Finite Group Databasebeta

← #26117057

Subgroups — #26117057

Order 12032.

500 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 101 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#20253427C211yesmaximal, characteristic
2#20253193C211yesmaximal, characteristic
3#20241951C211yesmaximal, characteristic
4#20241817C211yesmaximal, characteristic
5#20241783C211yesmaximal, characteristic
6#20241246C211yesmaximal, characteristic
7C47×#2581C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689458—21no—
10#15689430—22no—
11#15689418—21no—
12#15689418—21no—
13#15689408—21no—
14#15689333—21no—
15#15689279—21no—
16C4×#10625337—22no—
17#15689176C2211yescharacteristic
18#15689176C2211yescharacteristic
19#15689163—21no—
20#15689147C2211yescharacteristic
21#15689132—21no—
22#15688859—22no—
23Q8⋊(C47⋊C8)—22no—
24Q8⋊(C47⋊C8)—22no—
25C2×C4×Q8×C47C2211yescharacteristic
26C2×C4×Q8×C47C2211yescharacteristic
27C47×#400—21no—
28C47×#395—21no—
29C47×#391—21no—
30C47×#389—21no—
31C47×#387—22no—
32C47×#382C2211yescharacteristic
33C2×#10625337—22no—
34C2×#10625329—21no—
35#13094024D411yescharacteristic
36#13094024D411yescharacteristic
37#13094016—21no—
38#13094003—21no—
39#13094003—21no—
40C4×Dic94—21no—
41C4×Dic94—21no—
42#13093983—21no—
43#13093957—22no—
44#13093957—22no—
45#13093955—22no—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)—21no—
48C4⋊(C47⋊C8)—21no—
49C4⋊(C47⋊C8)D412yes—
50#13093948—22no—
51#13093948—22no—
52#13093948—22no—
53#13093947—22no—
54C22⋊(C47⋊C8)—21no—
55C22⋊(C47⋊C8)—21no—
56C4×C47⋊C8—21no—
57C4×C47⋊C8D412yes—
58C22×Q8×C47D411yescharacteristic
59C22×Q8×C47D411yescharacteristic
60C4×Q8×C47—21no—
61C4×Q8×C47—21no—
62C4×Q8×C47—21no—
63C4×Q8×C47—21no—
64C4×Q8×C47—21no—
65C4×Q8×C47—21no—
66C4×Q8×C47—21no—
67C4×Q8×C47—21no—
68C2×C4⋊C4×C47—22no—
69C2×C4⋊C4×C47—21no—
70C2×C4⋊C4×C47—21no—
71C2×C4⋊C4×C47—21no—
72C2×C4⋊C4×C47D411yescharacteristic
73C2×C4⋊C4×C47D411yescharacteristic
74C2×C42×C47—21no—
75C2×C42×C47—21no—
76C2×C42×C47C2311yescharacteristic
77#95×C47—22no—
78#95×C47—22no—
79#95×C47—22no—
80#95×C47—21no—
81#95×C47D412yes—
82C2×Q8×C47—21no—
83C2×Q8×C47—21no—
84C2×Q8×C47—21no—
85C2×Q8×C47—21no—
86C2×Q8×C47—21no—
87C2×Q8×C47—21no—
88C2×Q8×C47—21no—
89C2×Q8×C47—42no—
90C2×Q8×C47Q1612yescomplemented
91C22×C4×C47—21no—
92C22×C4×C47—21no—
93C22×C4×C47—21no—
94C22×C4×C47—21no—
95C22×C4×C47—22no—
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C2×Dic94—21no—
100C2×Dic94—21no—
101C4⋊C4×C47—21no—
102C4⋊C4×C47—21no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—44no—
106C4⋊C4×C47—41no—
107C4⋊C4×C47—41no—
108C4⋊C4×C47—41no—
109C4⋊C4×C47—41no—
110C4⋊C4×C47—41no—
111C4⋊C4×C47—41no—
112C42×C47—41no—
113C42×C47—41no—
114C42×C47—41no—
115C42×C47—41no—
116C42×C47C2×D411yescharacteristic
117C42×C47C2×D411yescharacteristic
118C42×C47C2×D411yescharacteristic
119C42×C47#4111yescharacteristic
120C22⋊Dic47—41no—
121#10625337—44no—
122C4⋊Dic47—21no—
123C4⋊Dic47—21no—
124C4⋊Dic47—21no—
125C4⋊Dic47—21no—
126Dic47⋊C4—41no—
127Dic47⋊C4—41no—
128C4×Dic47—41no—
129#10625329—41no—
130#10625329—41no—
131C2×C47⋊C8—22no—
132C2×C47⋊C8—22no—
133C2×C47⋊C8—41no—
134C23×C47#12011yescharacteristic
135Q8×C47—22no—
136Q8×C47—22no—
137Q8×C47—22no—
138Q8×C47—22no—
139Q8×C47—41no—
140Q8×C47—41no—
141Q8×C47—41no—
142Q8×C47—41no—
143C2×C4×C47—22no—
144C2×C4×C47—22no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—42no—
152C2×C4×C47—42no—
153C2×C4×C47—42no—
154C2×C4×C47—42no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—42no—
158C2×C4×C47#12011yescharacteristic
159C2×C4×C47#12011yescharacteristic
160C2×C4×C47#12111yescharacteristic
161C2×C4×C47#12111yescharacteristic
162C2×C4×C47#12111yescharacteristic
163C2×C4×C47#12711yescharacteristic
164C2×C4×C47C2×Q1611yescharacteristic
165C2×C4×C47#13511yescharacteristic
166C2×C4×C47#13711yescharacteristic
167C2×C4×C47#13711yescharacteristic
168C2×Dic47—41no—
169C2×Dic47—41no—
170Dic94—42no—
171Dic94—81no—
172C47⋊C8—42no—
173C47⋊C8—42no—
174C47⋊C8—81no—
175#10003—471nomaximal, Sylow
176C22×C47—21no—
177C22×C47—21no—
178C22×C47#39211yescharacteristic
179C22×C47#45111yescharacteristic
180C22×C47#45211yescharacteristic
181C4×C47—21no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—42no—
