Finite Group Databasebeta

← #26134455

Subgroups — #26134455

Order 12032.

438 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689238C211yesmaximal, characteristic
2C2×#15688943C211yesmaximal, characteristic, complemented
3C2×#15688908C211yesmaximal, characteristic, complemented
4C2×#15688907C211yesmaximal, characteristic, complemented
5#20245001C211yesmaximal, characteristic, complemented
6C2×C16×Dic47C211yesmaximal, characteristic, complemented
7C47×#2113C211yesmaximal, characteristic, complemented
8C2×#13094044C411yescharacteristic
9C2×#13094030C2211yescharacteristic
10C2×#13093964C2211yescharacteristic
11C22×C47⋊C16C2211yescharacteristic
12#15689238—22no—
13#15689238—22no—
14C2×#13093959C411yescharacteristic
15C2×#13093951C411yescharacteristic
16C2×#13093950C411yescharacteristic
17C2×C8×Dic47C2211yescharacteristic
18#15688943—22no—
19#15688908—22no—
20#15688907—22no—
21(C2×D47)⋊C16—22no—
22C16×Dic47—22no—
23C2×#131×C47C2211yescharacteristic
24C2×M32×C47C2211yescharacteristic
25C22×C16×C47C2211yescharacteristic
26C47×C22⋊C16—22no—
27C2×#10625350C2×C411yescharacteristic
28#13094044—22no—
29#13094044—22no—
30C2×#10625337C811yescharacteristic
31C2×#10625335C811yescharacteristic
32C2×#10625336C811yescharacteristic
33C2×#10625334C811yescharacteristic
34#13094030—21no—
35#13094030—21no—
36#13094030—21no—
37#13094030—21no—
38C2×#10625329C2×C411yescharacteristic
39C2×#10625324—21no—
40C22×C47⋊C8C2×C411yescharacteristic
41C2×C8×D47—21no—
42C2×C4×Dic47C2×C411yescharacteristic
43#13093964—21no—
44#13093964—21no—
45C2×C47⋊C16—21no—
46C2×C47⋊C16—21no—
47C2×C47⋊C16—21no—
48C2×C47⋊C16D412yes—
49#13093959—22no—
50#13093951—22no—
51#13093950—22no—
52C8×Dic47D412yes—
53C8×Dic47D412yes—
54C2×#41×C47C2×C411yescharacteristic
55#131×C47—21no—
56#131×C47—21no—
57#131×C47—21no—
58#131×C47—21no—
59C2×M16×C47—21no—
60C2×M16×C47C2×C411yescharacteristic
61C22×C8×C47—21no—
62C22×C8×C47C2311yescharacteristic
63M32×C47—21no—
64M32×C47—21no—
65C2×C16×C47—21no—
66C2×C16×C47—21no—
67C2×C16×C47—21no—
68C2×C16×C47D412yes—
69#41×C47—21no—
70#41×C47—21no—
71#41×C47—21no—
72#41×C47—21no—
73C2×Q8×C47C2×C811yescharacteristic
74C2×D4×C47—21no—
75C2×D4×C47C2×C811yescharacteristic
76C22×C4×C47—21no—
77C22×C4×C47C22×C411yescharacteristic
78C2×C22⋊D47—21no—
79C22×Dic47—21no—
80#10625350—21no—
81#10625350—21no—
82#10625350—21no—
83#10625350—21no—
84C2×D188C2×C811yescharacteristic
85C2×C4×D47—21no—
86C2×Dic94C2×C811yescharacteristic
87M16×C47—21no—
88M16×C47—21no—
89M16×C47—41no—
90M16×C47—41no—
91C2×C8×C47—21no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47C2×D411yescharacteristic
98C2×C8×C47#4111yescharacteristic
99C2×C8×C47#4111yescharacteristic
100#10625337—22no—
101#10625336—22no—
102#10625335—22no—
103#10625334—22no—
104C4×Dic47—21no—
105C4×Dic47C22⋊C412yes—
106#10625329—21no—
107#10625329—21no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8C22⋊C412yes—
