Finite Group Databasebeta

← #14645472

Subgroups — #14645472

Order 2816.

780 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 127 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×#10623072C211yesmaximal, characteristic
2#13068700C212yesmaximal, complemented
3#13067187C212yesmaximal, complemented
4#13066934C211yesmaximal, characteristic
5C11×#1799C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66988—21no—
8C2×#66979C411yescharacteristic, complemented
9C22×C4⋊Dic11C2211yescharacteristic
10C2×#66977C411yescharacteristic, complemented
11C2×#66977C2211yescharacteristic
12#10623072—24no—
13#10623072—24no—
14C2×#66942—21no—
15C2×#66932—21no—
16C2×#66930—21no—
17C2×#66923C411yescharacteristic, complemented
18C2×C4×Dic22C411yescharacteristic, complemented
19C2×C11×#99—21no—
20C11×#380C2212yes—
21C2×C22⋊(C11⋊C8)C2212yes—
22C11×#342—21no—
23#10622167—24no—
24#10622166—21no—
25#10622163—21no—
26#10622090—24no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C22×Dic22C2×C411yescharacteristic
32C4×D4×C11—22no—
33C4×D4×C11—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43#66988—28no—
44#66979—22no—
45#66979—22no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×C4⋊Dic11D414yes—
52#66977—22no—
53#66977—22no—
54#66977—22no—
55#66977D414yes—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×Dic11⋊C4—21no—
59C2×Dic11⋊C4—21no—
60C2×Dic11⋊C4—21no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11—21no—
63C22×C11⋊C8—22no—
64#66942—28no—
65#66932—28no—
66#66930—28no—
67#66923—22no—
68#66923—22no—
69C4×Dic22—22no—
70C4×Dic22—22no—
71C11×#99—42no—
72C11×#95—22no—
73C22⋊(C11⋊C8)—22no—
74C22⋊(C11⋊C8)—22no—
75#8382—111nomaximal, Sylow
76C24×C11C22⋊C411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—24no—
99C22×Dic11—42no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C2×Dic22—21no—
103C2×Dic22—42no—
104C2×Dic22C22⋊C412yes—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—44no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C42×C11—21no—
112C42×C11—21no—
113C22⋊Dic11—24no—
114C22⋊Dic11—24no—
115C22⋊Dic11—24no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—24no—
120C4⋊Dic11C22⋊C412yes—
121C4⋊Dic11C22⋊C412yes—
122C4⋊Dic11C22⋊C412yes—
123Dic11⋊C4—24no—
124Dic11⋊C4—24no—
125Dic11⋊C4—24no—
126Dic11⋊C4—24no—
127Dic11⋊C4—24no—
128C4×Dic11—24no—
129C4×Dic11—24no—
130C2×C11⋊C8—44no—
131C2×C11⋊C8—42no—
132C2×#552—111no—
133#1823—112no—
134#1799D1111yescharacteristic
135#1520—112no—
136#1459—111no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11C2×C22⋊C411yescharacteristic
145C23×C11#12012yes—
146C23×C11#13512yes—
147C23×C11AGL(1,ℤ/8)11yescharacteristic
148C23×C11#13711yescharacteristic
149D4×C11—42no—
150D4×C11—42no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—82no—
165C2×C4×C11—82no—
166C2×C4×C11—82no—
167C2×C4×C11C2×C22⋊C411yescharacteristic
168C2×C4×C11C2×C22⋊C411yescharacteristic
169C2×C4×C11#12012yes—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—44no—
181C2×Dic11—44no—
182Dic22—42no—
183Dic22—42no—
184C11⋊C8—82no—
185#552—224no—
186#552—224no—
187C2×#126—221no—
188C2×#125—111no—
189C2×#125—221no—
190C2×#123—221no—
191C2×C22⋊Q8—111no—
192C2×C22⋊Q8—111no—
193C2×C4×Q8—111no—
194C2×C4×D4C2×D1111yescharacteristic
195C2×#117—111no—
196C2×#117—221no—
197C22×C4⋊C4—111no—
198C2×#99—21no—
199C2×C22⋊C8—112no—
200#380C2×D1112yes—
201#342—21no—
202#340—224no—
203#328—224no—
204#324—221no—
205#323—221no—
206C22×C11—21no—
207C22×C11—22no—
208C22×C11—21no—
209C22×C11—22no—
210C22×C11—42no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11#37911yescharacteristic
219C22×C11#41611yescharacteristic
220C22×C11#41711yescharacteristic
221C22×C11#44912yes—
