Finite Group Databasebeta

← #14727692

Subgroups — #14727692

Order 2816.

1002 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 187 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
1C2×#10623031C211yesmaximal, characteristic, complemented
2#13079374C212yesmaximal
3#13074358C211yesmaximal, characteristic
4#13067626C214yesmaximal, complemented
5#13067558C214yesmaximal, complemented
6#13067189C212yesmaximal, complemented
7C2×C11×#324C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×#66982—21no—
11C2×#66979—21no—
12C2×#66977—21no—
13C2×#66977C2212yes—
14#10623031—22no—
15#10623031—24no—
16#10623031C2214yes—
17C2×#66943—22no—
18C2×#66941—22no—
19C2×C11×C22⋊C8C2212yes—
20#10622826—21no—
21#10622825C2211yescharacteristic
22#10622727—24no—
23#10622607—22no—
24#10622604C2212yes—
25#10622596C2212yes—
26#10622351—22no—
27#10622348—22no—
28#10622344C2214yes—
29#10622334C2214yes—
30C11×#324C2214yes—
31#10622105C2218yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—21no—
36C22×D44C2311yescharacteristic
37C22×Dic22—21no—
38C22×Dic22D412yes—
39C22×C8×C11—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4D412yes—
43C2×C11×C4⋊C4C2312yes—
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11—21no—
46#66983—22no—
47#66983—22no—
48#66982—44no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—22no—
52#66979—24no—
53#66979—24no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D412yes—
59C2×C4⋊Dic11C2311yescharacteristic
60#66977—24no—
61#66977—22no—
62#66977—22no—
63#66977—24no—
64#66977D414yes—
65#66977C2314yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—22no—
70C2×#4314—24no—
71#66943—28no—
72#66943—28no—
73#66941—28no—
74#66941—28no—
75C11×C22⋊C8—22no—
76C11×C22⋊C8C2314yes—
77C11⋊#95—22no—
78C11⋊#95C2312yes—
79#66885—24no—
80#66881—24no—
81#66880—24no—
82#18294—111nomaximal, Sylow
83C24×C11C2×D411yescharacteristic
84C23×D11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—81no—
91C22×C4×C11—81no—
92C22×C4×C11SD1614yescomplemented
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2411yescharacteristic
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—42no—
102C2×C22⋊D11—42no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—21no—
106C22×Dic11—22no—
107C2×D44—22no—
108C2×D44—81no—
109C2×Dic22—24no—
110C2×Dic22—22no—
111C2×Dic22—82no—
112C2×Dic22—82no—
113C2×Dic22C2×D414yes—
114C2×C8×C11—24no—
115C2×C8×C11—82no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C22⋊Dic11—24no—
119C22⋊Dic11—24no—
120C22⋊Dic11—42no—
121(C2×D11)⋊C4—42no—
122(C2×D11)⋊C4—44no—
123(C2×D11)⋊C4—82no—
124C4⋊Dic11—24no—
125C4⋊Dic11—24no—
126C4⋊Dic11—24no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—81no—
130C4⋊Dic11C2×D414yes—
131Dic11⋊C4—28no—
132Dic11⋊C4—24no—
133Dic11⋊C4—24no—
134Dic11⋊C4—44no—
135C4×Dic11—28no—
136#4314—84no—
137C2×#544—111no—
138#3187—112no—
139#2618—111no—
140#1611—114no—
141#1599—114no—
142#1520—112no—
143C2×#324D1111yescharacteristic, complemented
144C23×C11—41no—
145C23×C11—41no—
146C23×C11#12011yescharacteristic
147C23×C11#12011yescharacteristic
148C23×C11C2×SD1612yes—
149C23×C11#13712yes—
150C23×C11C22×D411yescharacteristic
151C22×D11—42no—
152C22×D11—42no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—81no—
168C2×C4×C11#12012yes—
169C2×C4×C11C2×SD1614yes—
170C2×C4×C11C22×D412yes—
171C22⋊D11—82no—
172C22⋊D11—82no—
173C2×Dic11—24no—
174C2×Dic11—24no—
175C2×Dic11—44no—
176C2×Dic11—44no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—41no—
183D44—44no—
184Dic22—44no—
185Dic22—82no—
186Dic22—84no—
187C8×C11—44no—
188#544—114no—
189#544—224no—
190#544—222no—
191C2×C4⋊Q8—222no—
192C2×#125—222no—
193C2×#123—221no—
194C2×C22⋊Q8—112no—
195C2×C22⋊Q8—221no—
196C2×#121—111no—
197C2×#117—221no—
198C22×C4⋊C4C2×D1111yescharacteristic
199#483—114no—
200#481—222no—
201#465—224no—
202#450—114no—
203#448—222no—
204C2×C22⋊C8C2×D1112yes—
205#398—112no—
206#396—222no—
207#394—112no—
208#386—221no—
209#380—111no—
210#328—118no—
211#324C2×D1114yes—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11#44812yes—