110C2×C47⋊C8C2×C811yescharacteristic
111C2×C47⋊C8C2×C811yescharacteristic
112C2×C47⋊C8M1612yes—
113#10625324—41no—
114#10625324—41no—
115C8×D47—41no—
116C8×D47—41no—
117C16×C47—22no—
118C16×C47—41no—
119C47⋊C16—22no—
120C47⋊C16—41no—
121C23×C47—21no—
122C23×C47#13111yescharacteristic
123C22×D47—21no—
124Q8×C47—21no—
125Q8×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—41no—
129D4×C47—41no—
130C2×C4×C47—21no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47C2×C22⋊C411yescharacteristic
134C2×C4×C47C4×D411yescharacteristic
135C2×C4×C47C4×D411yescharacteristic
136C2×C4×C47C22×C811yescharacteristic
137C2×C4×C47C2×M1611yescharacteristic
138C2×C4×C47#13111yescharacteristic
139C22⋊D47—41no—
140C22⋊D47—41no—
141C2×Dic47—24no—
142C2×Dic47—22no—
143C2×Dic47—21no—
144D188—21no—
145D188—21no—
146C4×D47—41no—
147C4×D47—41no—
148Dic94—21no—
149Dic94—21no—
150C8×C47—41no—
151C8×C47#12111yescharacteristic
152C8×C47#12111yescharacteristic
153C8×C47#12411yescharacteristic
154C8×C47#12711yescharacteristic
155C47⋊C8—41no—
156C47⋊C8C22⋊C812yes—
157C47⋊C8C22⋊C812yes—
158#13195—471nomaximal, Sylow
159C22×C47—22no—
160C22×C47—42no—
161C22×C47—41no—
162C22×C47#40811yescharacteristic
163C22×C47C8×D411yescharacteristic
164C22×C47#43611yescharacteristic
165C2×D47—42no—
166C2×D47—41no—
167C4×C47—41no—
168C4×C47#39011yescharacteristic
169C4×C47C2×C22⋊C811yescharacteristic
170C4×C47C8×D411yescharacteristic
171C4×C47#43611yescharacteristic
172Dic47—24no—
173Dic47—41no—
174C2×#443—471no—
175C2×#364—471no—
176C2×#350—471no—
177C2×#350—471no—
178#2113—471no—
179#2113D4711yescharacteristic, complemented
180C2×C4×C16—471no—
181C2×C47—21no—
182C2×C47—21no—
183C2×C47—81no—
184C2×C47#195411yescharacteristic
185C2×C47#217012yes—
186D47—81no—
187C2×#135—471no—
188C2×#131—471no—
189C2×#131C2×D4711yescharacteristic
190C2×M32—471no—
191C2×M32C2×D4711yescharacteristic
192C22×C16—471no—
193C22×C16C2×D4711yescharacteristic
194#443—942no—
195#443—942no—
196C2×#108—471no—
197C2×#104—471no—
198C2×#104—471no—
199C2×C4×C8—471no—
200#364—942no—
201#350—942no—
202#350—942no—
203C22⋊C16—22no—
204C22⋊C16—942no—
205C4×C16—942no—
206C47#1319511yescharacteristic, complemented, Sylow
207C2×#41—471no—
208C2×#41C4×D4711yescharacteristic
209#135—942no—
210#135—942no—
211C2×Q16—471no—
212C2×SD16—471no—
213C2×SD16—471no—
214C2×D8—471no—
215#131—21no—
216#131—21no—
217#131—21no—
218#131—21no—
219#131—941no—
220#131—941no—
221#131—941no—
222#131—941no—
223C2×M16—21no—
224C2×M16—471no—
225C2×M16—941no—
226C2×M16C4×D4711yescharacteristic
227C22×C8—21no—
228C22×C8—471no—
229C22×C8—941no—
230C22×C8C22×D4711yescharacteristic
231C2×C42—471no—
232M32—21no—
233M32—21no—
234M32—941no—
235M32—941no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—472no—
240C2×C16—941no—
241C2×C16—941no—
242C2×C16—941no—
243C2×C16C22⋊D4712yes—
244#108—942no—
245#104—942no—
246#104—942no—
247C4×C8—472no—
248C4×C8—472no—
249#41—21no—
