Finite Group Databasebeta

← #28393851

Subgroups — #28393851

Order 14464.

528 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813587C211yesmaximal, characteristic, complemented
2C2×#16813580C211yesmaximal, characteristic
3#20298540C211yesmaximal, characteristic, complemented
4#20298533C211yesmaximal, characteristic
5#20298531C211yesmaximal, characteristic, complemented
6#20298520C211yesmaximal, characteristic
7#20298520C211yesmaximal, characteristic
8#20298519C211yesmaximal, characteristic, complemented
9#20298511C211yesmaximal, characteristic
10C4⋊C4×Dic113C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic113C211yesmaximal, characteristic, complemented
12#20298449C211yesmaximal, characteristic, complemented
13#20298445C211yesmaximal, characteristic
14#20298445C211yesmaximal, characteristic
15#398×C113C211yesmaximal, characteristic, complemented
16C22×Dic226C2211yescharacteristic
17C22×C4×D113C2211yescharacteristic
18#16813587—24no—
19#16813580—24no—
20C2×C4⋊Dic113C2211yescharacteristic
21C2×C4⋊Dic113C2211yescharacteristic
22C2×C4⋊Dic113C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268626C2211yescharacteristic
27C2×#14268624C2211yescharacteristic
28C2×#14268624C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×#14268624C2211yescharacteristic
31C2×#14268624C2211yescharacteristic
32C2×#14268624C2211yescharacteristic
33C2×C4×Dic113C2211yescharacteristic
34C2×C4×Dic113C2211yescharacteristic
35C2×C4×Dic113C2211yescharacteristic
36C2×C4×Dic113C2211yescharacteristic
37C2×C4×Dic113C2211yescharacteristic
38C2×C4×Dic113C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46C2×C4⋊C4×C113C2211yescharacteristic
47C2×C4⋊C4×C113C2211yescharacteristic
48C2×C4⋊C4×C113C2211yescharacteristic
49C2×C4⋊C4×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52#95×C113C2211yescharacteristic
53C23×D113C2311yescharacteristic
54C2×Dic226—22no—
55C2×Dic226—22no—
56C2×Dic226—22no—
57C22×Dic113C2311yescharacteristic
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C2×C4×D113—22no—
65C2×C4×D113—22no—
66C2×C4×D113Q814yescomplemented
67C4⋊Dic113—22no—
68C4⋊Dic113—22no—
69C4⋊Dic113—22no—
70#14268626—22no—
71#14268626—22no—
72#14268626—22no—
73#14268626—22no—
74#14268624—22no—
75#14268624—22no—
76#14268624—22no—
77#14268624—22no—
78#14268624—22no—
79#14268624—22no—
80C4×Dic113—22no—
81C4×Dic113—22no—
82C4×Dic113—22no—
83C4×Dic113—22no—
84C4×Dic113—22no—
85C4×Dic113D414yes—
86C22×C4×C113C2311yescharacteristic
87C22×C4×C113C2311yescharacteristic
88C22×C4×C113C2311yescharacteristic
89C22×C4×C113C2311yescharacteristic
90C22×C4×C113C2311yescharacteristic
91C22×C4×C113C2311yescharacteristic
92C22×C4×C113C2311yescharacteristic
93C4⋊C4×C113—22no—
94C4⋊C4×C113—22no—
95C4⋊C4×C113—22no—
96C4⋊C4×C113—22no—
97C23×C113C2411yescharacteristic
98C22×D113—21no—
99C22×D113—21no—
100C22×D113—21no—
101C22×D113—21no—
102C22×D113—21no—
103C22×D113—21no—
104C22×D113C2×Q812yes—
105C2×C4×C113—21no—
106C2×C4×C113—21no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113C2×D412yes—
123C2×C4×C113C2×Q812yes—
124C2×C4×C113#4112yes—
125C2×C4×C113#4112yes—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113C2×D412yes—
142C2×Dic113C2×D412yes—
143C2×Dic113C2×Q812yes—
144C2×Dic113#4112yes—
145C2×Dic113#4112yes—
146C2×Dic113#4112yes—
147C4×D113—28no—
148Dic226—28no—
149C22×C113C22×D411yescharacteristic
150C22×C113C22×Q811yescharacteristic
151C22×C113C2×#4111yescharacteristic
152C22×C113C2×#4111yescharacteristic
153C22×C113C2×#4111yescharacteristic
154C22×C113C2×#4111yescharacteristic
155C22×C113C2×#4111yescharacteristic
156C2×D113—22no—
157C2×D113—22no—
158C2×D113—22no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—41no—
163C4×C113—22no—
164C4×C113—22no—
165C4×C113—22no—
166C4×C113—22no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113—41no—
170Dic113—22no—
171Dic113—22no—
172Dic113—22no—
173Dic113—41no—
174Dic113—41no—
175Dic113—41no—
176Dic113C22⋊Q814yes—
177C2×C113C2×C22⋊Q811yescharacteristic
178C2×C113#52511yescharacteristic
179C2×C113#52911yescharacteristic
