Finite Group Databasebeta

← #26113685

Subgroups — #26113685

Order 12032.

486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252471C211yesmaximal, characteristic
2#20248377C211yesmaximal, characteristic
3#20243381C211yesmaximal, characteristic
4#20242060C211yesmaximal, characteristic
5#20241290C211yesmaximal, characteristic
6#20241289C211yesmaximal, characteristic
7C47×#1546C211yesmaximal, characteristic
8C2×#13094022—21no—
9C2×C4×Dic94C2211yescharacteristic
10#15689253—22no—
11#15689250—22no—
12#15689177—22no—
13#15689176C2211yescharacteristic
14#15689147C2211yescharacteristic
15C2×#13093942—21no—
16#15689054C414yes—
17#15689030—21no—
18#15689019—22no—
19C4×C4⋊Dic47C2211yescharacteristic
20#15688891—21no—
21#15688869—22no—
22C2×C4⋊Q8×C47C2211yescharacteristic
23C47×#431C2211yescharacteristic
24C47×#423C2211yescharacteristic
25C47×#332—22no—
26C22×Dic94D411yescharacteristic
27C2×#10625329—21no—
28#13094022—42no—
29#13094022—42no—
30C4×Dic94—21no—
31C4×Dic94—21no—
32C4×Dic94—21no—
33C4×Dic94—21no—
34C2×C4⋊Dic47—21no—
35C2×C4⋊Dic47D411yescharacteristic
36C2×Dic47⋊C4—24no—
37C2×Dic47⋊C4C2×C412yes—
38C2×C4×Dic47—21no—
39C2×C4×Dic47D412yes—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)D412yes—
43Dic47⋊C8—24no—
44#13093942—42no—
45C22⋊(C47⋊C8)—21no—
46#13093934—24no—
47C4×C47⋊C8—21no—
48C47⋊#95—24no—
49C47⋊#95C2×C412yes—
50C22×Q8×C47—21no—
51C2×M16×C47—21no—
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47—21no—
54C4⋊Q8×C47—21no—
55C4⋊Q8×C47—21no—
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47C2×C412yes—
58C2×C42×C47C2311yescharacteristic
59C4⋊C8×C47—21no—
60C4⋊C8×C47—21no—
61C4⋊C8×C47D412yes—
62C22⋊C8×C47—21no—
63C4×C8×C47—21no—
64C2×Q8×C47—41no—
65C2×Q8×C47—41no—
66C2×Q8×C47—41no—
67C2×Q8×C47—41no—
68C2×Q8×C47—41no—
69C2×Q8×C47—41no—
70C22×C4×C47—22no—
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—22no—
75C22×Dic47C22⋊C412yes—
76C22×Dic47C22⋊C412yes—
77C2×Dic94—21no—
78C2×Dic94—21no—
79C2×Dic94—21no—
80C2×Dic94—21no—
81C2×Dic94—21no—
82C2×Dic94—21no—
83M16×C47—41no—
84M16×C47—41no—
85C2×C8×C47—22no—
86C2×C8×C47—41no—
87C4⋊C4×C47—22no—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—41no—
91C42×C47C2×D411yescharacteristic
92C42×C47C2×D411yescharacteristic
93C42×C47#4111yescharacteristic
94C42×C47#4111yescharacteristic
95C4⋊Dic47—24no—
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98Dic47⋊C4—22no—
99Dic47⋊C4—22no—
100Dic47⋊C4—48no—
101C4×Dic47—22no—
102C4×Dic47—22no—
103C4×Dic47—41no—
104C4×Dic47—41no—
105#10625329—41no—
106#10625329—41no—
107C2×C47⋊C8—22no—
108C2×C47⋊C8—41no—
109C23×C47C2×C22⋊C411yescharacteristic
110Q8×C47—81no—
111Q8×C47—81no—
112Q8×C47—81no—
113Q8×C47—81no—
114C2×C4×C47—22no—
115C2×C4×C47—41no—
116C2×C4×C47—42no—
117C2×C4×C47—42no—
118C2×C4×C47—42no—
119C2×C4×C47C4×D411yescharacteristic
120C2×C4×C47C4×D411yescharacteristic
121C2×C4×C47#12011yescharacteristic
122C2×C4×C47#12111yescharacteristic
123C2×C4×C47#12111yescharacteristic
124C2×C4×C47#12311yescharacteristic
125C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C47#13711yescharacteristic
129C2×Dic47—24no—
130C2×Dic47—22no—
131C2×Dic47—22no—
132C2×Dic47—22no—
133C2×Dic47—22no—
134C2×Dic47—42no—
135C2×Dic47—42no—
136C2×Dic47—42no—
137Dic94—41no—
138Dic94—41no—
139Dic94—41no—
140Dic94—41no—
141C8×C47—42no—
142C8×C47—81no—
143C47⋊C8—42no—
144C47⋊C8—81no—
145#9402—471nomaximal, Sylow
146C22×C47—21no—
147C22×C47—21no—
148C22×C47#38611yescharacteristic
149C22×C47#41711yescharacteristic
150C22×C47#41811yescharacteristic
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—82no—
155C4×C47#45612yes—
156C4×C47#46811yescharacteristic
157C4×C47#46811yescharacteristic
158C4×C47#46911yescharacteristic
159C4×C47#46911yescharacteristic
160Dic47—44no—
161Dic47—42no—