222C22×C11#45212yes—
223C4×C11—21no—
224C4×C11—22no—
225C4×C11—41no—
226C4×C11—41no—
227C4×C11—41no—
228C4×C11—162no—
229C4×C11#41012yes—
230Dic11—42no—
231Dic11—42no—
232Dic11—42no—
233Dic11—42no—
234C22×Q8—111no—
235C22×D4C22⋊D1111yescharacteristic
236C23×C4—221no—
237C23×C4C4×D1111yescharacteristic
238C23×C4C22×D1111yescharacteristic
239C22×C8—222no—
240#126—228no—
241#125—222no—
242#125—222no—
243#125—228no—
244#123—228no—
245C22⋊Q8—114no—
246C22⋊Q8—222no—
247C22⋊Q8—222no—
248C22⋊Q8—222no—
249C4×Q8—222no—
250C4×Q8—222no—
251C4×D4—22no—
252C4×D4—22no—
253#117—228no—
254#117—222no—
255#117—222no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—114no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4D4411yescharacteristic
269C2×C22⋊C4—22no—
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4D4411yescharacteristic
274C2×C22⋊C4C22⋊D1111yescharacteristic
275C2×C42—221no—
276C2×C42—221no—
277C2×C42C4×D1111yescharacteristic
278#99—42no—
279C22⋊C8—222no—
280C22⋊C8—222no—
281#95—22no—
282C2×C11—22no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—22no—
286C2×C11—81no—
287C2×C11#178211yescharacteristic
288C2×C11#178811yescharacteristic
289C2×C11#179611yescharacteristic
290C24(C2×D11)⋊C411yescharacteristic
291C24C2×C22⋊D1111yescharacteristic
292C2×Q8—112no—
293C2×Q8—221no—
294C2×Q8—442no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—21no—
298C2×D4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—224no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—442no—
312C22×C4(C2×D11)⋊C411yescharacteristic
313C22×C4(C2×D11)⋊C411yescharacteristic
314C22×C4(C2×D11)⋊C411yescharacteristic
315C22×C4C2×C4×D1111yescharacteristic
316C22×C4C2×D4411yescharacteristic
317C22×C4D4×D1112yes—
318C22×C4D4×D1112yes—
319C2×C8—444no—
320C2×C8—442no—
321C4⋊C4—22no—
322C4⋊C4—44no—
323C4⋊C4—112no—
324C4⋊C4—112no—
325C4⋊C4—112no—
326C4⋊C4—224no—
327C4⋊C4—224no—
328C4⋊C4—224no—
329C4⋊C4—224no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—224no—
334C4⋊C4—224no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—224no—
340C22⋊C4—224no—
341C22⋊C4—224no—
342C42—21no—
343C42—21no—
344C42—224no—
345C42—224no—
346C11#838211yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23C2×(C2×D11)⋊C411yescharacteristic
355C23#6698511yescharacteristic
356C23#6699012yes—
357C23#6699511yescharacteristic
358C23#6700312yes—
359Q8—442no—
360Q8—442no—
361D4—42no—
362D4—42no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—222no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—444no—
390C2×C4—444no—
391C2×C4C22⋊C4×D1111yescharacteristic
392C2×C4C22⋊C4×D1111yescharacteristic
393C2×C4#6693512yes—
394C8—882no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22#1062256811yescharacteristic
408C22#1062257911yescharacteristic
409C22#1062261511yescharacteristic
410C22#1062265012yes—
411C22#1062266012yes—
412C4—22no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—162no—
418C4—442no—
419C4—442no—
420C4—442no—
421C4—442no—
422C4#1062235312yes—
423C2—22no—
424C2—21no—
425C2—21no—
426C2—22no—
427C2—81no—
428C2#1306853211yescharacteristic
429C2#1306855411yescharacteristic
430C2#1306858911yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1799C2
socleC22×C11#379
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#1799D11
hypocenterC11#8382
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #13068700C2semidirect
3. #13067187C2semidirect
8. C2×#66979C4semidirect
10. C2×#66977C4semidirect
17. C2×#66923C4semidirect
18. C2×C4×Dic22C4semidirect
346. C11#8382semidirect

Maximal subgroups

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

subgroupindex
C2×#106230722
#130687002
#130671872
#130669342
C11×#17992
#838211