Finite Group Databasebeta

← #26127212

Subgroups — #26127212

Order 12032.

412 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 83 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#20248768C211yesmaximal, characteristic
2#20243468C211yesmaximal, characteristic
3#20241419C212yesmaximal, complemented
4#20241395C212yesmaximal, complemented
5C2×C47×#324C211yesmaximal, characteristic
6C2×#13094003C411yescharacteristic
7#15689087—21no—
8#15689053C411yescharacteristic
9#15689053C2211yescharacteristic
10#15689043C411yescharacteristic
11#15689043C2211yescharacteristic
12#15689018—21no—
13#15689018—21no—
14#15688996—21no—
15#15688996—21no—
16C4×C22⋊Dic47C411yescharacteristic
17#15688892—21no—
18#15688892C2212yes—
19C22×C4⋊C4×C47C2211yescharacteristic
20C2×C22⋊C8×C47—21no—
21C47×#324—21no—
22C47×#324C2212yes—
23C22×Dic94C2×C411yescharacteristic
24C2×#10625329—22no—
25#13094003—41no—
26#13094003—41no—
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×Dic47⋊C4—21no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C2×C22⋊Dic47—21no—
34C2×C22⋊Dic47—21no—
35C2×C4×Dic47—21no—
36C22⋊(C47⋊C8)—41no—
37C22⋊(C47⋊C8)—41no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95C2×C411yescharacteristic
43C47⋊#95C2×C411yescharacteristic
44C23×C4×C47C2×C411yescharacteristic
45C23×C4×C47D411yescharacteristic
46C23×C4×C47D411yescharacteristic
47C22×C8×C47—41no—
48C2×C4⋊C4×C47—41no—
49C2×C4⋊C4×C47—41no—
50C2×C4⋊C4×C47C2×C411yescharacteristic
51C2×C4⋊C4×C47D411yescharacteristic
52C2×C4⋊C4×C47D411yescharacteristic
53C2×C4⋊C4×C47C2311yescharacteristic
54C22⋊C8×C47—22no—
55C22⋊C8×C47—41no—
56C24×C47C22⋊C411yescharacteristic
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—22no—
64C22×C4×C47—41no—
65C22×C4×C47—81no—
66C22×C4×C47—81no—
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22×C411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C2×Dic94—41no—
78C2×Dic94—81no—
79C2×C8×C47—42no—
80C2×C8×C47—82no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85C22⋊Dic47—24no—
86C22⋊Dic47—41no—
87C22⋊Dic47—41no—
88C4⋊Dic47—41no—
89Dic47⋊C4—42no—
90Dic47⋊C4—42no—
91Dic47⋊C4—42no—
92Dic47⋊C4—81no—
93Dic47⋊C4—81no—
94C4×Dic47—81no—
95#10625329—42no—
96#10625329—42no—
97C2×C47⋊C8—42no—
98C23×C47—22no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—41no—
102C23×C47#9911yescharacteristic
103C23×C47#9911yescharacteristic
104C23×C47C2×C22⋊C411yescharacteristic
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—42no—
115C2×C4×C47—42no—
116C2×C4×C47—42no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—41no—
121C2×C4×C47—81no—
122C2×C4×C47—81no—
123C2×C4×C47—81no—
124C2×C4×C47#13512yes—
125C2×Dic47—22no—
126C2×Dic47—22no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137Dic94—82no—
138C8×C47—82no—
139C47⋊C8—82no—
140#11854—471nomaximal, Sylow
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—42no—
149C22×C47—42no—
150C22×C47#35612yes—
151C22×C47C2×#9911yescharacteristic
152C22×C47#41611yescharacteristic
153C22×C47#42111yescharacteristic
154C4×C47—22no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47—41no—
160Dic47—42no—
161Dic47—42no—
162Dic47—81no—
163Dic47—81no—
164#2583—471no—
165#1821—471no—
166C2×#324D4711yescharacteristic
167#1354—472no—
168#1346—472no—
169C2×C47—21no—
