Finite Group Databasebeta

← #26219481

Subgroups — #26219481

Order 12032.

814 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic188C211yesmaximal, characteristic
2#20246040C211yesmaximal, characteristic
3#20245751C211yesmaximal, characteristic
4#20244030C212yesmaximal
5#20243960C212yesmaximal
6#20243728C212yesmaximal
7#20243645C212yesmaximal
8C4×#13093958C211yesmaximal, characteristic
9#20243219C211yesmaximal, characteristic
10#20243219C211yesmaximal, characteristic
11C47×#1746C211yesmaximal, characteristic
12C22×Dic188C2211yescharacteristic
13C2×C4×Dic94C2212yes—
14C2×C4×Dic94C2211yescharacteristic
15C2×C4×Dic94C2211yescharacteristic
16C4×Dic188C418yescomplemented
17C2×#13093958C2212yes—
18C2×#13093958C2211yescharacteristic
19C2×#13093949C2212yes—
20C2×#13093949C2212yes—
21C2×#13093949C2211yescharacteristic
22C2×#13093949C2211yescharacteristic
23#15689029C2212yes—
24#15689021C2212yes—
25#15689005—22no—
26#15688990—21no—
27#15688987—21no—
28C4×C4⋊Dic47C2211yescharacteristic
29C4×C4⋊Dic47C2211yescharacteristic
30C4×C4⋊Dic47C2212yes—
31#15688974—21no—
32#15688974—22no—
33#15688968—21no—
34#15688886C2212yes—
35#15688886C2212yes—
36#15688886C2212yes—
37C2×#97×C47C2211yescharacteristic
38C2×C4×C8×C47C2211yescharacteristic
39C47×#376C2211yescharacteristic
40C47×#336C2212yes—
41C47×#336C2212yes—
42C22×Dic94C2311yescharacteristic
43C22×Dic94C2311yescharacteristic
44C2×Dic188—24no—
45C2×Dic188C2×C414yes—
46C4×Dic94—24no—
47C4×Dic94—22no—
48C4×Dic94—22no—
49C4×Dic94—24no—
50C4×Dic94C2×C414yes—
51C4×Dic94C2×C414yes—
52C2×C4⋊Dic47C2312yes—
53C2×C4⋊Dic47C2311yescharacteristic
54C2×C4⋊Dic47C2311yescharacteristic
55C2×C4⋊Dic47C2312yes—
56C2×Dic47⋊C4—22no—
57C2×Dic47⋊C4—21no—
58C2×Dic47⋊C4—21no—
59C2×Dic47⋊C4—22no—
60C2×C4×Dic47—22no—
61C2×C4×Dic47—21no—
62C2×C4×Dic47—21no—
63C2×C4×Dic47—22no—
64C2×C4×Dic47—21no—
65C2×C4×Dic47—21no—
66#13093958—24no—
67#13093958C2×C414yes—
68#13093949—24no—
69#13093949—24no—
70#13093949C2×C414yes—
71#13093949C2×C414yes—
72C47⋊#95—22no—
73C47⋊#95—21no—
74C47⋊#95—21no—
75C47⋊#95—22no—
76C47⋊#95—22no—
77C47⋊#95—22no—
78C22×C8×C47C2312yes—
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C2×C42×C47C2312yes—
82C2×C42×C47C2311yescharacteristic
83#97×C47—22no—
84C4×C8×C47C2×C414yes—
85#95×C47D411yescharacteristic
86#95×C47D411yescharacteristic
87#95×C47D412yes—
88C22×C4×C47C2×D412yes—
89C22×C4×C47C2×D412yes—
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47C2411yescharacteristic
93C22×Dic47—21no—
94C22×Dic47—21no—
95C22×Dic47—21no—
96C22×Dic47—22no—
97C22×Dic47—21no—
98C22×Dic47—22no—
99C2×Dic94—22no—
100C2×Dic94—21no—
101C2×Dic94—22no—
102C2×Dic94—22no—
103C2×Dic94—21no—
104C2×Dic94C22×C412yes—
105C2×Dic94C22×C412yes—
106C2×Dic94#4114yes—
107C2×C8×C47—22no—
108C2×C8×C47—22no—
109C2×C8×C47—22no—
110C2×C8×C47—22no—
111C2×C8×C47—22no—
112C2×C8×C47C22×C412yes—
113C2×C8×C47C22×C412yes—
114C42×C47—22no—
115C42×C47—22no—
116C42×C47C22×C412yes—
117C42×C47#4112yes—
118C4⋊Dic47—21no—
