Finite Group Databasebeta

← #28393921

Subgroups — #28393921

Order 14464.

908 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14268648C211yesmaximal, characteristic, complemented
2C2×#16813596C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D113C211yesmaximal, characteristic, complemented
4#20298515C212yesmaximal, complemented
5#20298507C212yesmaximal, complemented
6#20298505C211yesmaximal, characteristic, complemented
7#20298499C211yesmaximal, characteristic, complemented
8#20298474C212yesmaximal, complemented
9#20298469C212yesmaximal, complemented
10#20298455C211yesmaximal, characteristic, complemented
11C2×C22⋊Q8×C113C211yesmaximal, characteristic, complemented
12C2×#14268648—24no—
13C2×#14268648—24no—
14C2×#14268648—24no—
15C22×D452C2212yes—
16C22×D452C2211yescharacteristic
17C22×C22⋊D113C2211yescharacteristic
18C22×C22⋊D113C2212yes—
19C22×C4×D113C2212yes—
20C22×C4×D113C2211yescharacteristic
21#16813596—24no—
22C4×C22⋊D113—24no—
23C2×C4⋊Dic113C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×C22⋊Dic113C2211yescharacteristic
26C2×#14268624C2212yes—
27C2×#14268624C2211yescharacteristic
28C2×#14268624C2212yes—
29C2×#14268624C2212yes—
30C2×#14268624C2212yes—
31C2×C4×Dic113C2211yescharacteristic
32#16813529C2212yes—
33#16813529C2212yes—
34#16813529C2212yes—
35C22×Q8×C113C2211yescharacteristic
36C23×C4×C113C2211yescharacteristic
37C22⋊Q8×C113—24no—
38C2×C4⋊C4×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2212yes—
40C2×C22⋊C4×C113C2212yes—
41C23×D113C2312yes—
42C23×D113C2311yescharacteristic
43#14268648—232no—
44C2×D452—24no—
45C2×D452—24no—
46C2×D452—22no—
47C2×D452—24no—
48C2×D452—22no—
49C2×D452D414yescomplemented
50C2×C22⋊D113—22no—
51C2×C22⋊D113—22no—
52C2×C22⋊D113—24no—
53C2×C22⋊D113—24no—
54C2×C22⋊D113—22no—
55C2×C22⋊D113—42no—
56C22×Dic113C2311yescharacteristic
57C22×Dic113C2312yes—
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C2×C4×D113—24no—
61C2×C4×D113—22no—
62C2×C4×D113—24no—
63C2×C4×D113—22no—
64C2×C4×D113—24no—
65C2×C4×D113D414yescomplemented
66C4⋊Dic113—22no—
67#14268626—22no—
68C22⋊Dic113—22no—
69#14268624—22no—
70#14268624—24no—
71#14268624—24no—
72#14268624—42no—
73#14268624—42no—
74C4×Dic113—22no—
75C24×C113C2311yescharacteristic
76C2×Q8×C113—22no—
77C2×Q8×C113—22no—
78C2×Q8×C113D414yescomplemented
79C22×C4×C113—22no—
80C22×C4×C113—22no—
81C22×C4×C113—22no—
82C22×C4×C113C2311yescharacteristic
83C22×C4×C113C2312yes—
84C22×C4×C113C2312yes—
85C22×C4×C113C2311yescharacteristic
86C4⋊C4×C113—22no—
87C4⋊C4×C113—24no—
88C22⋊C4×C113—24no—
89C23×C113—21no—
90C23×C113—21no—
91C23×C113—21no—
92C23×C113—21no—
93C23×C113—21no—
94C23×C113—21no—
95C23×C113#4112yescomplemented
96C23×C113C2411yescharacteristic
97C22×D113—22no—
98C22×D113—21no—
99C22×D113—22no—
100C22×D113—21no—
101C22×D113—22no—
102C22×D113—21no—
103C22×D113—21no—
104C22×D113—22no—
105C22×D113—21no—
106C22×D113—22no—
107C22×D113—21no—
108C22×D113—22no—
109C22×D113C2×D414yes—
110C22×D113C2×D412yes—
111Q8×C113—28no—
112C2×C4×C113—22no—
