Finite Group Databasebeta

← #28393837

Subgroups — #28393837

Order 14464.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D452C211yesmaximal, characteristic
2C2×#16813579C211yesmaximal, characteristic, complemented
3#20298540C211yesmaximal, characteristic, complemented
4#20298533C211yesmaximal, characteristic, complemented
5#20298531C211yesmaximal, characteristic, complemented
6#20298527C211yesmaximal, characteristic, complemented
7#20298527C211yesmaximal, characteristic, complemented
8#20298524C211yesmaximal, characteristic, complemented
9#20298516C211yesmaximal, characteristic
10#20298515C211yesmaximal, characteristic
11C4×#14268626C211yesmaximal, characteristic, complemented
12C4×#14268624C211yesmaximal, characteristic, complemented
13C4×#14268624C211yesmaximal, characteristic, complemented
14C4×#14268624C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C22×C4×D113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C4×D452—24no—
20#16813579—24no—
21C2×C4⋊Dic113C2211yescharacteristic
22C2×#14268626C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268624C2211yescharacteristic
27C2×#14268624C2211yescharacteristic
28C2×#14268624C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×#14268624C2211yescharacteristic
31C2×#14268624C2211yescharacteristic
32C2×#14268624C2211yescharacteristic
33C2×#14268624C2211yescharacteristic
34C2×#14268624C2211yescharacteristic
35C2×#14268624C2211yescharacteristic
36C2×C4×Dic113C2211yescharacteristic
37C2×C4×Dic113C2211yescharacteristic
38#16813529C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46C2×C4⋊C4×C113C2211yescharacteristic
47C2×C4⋊C4×C113C2211yescharacteristic
48C2×C42×C113C2211yescharacteristic
49C2×C42×C113C2211yescharacteristic
50C2×C42×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52#95×C113C2211yescharacteristic
53C23×D113C2311yescharacteristic
54C23×D113C2311yescharacteristic
55C2×D452—22no—
56C2×D452—22no—
57C2×D452—22no—
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C2×C4×D113—22no—
65C2×C4×D113—22no—
66C2×C4×D113—22no—
67C2×C4×D113—22no—
68C2×C4×D113—22no—
69C2×C4×D113D414yes—
70C4⋊Dic113—22no—
71#14268626—22no—
72#14268626—22no—
73#14268626—22no—
74#14268626—22no—
75#14268624—22no—
76#14268624—22no—
77#14268624—22no—
78#14268624—22no—
79#14268624—22no—
80#14268624—22no—
81#14268624—22no—
82#14268624—22no—
83#14268624—22no—
84#14268624—22no—
85C4×Dic113—22no—
86C4×Dic113—22no—
87C22×C4×C113C2311yescharacteristic
88C22×C4×C113C2311yescharacteristic
89C22×C4×C113C2311yescharacteristic
90C22×C4×C113C2311yescharacteristic
91C22×C4×C113C2311yescharacteristic
92C22×C4×C113C2311yescharacteristic
93C22×C4×C113C2311yescharacteristic
94C4⋊C4×C113—22no—
95C4⋊C4×C113—22no—
96C42×C113—22no—
97C42×C113—22no—
98C42×C113—22no—
99C23×C113C2411yescharacteristic
100C22×D113—21no—
101C22×D113—21no—
102C22×D113—21no—
103C22×D113—21no—
104C22×D113—21no—
105C22×D113—21no—
106C22×D113—21no—
107C22×D113—21no—
108C22×D113—21no—
109C22×D113—21no—
110C22×D113—21no—
111C22×D113—21no—
112C22×D113C2×D412yes—
113C22×D113#4112yes—
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×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113C2×D412yes—
131C2×C4×C113#4112yes—
132C2×C4×C113#4112yes—
133C2×C4×C113#4112yes—
134C2×C4×C113#4112yes—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—21no—
151C2×Dic113C2×D412yes—
152C2×Dic113#4112yes—
153D452—28no—
154C4×D113—28no—
155C4×D113—44no—
156C22×C113C22×D411yescharacteristic
157C22×C113C2×#4111yescharacteristic
158C22×C113C2×#4111yescharacteristic
159C22×C113C2×#4111yescharacteristic
160C22×C113C2×#4111yescharacteristic
161C22×C113C2×#4111yescharacteristic
162C22×C113C2×#4111yescharacteristic
163C2×D113—22no—
164C2×D113—22no—
165C2×D113—22no—
166C2×D113—22no—
167C2×D113—22no—
168C2×D113—22no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C4×C113—22no—
178C4×C113—22no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113—41no—
183C4×C113#12314yes—
184Dic113—22no—
185Dic113—22no—
186Dic113—41no—
187Dic113—41no—
188Dic113—41no—
189Dic113—41no—
190C2×C113C2×#12311yescharacteristic
191C2×C113#52511yescharacteristic
192C2×C113#52911yescharacteristic
193C2×C113#52911yescharacteristic
194C2×C113#52911yescharacteristic
195C2×C113#52911yescharacteristic
196C2×C113#53211yescharacteristic
197D113—42no—
198D113—42no—
199#2395—1131nomaximal, Sylow
