, characteristic, complemented
5#13067040C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×#66948—21no—
9C2×C4×D44C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C11×#382C2211yescharacteristic
14C2×#66887—21no—
15#10622600—21no—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622447—22no—
19D11×C22⋊C8—22no—
20C8×D44—22no—
21#10622287C412yes—
22#10622284C412yes—
23#10622278—22no—
24#10622192—21no—
25#10622121—22no—
26#10622097—22no—
27C22×D44—22no—
28C22×D44C2×C411yescharacteristic
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C22×C4×D11D412yes—
32C2×C11×M16—21no—
33C2×C11×C4⋊C4—21no—
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4C2×C412yes—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×#4318—21no—
42C2×C8×D11—24no—
43#66948—42no—
44#66948—42no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C22⋊C8—21no—
57C4×C8×C11D412yescomplemented
58C11×#95—21no—
59C11×#95C2×C412yes—
60C11⋊#95—22no—
61C22⋊(C11⋊C8)—21no—
62#66887—42no—
63(C2×D11)⋊C8—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4×C11⋊C8D412yescomplemented
68#9485—111nomaximal, Sylow
69C23×D11—21no—
70C23×D11C22⋊C412yes—
71C22×C4×C11—22no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11C22⋊C412yes—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—42no—
84C2×D44—44no—
85C2×D44—44no—
86C2×D44—82no—
87C2×D44D812yes—
88C2×D44SD1612yes—
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C4×D11—82no—
98C11×M16—41no—
99C11×M16—41no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—44no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—82no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118#4318—41no—
119#4318—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C8×D11—84no—
123#2972—111no—
124#2535—111no—
125#1800—111no—
126#1486—111no—
127#1486—111no—
128#1286—111no—
129#1286D1111yescharacteristic, complemented
130C23×C11C2×C22⋊C411yescharacteristic
131C22×D11—22no—
132C22×D11—22no—
133C22×D11—22no—
134C22×D11—42no—
135C22×D11—42no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11#10214yes—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×SD1611yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11#13511yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163D44—22no—
164D44—22no—
165D44—22no—
166D44—22no—
167D44—22no—
168D44—22no—
169D44—41no—
170D44—41no—
171D44—88no—
172C4×D11—44no—
173C4×D11—82no—
174C4×D11—81no—
175C4×D11—81no—
176C4×D11—81no—
177C4×D11—81no—
178C8×C11—42no—
179C8×C11—81no—
180C11⋊C8—42no—
181C11⋊C8—81no—
182C2×#121—221no—
183C2×C4×D4—111no—
184C2×C4×D4—111no—
185C8×D4—222no—
186C8×D4—222no—
187#431—111no—
188#431C2×D1111yescharacteristic
189#423—111no—
190#423C2×D1111yescharacteristic
191C2×#100—221no—
192C2×C22⋊C8—222no—
193#397—112no—
194#392—112no—
195#386—222no—
196#382C2×D1111yescharacteristic
197#380—221no—
198#343—221no—
199D4⋊C8—222no—
200D4⋊C8—222no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11#38611yescharacteristic
204C22×C11C2×#10211yescharacteristic
205C22×C11#41611yescharacteristic
206C2×D11—24no—
207C2×D11—42no—
208C2×D11—42no—
209C2×D11—44no—
210C2×D11—42no—
211C2×D11—42no—
212C2×D11—42no—
213C2×D11—82no—
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—81no—
217C2×D11—81no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—82no—
223C4×C11#46511yescharacteristic
224C4×C11#46511yescharacteristic
225C4×C11#46611yescharacteristic
226C4×C11#46611yescharacteristic
227Dic11—42no—
228Dic11—81no—
229C22×D4—111no—
230C22×D4—111no—
231C22×D4—222no—
232C23×C4—112no—
233C23×C4—221no—
234C2×M16—21no—
235C2×M16—221no—
236C22×C8—224no—
237#121—442no—
238#121—442no—
239C4×D4—221no—
240C4×D4—221no—
241C4×D4—221no—
242C4×D4—221no—
243C4×D4—221no—
244C4×D4—221no—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—111no—