113C2×C4×C113—22no—
114C2×C4×C113—22no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—22no—
119C2×C4×C113—22no—
120C2×C4×C113—44no—
121C2×C4×C113C2×D412yes—
122C2×C4×C113C2×D412yes—
123C2×C4×C113C2×D414yes—
124C2×C4×C113C2×D412yes—
125C22⋊D113—28no—
126C22⋊D113—48no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—22no—
133C2×Dic113—22no—
134C2×Dic113—21no—
135C2×Dic113—22no—
136C2×Dic113—21no—
137C2×Dic113C2×D412yes—
138C2×Dic113#4112yescomplemented
139D452—216no—
140D452—28no—
141C4×D113—216no—
142C4×D113—28no—
143C22×C113—22no—
144C22×C113—22no—
145C22×C113—22no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113C22×D411yescharacteristic
151C22×C113C22×D411yescharacteristic
152C22×C113C22×D411yescharacteristic
153C22×C113C2×#4111yescharacteristic
154C22×C113C2×#4111yescharacteristic
155C22×C113H(5,𝔽2)11yescharacteristic
156C22×C1132−1+411yescharacteristic
157C2×D113—24no—
158C2×D113—22no—
159C2×D113—22no—
160C2×D113—22no—
161C2×D113—24no—
162C2×D113—24no—
163C2×D113—42no—
164C2×D113—42no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—41no—
168C2×D113—42no—
169C2×D113—42no—
170C2×D113—41no—
171C4×C113—24no—
172C4×C113—41no—
173C4×C113—42no—
174C4×C113#12014yes—
175Dic113—22no—
176Dic113—22no—
177Dic113—41no—
178Dic113—42no—
179C2×C113—42no—
180C2×C113C2×#12011yescharacteristic
181C2×C113#52511yescharacteristic
182C2×C113#53711yescharacteristic
183C2×C113#54611yescharacteristic
184C2×C113#54711yescharacteristic
185C2×C113#54811yescharacteristic
186C2×C113#55011yescharacteristic
187D113—42no—
188D113—44no—
189#2407—1131nomaximal, Sylow
190C113#240711yescharacteristic, complemented, Sylow
191C22×#41—1131no—
192C2×C22⋊Q8D11311yescharacteristic, complemented
193C2×#121—1131no—
194C2×C4×D4—1131no—
195#394—1132no—
196#392—1132no—
197#391—1131no—
198#390—1131no—
199#386—1132no—
200#385—1132no—
201#380—1131no—
202C2×#41—2264no—
203C2×#41—2264no—
204C2×#41—2264no—
205C22×Q8C2×D11311yescharacteristic
206C22×D4—1132no—
207C22×D4—1131no—
208C22×D4—1131no—
209C22×D4—1132no—
210C23×C4—1131no—
211C23×C4—1132no—
212C23×C4C2×D11311yescharacteristic
213C22⋊Q8—24no—
214#121—2264no—
215C4×D4—2264no—
216C2×C4⋊C4—1131no—
217C2×C4⋊C4—1131no—
218C2×C4⋊C4C2×D11311yescharacteristic
219C2×C4⋊C4C2×D11312yes—
220C2×C22⋊C4—1132no—
221C2×C22⋊C4—1132no—
222C2×C22⋊C4—1131no—
223C2×C22⋊C4—1131no—
224C2×C22⋊C4—1132no—
225C2×C22⋊C4—1132no—
226C2×C22⋊C4C2×D11312yes—
227C2×C42—1131no—
228#95—1132no—
229#95—1132no—
230#95—1132no—
231C24—1131no—
232C24—1132no—
233C24C22×D11311yescharacteristic
234#41—22632no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8C22⋊D11314yescomplemented
238C2×D4—1134no—
239C2×D4—4522no—
240C2×D4—2264no—
241C2×D4—2264no—
242C2×D4—2262no—
243C2×D4—2264no—
244C2×D4—2264no—
245C2×D4—2262no—
246C2×D4—2262no—
247C2×D4—2262no—
248C2×D4—2264no—
249C2×D4—2262no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—1131no—
254C22×C4—1131no—
255C22×C4—1134no—
256C22×C4—1132no—
257C22×C4—1131no—
258C22×C4—2264no—
