Finite Group Databasebeta

← C47×#61013 #26100711

Subgroups — C47×#61013 #26100711

Order 12032.

1656 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3509C212yesmaximal
2C47×#3261C214yesmaximal, complemented
3C47×#3231C214yesmaximal, complemented
4C47×#3209C214yesmaximal, complemented
5C47×#3202C214yesmaximal
6C47×#3185C212yesmaximal, complemented
7C47×#3170C212yesmaximal, complemented
8C47×#3127C218yesmaximal, complemented
9C47×#2922C211yesmaximal, characteristic
10C47×#557—24no—
11C47×#556—24no—
12C47×#552—24no—
13C47×#552—24no—
14C47×#541C2214yes—
15C47×#541C2214yes—
16C47×#536C2214yes—
17C47×#533C2214yes—
18C47×#533C2214yes—
19C47×#533C2212yes—
20C2×C4⋊Q8×C47C2212yes—
21C47×#519C2214yes—
22C4×#41×C47C2211yescharacteristic
23C47×#500C2212yes—
24C47×#498C2212yes—
25C47×#494C2212yes—
26C47×#494C2212yes—
27C47×#487C2214yes—
28C47×#487C2214yes—
29C47×#485C22116yes—
30C47×#479C22116yes—
31C47×#470C2218yes—
32C47×#467C2218yes—
33C47×#462C22116yes—
34C47×#451C22116yes—
35C47×#441C2218yes—
36C4×Q16×C47C2218yes—
37C47×#433C2214yes—
38C47×#431C2214yes—
39C47×#424C2212yes—
40C47×#408C2212yes—
41C4×M16×C47C2211yescharacteristic
42C2×C4×C8×C47C2211yescharacteristic
43C2×#41×C47C2311yescharacteristic
44C22×Q8×C47C2314yes—
45C2×Q16×C47C2318yes—
46C2×Q16×C47C2318yes—
47C2×M16×C47C2312yes—
48C22×C8×C47C2312yes—
49C4⋊Q8×C47—24no—
50C4⋊Q8×C47—24no—
51C4⋊Q8×C47C2314yes—
52C4⋊Q8×C47C2314yes—
53C4⋊Q8×C47C2314yes—
54#126×C47—28no—
55#126×C47—28no—
56#125×C47—28no—
57#125×C47—28no—
58#125×C47—24no—
59#125×C47—24no—
60#125×C47C2314yes—
61#124×C47—24no—
62#123×C47—24no—
63#123×C47—24no—
64C22⋊Q8×C47—24no—
65C22⋊Q8×C47—24no—
66C22⋊Q8×C47—24no—
67C22⋊Q8×C47C2318yes—
68C22⋊Q8×C47C2318yes—
69C4×Q8×C47—28no—
70C4×Q8×C47—24no—
71C4×Q8×C47—24no—
72C4×Q8×C47—24no—
73C4×Q8×C47D412yes—
74C4×Q8×C47C2318yes—
75C4×Q8×C47C2318yes—
76C4×D4×C47D412yes—
77C4×D4×C47D414yes—
78#117×C47—24no—
79#117×C47—24no—
80#117×C47—28no—
81#117×C47C2314yes—
82#117×C47C2312yes—
83#117×C47C2311yescharacteristic
84C2×C4⋊C4×C47—24no—
85C2×C42×C47C2312yes—
86C2×C42×C47C2311yescharacteristic
87#107×C47C2318yes—
88#106×C47C2318yes—
89C4⋊C8×C47C2318yes—
90#103×C47C23116yes—
91#103×C47C23116yes—
92C22⋊C8×C47C2318yes—
93#97×C47C2312yes—
94C4×C8×C47C2312yes—
95C4×C8×C47C2312yes—
96C4×C8×C47C2312yes—
97#41×C47—42no—
98C2×Q8×C47—24no—
99C2×Q8×C47—24no—
100C2×Q8×C47—48no—
101C2×Q8×C47C2×D411yescharacteristic
102C2×Q8×C47C2418yes—
103C2×D4×C47C2×D411yescharacteristic
104C2×D4×C47C2×D412yes—
105C22×C4×C47—24no—
106C22×C4×C47C2×D414yes—
107C22×C4×C47C2×D412yes—
108C22×C4×C47C2412yes—
109C22×C4×C47C2411yescharacteristic
110Q16×C47—48no—
111Q16×C47—48no—
112M16×C47—42no—
113C2×C8×C47—42no—
114C2×C8×C47C2414yes—
115C2×C8×C47C2414yes—
116C4⋊C4×C47—24no—
117C4⋊C4×C47—24no—
118C4⋊C4×C47—28no—
119C4⋊C4×C47—24no—
120C4⋊C4×C47—28no—
121C4⋊C4×C47—28no—