180C2×C113#52911yescharacteristic
181C2×C113#53211yescharacteristic
182C2×C113#53311yescharacteristic
183C2×C113#53311yescharacteristic
184D113—42no—
185#2396—1131nomaximal, Sylow
186C113#239611yescharacteristic, complemented, Sylow
187C2×C4×Q8—1131no—
188C2×#117—1131no—
189#400—1131no—
190#399—1131no—
191#398—1131no—
192#398D11311yescharacteristic, complemented
193#396—1131no—
194#396—1131no—
195#395—1131no—
196#393—1131no—
197C4×C4⋊C4—1131no—
198C4×C4⋊C4—1131no—
199C4×C4⋊C4—1131no—
200C4×C22⋊C4—1131no—
201C4×C22⋊C4—1131no—
202C22×Q8—1131no—
203C23×C4—1131no—
204C4×Q8—2264no—
205#117—2264no—
206C2×C4⋊C4—1131no—
207C2×C4⋊C4—1131no—
208C2×C4⋊C4—1131no—
209C2×C4⋊C4—1131no—
210C2×C4⋊C4—1131no—
211C2×C4⋊C4—1131no—
212C2×C4⋊C4—1131no—
213C2×C4⋊C4C2×D11311yescharacteristic
214C2×C4⋊C4C2×D11311yescharacteristic
215C2×C4⋊C4C2×D11311yescharacteristic
216C2×C4⋊C4C2×D11311yescharacteristic
217C2×C22⋊C4—1131no—
218C2×C22⋊C4—1131no—
219C2×C22⋊C4—1131no—
220C2×C22⋊C4—1131no—
221C2×C22⋊C4—1131no—
222C2×C22⋊C4—1131no—
223C2×C42—1131no—
224C2×C42—1131no—
225C2×C42—1131no—
226C2×C42—1131no—
227C2×C42—1131no—
228C2×C42—1131no—
229#95—1131no—
230#95—1131no—
231#95—1131no—
232#95—1131no—
233#95—1131no—
234#95—1131no—
235#95—1131no—
236#95C2×D11311yescharacteristic
237#95C2×D11311yescharacteristic
238#95C2×D11311yescharacteristic
239C24—1131no—
240C2×Q8—2262no—
241C2×Q8—2262no—
242C2×Q8—2262no—
243C22×C4—1131no—
244C22×C4—1131no—
245C22×C4—1131no—
246C22×C4—1131no—
247C22×C4—1134no—
248C22×C4—1131no—
249C22×C4—1131no—
250C22×C4—1131no—
251C22×C4—2262no—
252C22×C4—2262no—
253C22×C4C22×D11311yescharacteristic
254C22×C4C22×D11311yescharacteristic
255C22×C4C22×D11311yescharacteristic
256C22×C4C22×D11311yescharacteristic
257C22×C4C22×D11311yescharacteristic
258C22×C4C22×D11311yescharacteristic
259C22×C4C22×D11311yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—2262no—
265C4⋊C4—2262no—
266C4⋊C4—2262no—
267C4⋊C4—2262no—
268C4⋊C4—2262no—
269C4⋊C4—2262no—
270C4⋊C4—2262no—
271C22⋊C4—2262no—
272C22⋊C4—2262no—
273C22⋊C4—2262no—
274C22⋊C4—2262no—
275C22⋊C4—2262no—
276C22⋊C4—2262no—
277C42—1134no—
278C42—2262no—
279C42—2262no—
280C42—2262no—
281C42—2262no—
282C42—2262no—
283C23—1132no—
284C23—2261no—
285C23—2261no—
286C23—2261no—
287C23—2261no—
288C23—2261no—
289C23—2261no—
290C23C23×D11311yescharacteristic
291Q8—2268no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1132no—
310C2×C4—1132no—
311C2×C4—1132no—
312C2×C4—1132no—
313C2×C4—1132no—
314C2×C4—1132no—
315C2×C4—2268no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4D4×D11312yes—
332C2×C4Q8×D11312yes—
333C2×C4#1426864612yes—
334C2×C4#1426864812yes—
335C22—4521no—
336C22—4521no—
337C22—4521no—
338C22—4521no—
339C22—2262no—
340C22—2262no—
341C22—2262no—
342C22C2×D4×D11311yescharacteristic
343C22C2×Q8×D11311yescharacteristic
344C22#41×D11311yescharacteristic
345C22#41×D11311yescharacteristic
346C22#41×D11311yescharacteristic
347C22C2×#1426864611yescharacteristic
348C22C2×#1426864811yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—1134no—
357C4—4521no—
358C4—4521no—
359C4—4521no—
360C4—2262no—
361C4—2262no—
362C4—2262no—
363C2—4522no—
364C2C22⋊Q8×D11311yescharacteristic
365C2#2029911111yescharacteristic
366C2#2029912511yescharacteristic
367C2#2029913311yescharacteristic
368C2#2029914311yescharacteristic
369C2#2029915311yescharacteristic
370C2#2029915411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#398×C113C2
prime radicalC23×D113C23
hypercenter#398D113
hypocenterC113#2396
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#16813587C2semidirect
3. #20298540C2semidirect
5. #20298531C2semidirect
8. #20298519C2semidirect
10. C4⋊C4×Dic113C2semidirect
11. C4⋊C4×Dic113C2semidirect
12. #20298449C2semidirect
15. #398×C113C2semidirect
66. C2×C4×D113Q8semidirect
186. C113#2396semidirect
192. #398D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135872
C2×#168135802
#202985402
#202985332
#202985312
#202985202
#202985192
#202985112
C4⋊C4×Dic1132
#202984492
#202984452
#398×C1132
#2396113