Finite Group Databasebeta

← #26127396

Subgroups — #26127396

Order 12032.

452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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#20248742C211yesmaximal, characteristic
2#20241706C211yesmaximal, characteristic
3#20241411C212yesmaximal, complemented
4#20241408C212yesmaximal, complemented
5C47×#1799C211yesmaximal, characteristic
6C2×C4×Dic94C411yescharacteristic, complemented
7C2×C22⋊(C47⋊C8)—21no—
8#15689059C411yescharacteristic, complemented
9#15689059C2211yescharacteristic
10#15689035C411yescharacteristic, complemented
11#15689035C2211yescharacteristic
12#15689026—21no—
13#15689019—21no—
14#15688996—21no—
15#15688996—21no—
16#15688989C411yescharacteristic, complemented
17#15688849—21no—
18#15688847C2212yes—
19C2×C4×D4×C47C2211yescharacteristic
20C2×#99×C47—21no—
21C47×#380—21no—
22C47×#342C2212yes—
23C22×Dic94C2×C411yescharacteristic
24C22×C47⋊C8—41no—
25C4×Dic94—41no—
26C4×Dic94—41no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—21no—
32C2×C22⋊Dic47—21no—
33C2×C22⋊Dic47—21no—
34C2×C22⋊Dic47—21no—
35C2×C22⋊Dic47—21no—
36C2×C4×Dic47—21no—
37C22⋊(C47⋊C8)—22no—
38C22⋊(C47⋊C8)—41no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95C2×C411yescharacteristic
43C47⋊#95C2×C411yescharacteristic
44C22×D4×C47D411yescharacteristic
45C23×C4×C47D411yescharacteristic
46C23×C4×C47D411yescharacteristic
47C4×D4×C47—41no—
48C4×D4×C47—41no—
49C2×C4⋊C4×C47—41no—
50C2×C4⋊C4×C47D411yescharacteristic
51C2×C22⋊C4×C47—22no—
52C2×C22⋊C4×C47C2×C411yescharacteristic
53C2×C22⋊C4×C47C2311yescharacteristic
54C2×C42×C47C2×C411yescharacteristic
55#99×C47—42no—
56#95×C47—41no—
57C24×C47C22⋊C411yescharacteristic
58C24×C47C2×D411yescharacteristic
59C2×D4×C47—41no—
60C2×D4×C47—41no—
61C2×D4×C47SD1612yes—
62C2×D4×C47Q1612yes—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—42no—
68C22×C4×C47—81no—
69C22×C4×C47—81no—
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C22⋊C411yescharacteristic
73C22×C4×C47C22×C411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C22×Dic47—21no—
79C2×Dic94—41no—
80C2×Dic94—42no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—82no—
83C22⋊C4×C47—41no—
84C22⋊C4×C47—41no—
85C22⋊C4×C47—42no—
86C22⋊C4×C47—42no—
87C42×C47—21no—
88C42×C47—21no—
89C22⋊Dic47—42no—
90C22⋊Dic47—42no—
91C22⋊Dic47—81no—
92C22⋊Dic47—81no—
93C4⋊Dic47—42no—
94C4⋊Dic47—41no—
95Dic47⋊C4—41no—
96Dic47⋊C4—41no—
97Dic47⋊C4—81no—
98Dic47⋊C4—81no—
99C4×Dic47—42no—
100C2×C47⋊C8—42no—
101C2×C47⋊C8—82no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—41no—
107C23×C47—41no—
108C23×C47—41no—
109C23×C47—41no—
110C23×C47#10312yes—
111C23×C47C2×C22⋊C411yescharacteristic
112C23×C47C2×SD1611yescharacteristic
113C23×C47C2×Q1611yescharacteristic
114D4×C47—42no—
115D4×C47—42no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—41no—
122C2×C4×C47—42no—
123C2×C4×C47—42no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—81no—
128C2×C4×C47—81no—
129C2×C4×C47—82no—
130C2×C4×C47—82no—
131C2×C4×C47—82no—
132C2×C4×C47#9911yescharacteristic
133C2×C4×C47#9911yescharacteristic
134C2×C4×C47#10312yes—
135C2×Dic47—22no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144C2×Dic47—41no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147Dic94—42no—
148Dic94—42no—
149C47⋊C8—82no—
150#11897—471nomaximal, Sylow
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—22no—
155C22×C47—21no—
156C22×C47—42no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—81no—
164C22×C47—81no—
165C22×C47C2×#9911yescharacteristic
166C22×C47C2×#10311yescharacteristic
167C22×C47#42111yescharacteristic
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—22no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47—162no—
175Dic47—42no—
176Dic47—81no—