162Dic47—42no—
163#2983—471no—
164#2546—471no—
165#1801—471no—
166#1546—471no—
167#1546D4711yescharacteristic
168#1303—471no—
169#1303—471no—
170C2×C47—21no—
171C2×C47—21no—
172C2×C47#188611yescharacteristic
173C2×C47#189511yescharacteristic
174C2×C47#191511yescharacteristic
175C2×C4⋊Q8—941no—
176C2×C4⋊Q8C2×D4711yescharacteristic
177C2×C4×Q8—471no—
178#446—942no—
179#446—942no—
180#432—942no—
181#431—471no—
182#431C2×D4711yescharacteristic
183#423—471no—
184#423C2×D4711yescharacteristic
185C2×#101—941no—
186#398—474no—
187#391—941no—
188#389—942no—
189C4×C4⋊C4—471no—
190#343—941no—
191#332—22no—
192#332—942no—
193C47#940211yescharacteristic, complemented, Sylow
194C22×Q8—21no—
195C22×Q8—471no—
196C2×M16—21no—
197C2×M16—941no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—1882no—
203C4⋊Q8—1882no—
204C4×Q8—941no—
205C4×Q8—941no—
206C4×Q8—941no—
207C4×Q8—941no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—472no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—941no—
212C2×C4⋊C4—944no—
213C2×C4⋊C4C4×D4712yes—
214C2×C42—472no—
215C2×C42—941no—
216C2×C42C22×D4711yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—472no—
220C4⋊C8—944no—
221C4⋊C8—941no—
222C4⋊C8—941no—
223C4⋊C8C22⋊D4712yes—
224#101—1882no—
225C22⋊C8—21no—
226C22⋊C8—941no—
227#97—944no—
228C4×C8—21no—
229C4×C8—941no—
230#95—472no—
231#95—944no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—941no—
239C2×Q8—941no—
240C2×Q8—941no—
241C2×Q8—941no—
242C2×Q8—941no—
243C2×Q8—941no—
244C22×C4—22no—
245C22×C4—472no—
246C22×C4—472no—
247C22×C4—942no—
248C22×C4C2×C4×D4711yescharacteristic
249C22×C4D4×D4711yescharacteristic
250C22×C4D4×D4711yescharacteristic
251M16—41no—
252M16—41no—
253M16—1881no—
254M16—1881no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—942no—
258C2×C8—1881no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—944no—
264C4⋊C4—942no—
265C4⋊C4—942no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—1888no—
269C42—942no—
270C42—942no—
271C42—1881no—
272C42—1881no—
273C42#1062535011yescharacteristic
274C42D4×D4711yescharacteristic
275C42#1062535211yescharacteristic
276C42C2×C22⋊D4711yescharacteristic
277C23C22⋊C4×D4711yescharacteristic
278Q8—81no—
279Q8—81no—
280Q8—81no—
281Q8—81no—
282Q8—1881no—
283Q8—1881no—
284Q8—1881no—
285Q8—1881no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—944no—
292C2×C4—942no—
293C2×C4—942no—
294C2×C4—942no—
295C2×C4—942no—
296C2×C4—1882no—
297C2×C4—1882no—
298C2×C4—1882no—
299C2×C4(C22⋊D47)⋊C411yescharacteristic
300C2×C4C4×C22⋊D4711yescharacteristic
301C2×C4#1309399211yescharacteristic
302C2×C4#1309399511yescharacteristic
303C2×C4#1309399711yescharacteristic
304C2×C4#1309400611yescharacteristic
305C2×C4#1309404811yescharacteristic
306C2×C4#1309404811yescharacteristic
307C2×C4#1309405111yescharacteristic
308C2×C4#1309405311yescharacteristic
309C8—42no—
310C8—81no—
311C8—3761no—
312C8—1882no—
313C22—21no—
314C22—21no—
315C22#1568899911yescharacteristic
316C22#1568912111yescharacteristic
317C22#1568912611yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—1884no—
323C4—1882no—
324C4—1882no—
325C4#1568930412yes—
326C4#1568936611yescharacteristic
327C4#1568936811yescharacteristic
328C4#1568937311yescharacteristic
329C4#1568937511yescharacteristic
330C2—21no—
331C2—21no—
332C2#2024377811yescharacteristic
333C2#2024382311yescharacteristic
334C2#2024393711yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1546C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1546D47
hypocenterC47#9402
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
193. C47#9402semidirect

Maximal subgroups

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

subgroupindex
#202524712
#202483772
#202433812
#202420602
#202412902
#202412892
C47×#15462
#940247