221C22×C11#44812yes—
222C22×C11C2×#12011yescharacteristic
223C22×C11C22×SD1611yescharacteristic
224C22×C11C2×#13711yescharacteristic
225C2×D11—82no—
226C2×D11—82no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C4×C11—24no—
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—42no—
234Dic11—44no—
235Dic11—44no—
236Dic11—82no—
237Dic11—81no—
238C22×Q8—112no—
239C22×Q8—221no—
240C22×D4—111no—
241C22×D4—221no—
242C23×C4D4411yescharacteristic
243C23×C4D4411yescharacteristic
244C23×C4C22×D1111yescharacteristic
245C2×SD16—224no—
246C22×C8—22no—
247C4⋊Q8—228no—
248C4⋊Q8—228no—
249#125—228no—
250#125—228no—
251#123—444no—
252C22⋊Q8—114no—
253C22⋊Q8—114no—
254C22⋊Q8—224no—
255C22⋊Q8—222no—
256C22⋊Q8—224no—
257C22⋊Q8—222no—
258#121—222no—
259#121—222no—
260#117—224no—
261#117—224no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4—222no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4D4412yes—
274C2×C4⋊C4C22×D1112yes—
275C2×C22⋊C4—222no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—221no—
278C2×C22⋊C4—222no—
279C2×C22⋊C4—222no—
280C2×C42—222no—
281#106—224no—
282#103—224no—
283#102—224no—
284C22⋊C8—22no—
285C22⋊C8C22×D1114yes—
286#95—112no—
287#95—222no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—22no—
291C2×C11—22no—
292C2×C11C2×#44811yescharacteristic
293C2×C11#302011yescharacteristic
294C2×C11#302611yescharacteristic
295D11—161no—
296C24—221no—
297C24C2×D4411yescharacteristic
298C2×Q8—114no—
299C2×Q8—224no—
300C2×Q8—222no—
301C2×Q8—882no—
302C2×Q8—882no—
303C2×D4—222no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—442no—
307C2×D4—442no—
308C2×D4—881no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—81no—
315C22×C4—81no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—222no—
319C22×C4—221no—
320C22×C4#431414yescomplemented
321C22×C4C2×D4412yes—
322C22×C4C2×D4412yes—
323C22×C4C2×D4411yescharacteristic
324C22×C4D4×D1112yes—
325C22×C4D4×D1112yes—
326C22×C4C23×D1111yescharacteristic
327SD16—884no—
328C2×C8—24no—
329C2×C8—82no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—114no—
333C4⋊C4—224no—
334C4⋊C4—224no—
335C4⋊C4—224no—
336C4⋊C4—228no—
337C4⋊C4—222no—
338C4⋊C4—224no—
339C4⋊C4—224no—
340C4⋊C4—222no—
341C4⋊C4—444no—
342C4⋊C4—881no—
343C22⋊C4—224no—
344C22⋊C4—224no—
345C22⋊C4—442no—
346C22⋊C4—442no—
347C22⋊C4—444no—
348C22⋊C4—882no—
349C42—228no—
350C11#1829411yescharacteristic, complemented, Sylow
351C23—41no—
352C23—41no—
353C23—442no—
354C23—442no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23#6693511yescharacteristic
359C23#6693511yescharacteristic
360C23C2×#431412yes—
361C23#6696212yes—
362C23C22×D4411yescharacteristic
363Q8—444no—
364Q8—882no—
365Q8—884no—
366D4—444no—
367D4—882no—
368D4—882no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—224no—
382C2×C4—224no—
383C2×C4—444no—
384C2×C4—444no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4#6693512yes—
392C2×C4C2×#431414yes—
393C2×C4C2×D4×D1112yes—
394C8—44no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—882no—
404C22—882no—
405C22—881no—
406C22—881no—
407C22—881no—
408C22#1062235112yes—
409C22#1062235112yes—
410C22C2×#6693511yescharacteristic
411C22C22×#431411yescharacteristic
412C22C2×#6696211yescharacteristic
413C4—24no—
414C4—22no—
415C4—22no—
416C4—42no—
417C4—444no—
418C4—444no—
419C4—882no—
420C4—881no—
421C2—21no—
422C2—21no—
423C2—22no—
424C2—22no—
425C2—1761no—
426C2C2×#1062235111yescharacteristic
427C2#1307798311yescharacteristic
428C2#1307801511yescharacteristic
subgroupG/H
centerC22C2×#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC22×C11C2×#120
prime radicalC2×#66983C22
hypercenterC2×#324D11
hypocenterC11#18294
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
1. C2×#10623031C2semidirect
4. #13067626C2semidirect
5. #13067558C2semidirect
6. #13067189C2semidirect
7. C2×C11×#324C2semidirect
92. C22×C4×C11SD16semidirect
143. C2×#324D11semidirect
320. C22×C4#4314semidirect
350. C11#18294semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
#130793742
#130743582
#130676262
#130675582
#130671892
C2×C11×#3242
#1829411