Finite Group Databasebeta

← #28404342

Subgroups — #28404342

Order 14464.

1492 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813670C211yesmaximal, characteristic, complemented
2C2×#16813669C211yesmaximal, characteristic, complemented
3#20299267C211yesmaximal, characteristic, complemented
4#20299266C213yesmaximal, complemented
5Q8×C22⋊D113C211yesmaximal, characteristic, complemented
6#20299261C213yesmaximal, complemented
7#20299260C211yesmaximal, characteristic, complemented
8#20299257C213yesmaximal, complemented
9#20299256C213yesmaximal, complemented
10#20299178C213yesmaximal, complemented
11#20299177C213yesmaximal, complemented
12#20299147C213yesmaximal, complemented
13#20299145C213yesmaximal, complemented
14C4×Q8×D113C211yesmaximal, characteristic, complemented
15#548×C113C211yesmaximal, characteristic, complemented
16#16813670—28no—
17#16813669—28no—
18C2×#14268648C2211yescharacteristic
19C2×#14268648C2213yes—
20C2×#14268647C2213yes—
21C2×#14268647C2213yes—
22C2×#14268647C2213yes—
23C2×#14268646C2213yes—
24C2×#14268646C2213yes—
25C22×Dic226C2213yes—
26C2×Q8×D113C2211yescharacteristic
27C2×Q8×D113C2213yes—
28C2×Q8×D113C2211yescharacteristic
29#16813621C2213yes—
30#16813620C2213yes—
31#16813618C2213yes—
32#16813618C2213yes—
33#16813610C2213yes—
34#16813608C2213yes—
35#16813608C2213yes—
36#16813602C2213yes—
37#16813601C2213yes—
38#16813600C2216yes—
39#16813599C2216yes—
40#16813598C2213yes—
41#16813597C2213yes—
42#16813597C2213yes—
43#16813596C2213yes—
44#16813595C2216yes—
45#16813595C2211yescharacteristic
46#16813595C2213yes—
47#16813595C2216yes—
48#16813594C2216yes—
49#16813593C2213yes—
50#16813593C2213yes—
51Q8×Dic113C2211yescharacteristic
52C4×Dic226C2213yes—
53#16813587C2213yes—
54C4×D452C2213yes—
55C4×C22⋊D113C2213yes—
56C4×C22⋊D113C2213yes—
57#16813582C2216yes—
58#16813582C2216yes—
59C4⋊C4×D113C2213yes—
60C42×D113C2213yes—
61C2×#41×C113C2211yescharacteristic
62C22×Q8×C113C2211yescharacteristic
63#124×C113C2213yes—
64C22⋊Q8×C113C2213yes—
65#121×C113C2213yes—
66C4×Q8×C113C2211yescharacteristic
67C4×D4×C113C2213yes—
68#14268648—24no—
69#14268648—212no—
70#14268647—212no—
71#14268647—212no—
72#14268647—212no—
73#14268646—212no—
74#14268646—212no—
75C2×Dic226—212no—
76C2×Dic226C2313yes—
77C2×Dic226C2313yes—
78C2×Dic226C2313yes—
79C2×Dic226C2313yes—
80Q8×D113—24no—
81Q8×D113—212no—
82Q8×D113D418yescomplemented
83C2×D452C2313yes—
84C2×D452C2311yescharacteristic
85C2×D452C2313yes—
86C2×D452C2313yes—
87C2×C22⋊D113C2313yes—
88C2×C22⋊D113C2311yescharacteristic
89C2×C22⋊D113C2311yescharacteristic
90C2×C22⋊D113C2313yes—
91C2×C22⋊D113C2313yes—
92C2×C22⋊D113C2313yes—
93C2×C22⋊D113C2316yes—
94C22×Dic113C2316yes—
95C2×C4×D113C2311yescharacteristic
96C2×C4×D113C2316yes—
97C2×C4×D113C2313yes—
98C2×C4×D113C2313yes—
99C2×C4×D113C2313yes—
100C2×C4×D113C2313yes—
101C4⋊Dic113C2313yes—
102C4⋊Dic113C2313yes—
103#14268626C2316yes—
104#14268626C2313yes—
105#14268626C2316yes—
106#14268626C2311yescharacteristic
107C22⋊Dic113C2313yes—
108C22⋊Dic113C2313yes—
109#14268624C2313yes—
110#14268624C2316yes—
111#14268624C2313yes—
112#14268624C2313yes—
113#14268624C2311yescharacteristic
114C4×Dic113C2313yes—
115C4×Dic113C2313yes—
116C4×Dic113C2313yes—
117#41×C113—24no—
118C2×Q8×C113—24no—
119C2×Q8×C113C2313yes—
