Finite Group Databasebeta

← #26117001

Subgroups — #26117001

Order 12032.

510 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 89 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#20254209C211yesmaximal, characteristic
2C2×#15689453C211yesmaximal, characteristic
3#20243468C211yesmaximal, characteristic
4#20241752C211yesmaximal, characteristic
5#20241751C211yesmaximal, characteristic
6#20241276C211yesmaximal, characteristic
7C2×C47×#484C211yesmaximal, characteristic
8C2×#13094003C2211yescharacteristic
9#15689453—22no—
10#15689453—21no—
11#15689453—22no—
12#15689451—21no—
13#15689379—22no—
14#15689279—21no—
15#15689278—21no—
16C2×#13093955—21no—
17C2×#13093947—21no—
18#15689087C2211yescharacteristic
19#15689087C2211yescharacteristic
20C2×C22⋊(C47⋊C8)C2211yescharacteristic
21#15688892—22no—
22#15688849—22no—
23#15688848—22no—
24C2×C22⋊Q8×C47C2211yescharacteristic
25C22×C4⋊C4×C47C2211yescharacteristic
26C47×#484—22no—
27C47×#484—22no—
28C2×#107×C47—21no—
29C2×#103×C47—21no—
30C2×C22⋊C8×C47C2211yescharacteristic
31C22×Dic94D411yescharacteristic
32C2×#10625337—22no—
33C2×#10625329—21no—
34C2×#10625329D412yes—
35C22×C47⋊C8—21no—
36#13094003—21no—
37#13094003—21no—
38#13094003—21no—
39#13094003—21no—
40C2×C4⋊Dic47D411yescharacteristic
41C2×Dic47⋊C4—21no—
42C2×C22⋊Dic47—21no—
43#13093955—22no—
44#13093955—24no—
45#13093948—22no—
46#13093947—22no—
47#13093947—24no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50C22⋊(C47⋊C8)—21no—
51C22⋊(C47⋊C8)—21no—
52C22⋊(C47⋊C8)—21no—
53C22⋊(C47⋊C8)D412yes—
54C22×Q8×C47D411yescharacteristic
55C23×C4×C47—21no—
56C23×C4×C47C2311yescharacteristic
57C22×C8×C47—21no—
58C22⋊Q8×C47—21no—
59C22⋊Q8×C47—21no—
60C22⋊Q8×C47—21no—
61C22⋊Q8×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47—21no—
64C2×C4⋊C4×C47—21no—
65C2×C4⋊C4×C47—21no—
66C2×C4⋊C4×C47—21no—
67C2×C4⋊C4×C47—21no—
68C2×C4⋊C4×C47D412yes—
69C2×C4⋊C4×C47D411yescharacteristic
70C2×C22⋊C4×C47—21no—
71#107×C47—24no—
72#103×C47—24no—
73C22⋊C8×C47—21no—
74C22⋊C8×C47D412yes—
75C24×C47#4111yescharacteristic
76C2×Q8×C47—21no—
77C2×Q8×C47—21no—
78C2×Q8×C47—42no—
79C22×C4×C47—21no—
80C22×C4×C47—21no—
81C22×C4×C47—22no—
82C22×C4×C47—42no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47—82no—
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×Dic47—21no—
93C22×Dic47—21no—
94C2×Dic94—21no—
95C2×Dic94—21no—
96C2×Dic94—42no—
97C2×C8×C47—22no—
98C2×C8×C47—42no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47—22no—
102C4⋊C4×C47—21no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47—41no—
106C4⋊C4×C47—41no—
107C22⋊C4×C47—41no—
108C22⋊C4×C47—41no—
109C22⋊Dic47—41no—
110C22⋊Dic47—41no—
111#10625337—82no—
112C4⋊Dic47—21no—
113C4⋊Dic47—21no—
114Dic47⋊C4—41no—
115Dic47⋊C4—41no—
116#10625329—42no—
117#10625329—42no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—42no—
121C2×C47⋊C8—41no—
122C23×C47—22no—
123C23×C47—22no—
124C23×C47—41no—
125C23×C47#12111yescharacteristic
126C23×C47#12111yescharacteristic
127C23×C47#12111yescharacteristic
128Q8×C47—42no—
129Q8×C47—42no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—42no—
139C2×C4×C47—42no—
140C2×C4×C47—82no—
141C2×C4×C47—82no—
142C2×C4×C47—82no—
143C2×C4×C47—81no—
144C2×C4×C47#12011yescharacteristic
145C2×C4×C47#12011yescharacteristic
146C2×C4×C47#12011yescharacteristic
147C2×C4×C47#12711yescharacteristic
148C2×Dic47—41no—
149C2×Dic47—41no—
150C2×Dic47—42no—
151C2×Dic47—81no—
152Dic94—42no—
153Dic94—42no—
154C8×C47—42no—
155C47⋊C8—42no—
156C47⋊C8—42no—
157C47⋊C8—81no—
158#9995—471nomaximal, Sylow
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—44no—
167C22×C47#39211yescharacteristic
168C22×C47#47112yes—
169C22×C47#47312yes—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47—21no—
173C4×C47—81no—
