Finite Group Databasebeta

← C4×#15688921 #26131461

Subgroups — C4×#15688921 #26131461

Order 12032.

500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4×#13094022C211yesmaximal, characteristic
2C2×#15688921C212yesmaximal
3C4×#13093943C211yesmaximal, characteristic
4#20241514C212yesmaximal
5C4×#101×C47C211yesmaximal, characteristic
6C2×#13094022C2211yescharacteristic
7C2×C4×Dic94C411yescharacteristic
8C2×#13093943C2212yes—
9C4×#10625329—21no—
10#15689030C2211yescharacteristic
11#15689028C411yescharacteristic
12#15689018—21no—
13#15689018—21no—
14#15688992C411yescharacteristic
15C4×Dic47⋊C4—21no—
16C4×Dic47⋊C4—21no—
17C42×Dic47C411yescharacteristic
18#15688921C418yesdirect product factor
19#15688892—21no—
20C2×C4×Q8×C47C2211yescharacteristic
21C2×#101×C47C2212yes—
22C4×M16×C47—21no—
23C47×#343—21no—
24C22×Dic94C2×C411yescharacteristic
25C2×#10625329—22no—
26#13094022—22no—
27#13094022C2×C414yes—
28C4×Dic94—41no—
29C4×Dic94—41no—
30C2×C4⋊Dic47C2×C411yescharacteristic
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×Dic47⋊C4—21no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47—21no—
39C2×C4×Dic47C2×C411yescharacteristic
40C2×C4×Dic47C2×C411yescharacteristic
41#13093943—22no—
42#13093943C2×C414yes—
43#13093935—41no—
44C4×C47⋊C8—41no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C22×Q8×C47C2311yescharacteristic
50C2×M16×C47—22no—
51C4×Q8×C47—41no—
52C4×Q8×C47—41no—
53C2×C4⋊C4×C47C2×C411yescharacteristic
54C2×C4⋊C4×C47D411yescharacteristic
55C2×C4⋊C4×C47D411yescharacteristic
56C2×C42×C47C2×C411yescharacteristic
57C2×C42×C47D411yescharacteristic
58C2×C42×C47D411yescharacteristic
59#101×C47—22no—
60#101×C47C2×C414yes—
61#97×C47—41no—
62C4×C8×C47—41no—
63C2×Q8×C47—41no—
64C2×Q8×C47—41no—
65C2×Q8×C47C22×C412yes—
66C2×Q8×C47#4112yes—
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C2×Dic94—21no—
79C2×Dic94—41no—
80C2×Dic94—41no—
81C2×Dic94C4212yes—
82M16×C47—24no—
83M16×C47—42no—
84C2×C8×C47—42no—
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87C4⋊C4×C47—41no—
88C42×C47—21no—
89C42×C47—21no—
90C42×C47—21no—
91C42×C47—21no—
92C42×C47—21no—
93C42×C47—21no—
94C4⋊Dic47—41no—
95Dic47⋊C4—24no—
96Dic47⋊C4—24no—
97Dic47⋊C4—42no—
98Dic47⋊C4—42no—
99Dic47⋊C4—42no—
100C4×Dic47—24no—
101C4×Dic47—21no—
102C4×Dic47—42no—
103C4×Dic47—41no—
104C4×Dic47—41no—
105C4×Dic47—41no—
106C4×Dic47C4212yes—
107#10625329—24no—
108#10625329—42no—
109C2×C47⋊C8—42no—
110C23×C47C2×C22⋊C411yescharacteristic
111Q8×C47—42no—
112Q8×C47—42no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—22no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47#9911yescharacteristic
127C2×C4×C47#9911yescharacteristic
128C2×C4×C47C2×C4211yescharacteristic
129C2×C4×C47#11711yescharacteristic
130C2×C4×C47C4×D412yes—
131C2×C4×C47C4×D412yes—
132C2×Dic47—22no—
133C2×Dic47—22no—
134C2×Dic47—22no—
135C2×Dic47—22no—
136C2×Dic47—22no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144Dic94—42no—
145Dic94—42no—
146C8×C47—44no—
147C47⋊C8—44no—
148C4×#356—471nomaximal, Sylow
149C22×C47—21no—
150C22×C47—21no—
151C22×C47C4×C22⋊C411yescharacteristic
152C22×C47C2×#9911yescharacteristic
153C22×C47#41011yescharacteristic
154C4×C47—21no—
155C4×C47—22no—
156C4×C47—22no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47#35612yescomplemented
163Dic47—24no—
164Dic47—42no—
165Dic47—42no—
166Dic47—81no—
167C4×C4⋊Q8—471no—
168C2×#356—472no—
169C4×#101—471no—
170C4×#101D4711yescharacteristic
171#1394—472no—
172C2×C47—21no—
173C2×C47—21no—
174C2×C47C4×#9911yescharacteristic