120C2×Q8×C113C2311yescharacteristic
121C2×D4×C113C2313yes—
122C2×D4×C113C2313yes—
123C22×C4×C113C2313yes—
124C22×C4×C113C2313yes—
125C4⋊C4×C113C2313yes—
126C4⋊C4×C113C2313yes—
127C22⋊C4×C113C2313yes—
128C22⋊C4×C113C2316yes—
129C22⋊C4×C113C2311yescharacteristic
130C42×C113C2313yes—
131C23×C113C2413yes—
132C23×C113C2411yescharacteristic
133C22×D113C2413yes—
134C22×D113C2411yescharacteristic
135C22×D113C2411yescharacteristic
136Q8×C113—26no—
137Q8×C113C2×D414yes—
138D4×C113—26no—
139D4×C113—43no—
140C2×C4×C113—26no—
141C2×C4×C113—26no—
142C2×C4×C113C2411yescharacteristic
143C2×C4×C113C2413yes—
144C2×C4×C113C2413yes—
145C2×C4×C113C2411yescharacteristic
146C2×C4×C113C2413yes—
147C22⋊D113—26no—
148C22⋊D113—22no—
149C22⋊D113—26no—
150C22⋊D113—26no—
151C22⋊D113—26no—
152C22⋊D113—22no—
153C22⋊D113—46no—
154C2×Dic113—212no—
155C2×Dic113C2413yes—
156C2×Dic113C2413yes—
157C2×Dic113C2411yescharacteristic
158C2×Dic113C2413yes—
159C2×Dic113C2411yescharacteristic
160D452—22no—
161D452—26no—
162D452—26no—
163D452—43no—
164C4×D113—26no—
165C4×D113—26no—
166C4×D113—212no—
167C4×D113—22no—
168C4×D113—43no—
169C4×D113C2×D4112yes—
170Dic226—26no—
171Dic226—26no—
172Dic226—26no—
173Dic226C2×D4112yes—
174C22×C113—23no—
175C22×C113—21no—
176C22×C113—23no—
177C22×C113—21no—
178C22×C113—23no—
179C22×C113—21no—
180C22×C113C2511yescharacteristic
181C2×D113—21no—
182C2×D113—21no—
183C2×D113—23no—
184C2×D113—21no—
185C2×D113—23no—
186C2×D113—21no—
187C2×D113—21no—
188C2×D113—23no—
189C2×D113C22×D412yes—
190C4×C113—21no—
191C4×C113—23no—
192C4×C113—21no—
193C4×C113—23no—
194C4×C113C22×D416yes—
195Dic113—21no—
196Dic113—23no—
197Dic113—23no—
198Dic113C22×D416yes—
199Dic1132−1+412yescomplemented
200C2×C113—43no—
201C2×C113—41no—
202C2×C113C23×D411yescharacteristic
203C2×C113C2×2−1+411yescharacteristic
204C2×C113#58511yescharacteristic
205D113—22no—
206D113—43no—
207D113—41no—
208#3497—1131nomaximal, Sylow
209C113#349711yescharacteristic, complemented, Sylow
210C2×2−1+4—1131no—
211C2×2−1+4—1131no—
212#550—1131no—
213#550—1133no—
214D4×Q8—1131no—
215D4×Q8—1133no—
216#548—1133no—
217#548—1131no—
218#548—1133no—
219#548D11311yescharacteristic, complemented
220#537—1133no—
221#537—1133no—
222#532—1133no—
223#532—1133no—
224C2×C4×Q8—1131no—
2252−1+4—2268no—
2262−1+4—2268no—
227C2×#41—1133no—
228C2×#41—1131no—
229C2×#41—1133no—
230C2×#41—1133no—
231C2×#41—1133no—
232C2×#41—1133no—
233C2×#41—1133no—
234C2×#41C2×D11311yescharacteristic
235C22×Q8—1131no—
236C22×Q8—1133no—
237C22×Q8—1131no—
238C22×Q8—1133no—
239C22×Q8C2×D11311yescharacteristic
240C4⋊Q8—1133no—
241C4⋊Q8—1133no—
242#127—1133no—
243#127—1133no—
244#124—1133no—
245#124—1133no—
246#124—1133no—
247#124C2×D11313yes—
248C22⋊Q8—1133no—
249C22⋊Q8—1133no—
250C22⋊Q8—1136no—
251C22⋊Q8—1133no—
252C22⋊Q8—1136no—
253C22⋊Q8C2×D11313yes—
254#121—1133no—
255#121—1133no—
256#121—1136no—
257#121—1133no—
258#121—1133no—
259#121—1133no—
260#121—1133no—
261#121—1131no—
262#121—1136no—
263#121—1136no—
264#121C2×D11313yes—
265C4×Q8—1131no—
266C4×Q8—1133no—
267C4×Q8—1133no—
268C4×Q8C2×D11311yescharacteristic
269C4×D4—1133no—
270C4×D4—1133no—
271C4×D4—1136no—
272C4×D4—1136no—
273C4×D4—1133no—
274C4×D4C2×D11313yes—
275C2×C4⋊C4—1133no—
276C2×C42—1133no—
277#41—24no—
278#41—22612no—
279#41—22612no—
280#41—22612no—