200C113#239511yescharacteristic, complemented, Sylow
201C2×C4×D4—1131no—
202C2×#117—1131no—
203#400—1131no—
204#399—1131no—
205#398—1131no—
206#397—1131no—
207#397—1131no—
208#397—1131no—
209#394—1131no—
210#394—1131no—
211C4×C4⋊C4—1131no—
212C4×C4⋊C4D11311yescharacteristic, complemented
213C4×C22⋊C4—1131no—
214C4×C22⋊C4—1131no—
215C4×C22⋊C4—1131no—
216C22×D4—1131no—
217C23×C4—1131no—
218C23×C4—1131no—
219C4×D4—2264no—
220#117—2264no—
221C2×C4⋊C4—1131no—
222C2×C4⋊C4—1131no—
223C2×C4⋊C4—1131no—
224C2×C4⋊C4—1131no—
225C2×C4⋊C4—1131no—
226C2×C4⋊C4C2×D11311yescharacteristic
227C2×C4⋊C4C2×D11311yescharacteristic
228C2×C22⋊C4—1131no—
229C2×C22⋊C4—1131no—
230C2×C22⋊C4—1131no—
231C2×C22⋊C4—1131no—
232C2×C22⋊C4—1131no—
233C2×C22⋊C4—1131no—
234C2×C22⋊C4—1131no—
235C2×C22⋊C4—1131no—
236C2×C22⋊C4—1131no—
237C2×C22⋊C4—1131no—
238C2×C42—1131no—
239C2×C42—1131no—
240C2×C42C2×D11311yescharacteristic
241C2×C42C2×D11311yescharacteristic
242C2×C42C2×D11311yescharacteristic
243#95—1131no—
244#95—1131no—
245#95—1131no—
246#95—1131no—
247#95—1131no—
248#95—1131no—
249#95—1131no—
250#95—1131no—
251#95C2×D11311yescharacteristic
252#95C2×D11311yescharacteristic
253C24—1131no—
254C24—1131no—
255C2×D4—2262no—
256C2×D4—2262no—
257C2×D4—2262no—
258C22×C4—1131no—
259C22×C4—1131no—
260C22×C4—1134no—
261C22×C4—1131no—
262C22×C4—1131no—
263C22×C4—1131no—
264C22×C4—1131no—
265C22×C4—2262no—
266C22×C4—2262no—
267C22×C4—2262no—
268C22×C4—2262no—
269C22×C4—2262no—
270C22×C4C22×D11311yescharacteristic
271C22×C4C22×D11311yescharacteristic
272C22×C4C22×D11311yescharacteristic
273C22×C4C22×D11311yescharacteristic
274C22×C4C22×D11311yescharacteristic
275C22×C4C22×D11311yescharacteristic
276C22×C4C22×D11311yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—2262no—
280C4⋊C4—2262no—
281C4⋊C4—2262no—
282C4⋊C4—2262no—
283C4⋊C4—2262no—
284C22⋊C4—2262no—
285C22⋊C4—2262no—
286C22⋊C4—2262no—
287C22⋊C4—2262no—
288C22⋊C4—2262no—
289C22⋊C4—2262no—
290C22⋊C4—2262no—
291C22⋊C4—2262no—
292C22⋊C4—2262no—
293C22⋊C4—2262no—
294C42—22no—
295C42—22no—
296C42—22no—
297C42—2262no—
298C42—2262no—
299C23—1132no—
300C23—1132no—
301C23—2261no—
302C23—2261no—
303C23—2261no—
304C23—2261no—
305C23—2261no—
306C23—2261no—
307C23—2261no—
308C23—2261no—
309C23—2261no—
310C23—2261no—
311C23—2261no—
312C23—2261no—
313C23C23×D11311yescharacteristic
314D4—2268no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—1132no—
332C2×C4—1132no—
333C2×C4—4524no—
334C2×C4—2261no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4—2261no—
348C2×C4—2261no—
349C2×C4—2261no—
350C2×C4—2268no—
351C2×C4D4×D11312yes—
352C2×C4#1426864712yes—
353C2×C4#1426864712yes—
354C2×C4#1426864712yes—
355C2×C4#1426864812yes—
356C22—4521no—
357C22—4521no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22—4521no—
362C22—4521no—
363C22—4521no—
364C22—2262no—
365C22—2262no—
366C22—2262no—
367C22—2262no—
368C22—2262no—
369C22—2262no—
370C22C2×D4×D11311yescharacteristic
371C22#41×D11311yescharacteristic
372C22#41×D11311yescharacteristic
373C22C2×#1426864711yescharacteristic
374C22C2×#1426864711yescharacteristic
375C22C2×#1426864711yescharacteristic
376C22C2×#1426864811yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—4521no—
384C4—4521no—
385C4—4521no—
386C4—4521no—
387C4—2262no—
388C4—2262no—
389C4#1681360714yes—
390C2—4522no—
391C2—4522no—
392C2C2×#1681360711yescharacteristic
393C2#2029910711yescharacteristic
394C2#2029912611yescharacteristic
395C2#2029913211yescharacteristic
396C2#2029913511yescharacteristic
397C2#2029913511yescharacteristic
398C2#2029914511yescharacteristic
subgroupG/H
centerC22×C4C22×D113
commutator, socle, cosocleC23×C113C24
FrattiniC23C23×D113
FittingC4×C4⋊C4×C113C2
prime radicalC22×D452C22
hypercenterC4×C4⋊C4D113
hypocenterC113#2395
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16813579C2semidirect
3. #20298540C2semidirect
4. #20298533C2semidirect
5. #20298531C2semidirect
6. #20298527C2semidirect
7. #20298527C2semidirect
8. #20298524C2semidirect
11. C4×#14268626C2semidirect
12. C4×#14268624C2semidirect
13. C4×#14268624C2semidirect
14. C4×#14268624C2semidirect
15. C4×C4⋊C4×C113C2semidirect
200. C113#2395semidirect
212. C4×C4⋊C4D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4522
C2×#168135792
#202985402
#202985332
#202985312
#202985272
#202985242
#202985162
#202985152
C4×#142686262
C4×#142686242
C4×C4⋊C4×C1132
#2395113