122C4⋊C4×C47—28no—
123C4⋊C4×C47—28no—
124C4⋊C4×C47—28no—
125C4⋊C4×C47C2×D414yes—
126C4⋊C4×C47C2×D412yes—
127C4⋊C4×C47C2418yes—
128C22⋊C4×C47—24no—
129C22⋊C4×C47—28no—
130C22⋊C4×C47—28no—
131C22⋊C4×C47C2×D414yes—
132C22⋊C4×C47C2×D412yes—
133C42×C47—28no—
134C42×C47—28no—
135C42×C47—24no—
136C42×C47C2×D412yes—
137C42×C47C2×D414yes—
138C42×C47C2412yes—
139C42×C47C2411yescharacteristic
140C42×C47C2411yescharacteristic
141C23×C47C22×D411yescharacteristic
142C23×C47C22×D412yes—
143Q8×C47—216no—
144Q8×C47—41no—
145Q8×C47—48no—
146Q8×C47—48no—
147D4×C47—41no—
148D4×C47—42no—
149C2×C4×C47—28no—
150C2×C4×C47—24no—
151C2×C4×C47—22no—
152C2×C4×C47—24no—
153C2×C4×C47—28no—
154C2×C4×C47—28no—
155C2×C4×C47—48no—
156C2×C4×C47C22×D412yes—
157C2×C4×C47C22×D412yes—
158C2×C4×C47C22×D414yes—
159C2×C4×C47C22×D411yescharacteristic
160C2×C4×C47C22×D412yes—
161C2×C4×C47C2511yescharacteristic
162C8×C47—24no—
163C8×C47—24no—
164#61013C4711yesmaximal, characteristic, direct product factor, Sylow
165C22×C47—22no—
166C22×C47—21no—
167C22×C47—22no—
168C22×C47—24no—
169C22×C47C23×D411yescharacteristic
170C4×C47—21no—
171C4×C47—22no—
172C4×C47—22no—
173C4×C47—24no—
174C4×C47—48no—
175C4×C47—48no—
176C4×C47#57814yes—
177C4×C47#58512yes—
178#3509C2×C4712yes—
179#3261C2×C4714yescomplemented
180#3231C2×C4714yescomplemented
181#3209C2×C4714yescomplemented
182#3202C2×C4714yes—
183#3185C2×C4712yescomplemented
184#3170C2×C4712yescomplemented
185#3127C2×C4718yescomplemented
186#2922C2×C4711yescharacteristic
187C2×C47—42no—
188C2×C47—41no—
189C2×C47#344911yescharacteristic
190C2×C47C2×#57812yes—
191#557—24no—
192#556—24no—
193#552—24no—
194#552—24no—
195#541C22×C4714yes—
196#541C22×C4714yes—
197#536C22×C4714yes—
198#533C22×C4714yes—
199#533C22×C4714yes—
200#533C22×C4712yes—
201C2×C4⋊Q8C22×C4712yes—
202#519C22×C4714yes—
203C4×#41C22×C4711yescharacteristic
204#500C22×C4712yes—
205#498C22×C4712yes—
206#494C22×C4712yes—
207#494C22×C4712yes—
208#487C22×C4714yes—
209#487C22×C4714yes—
210#485C22×C47116yes—
211#479C22×C47116yes—
212#470C22×C4718yes—
213#467C22×C4718yes—
214#462C22×C47116yes—
215#451C22×C47116yes—
216#441C22×C4718yes—
217C4×Q16C22×C4718yes—
218#433C22×C4714yes—
219#431C22×C4714yes—
220#424C22×C4712yes—
221#408C22×C4712yes—
222C4×M16C22×C4711yescharacteristic
223C2×C4×C8C22×C4711yescharacteristic
224C47#6101311yescharacteristic, direct product factor, Sylow
225C2×#41C23×C4711yescharacteristic
226C22×Q8C23×C4714yes—
227C2×Q16C23×C4718yes—
228C2×Q16C23×C4718yes—
229C2×M16C23×C4712yes—
230C22×C8C23×C4712yes—
231C4⋊Q8—24no—
232C4⋊Q8—24no—
233C4⋊Q8C23×C4714yes—
234C4⋊Q8C23×C4714yes—
235C4⋊Q8C23×C4714yes—
236#126—28no—
237#126—28no—
238#125—28no—
239#125—28no—
240#125—24no—
241#125—24no—
242#125C23×C4714yes—
243#124—24no—
244#123—24no—
245#123—24no—
246C22⋊Q8—24no—
247C22⋊Q8—24no—
248C22⋊Q8—24no—
249C22⋊Q8C23×C4718yes—