186C4×C47—42no—
187C4×C47—82no—
188C4×C47—81no—
189C4×C47—81no—
190C4×C47#45111yescharacteristic
191C4×C47#45211yescharacteristic
192C4×C47#46711yescharacteristic
193C4×C47#47011yescharacteristic
194Dic47—81no—
195Dic47—81no—
196#3104—471no—
197#3078—471no—
198#2581D4711yescharacteristic
199#1518—471no—
200#1487—471no—
201#1479—471no—
202#1286—471no—
203C2×C47—21no—
204C2×C47—21no—
205C2×C47#200111yescharacteristic
206C2×C47#200911yescharacteristic
207C2×C47#201011yescharacteristic
208#533—471no—
209C2×C4×Q8C2×D4711yescharacteristic
210C2×C4×Q8C2×D4711yescharacteristic
211#484—941no—
212#479—942no—
213#477—941no—
214#477—941no—
215#475—941no—
216#462—941no—
217#451—941no—
218C4×Q16—942no—
219#431—471no—
220#431—471no—
221#428—941no—
222#423—471no—
223#419—941no—
224#400—21no—
225#395—21no—
226#391—21no—
227#389—21no—
228#387—22no—
229#382C2×D4711yescharacteristic
230#328—942no—
231Q8⋊C8—942no—
232Q8⋊C8—942no—
233C47#1000311yescharacteristic, complemented, Sylow
234C22×Q8C22⋊D4711yescharacteristic
235C22×Q8C22⋊D4711yescharacteristic
236C2×Q16—942no—
237C2×M16—941no—
238C4⋊Q8—471no—
239C4⋊Q8—471no—
240#125—941no—
241C22⋊Q8—941no—
242C22⋊Q8—941no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—941no—
252C4×Q8—941no—
253#117—941no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4C22⋊D4711yescharacteristic
259C2×C4⋊C4C22⋊D4711yescharacteristic
260C2×C42—21no—
261C2×C42—21no—
262C2×C42C22×D4711yescharacteristic
263#107—942no—
264#107—942no—
265#106—942no—
266C4⋊C8—472no—
267C4⋊C8—941no—
268C4⋊C8—941no—
269C4⋊C8—941no—
270#103—942no—
271#103—942no—
272#103—942no—
273#103—942no—
274C22⋊C8—941no—
275C22⋊C8—941no—
276C4×C8—472no—
277C4×C8—941no—
278#95—22no—
279#95—22no—
280#95—22no—
281#95—21no—
282#95C22⋊D4712yes—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—42no—
291C2×Q8—941no—
292C2×Q8—941no—
293C2×Q8#1062533712yescomplemented
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4C2×C22⋊D4711yescharacteristic
300C22×C4C2×C22⋊D4711yescharacteristic
301C22×C4C2×C22⋊D4711yescharacteristic
302Q16—1884no—
303M16—1881no—
304M16—1881no—
305C2×C8—942no—
306C2×C8—942no—
307C2×C8—1881no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—44no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—941no—
320C4⋊C4—941no—
321C4⋊C4—941no—
322C4⋊C4—941no—
323C4⋊C4—1881no—
324C4⋊C4—1881no—
325C22⋊C4—1881no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42—1881no—
331C42D4×D4711yescharacteristic
332C42D4×D4711yescharacteristic
333C42D4×D4711yescharacteristic
334C42#1062535211yescharacteristic
335C23#1309399311yescharacteristic
336Q8—22no—
337Q8—22no—
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—3761no—
345Q8—1882no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—1881no—
362C2×C4—1881no—
363C2×C4#1309399211yescharacteristic
364C2×C4#1309399211yescharacteristic
365C2×C4#1309399511yescharacteristic
366C2×C4#1309399611yescharacteristic
367C2×C4#1309399611yescharacteristic
368C2×C4#1309402011yescharacteristic
369C2×C4C2×#1062533711yescharacteristic
370C2×C4#1309404411yescharacteristic
371C2×C4#1309405411yescharacteristic
372C2×C4#1309405511yescharacteristic
373C8—3761no—
374C8—1882no—
375C8—1882no—
376C22—21no—
377C22—21no—
378C22#1568903111yescharacteristic
379C22#1568927911yescharacteristic
380C22#1568928511yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—42no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—3761no—
391C4—3761no—
392C4#1568927811yescharacteristic
393C4#1568928311yescharacteristic
394C4#1568936211yescharacteristic
395C4#1568937911yescharacteristic
396C2—21no—
397C2—21no—
398C2#2024439611yescharacteristic
399C2#2024444811yescharacteristic
400C2#2024445311yescharacteristic
subgroupG/H
centerC22#15689031
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2581C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#2581D47
hypocenterC47#10003
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
90. C2×Q8×C47Q16semidirect
233. C47#10003semidirect
293. C2×Q8#10625337semidirect

Maximal subgroups

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

subgroupindex
#202534272
#202531932
#202419512
#202418172
#202417832
#202412462
C47×#25812
#1000347