Finite Group Databasebeta

← #28402130

Subgroups — #28402130

Order 14464.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813653C211yesmaximal, characteristic, complemented
2C2×#16813642C211yesmaximal, characteristic, complemented
3#20299253C211yesmaximal, characteristic, complemented
4#20298993C211yesmaximal, characteristic, complemented
5#20298842C211yesmaximal, characteristic, complemented
6#20298837C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298808C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298758C211yesmaximal, characteristic, complemented
11#20298754C211yesmaximal, characteristic, complemented
12#20298741C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#20298670C211yesmaximal, characteristic, complemented
15#548×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18#16813653—24no—
19#16813642—24no—
20C2×#14268637C2211yescharacteristic
21C2×#14268637C2211yescharacteristic
22C2×#14268637C2211yescharacteristic
23C2×#14268637C2211yescharacteristic
24C2×#14268635C2211yescharacteristic
25C2×#14268635C2211yescharacteristic
26C2×#14268634C2211yescharacteristic
27C2×#14268634C2211yescharacteristic
28C2×#14268632C2211yescharacteristic
29C2×#14268631C2211yescharacteristic
30C22×#11744751C2211yescharacteristic
31#16813622C2211yescharacteristic
32#16813604—21no—
33#16813604—21no—
34#16813601C2211yescharacteristic
35#16813601C2211yescharacteristic
36#16813593—21no—
37C4×D452C2211yescharacteristic
38C4⋊C4×D113—21no—
39#16813555C2211yescharacteristic
40C4⋊#11744751C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813542C2211yescharacteristic
47C22⋊#11744751C2211yescharacteristic
48C22⋊#11744751C2211yescharacteristic
49#16813533C2211yescharacteristic
50C2×#41×C113C2211yescharacteristic
51C22×Q8×C113C2211yescharacteristic
52#124×C113—21no—
53#124×C113C2211yescharacteristic
54C22⋊Q8×C113—21no—
55C22⋊Q8×C113C2211yescharacteristic
56#121×C113—21no—
57#121×C113C2211yescharacteristic
58C4×Q8×C113C2211yescharacteristic
59C4×D4×C113—21no—
60C4×D4×C113C2211yescharacteristic
61#14268647—22no—
62#14268647—22no—
63#14268647—41no—
64#14268647—41no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73#14268637—22no—
74#14268637—22no—
75#14268637—22no—
76#14268637—41no—
77#14268635—22no—
78#14268635—41no—
79#14268634—22no—
80#14268634D414yescomplemented
81#14268632—22no—
82#14268631—22no—
83C2×#11744751—22no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C2×#11744751C2311yescharacteristic
87C2×#11744751C2311yescharacteristic
88C4⋊Dic113—21no—
89C4⋊Dic113—21no—
90C4⋊Dic113C2311yescharacteristic
91#14268626—21no—
92#14268626—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95#14268624—21no—
96#41×C113—22no—
97#41×C113—41no—
98C2×Q8×C113—21no—
99C2×Q8×C113—22no—
100C2×Q8×C113—41no—
101C2×Q8×C113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113—21no—
104C2×D4×C113—21no—
105C2×D4×C113D411yescharacteristic
106C2×D4×C113C2311yescharacteristic
107C22×C4×C113—21no—
108C22×C4×C113—21no—
109C22×C4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
111C4⋊C4×C113—21no—
112C4⋊C4×C113—21no—
113C4⋊C4×C113D411yescharacteristic
114C4⋊C4×C113C2311yescharacteristic
115C22⋊C4×C113—21no—
116C22⋊C4×C113—21no—
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C22⋊C4×C113D411yescharacteristic
120C22⋊C4×C113D411yescharacteristic
121C42×C113—21no—
122C42×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C23×C113C2×D411yescharacteristic
126C22×D113—21no—
127Q8×C113—21no—
128Q8×C113—21no—
129Q8×C113—21no—
130Q8×C113—42no—
131Q8×C113C2×D412yes—
132D4×C113—21no—
133D4×C113—21no—
134D4×C113—41no—
135D4×C113—42no—
136D4×C113—42no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—42no—
145C2×C4×C113—42no—
146C2×C4×C113C2×D411yescharacteristic
147C2×C4×C113C2×D411yescharacteristic
148C2×C4×C113C2×D411yescharacteristic
149C2×C4×C113C2×D411yescharacteristic
150C2×C4×C113C2411yescharacteristic
151C22⋊D113—42no—
152C22⋊D113—42no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113—21no—
156D452—21no—
157D452C2×D412yes—
158C4×D113—42no—
159C4×D113—42no—
160C4×D113—42no—
161Dic226—21no—
162Dic226—21no—
163Dic226—21no—
164Dic226—21no—
165#11744751—21no—
166#11744751—21no—
167#11744751—21no—
168#11744751C2×D412yes—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113C22×D411yescharacteristic
179C2×D113—22no—
180C2×D113—41no—
181C2×D113—41no—
182C4×C113—21no—
183C4×C113—21no—
184C4×C113—22no—
185C4×C113—21no—
186C4×C113—21no—
187C4×C113—41no—
188C4×C113—41no—
189C4×C113C22×D411yescharacteristic
190C4×C113H(5,𝔽2)11yescharacteristic
191Dic113—41no—
192Dic113—41no—
193Dic113—41no—