250C22⋊Q8C23×C4718yes—
251C4×Q8—28no—
252C4×Q8—24no—
253C4×Q8—24no—
254C4×Q8—24no—
255C4×Q8D4×C4712yes—
256C4×Q8C23×C4718yes—
257C4×Q8C23×C4718yes—
258C4×D4D4×C4712yes—
259C4×D4D4×C4714yes—
260#117—24no—
261#117—24no—
262#117—28no—
263#117C23×C4714yes—
264#117C23×C4712yes—
265#117C23×C4711yescharacteristic
266C2×C4⋊C4—24no—
267C2×C42C23×C4712yes—
268C2×C42C23×C4711yescharacteristic
269#107C23×C4718yes—
270#106C23×C4718yes—
271C4⋊C8C23×C4718yes—
272#103C23×C47116yes—
273#103C23×C47116yes—
274C22⋊C8C23×C4718yes—
275#97C23×C4712yes—
276C4×C8C23×C4712yes—
277C4×C8C23×C4712yes—
278C4×C8C23×C4712yes—
279#41—42no—
280C2×Q8—24no—
281C2×Q8—24no—
282C2×Q8—48no—
283C2×Q8C2×D4×C4711yescharacteristic
284C2×Q8C24×C4718yes—
285C2×D4C2×D4×C4711yescharacteristic
286C2×D4C2×D4×C4712yes—
287C22×C4—24no—
288C22×C4C2×D4×C4714yes—
289C22×C4C2×D4×C4712yes—
290C22×C4C24×C4712yes—
291C22×C4C24×C4711yescharacteristic
292Q16—48no—
293Q16—48no—
294M16—42no—
295C2×C8—42no—
296C2×C8C24×C4714yes—
297C2×C8C24×C4714yes—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—28no—
301C4⋊C4—24no—
302C4⋊C4—28no—
303C4⋊C4—28no—
304C4⋊C4—28no—
305C4⋊C4—28no—
306C4⋊C4—28no—
307C4⋊C4C2×D4×C4714yes—
308C4⋊C4C2×D4×C4712yes—
309C4⋊C4C24×C4718yes—
310C22⋊C4—24no—
311C22⋊C4—28no—
312C22⋊C4—28no—
313C22⋊C4C2×D4×C4714yes—
314C22⋊C4C2×D4×C4712yes—
315C42—28no—
316C42—28no—
317C42—24no—
318C42C2×D4×C4712yes—
319C42C2×D4×C4714yes—
320C42C24×C4711yescharacteristic
321C42C24×C4711yescharacteristic
322C42C24×C4712yes—
323C23C22×D4×C4711yescharacteristic
324C23C22×D4×C4712yes—
325Q8—216no—
326Q8—41no—
327Q8—48no—
328Q8—48no—
329D4—42no—
330D4—41no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—48no—
338C2×C4C22×D4×C4712yes—
339C2×C4C22×D4×C4712yes—
340C2×C4C22×D4×C4714yes—
341C2×C4C22×D4×C4711yescharacteristic
342C2×C4C22×D4×C4712yes—
343C2×C4C25×C4711yescharacteristic
344C8—24no—
345C8—24no—
346C22—22no—
347C22—24no—
348C22—22no—
349C22—21no—
350C22C23×D4×C4711yescharacteristic
351C4—22no—
352C4—24no—
353C4—22no—
354C4—21no—
355C4—48no—
356C4—48no—
357C4C47×#57814yes—
358C4C47×#58512yes—
359C2—42no—
360C2—41no—
361C2C47×#344911yescharacteristic
362C2C2×C47×#57812yes—
subgroupG/H
center, socleC22×C47C23×D4
commutator, Frattini, cosocleC2×C4C25×C47
prime radicalC2×#41×C47C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3261C2semidirect
3. C47×#3231C2semidirect
4. C47×#3209C2semidirect
6. C47×#3185C2semidirect
7. C47×#3170C2semidirect
8. C47×#3127C2semidirect
164. #61013C47direct (N × H)
179. #3261C2×C47semidirect
180. #3231C2×C47semidirect
181. #3209C2×C47semidirect
183. #3185C2×C47semidirect
184. #3170C2×C47semidirect
185. #3127C2×C47semidirect
224. C47#61013direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35092
C47×#32612
C47×#32312
C47×#32092
C47×#32022
C47×#31852
C47×#31702
C47×#31272
C47×#29222
#6101347