281#41—22612no—
282#41—22612no—
283#41—22612no—
284#41—2264no—
285C2×Q8—24no—
286C2×Q8—1138no—
287C2×Q8—1133no—
288C2×Q8—1133no—
289C2×Q8—1133no—
290C2×Q8—1133no—
291C2×Q8—22612no—
292C2×Q8—22612no—
293C2×Q8—2264no—
294C2×Q8C22×D11313yes—
295C2×Q8C22×D11311yescharacteristic
296C2×D4—1136no—
297C2×D4—1131no—
298C2×D4—1133no—
299C2×D4—1131no—
300C2×D4—1133no—
301C2×D4—1133no—
302C2×D4—1133no—
303C2×D4—1133no—
304C2×D4—1131no—
305C2×D4—1133no—
306C2×D4—1133no—
307C2×D4C22×D11313yes—
308C2×D4C22×D11313yes—
309C22×C4—1133no—
310C22×C4—1136no—
311C22×C4—1133no—
312C22×C4—1131no—
313C22×C4—1136no—
314C22×C4—1133no—
315C22×C4—1133no—
316C22×C4C22×D11313yes—
317C22×C4C22×D11313yes—
318C4⋊C4—1136no—
319C4⋊C4—1133no—
320C4⋊C4—1131no—
321C4⋊C4—1133no—
322C4⋊C4—1136no—
323C4⋊C4—1133no—
324C4⋊C4C22×D11313yes—
325C4⋊C4C22×D11313yes—
326C22⋊C4—1133no—
327C22⋊C4—1133no—
328C22⋊C4—1133no—
329C22⋊C4—1131no—
330C22⋊C4—1133no—
331C22⋊C4—1133no—
332C22⋊C4—1136no—
333C22⋊C4C22×D11313yes—
334C22⋊C4C22×D11316yes—
335C22⋊C4C22×D11311yescharacteristic
336C42—1133no—
337C42—1133no—
338C42—1133no—
339C42C22×D11313yes—
340C23—1131no—
341C23—1133no—
342C23—1131no—
343C23C23×D11311yescharacteristic
344C23C23×D11313yes—
345Q8—26no—
346Q8—11312no—
347Q8—2266no—
348Q8—2266no—
349Q8—2266no—
350Q8D4×D11314yes—
351D4—26no—
352D4—43no—
353D4—4523no—
354D4—4526no—
355D4—2262no—
356D4—2266no—
357D4—2266no—
358D4—2266no—
359D4—2262no—
360D4—2266no—
361D4—2262no—
362D4—2266no—
363D4—2266no—
364C2×C4—26no—
365C2×C4—26no—
366C2×C4—1131no—
367C2×C4—1133no—
368C2×C4—11312no—
369C2×C4—1133no—
370C2×C4—1131no—
371C2×C4—1133no—
372C2×C4—4523no—
373C2×C4—22612no—
374C2×C4—2262no—
375C2×C4—22612no—
376C2×C4—2266no—
377C2×C4—2266no—
378C2×C4C23×D11311yescharacteristic
379C2×C4C23×D11313yes—
380C2×C4C23×D11311yescharacteristic
381C2×C4C23×D11313yes—
382C2×C4C23×D11313yes—
383C22—21no—
384C22—23no—
385C22—21no—
386C22—23no—
387C22—21no—
388C22—23no—
389C22—1132no—
390C22—2263no—
391C22—2261no—
392C22—2263no—
393C22—2261no—
394C22—2261no—
395C22—2263no—
396C22—2261no—
397C22—2261no—
398C22C24×D11311yescharacteristic
399C4—21no—
400C4—23no—
401C4—21no—
402C4—23no—
403C4—1136no—
404C4—1132no—
405C4—2263no—
406C4—2261no—
407C4—2263no—
408C4C2×D4×D11316yes—
409C2—41no—
410C2—43no—
411C2—4523no—
412C2—4521no—
413C2—2262no—
414C2C22×D4×D11311yescharacteristic
415C22−1+4×D11311yescharacteristic
416C2#2029943411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#548×C113C2
hypercenter#548D113
hypocenterC113#3497
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#16813670C2semidirect
2. C2×#16813669C2semidirect
3. #20299267C2semidirect
4. #20299266C2semidirect
5. Q8×C22⋊D113C2semidirect
6. #20299261C2semidirect
7. #20299260C2semidirect
8. #20299257C2semidirect
9. #20299256C2semidirect
10. #20299178C2semidirect
11. #20299177C2semidirect
12. #20299147C2semidirect
13. #20299145C2semidirect
14. C4×Q8×D113C2semidirect
15. #548×C113C2semidirect
82. Q8×D113D4semidirect
199. Dic1132−1+4semidirect
209. C113#3497semidirect
219. #548D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136702
C2×#168136692
#202992672
#202992662
Q8×C22⋊D1132
#202992612
#202992602
#202992572
#202992562
#202991782
#202991772
#202991472
#202991452
C4×Q8×D1132
#548×C1132
#3497113