119C4⋊Dic47—21no—
120C4⋊Dic47—22no—
121C4⋊Dic47—22no—
122C4⋊Dic47—22no—
123C4⋊Dic47C22×C412yes—
124C4⋊Dic47C22×C412yes—
125C4⋊Dic47#4114yes—
126Dic47⋊C4—28no—
127Dic47⋊C4—24no—
128Dic47⋊C4—24no—
129Dic47⋊C4—82no—
130C4×Dic47—28no—
131C4×Dic47—24no—
132C4×Dic47—24no—
133C4×Dic47—81no—
134C4×Dic47—82no—
135C4×Dic47—81no—
136Dic188—28no—
137C23×C47C22×D411yescharacteristic
138C2×C4×C47—21no—
139C2×C4×C47—22no—
140C2×C4×C47—21no—
141C2×C4×C47—22no—
142C2×C4×C47—22no—
143C2×C4×C47—22no—
144C2×C4×C47—22no—
145C2×C4×C47—22no—
146C2×C4×C47—22no—
147C2×C4×C47C4×D412yes—
148C2×C4×C47C4×D412yes—
149C2×C4×C47C23×C411yescharacteristic
150C2×C4×C47C2×#4112yes—
151C2×C4×C47C2×#4112yes—
152C2×C4×C47C2×#4111yescharacteristic
153C2×Dic47—22no—
154C2×Dic47—24no—
155C2×Dic47—22no—
156C2×Dic47—22no—
157C2×Dic47—22no—
158C2×Dic47—24no—
159C2×Dic47—42no—
160C2×Dic47—42no—
161C2×Dic47—41no—
162C2×Dic47—41no—
163C2×Dic47—42no—
164C2×Dic47—41no—
165C2×Dic47—41no—
166C2×Dic47—42no—
167C2×Dic47—42no—
168C2×Dic47—42no—
169Dic94—22no—
170Dic94—24no—
171Dic94—22no—
172Dic94—22no—
173Dic94—42no—
174Dic94#11714yes—
175C8×C47—22no—
176C8×C47—22no—
177C8×C47—42no—
178#21135—471nomaximal, Sylow
179C22×C47C2×C4×D411yescharacteristic
180C22×C47#52512yes—
181C22×C47#57611yescharacteristic
182C22×C47#57812yes—
183C22×C47#57811yescharacteristic
184C4×C47—22no—
185C4×C47—22no—
186C4×C47—42no—
187C4×C47—42no—
188C4×C47C2×#11711yescharacteristic
189C4×C47C4×#4111yescharacteristic
190C4×C47#52912yes—
191Dic47—24no—
192Dic47—44no—
193Dic47—42no—
194Dic47—42no—
195Dic47—42no—
196Dic47—82no—
197C2×C4×Q16—471no—
198#2320—471no—
199#2276—471no—
200#1928—472no—
201#1918—472no—
202#1878—472no—
203#1863—472no—
204C4×#107—471no—
205#1763—471no—
206#1763—471no—
207#1746D4711yescharacteristic
208C2×C47#229011yescharacteristic
209C2×C47#295011yescharacteristic
210C2×C47#295111yescharacteristic
211C2×C47#312412yes—
212C2×C47#312712yes—
213C22×Q16—471no—
214C2×C4×Q8—471no—
215C2×C4×Q8—471no—
216C2×C4×Q8—472no—
217C4×Q16—478no—
218C2×#107—471no—
219C2×#107—472no—
220C2×#103—471no—
221C2×#103—471no—
222C2×#103—472no—
223C2×#103—472no—
224C2×#97C2×D4711yescharacteristic
225C2×C4×C8C2×D4711yescharacteristic
226#391—472no—
227#389—472no—
228#387—942no—
229#383—941no—
230#382—941no—
231C4×C4⋊C4—471no—
232C4×C4⋊C4—472no—
233C4×C4⋊C4—471no—
234C4×C4⋊C4—941no—
235C4×C4⋊C4—942no—
236#376—941no—
237#376C2×D4711yescharacteristic
238#340—472no—
239#340—472no—
240#340—472no—
241#336C2×D4712yes—
242#336C2×D4712yes—
243C47#2113511yescharacteristic, complemented, Sylow
244C22×Q8—471no—
245C22×Q8—471no—
246C2×Q16—474no—
247C2×Q16—944no—
248C22×C8C22×D4712yes—
249C22×C8C22×D4711yescharacteristic
250C22×C8C22×D4711yescharacteristic
251C4×Q8—474no—
252C4×Q8—474no—
253C4×Q8—944no—
254C4×Q8—944no—
255C4×Q8—942no—
256C4×Q8—942no—
257C2×C4⋊C4—471no—
258C2×C4⋊C4—472no—
259C2×C4⋊C4—471no—
260C2×C4⋊C4—472no—
261C2×C4⋊C4—942no—
262C2×C4⋊C4—941no—
263C2×C4⋊C4—941no—
264C2×C4⋊C4—942no—