250#41—21no—
251#41—21no—
252#41—21no—
253#41—941no—
254#41—941no—
255#41—941no—
256#41—941no—
257C2×Q8—471no—
258C2×Q8C8×D4711yescharacteristic
259C2×D4—21no—
260C2×D4—471no—
261C2×D4—941no—
262C2×D4C8×D4711yescharacteristic
263C22×C4—21no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4C2×C4×D4711yescharacteristic
267Q16—942no—
268SD16—942no—
269SD16—942no—
270D8—942no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—941no—
276M16—941no—
277M16—1881no—
278M16—1881no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—472no—
283C2×C8—471no—
284C2×C8—471no—
285C2×C8—472no—
286C2×C8—941no—
287C2×C8—1881no—
288C2×C8—1881no—
289C2×C8#1062535011yescharacteristic
290C2×C8D4×D4711yescharacteristic
291C2×C8D4×D4711yescharacteristic
292C2×C8D4×D4711yescharacteristic
293C2×C8#1062535211yescharacteristic
294C2×C8C2×C22⋊D4711yescharacteristic
295C42—472no—
296C42—941no—
297C16—22no—
298C16—41no—
299C16—942no—
300C16—1881no—
301C23—21no—
302C23—941no—
303C23#1309403011yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—941no—
307Q8—941no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—941no—
313D4—941no—
314D4—1881no—
315D4—1881no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—944no—
320C2×C4—942no—
321C2×C4—941no—
322C2×C4—1881no—
323C2×C4—1881no—
324C2×C4C22⋊C4×D4711yescharacteristic
325C2×C4(C22⋊D47)⋊C411yescharacteristic
326C2×C4C4×C22⋊D4711yescharacteristic
327C2×C4C2×C8×D4711yescharacteristic
328C2×C4M16×D4711yescharacteristic
329C2×C4#1309403211yescharacteristic
330C8—41no—
331C8—472no—
332C8—472no—
333C8—1881no—
334C8#1309399611yescharacteristic
335C8#1309399711yescharacteristic
336C8#1309401011yescharacteristic
337C8#1309402011yescharacteristic
338C22—22no—
339C22—41no—
340C22—42no—
341C22—1881no—
342C22—1882no—
343C22#1568908811yescharacteristic
344C22C8×C22⋊D4711yescharacteristic
345C22#1568919811yescharacteristic
346C4—41no—
347C4—944no—
348C4—1881no—
349C4#1568902311yescharacteristic
350C4C22⋊C8×D4711yescharacteristic
351C4(C22⋊D47)⋊C811yescharacteristic
352C4#1568919911yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2—3761no—
357C2#2024418011yescharacteristic
358C2#2024522312yes—
subgroupG/H
centerC2×C8C2×C22⋊D47
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#2113C2
socleC22×C47C8×D4
prime radicalC2×#13094044C4
cosocleC22×C8×C47C23
hypercenter#2113D47
hypocenterC47#13195
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ #2113

Complements

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

NH ≅ G/Ntype
2. C2×#15688943C2semidirect
3. C2×#15688908C2semidirect
4. C2×#15688907C2semidirect
5. #20245001C2semidirect
6. C2×C16×Dic47C2semidirect
7. C47×#2113C2semidirect
179. #2113D47semidirect
206. C47#13195semidirect

Maximal subgroups

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

subgroupindex
C2×#156892382
C2×#156889432
C2×#156889082
C2×#156889072
#202450012
C2×C16×Dic472
C47×#21132
#1319547