177Dic47—81no—
178Dic47—81no—
179#2580—471no—
180#1799D4711yescharacteristic
181#1459—471no—
182#1352—472no—
183#1351—472no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—41no—
187C2×C47—42no—
188C2×C47—41no—
189C2×C47#152011yescharacteristic
190C2×C47#212011yescharacteristic
191C2×C47#212711yescharacteristic
192C2×C4×Q8—471no—
193C2×C4×D4C2×D4711yescharacteristic
194C2×#99—21no—
195C2×C22⋊C8—941no—
196#399—471no—
197#399—471no—
198#393—471no—
199#393—471no—
200#390—941no—
201#389—941no—
202#385—941no—
203#385—941no—
204#382—471no—
205#380—21no—
206#342C2×D4712yes—
207#324—941no—
208#323—472no—
209C47#1189711yescharacteristic, complemented, Sylow
210C22×Q8—471no—
211C22×D4C22⋊D4711yescharacteristic
212C23×C4D18811yescharacteristic
213C23×C4C22⋊D4711yescharacteristic
214C22×C8—1881no—
215C4×Q8—1881no—
216C4×Q8—1881no—
217C4×D4—41no—
218C4×D4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—941no—
222C2×C4⋊C4—941no—
223C2×C4⋊C4—941no—
224C2×C4⋊C4—941no—
225C2×C4⋊C4D18811yescharacteristic
226C2×C22⋊C4—22no—
227C2×C22⋊C4—941no—
228C2×C22⋊C4—941no—
229C2×C22⋊C4—941no—
230C2×C22⋊C4—941no—
231C2×C22⋊C4C4×D4711yescharacteristic
232C2×C22⋊C4C22×D4711yescharacteristic
233C2×C42—941no—
234C2×C42C4×D4711yescharacteristic
235#99—42no—
236C22⋊C8—942no—
237C22⋊C8—1881no—
238#95—41no—
239#95—471no—
240#95—471no—
241#95—941no—
242#95—941no—
243#95—941no—
244C24(C2×D47)⋊C411yescharacteristic
245C24C2×C22⋊D4711yescharacteristic
246C2×Q8—1881no—
247C2×Q8—1882no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4#1062533512yes—
251C2×D4#1062533712yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4(C2×D47)⋊C411yescharacteristic
264C22×C4(C2×D47)⋊C411yescharacteristic
265C22×C4(C2×D47)⋊C411yescharacteristic
266C22×C4C2×C4×D4711yescharacteristic
267C22×C4C2×D18811yescharacteristic
268C2×C8—3762no—
269C2×C8—1882no—
270C4⋊C4—41no—
271C4⋊C4—82no—
272C4⋊C4—3761no—
273C4⋊C4—3761no—
274C4⋊C4—1881no—
275C4⋊C4—1882no—
276C4⋊C4—1881no—
277C4⋊C4—1881no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—3761no—
283C22⋊C4—3761no—
284C22⋊C4—1882no—
285C22⋊C4—1882no—
286C42—21no—
287C42—21no—
288C42—1882no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#1309394712yes—
298C23C2×(C2×D47)⋊C411yescharacteristic
299C23C2×#1062533511yescharacteristic
300C23C2×#1062533711yescharacteristic
301Q8—1882no—
302Q8—1882no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—942no—
322C2×C4—1881no—
323C2×C4—1881no—
324C2×C4—1881no—
325C2×C4—1881no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4—1881no—
329C2×C4—1881no—
330C2×C4—1881no—
331C2×C4—1881no—
332C2×C4—1881no—
333C2×C4#1309393811yescharacteristic
334C2×C4#1309393811yescharacteristic
335C2×C4#1309394712yes—
336C8—3762no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22C2×#1309393811yescharacteristic
352C22C2×#1309394711yescharacteristic
353C22#1568914111yescharacteristic
354C4—22no—
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—162no—
361C4—3761no—
362C4—3761no—
363C4—3761no—
364C4—1882no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—42no—
369C2—41no—
370C2#2024195911yescharacteristic
371C2#2024502711yescharacteristic
372C2#2024505511yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C22⋊C4C22×D47
FittingC47×#1799C2
socleC22×C47C2×#99
prime radicalC22×D4×C47D4
cosocleC2×C22⋊C4×C47C23
hypercenter#1799D47
hypocenterC47#11897
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #20241411C2semidirect
4. #20241408C2semidirect
6. C2×C4×Dic94C4semidirect
8. #15689059C4semidirect
10. #15689035C4semidirect
16. #15688989C4semidirect
209. C47#11897semidirect

Maximal subgroups

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

subgroupindex
#202487422
#202417062
#202414112
#202414082
C47×#17992
#1189747