265C2×C42—942no—
266C2×C42—941no—
267C2×C42—941no—
268C2×C42—942no—
269C2×C42—941no—
270C2×C42—941no—
271C2×C42C22×D4712yes—
272C2×C42C22×D4711yescharacteristic
273#107—474no—
274#107—944no—
275#103—474no—
276#103—474no—
277#103—944no—
278#103—944no—
279#97—22no—
280C4×C8C4×D4714yes—
281#95—942no—
282#95—941no—
283#95—941no—
284#95—942no—
285#95—942no—
286#95—942no—
287#95D18811yescharacteristic
288#95D18811yescharacteristic
289#95D18812yes—
290C2×Q8—472no—
291C2×Q8—472no—
292C2×Q8—474no—
293C2×Q8—942no—
294C2×Q8—941no—
295C2×Q8—941no—
296C2×Q8—942no—
297C2×Q8—942no—
298C22×C4—941no—
299C22×C4—941no—
300C22×C4—941no—
301C22×C4—942no—
302C22×C4—941no—
303C22×C4—942no—
304C22×C4C2×D18812yes—
305C22×C4C2×D18812yes—
306C22×C4C2×D18811yescharacteristic
307C22×C4C2×D18811yescharacteristic
308C22×C4C23×D4711yescharacteristic
309Q16—948no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8C2×C4×D4712yes—
316C2×C8C2×C4×D4712yes—
317C4⋊C4—472no—
318C4⋊C4—472no—
319C4⋊C4—474no—
320C4⋊C4—948no—
321C4⋊C4—944no—
322C4⋊C4—944no—
323C4⋊C4—942no—
324C4⋊C4—941no—
325C4⋊C4—941no—
326C4⋊C4—942no—
327C4⋊C4—942no—
328C4⋊C4—3762no—
329C42—22no—
330C42—22no—
331C42—948no—
332C42—944no—
333C42—944no—
334C42—3761no—
335C42—3761no—
336C42—3762no—
337C42C2×C4×D4712yes—
338C42#1062535012yes—
339C23C22×D18811yescharacteristic
340Q8—474no—
341Q8—942no—
342Q8—944no—
343Q8—942no—
344Q8—942no—
345Q8—1882no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—942no—
356C2×C4—944no—
357C2×C4—942no—
358C2×C4—942no—
359C2×C4—942no—
360C2×C4—944no—
361C2×C4—1882no—
362C2×C4—1882no—
363C2×C4—1882no—
364C2×C4—1882no—
365C2×C4—1881no—
366C2×C4—1882no—
367C2×C4—1881no—
368C2×C4—1881no—
369C2×C4—1881no—
370C2×C4—1882no—
371C2×C4C4×D18812yes—
372C2×C4C4×D18812yes—
373C2×C4C22×C4×D4711yescharacteristic
374C2×C4#41×D4712yes—
375C2×C4#41×D4712yes—
376C2×C4C2×#1062535011yescharacteristic
377C8—22no—
378C8—22no—
379C8—42no—
380C22C2×C4×D18811yescharacteristic
381C22#1568963512yes—
382C22#1568992811yescharacteristic
383C22#1568994012yes—
384C22#1568994011yescharacteristic
385C4—22no—
386C4—22no—
387C4—42no—
388C4—42no—
389C4—944no—
390C4—3762no—
391C4—1882no—
392C4—1882no—
393C4—1882no—
394C4—1884no—
395C4#117×D4711yescharacteristic
396C4#1568959111yescharacteristic
397C4#1568965112yes—
398C2#2024583211yescharacteristic
399C2#2025225711yescharacteristic
400C2#2025226511yescharacteristic
401C2#2025365212yes—
402C2#2025368912yes—
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1746C2
socle, prime radicalC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenter#1746D47
hypocenterC47#21135
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #1746

Complements

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

NH ≅ G/Ntype
16. C4×Dic188C4semidirect
243. C47#21135semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic1882
#202460402
#202457512
#202440302
#202439602
#202437282
#202436452
C4×#130939582
#202432192
C47×#17462
#2113547