174C4×C47—82no—
175C4×C47—81no—
176C4×C47#45812yes—
177Dic47—81no—
178Dic47—81no—
179#3195—471no—
180C2×#484D4711yescharacteristic
181C2×#483—471no—
182#1821—471no—
183#1472—471no—
184#1472—471no—
185#1298—471no—
186C2×C47—22no—
187C2×C47—22no—
188C2×C47—41no—
189C2×C47#201911yescharacteristic
190C2×C47#202011yescharacteristic
191C2×C47#202211yescharacteristic
192C2×C22⋊Q8—471no—
193C2×C22⋊Q8C2×D4711yescharacteristic
194C22×C4⋊C4C2×D4711yescharacteristic
195#484—22no—
196#484—22no—
197#483—942no—
198#483—941no—
199#483—942no—
200#483—941no—
201#470—942no—
202#451—941no—
203#451—941no—
204C2×#107—21no—
205C2×#106—941no—
206C2×#103—21no—
207C2×#103—941no—
208#407—471no—
209#407—471no—
210C2×C22⋊C8—471no—
211C2×C22⋊C8C2×D4711yescharacteristic
212#343—942no—
213#324—942no—
214#324—942no—
215C47#999511yescharacteristic, complemented, Sylow
216C22×Q8—471no—
217C22×Q8C22⋊D4711yescharacteristic
218C23×C4—21no—
219C23×C4C22×D4711yescharacteristic
220C2×Q16—942no—
221C2×M16—472no—
222C2×M16—941no—
223C22×C8—21no—
224C22×C8—941no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C22⋊Q8—941no—
230C22⋊Q8—941no—
231C22⋊Q8—941no—
232C22⋊Q8—941no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—471no—
240C2×C4⋊C4—941no—
241C2×C4⋊C4C22⋊D4712yes—
242C2×C4⋊C4C22⋊D4711yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—941no—
245#107—24no—
246#106—944no—
247#106—942no—
248#103—24no—
249#103—944no—
250#103—942no—
251#103—942no—
252C22⋊C8—21no—
253C22⋊C8—472no—
254C22⋊C8—941no—
255C22⋊C8—941no—
256C22⋊C8—941no—
257C22⋊C8—941no—
258C22⋊C8—941no—
259C22⋊C8C22⋊D4712yes—
260C24#1062535211yescharacteristic
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—42no—
264C2×Q8—941no—
265C2×Q8—941no—
266C2×Q8—1882no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—82no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4D4×D4711yescharacteristic
277C22×C4D4×D4711yescharacteristic
278C22×C4D4×D4711yescharacteristic
279C22×C4C2×C22⋊D4711yescharacteristic
280C22×C4C2×C22⋊D4711yescharacteristic
281C22×C4C2×C22⋊D4711yescharacteristic
282Q16—3762no—
283M16—1882no—
284M16—1882no—
285C2×C8—22no—
286C2×C8—42no—
287C2×C8—942no—
288C2×C8—942no—
289C2×C8—1881no—
290C2×C8—1882no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—941no—
300C4⋊C4—941no—
301C4⋊C4—1881no—
302C4⋊C4—1881no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—1881no—
306C22⋊C4—1881no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23#1309399511yescharacteristic
311C23#1309399611yescharacteristic
312C23#1309399611yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—1882no—
316Q8—1882no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—81no—
331C2×C4—3761no—
332C2×C4—1881no—
333C2×C4—1881no—
334C2×C4—1882no—
335C2×C4#1309399211yescharacteristic
336C2×C4#1309399211yescharacteristic
337C2×C4#1309399311yescharacteristic
338C2×C4#1309402011yescharacteristic
339C8—42no—
340C8—3761no—
341C8—1882no—
342C8—1882no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22#1568903111yescharacteristic
352C22#1568938412yes—
353C22#1568939512yes—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4—3761no—
361C4—3761no—
362C4#1568931212yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#2024450211yescharacteristic
367C2#2024450711yescharacteristic
368C2#2024451611yescharacteristic
subgroupG/H
centerC22#15689031
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC2×C47×#484C2
socleC22×C47#392
prime radicalC24×C47#41
hypercenterC2×#484D47
hypocenterC47#9995
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
215. C47#9995semidirect

Maximal subgroups

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

subgroupindex
#202542092
C2×#156894532
#202434682
#202417522
#202417512
#202412762
C2×C47×#4842
#999547