Finite Group Databasebeta

← #28400027

Subgroups — #28400027

Order 14464.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813644C211yesmaximal, characteristic, complemented
2C2×#16813642C211yesmaximal, characteristic, complemented
3#20299144C211yesmaximal, characteristic, complemented
4#20299066C211yesmaximal, characteristic, complemented
5#20298823C211yesmaximal, characteristic, complemented
6#20298819C211yesmaximal, characteristic, complemented
7#20298816C211yesmaximal, characteristic, complemented
8#20298812C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298802C211yesmaximal, characteristic, complemented
11#20298797C211yesmaximal, characteristic, complemented
12#20298792C211yesmaximal, characteristic, complemented
13C2×#16813551C211yesmaximal, characteristic, complemented
14#20298592C211yesmaximal, characteristic, complemented
15#416×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18#16813644—24no—
19#16813642—24no—
20C2×Dic452C2211yescharacteristic
21C2×#14268637C2211yescharacteristic
22C2×#14268636C2211yescharacteristic
23C2×#14268636C2211yescharacteristic
24C2×#14268635C2211yescharacteristic
25C2×#14268634C2211yescharacteristic
26C2×D904C2211yescharacteristic
27C2×#14268632C2211yescharacteristic
28C22×#11744751C2211yescharacteristic
29#16813620C2211yescharacteristic
30#16813618C2211yescharacteristic
31#16813611C2211yescharacteristic
32#16813609C2211yescharacteristic
33#16813594—21no—
34#16813594—21no—
35#16813587C2211yescharacteristic
36#16813587C2211yescharacteristic
37#16813584C2211yescharacteristic
38#16813584C2211yescharacteristic
39C4×C22⋊D113—21no—
40C4×C22⋊D113—21no—
41#16813582—21no—
42#16813582—21no—
43#16813579—21no—
44C2×C4×Dic113C2211yescharacteristic
45C42×D113—21no—
46#16813551C2211yescharacteristic
47#16813551C2211yescharacteristic
48#16813551C2211yescharacteristic
49#16813551C2211yescharacteristic
50#16813545C2211yescharacteristic
51#16813545C2211yescharacteristic
52#16813542C2211yescharacteristic
53#16813542C2211yescharacteristic
54C2×#41×C113C2211yescharacteristic
55C22×C8×C113C2211yescharacteristic
56#117×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#102×C113C2211yescharacteristic
60#102×C113C2211yescharacteristic
61#14268647—22no—
62#14268647—22no—
63#14268647—22no—
64#14268647D414yescomplemented
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C22×Dic113D411yescharacteristic
74C22×Dic113D411yescharacteristic
75C2×C4×D113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79Dic452—22no—
80#14268637—22no—
81#14268636—22no—
82#14268636—22no—
83#14268635—22no—
84#14268634—22no—
85D904—22no—
86#14268632—22no—
87C2×#11744751—22no—
88C2×#11744751C2311yescharacteristic
89C2×#11744751C2311yescharacteristic
90#14268626—21no—
91#14268626—21no—
92#14268626—21no—
93#14268626—21no—
94C22⋊Dic113—21no—
95C22⋊Dic113—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624—21no—
100C4×Dic113—21no—
101C4×Dic113—21no—
102C4×Dic113D411yescharacteristic
103C4×Dic113D411yescharacteristic
104C4×Dic113C2311yescharacteristic
105C4×Dic113C2311yescharacteristic
106#41×C113—22no—
107#41×C113—22no—
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113—21no—
110C2×D4×C113C2311yescharacteristic
111C22×C4×C113—21no—
112C22×C4×C113C2311yescharacteristic
113C2×C8×C113—22no—
114C2×C8×C113C2311yescharacteristic
115C2×C8×C113C2311yescharacteristic
116C4⋊C4×C113C2311yescharacteristic
117C4⋊C4×C113C2311yescharacteristic
118C22⋊C4×C113—21no—
119C42×C113—21no—
120C23×C113—21no—
121C23×C113C2×D411yescharacteristic
122C22×D113—21no—
123C22×D113—21no—
124Q8×C113—21no—
125Q8×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—42no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—42no—
133C2×C4×C113C2×D412yes—
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113#4112yes—
136C2×C4×C113C2411yescharacteristic
137C22⋊D113—24no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—42no—
141C2×Dic113—21no—
142C2×Dic113—22no—
143C2×Dic113—21no—
144C2×Dic113—41no—
145C2×Dic113C2×D411yescharacteristic
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149D452—21no—
150D452—21no—
151D452—21no—
152D452C2×D412yes—
153C4×D113—24no—
154C4×D113—42no—
155C4×D113—42no—
156C4×D113—42no—
157Dic226—21no—
158Dic226—21no—
159Dic226—21no—
160Dic226C2×D412yes—
161C8×C113—21no—
162C8×C113—21no—
163#11744751—21no—
164#11744751—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113#12112yes—
171C22×C113C22×D411yescharacteristic
172C2×D113—22no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113—41no—
178C4×C113—41no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113#12112yes—
182C4×C113C22×D411yescharacteristic
183C4×C113C2×#4111yescharacteristic
184Dic113—22no—
