Finite Group Databasebeta

← #28402125

Subgroups — #28402125

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×#16813652C211yesmaximal, characteristic, complemented
2C2×#16813642C211yesmaximal, characteristic, complemented
3#20299257C211yesmaximal, characteristic, complemented
4#20298990C211yesmaximal, characteristic, complemented
5#20298846C211yesmaximal, characteristic, complemented
6#20298837C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298805C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298758C211yesmaximal, characteristic, complemented
11#20298753C211yesmaximal, characteristic, complemented
12#20298743C211yesmaximal, characteristic, complemented
13#20298698C211yesmaximal, characteristic, complemented
14#20298670C211yesmaximal, characteristic, complemented
15#547×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18#16813652—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#16813610C2211yescharacteristic
32#16813608—21no—
33#16813601C2211yescharacteristic
34#16813600—21no—
35#16813596C2211yescharacteristic
36#16813594—21no—
37C4×Dic226C2211yescharacteristic
38#16813582—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
51C2×#41×C113C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53#123×C113—21no—
54#123×C113—21no—
55C22⋊Q8×C113C2211yescharacteristic
56C22⋊Q8×C113C2211yescharacteristic
57#121×C113—21no—
58C4×D4×C113C2211yescharacteristic
59C4×D4×C113C2211yescharacteristic
60C2×C4⋊C4×C113—21no—
61#14268647—22no—
62#14268647—41no—
63C2×Dic226—22no—
64C2×Dic226—21no—
65C2×Dic226—41no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73#14268637—22no—
74#14268637—22no—
75#14268637—22no—
76#14268637—41no—
77#14268635—22no—
78#14268635D414yescomplemented
79#14268634—22no—
80#14268634—41no—
81#14268632—22no—
82#14268631—22no—
83C2×#11744751—22no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C2×#11744751C2311yescharacteristic
87C2×#11744751C2311yescharacteristic
88C4⋊Dic113C2311yescharacteristic
89#14268626—21no—
90#14268626—21no—
91C22⋊Dic113—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95C4×Dic113—21no—
96#41×C113—22no—
97#41×C113—22no—
98#41×C113—41no—
99#41×C113—41no—
100C2×Q8×C113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113—21no—
103C2×D4×C113—21no—
104C2×D4×C113D411yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C22×C4×C113—21no—
107C22×C4×C113—21no—
108C22×C4×C113—21no—
109C22×C4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
111C4⋊C4×C113—21no—
112C4⋊C4×C113—21no—
113C4⋊C4×C113—21no—
114C4⋊C4×C113—21no—
115C4⋊C4×C113D411yescharacteristic
116C4⋊C4×C113C2311yescharacteristic
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C22⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
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—21no—
131D4×C113—21no—
132D4×C113—41no—
133D4×C113—42no—
134D4×C113—42no—
135D4×C113C2×D412yes—
136C2×C4×C113—21no—
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—42no—
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—
156C2×Dic113—42no—
157D452—21no—
158D452—21no—
159C4×D113—42no—
160Dic226—21no—
161Dic226—21no—
162Dic226—21no—
163Dic226—42no—
164Dic226C2×D412yes—
165#11744751—21no—
166#11744751—21no—
167#11744751—21no—
168#11744751C2×D412yes—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—22no—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—21no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113C22×D411yescharacteristic
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C4×C113—21no—
183C4×C113—21no—
184C4×C113—21no—
185C4×C113—21no—
186C4×C113—41no—
187C4×C113—41no—
188C4×C113—41no—
189C4×C113C22×D411yescharacteristic
190C4×C113H(5,𝔽2)11yescharacteristic
191Dic113—22no—
192Dic113—41no—
193Dic113—41no—
194C2×C113—41no—
195C2×C113—41no—
196C2×C113—42no—
197C2×C113D4211yescharacteristic
198C2×C113#57511yescharacteristic
199C2×C113#57811yescharacteristic
200D113—81no—
201#3269—1131nomaximal, Sylow
202C113#326911yescharacteristic, complemented, Sylow
203C2×#137—1131no—
204C2×#135—1131no—
205#548—1131no—
206#547D11311yescharacteristic, complemented
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×#41C2×D11311yescharacteristic
220C2×#41C2×D11311yescharacteristic
221C22×Q8—1131no—
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⋊Q8C2×D11311yescharacteristic
236#124—1131no—
237#124—2261no—
238#123—21no—
239#123—21no—
240C22⋊Q8—1131no—
241C22⋊Q8—2261no—
242C22⋊Q8C2×D11311yescharacteristic
243C22⋊Q8C2×D11311yescharacteristic
244#121—21no—
245#121—1131no—
246#121—2261no—
247C4×Q8—1131no—
248C4×D4—2261no—
249C4×D4C2×D11311yescharacteristic
250C4×D4C2×D11311yescharacteristic
251C2×C4⋊C4—21no—
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—22no—
265#41—41no—
266#41—41no—
267#41—4521no—
268#41—2262no—
269C2×Q8—1131no—
270C2×Q8—1131no—
271C2×Q8—4521no—
272C2×Q8—2262no—
273C2×Q8—2261no—
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—21no—
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—21no—
308C4⋊C4—21no—
309C4⋊C4—1131no—
310C4⋊C4—2261no—
311C4⋊C4—2261no—
312C4⋊C4C22⋊D11311yescharacteristic
313C4⋊C4C22×D11311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—2261no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4C22⋊D11311yescharacteristic
322C22⋊C4C22⋊D11311yescharacteristic
323C42—2261no—
324C42C22×D11311yescharacteristic
325C23—21no—
326C23—2261no—
327C23C2×C22⋊D11311yescharacteristic
328C23C2×C22⋊D11311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—1132no—
334Q8—4522no—
335Q8—2261no—
336Q8—2261no—
337Q8—2261no—
338D4—21no—
339D4—41no—
340D4—42no—
341D4—42no—
342D4—4522no—
343D4—4522no—
344D4—2261no—
345D4—2261no—
346D4D4×D11312yes—
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—42no—
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—22no—
378C22—41no—
379C22—41no—
380C22—4521no—
381C22—4521no—
382C22—4521no—
383C22C22×C22⋊D11311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—4521no—
392C4—4521no—
393C4—2262no—
394C4C2×D4×D11311yescharacteristic
395C4#1681366711yescharacteristic
396C2—41no—
397C2—41no—
398C2—42no—
399C2—9041no—
400C2D4×C22⋊D11311yescharacteristic
401C2#2029939611yescharacteristic
402C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#547×C113C2
socleC22×C113C22×D4
hypercenter#547D113
hypocenterC113#3269
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#16813652C2semidirect
2. C2×#16813642C2semidirect
3. #20299257C2semidirect
4. #20298990C2semidirect
5. #20298846C2semidirect
6. #20298837C2semidirect
7. #20298813C2semidirect
8. #20298805C2semidirect
9. #20298760C2semidirect
10. #20298758C2semidirect
11. #20298753C2semidirect
12. #20298743C2semidirect
13. #20298698C2semidirect
14. #20298670C2semidirect
15. #547×C113C2semidirect
78. #14268635D4semidirect
202. C113#3269semidirect
206. #547D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136522
C2×#168136422
#202992572
#202989902
#202988462
#202988372
#202988132
#202988052
#202987602
#202987582
#202987532
#202987432
#202986982
#202986702
#547×C1132
#3269113