259C22×C4—2264no—
260C22×C4—2262no—
261C22×C4—2264no—
262C22×C4—2262no—
263C22×C4C22×D11312yes—
264C22×C4C22×D11311yescharacteristic
265C22×C4C22×D11312yes—
266C22×C4C22×D11311yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—24no—
269C4⋊C4—2262no—
270C4⋊C4—2262no—
271C22⋊C4—24no—
272C22⋊C4—4522no—
273C22⋊C4—4522no—
274C22⋊C4—2264no—
275C22⋊C4—2262no—
276C22⋊C4—2264no—
277C22⋊C4—2262no—
278C42—2262no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—1132no—
286C23—1134no—
287C23—2262no—
288C23—2261no—
289C23—2262no—
290C23—2261no—
291C23—2262no—
292C23—2261no—
293C23—2262no—
294C23—2261no—
295C23—2261no—
296C23—2262no—
297C23—2262no—
298C23—2261no—
299C23#1426864812yescomplemented
300C23C23×D11311yescharacteristic
301Q8—28no—
302D4—4528no—
303D4—22616no—
304D4—2268no—
305D4—2268no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—44no—
315C2×C4—1132no—
316C2×C4—1132no—
317C2×C4—22616no—
318C2×C4—2261no—
319C2×C4—2262no—
320C2×C4—2262no—
321C2×C4—2261no—
322C2×C4—2262no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2268no—
329C2×C4D4×D11312yes—
330C2×C4D4×D11312yes—
331C2×C4C2×C22⋊D11314yes—
332C2×C4C2×C22⋊D11312yes—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—4522no—
341C22—4521no—
342C22—4522no—
343C22—4522no—
344C22—4521no—
345C22—4521no—
346C22—4522no—
347C22—4521no—
348C22—2264no—
349C22—2262no—
350C22—2262no—
351C22—2262no—
352C22—2264no—
353C22—2264no—
354C22C2×D4×D11311yescharacteristic
355C22C2×D4×D11311yescharacteristic
356C22C22×C22⋊D11311yescharacteristic
357C22#41×D11311yescharacteristic
358C22C2×#1426864811yescharacteristic
359C22#1681366811yescharacteristic
360C22#1681367011yescharacteristic
361C4—24no—
362C4—42no—
363C4—41no—
364C4—4521no—
365C4—4522no—
366C4—2262no—
367C4—2262no—
368C4#1681359014yes—
369C2—42no—
370C2—4524no—
371C2—4522no—
372C2C2×#1681359011yescharacteristic
373C2#2029911111yescharacteristic
374C2#2029917811yescharacteristic
375C2#2029923911yescharacteristic
376C2#2029925011yescharacteristic
377C2#2029925911yescharacteristic
378C2#2029926711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
FittingC2×C22⋊Q8×C113C2
hypercenterC2×C22⋊Q8D113
hypocenterC113#2407
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14268648C2semidirect
2. C2×#16813596C2semidirect
3. C2×C4×C22⋊D113C2semidirect
4. #20298515C2semidirect
5. #20298507C2semidirect
6. #20298505C2semidirect
7. #20298499C2semidirect
8. #20298474C2semidirect
9. #20298469C2semidirect
10. #20298455C2semidirect
11. C2×C22⋊Q8×C113C2semidirect
49. C2×D452D4semidirect
65. C2×C4×D113D4semidirect
78. C2×Q8×C113D4semidirect
95. C23×C113#41semidirect
138. C2×Dic113#41semidirect
190. C113#2407semidirect
192. C2×C22⋊Q8D113semidirect
237. C2×Q8C22⋊D113semidirect
299. C23#14268648semidirect

Maximal subgroups

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

subgroupindex
C22×#142686482
C2×#168135962
C2×C4×C22⋊D1132
#202985152
#202985072
#202985052
#202984992
#202984742
#202984692
#202984552
C2×C22⋊Q8×C1132
#2407113