185Dic113—21no—
186Dic113—21no—
187Dic113—21no—
188Dic113—41no—
189Dic113#13512yescomplemented
190C2×C113—22no—
191C2×C113—81no—
192C2×C113C2×#12111yescharacteristic
193C2×C113C2×#13511yescharacteristic
194C2×C113#57511yescharacteristic
195D113—42no—
196D113—81no—
197#3035—1131nomaximal, Sylow
198C113#303511yescharacteristic, complemented, Sylow
199C2×#135—1131no—
200C2×#135—1131no—
201#532—1131no—
202C4×#41—1131no—
203#464—1131no—
204#464—1131no—
205#463—1131no—
206#463—1131no—
207#462—1131no—
208#461—1131no—
209#460—1131no—
210#459—1131no—
211C2×C4⋊C8—1131no—
212#416—1131no—
213#416D11311yescharacteristic, complemented
214C2×#41—1131no—
215C2×#41—1131no—
216C2×#41C2×D11311yescharacteristic
217#135—2264no—
218#135—2264no—
219C2×Q16—1131no—
220C2×Q16—1131no—
221C2×SD16—1131no—
222C2×SD16—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×D8—1131no—
226C2×D8—1131no—
227C22×C8—1131no—
228C22×C8C2×D11311yescharacteristic
229C4⋊Q8—1131no—
230#127—1131no—
231#124—1131no—
232#124—1131no—
233#121—2261no—
234#121—2261no—
235C4×Q8—1131no—
236C4×Q8—1131no—
237C4×D4—1131no—
238C4×D4—1131no—
239C4×D4—2261no—
240C4×D4—2261no—
241C4×D4—2261no—
242C4×D4—2261no—
243#117—2261no—
244#117C2×D11311yescharacteristic
245C2×C42—1131no—
246C2×C42—2261no—
247C4⋊C8—1131no—
248C4⋊C8—1131no—
249C4⋊C8—1131no—
250C4⋊C8—1131no—
251#103—1131no—
252#103—1131no—
253#103C2×D11311yescharacteristic
254#103C2×D11311yescharacteristic
255#102—1131no—
256#102—1131no—
257#102C2×D11311yescharacteristic
258#102C2×D11311yescharacteristic
259#41—22no—
260#41—22no—
261#41—1134no—
262#41—2262no—
263#41—2262no—
264#41—2262no—
265C2×Q8—1131no—
266C2×Q8—1131no—
267C2×Q8C22×D11311yescharacteristic
268C2×D4—21no—
269C2×D4—1131no—
270C2×D4—1131no—
271C2×D4—2261no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4—2261no—
275C2×D4C22×D11311yescharacteristic
276C22×C4—21no—
277C22×C4—1131no—
278C22×C4—1131no—
279C22×C4—2261no—
280C22×C4—2261no—
281C22×C4—2261no—
282C22×C4—2261no—
283C22×C4C22×D11311yescharacteristic
284Q16—2262no—
285Q16—2262no—
286SD16—2262no—
287SD16—2262no—
288SD16—2262no—
289SD16—2262no—
290D8—2262no—
291D8—2262no—
292C2×C8—22no—
293C2×C8—1131no—
294C2×C8—1131no—
295C2×C8—2262no—
296C2×C8C22×D11311yescharacteristic
297C2×C8C22×D11311yescharacteristic
298C4⋊C4—2261no—
299C4⋊C4—2261no—
300C4⋊C4—2261no—
301C4⋊C4—2261no—
302C4⋊C4C22×D11311yescharacteristic
303C4⋊C4C22×D11311yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C42—21no—
312C42—1131no—
313C42—1131no—
314C42—1131no—
315C42—1131no—
316C42—2261no—
317C42—2261no—
318C23—21no—
319C23—2261no—
320C23—2261no—
321C23D4×D11311yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—1132no—
325Q8—2261no—
326Q8—2261no—
327Q8—2261no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—1132no—
332D4—4522no—
333D4—4522no—
334D4—4522no—
335D4—2264no—
336D4—2261no—
337D4—2261no—
338D4—2261no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—1131no—
344C2×C4—1131no—
345C2×C4—1131no—
346C2×C4—1131no—
347C2×C4—4522no—
348C2×C4—4522no—
349C2×C4—4522no—
350C2×C4—4521no—
351C2×C4—2262no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4—2264no—
355C2×C4D4×D11312yes—
356C2×C4D4×D11311yescharacteristic
357C2×C4#1426864712yes—
358C2×C4C23×D11311yescharacteristic
359C8—21no—
360C8—21no—
361C8—2261no—
362C8—2261no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—4521no—
369C22—4521no—
370C22—4521no—
371C22—4521no—
372C22—4521no—
373C22—2262no—
374C22#1681359512yes—
375C22C2×D4×D11311yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—1132no—
380C4—4521no—
381C4—2262no—
382C4—2261no—
383C4—2261no—
384C4—2261no—
385C4#1681359512yes—
386C4C2×D4×D11311yescharacteristic
387C4C2×#1426864711yescharacteristic
388C2—22no—
389C2—81no—
390C2—9041no—
391C2—4522no—
392C2C2×#1681359511yescharacteristic
393C2#135×D11311yescharacteristic
394C2#2029939511yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
hypercenter#416D113
hypocenterC113#3035
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#16813644C2semidirect
2. C2×#16813642C2semidirect
3. #20299144C2semidirect
4. #20299066C2semidirect
5. #20298823C2semidirect
6. #20298819C2semidirect
7. #20298816C2semidirect
8. #20298812C2semidirect
9. #20298807C2semidirect
10. #20298802C2semidirect
11. #20298797C2semidirect
12. #20298792C2semidirect
13. C2×#16813551C2semidirect
14. #20298592C2semidirect
15. #416×C113C2semidirect
64. #14268647D4semidirect
189. Dic113#135semidirect
198. C113#3035semidirect
213. #416D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136442
C2×#168136422
#202991442
#202990662
#202988232
#202988192
#202988162
#202988122
#202988072
#202988022
#202987972
#202987922
C2×#168135512
#202985922
#416×C1132
#3035113