170C2×C47—21no—
171C2×C47—22no—
172C2×C47—41no—
173C2×C47#151611yescharacteristic
174C2×C47#212111yescharacteristic
175C2×C47C2×#35611yescharacteristic
176C2×C22⋊Q8—471no—
177C22×C4⋊C4C2×D4711yescharacteristic
178#407—941no—
179C2×C22⋊C8—21no—
180#398—471no—
181#398—471no—
182#395—471no—
183#395—471no—
184#389—941no—
185#389—941no—
186#385—941no—
187#385—941no—
188C4×C22⋊C4—471no—
189#343—472no—
190#343—941no—
191#324—21no—
192#324C2×D4712yes—
193C47#1185411yescharacteristic, complemented, Sylow
194C22×Q8—471no—
195C23×C4C4×D4711yescharacteristic
196C23×C4D18811yescharacteristic
197C23×C4C22⋊D4711yescharacteristic
198C2×M16—942no—
199C22×C8—41no—
200C22⋊Q8—1881no—
201C22⋊Q8—1881no—
202C2×C4⋊C4—41no—
203C2×C4⋊C4—41no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—941no—
206C2×C4⋊C4—941no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4C4×D4711yescharacteristic
211C2×C4⋊C4D18811yescharacteristic
212C2×C4⋊C4C22⋊D4711yescharacteristic
213C2×C4⋊C4C22×D4711yescharacteristic
214C2×C22⋊C4—941no—
215C2×C22⋊C4—941no—
216C2×C42—941no—
217C22⋊C8—22no—
218C22⋊C8—41no—
219C22⋊C8—1881no—
220C22⋊C8—1881no—
221#95—471no—
222#95—471no—
223#95—941no—
224#95—941no—
225#95—941no—
226#95—941no—
227C24(C2×D47)⋊C411yescharacteristic
228C2×Q8—3761no—
229C2×Q8—1881no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244C22×C4(C2×D47)⋊C411yescharacteristic
245C22×C4(C2×D47)⋊C411yescharacteristic
246C22×C4(C2×D47)⋊C411yescharacteristic
247C22×C4C2×C4×D4711yescharacteristic
248C22×C4C2×D18811yescharacteristic
249C22×C4C2×C22⋊D4711yescharacteristic
250M16—1882no—
251M16—1882no—
252C2×C8—42no—
253C2×C8—82no—
254C2×C8—1882no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—3761no—
260C4⋊C4—3761no—
261C4⋊C4—1881no—
262C4⋊C4—1882no—
263C4⋊C4—1882no—
264C4⋊C4—1882no—
265C22⋊C4—944no—
266C22⋊C4—1881no—
267C22⋊C4—1881no—
268C42—3761no—
269C23—21no—
270C23—21no—
271C23—22no—
272C23—41no—
273C23#1309393811yescharacteristic
274C23#1309393811yescharacteristic
275C23C2×(C2×D47)⋊C411yescharacteristic
276Q8—3762no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—942no—
297C2×C4—942no—
298C2×C4—1881no—
299C2×C4—1881no—
300C2×C4—1881no—
301C2×C4—1881no—
302C2×C4—1881no—
303C2×C4—1881no—
304C2×C4—1881no—
305C2×C4—1881no—
306C2×C4—1881no—
307C2×C4—1881no—
308C2×C4#1309404612yes—
309C8—82no—
310C8—3762no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—42no—
319C22—42no—
320C22#1568892112yes—
321C22C2×#1309393811yescharacteristic
322C22#1568912011yescharacteristic
323C22#1568913911yescharacteristic
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—3761no—
331C4—3761no—
332C4—1882no—
333C4—1882no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—41no—
338C2#2024194511yescharacteristic
339C2#2024503211yescharacteristic
340C2C2×#1568892111yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC2×C47×#324C2
socleC22×C47C2×#99
prime radicalC24×C47C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenterC2×#324D47
hypocenterC47#11854
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #20241419C2semidirect
4. #20241395C2semidirect
193. C47#11854semidirect

Maximal subgroups

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

subgroupindex
#202487682
#202434682
#202414192
#202413952
C2×C47×#3242
#1185447