175C2×C47C2×#35611yescharacteristic
176C2×C47#213211yescharacteristic
177C2×C4⋊Q8—471no—
178C2×C4×Q8—471no—
179C2×C4×Q8C2×D4711yescharacteristic
180C2×#101—472no—
181C2×#101C2×D4712yes—
182C4×M16—21no—
183C4×M16—941no—
184#391—471no—
185#391—471no—
186#389—941no—
187#389—941no—
188#384—471no—
189C4×C4⋊C4—941no—
190C4×C4⋊C4—941no—
191C43—471no—
192#356—478no—
193#343—21no—
194#343—941no—
195C47C4×#35611yescharacteristic, complemented, Sylow
196C22×Q8—471no—
197C22×Q8C22×D4711yescharacteristic
198C2×M16—22no—
199C2×M16—942no—
200C4⋊Q8—474no—
201C4⋊Q8—942no—
202C4×Q8—41no—
203C4×Q8—41no—
204C4×Q8—1881no—
205C4×Q8—1881no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4—941no—
211C2×C4⋊C4—941no—
212C2×C4⋊C4C4×D4711yescharacteristic
213C2×C4⋊C4D18811yescharacteristic
214C2×C4⋊C4C22⋊D4711yescharacteristic
215C2×C42—471no—
216C2×C42—471no—
217C2×C42—941no—
218C2×C42—941no—
219C2×C42—941no—
220C2×C42C4×D4711yescharacteristic
221C2×C42D18811yescharacteristic
222C2×C42C22⋊D4711yescharacteristic
223#101—22no—
224#101—474no—
225#101—942no—
226#101C4×D4714yes—
227#97—41no—
228#97—1881no—
229C4×C8—41no—
230C4×C8—1881no—
231#95—941no—
232#95—941no—
233#95—941no—
234#95—941no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—472no—
238C2×Q8—941no—
239C2×Q8—1881no—
240C2×Q8—1881no—
241C2×Q8C2×C4×D4712yes—
242C2×Q8#1062535012yes—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4(C2×D47)⋊C411yescharacteristic
248C22×C4(C2×D47)⋊C411yescharacteristic
249C22×C4(C2×D47)⋊C411yescharacteristic
250C22×C4(C2×D47)⋊C411yescharacteristic
251C22×C4C2×C4×D4711yescharacteristic
252C22×C4C2×D18811yescharacteristic
253C22×C4C2×C22⋊D4711yescharacteristic
254M16—24no—
255M16—42no—
256M16—944no—
257M16—1882no—
258C2×C8—42no—
259C2×C8—1882no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—944no—
264C4⋊C4—944no—
265C4⋊C4—1881no—
266C4⋊C4—1882no—
267C4⋊C4—1882no—
268C4⋊C4—1882no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—472no—
276C42—944no—
277C42—941no—
278C42—1881no—
279C42—1882no—
280C42—1881no—
281C42—1881no—
282C23C2×(C2×D47)⋊C411yescharacteristic
283Q8—42no—
284Q8—42no—
285Q8—1882no—
286Q8—1882no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—942no—
301C2×C4—942no—
302C2×C4—942no—
303C2×C4—942no—
304C2×C4—942no—
305C2×C4—1881no—
306C2×C4—1881no—
307C2×C4—1881no—
308C2×C4—1881no—
309C2×C4—1881no—
310C2×C4—1881no—
311C2×C4—1881no—
312C2×C4#1309393811yescharacteristic
313C2×C4#1309393811yescharacteristic
314C2×C4C42×D4711yescharacteristic
315C2×C4#1309398111yescharacteristic
316C2×C4C4×C22⋊D4712yes—
317C2×C4C4×D18812yes—
318C8—44no—
319C8—1884no—
320C22—21no—
321C22—21no—
322C22C4×(C2×D47)⋊C411yescharacteristic
323C22C2×#1309393811yescharacteristic
324C22#1568909611yescharacteristic
325C4—21no—
326C4—22no—
327C4—22no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—944no—
334C4—3761no—
335C4—1882no—
336C4—1882no—
337C4#1568892112yesdirect product factor
338C2—21no—
339C2—21no—
340C2C4×#1309393811yescharacteristic
341C2C2×#1568892111yescharacteristic
342C2#2024507111yescharacteristic
subgroupG/H
centerC2×C4#13093938
commutatorC2×C4×C47C2×C42
FrattiniC22×Q8C22×D47
FittingC4×#101×C47C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC22×Q8×C47C23
hypercenterC4×#101D47
hypocenterC47C4×#356
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
18. #15688921C4direct (N × H)
162. C4×C47#356semidirect
195. C47C4×#356semidirect
337. C4#15688921direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130940222
C2×#156889212
C4×#130939432
#202415142
C4×#101×C472
C4×#35647