194C2×C113—41no—
195C2×C113—41no—
196C2×C113—81no—
197C2×C113D4211yescharacteristic
198C2×C113#57511yescharacteristic
199C2×C113#57811yescharacteristic
200D113—42no—
201#3269—1131nomaximal, Sylow
202C113#326911yescharacteristic, complemented, Sylow
203C2×#137—1131no—
204C2×#135—1131no—
205#548D11311yescharacteristic, complemented
206#547—1131no—
207#497—1131no—
208#468—1131no—
209#467—1131no—
210#463—1131no—
211#462—1131no—
212#452—1131no—
213#452—1131no—
214#451—1131no—
215#449—1131no—
216#440—1131no—
217#435—1131no—
218C2×#41—1131no—
219C2×#41—1131no—
220C2×#41C2×D11311yescharacteristic
221C22×Q8C2×D11311yescharacteristic
222#137—2264no—
223#135—2264no—
224C2×Q16—1131no—
225C2×Q16—1131no—
226C2×Q16—1131no—
227C2×Q16—1131no—
228C2×SD16—1131no—
229C2×SD16—1131no—
230C2×SD16—1131no—
231C2×SD16—1131no—
232C2×D8—1131no—
233C2×M16—1131no—
234C22×C8—1131no—
235C4⋊Q8—1131no—
236#124—21no—
237#124C2×D11311yescharacteristic
238#123—2261no—
239#123—2261no—
240C22⋊Q8—21no—
241C22⋊Q8—1131no—
242C22⋊Q8—1131no—
243C22⋊Q8C2×D11311yescharacteristic
244#121—21no—
245#121—2261no—
246#121C2×D11311yescharacteristic
247C4×Q8C2×D11311yescharacteristic
248C4×D4—21no—
249C4×D4—1131no—
250C4×D4C2×D11311yescharacteristic
251C2×C4⋊C4—2261no—
252#107—1131no—
253C4⋊C8—1131no—
254#103—1131no—
255#103—1131no—
256#103—1131no—
257#103—1131no—
258#102—1131no—
259#102—1131no—
260C22⋊C8—1131no—
261C22⋊C8—1131no—
262#97—1131no—
263#41—22no—
264#41—41no—
265#41—4521no—
266#41—4521no—
267#41—2262no—
268#41—2262no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—1131no—
273C2×Q8—1131no—
274C2×Q8C22×D11311yescharacteristic
275C2×Q8C22×D11311yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—1131no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4C22⋊D11311yescharacteristic
282C2×D4C22×D11311yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—2261no—
286C22×C4—2261no—
287C22×C4—2261no—
288C22×C4C22×D11311yescharacteristic
289C22×C4C22×D11311yescharacteristic
290Q16—4521no—
291Q16—2262no—
292Q16—2262no—
293Q16—2262no—
294SD16—1134no—
295SD16—4521no—
296SD16—2262no—
297SD16—2262no—
298D8—2262no—
299M16—2262no—
300C2×C8—1131no—
301C2×C8—1131no—
302C2×C8—1131no—
303C2×C8—1131no—
304C2×C8—2262no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—1131no—
308C4⋊C4—2261no—
309C4⋊C4—2261no—
310C4⋊C4—2261no—
311C4⋊C4—2261no—
312C4⋊C4C22⋊D11311yescharacteristic
313C4⋊C4C22×D11311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—21no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4C22⋊D11311yescharacteristic
322C22⋊C4C22⋊D11311yescharacteristic
323C42—21no—
324C42C22×D11311yescharacteristic
325C23—21no—
326C23—2261no—
327C23C2×C22⋊D11311yescharacteristic
328C23C2×C22⋊D11311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—2261no—
334Q8—2261no—
335Q8—2261no—
336Q8—2261no—
337Q8D4×D11312yes—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—42no—
342D4—42no—
343D4—1132no—
344D4—4522no—
345D4—4522no—
346D4—2261no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—4522no—
357C2×C4—4522no—
358C2×C4—4522no—
359C2×C4—2261no—
360C2×C4—2261no—
361C2×C4—2261no—
362C2×C4C2×C22⋊D11311yescharacteristic
363C2×C4C2×C22⋊D11311yescharacteristic
364C2×C4C2×C22⋊D11311yescharacteristic
365C2×C4C2×C22⋊D11311yescharacteristic
366C2×C4C23×D11311yescharacteristic
367C8—1132no—
368C8—2261no—
369C8—2261no—
370C8—2261no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—4521no—
381C22—4521no—
382C22—2262no—
383C22C22×C22⋊D11311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—4521no—
392C4—4521no—
393C4—4521no—
394C4C2×D4×D11311yescharacteristic
395C4#1681366711yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—4522no—
400C2D4×C22⋊D11311yescharacteristic
401C2#2029939611yescharacteristic
402C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#548×C113C2
socleC22×C113C22×D4
hypercenter#548D113
hypocenterC113#3269
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#16813653C2semidirect
2. C2×#16813642C2semidirect
3. #20299253C2semidirect
4. #20298993C2semidirect
5. #20298842C2semidirect
6. #20298837C2semidirect
7. #20298810C2semidirect
8. #20298808C2semidirect
9. #20298760C2semidirect
10. #20298758C2semidirect
11. #20298754C2semidirect
12. #20298741C2semidirect
13. #20298696C2semidirect
14. #20298670C2semidirect
15. #548×C113C2semidirect
80. #14268634D4semidirect
202. C113#3269semidirect
205. #548D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136532
C2×#168136422
#202992532
#202989932
#202988422
#202988372
#202988102
#202988082
#202987602
#202987582
#202987542
#202987412
#202986962
#202986702
#548×C1132
#3269113