250C2×C22⋊C4—112no—
251C2×C22⋊C4—222no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—222no—
254C2×C42C22×D1111yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—221no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261#100—442no—
262C22⋊C8—21no—
263C22⋊C8—224no—
264C22⋊C8—221no—
265C4×C8—112no—
266C4×C8D4412yescomplemented
267#95—21no—
268#95—222no—
269#95C4×D1112yes—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11#189111yescharacteristic
273C2×C11#189311yescharacteristic
274C2×C11#191111yescharacteristic
275D11—44no—
276D11—82no—
277C24—112no—
278C24—221no—
279C2×D4—112no—
280C2×D4—112no—
281C2×D4—221no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—442no—
288C2×D4—444no—
289C2×D4—444no—
290C2×D4—882no—
291C22×C4—22no—
292C22×C4—112no—
293C22×C4—222no—
294C22×C4—222no—
295C22×C4—221no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4—441no—
302C22×C4—882no—
303C22×C4C2×C4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4D4×D1111yescharacteristic
306M16—41no—
307M16—41no—
308M16—441no—
309M16—441no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—222no—
313C2×C8—441no—
314C2×C8—884no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—221no—
321C22⋊C4—222no—
322C22⋊C4—222no—
323C22⋊C4—444no—
324C22⋊C4—441no—
325C22⋊C4—441no—
326C22⋊C4—882no—
327C42C2×D4411yescharacteristic
328C42#433911yescharacteristic
329C42D4×D1111yescharacteristic
330C42#434311yescharacteristic
331C11#948511yescharacteristic, complemented, Sylow
332C23—114no—
333C23—222no—
334C23—222no—
335C23—222no—
336C23—442no—
337C23—442no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23—441no—
342C23—441no—
343C23—441no—
344C23C22⋊C4×D1111yescharacteristic
345D4—222no—
346D4—222no—
347D4—222no—
348D4—222no—
349D4—222no—
350D4—222no—
351D4—441no—
352D4—441no—
353D4—888no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—222no—
360C2×C4—444no—
361C2×C4—442no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—882no—
366C2×C4—881no—
367C2×C4—881no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4C4×D4411yescharacteristic
371C2×C4#6693511yescharacteristic
372C2×C4#6693711yescharacteristic
373C2×C4#6694611yescharacteristic
374C2×C4#6694711yescharacteristic
375C2×C4#6694811yescharacteristic
376C2×C4D8×D1111yescharacteristic
377C2×C4SD16×D1111yescharacteristic
378C2×C4#6696911yescharacteristic
379C2×C4#6697211yescharacteristic
380C8—42no—
381C8—81no—
382C8—442no—
383C8—881no—
384C22—21no—
385C22—21no—
386C22—224no—
387C22—444no—
388C22—442no—
389C22—442no—
390C22—442no—
391C22—442no—
392C22—442no—
393C22—882no—
394C22—881no—
395C22—881no—
396C22—881no—
397C22—881no—
398C22#1062227811yescharacteristic
399C22D11×#10211yescharacteristic
400C22#1062241711yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—82no—
406C4—442no—
407C4—881no—
408C4#1062238811yescharacteristic
409C4#1062242011yescharacteristic
410C4#1062247711yescharacteristic
411C4#1062249611yescharacteristic
412C2—21no—
413C2—21no—
414C2—444no—
415C2—882no—
416C2#1306903311yescharacteristic
417C2#1306904311yescharacteristic
418C2#1306914711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radical#13073518C2
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9485
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
1. #13077639C2semidirect
3. #13068605C2semidirect
4. #13067042C2semidirect
5. #13067040C2semidirect
6. #13066474C2semidirect
7. C11×#1286C2semidirect
57. C4×C8×C11D4semidirect
67. C4×C11⋊C8D4semidirect
129. #1286D11semidirect
266. C4×C8D44semidirect
331. C11#9485semidirect

Maximal subgroups

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

subgroupindex
#130776392
#130735182
#130686052
#130670422
#130670402
#130664742
C11×#12862
#948511