Finite Group Databasebeta

← #26110615

Subgroups — #26110615

Order 12032.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10625329C211yesmaximal, characteristic
2#20244164C211yesmaximal, characteristic
3#20242147C211yesmaximal, characteristic
4#20241817C211yesmaximal, characteristic
5#20241285C211yesmaximal, characteristic
6#20241225C211yesmaximal, characteristic
7C2×C47×Q8⋊C8C211yesmaximal, characteristic
8#15689254—22no—
9#15689254—21no—
10Q8×C47⋊C8—21no—
11#15689176C2211yescharacteristic
12C2×#13093960—21no—
13#15689147—21no—
14#15689147C2211yescharacteristic
15#15689147C2211yescharacteristic
16C4×#10625329—21no—
17C4×#10625329C2211yescharacteristic
18#15688888—21no—
19#15688876—22no—
20Q8⋊(C47⋊C8)—21no—
21Q8⋊(C47⋊C8)—21no—
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4×C8×C47C2211yescharacteristic
25C47×Q8⋊C8C411yescharacteristic
26C47×Q8⋊C8C411yescharacteristic
27C47×Q8⋊C8C411yescharacteristic
28C47×Q8⋊C8C411yescharacteristic
29C2×#10625329—21no—
30C2×#10625329—21no—
31C2×#10625329D411yescharacteristic
32C2×#10625329D411yescharacteristic
33#13093960—42no—
34C4⋊(C47⋊C8)—22no—
35C4⋊(C47⋊C8)—22no—
36C4⋊(C47⋊C8)—21no—
37C4⋊(C47⋊C8)—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)D412yes—
41C22⋊(C47⋊C8)—21no—
42#13093935—22no—
43#13093935—21no—
44C4×C47⋊C8—22no—
45C4×C47⋊C8—21no—
46C4×C47⋊C8—21no—
47C22×Q8×C47Q811yescharacteristic
48C22×C8×C47—21no—
49C22×C8×C47—21no—
50C4×Q8×C47—21no—
51C4×Q8×C47—21no—
52C4×Q8×C47C2×C411yescharacteristic
53C4×Q8×C47C2×C411yescharacteristic
54C4×Q8×C47D411yescharacteristic
55C4×Q8×C47D411yescharacteristic
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47Q811yescharacteristic
58C2×C42×C47—21no—
59C2×C42×C47C2311yescharacteristic
60C4⋊C8×C47—21no—
61C4⋊C8×C47C2×C411yescharacteristic
62C4⋊C8×C47C2×C411yescharacteristic
63C4×C8×C47—21no—
64C4×C8×C47C2×C411yescharacteristic
65C4×C8×C47C2×C411yescharacteristic
66C2×Q8×C47—21no—
67C2×Q8×C47—22no—
68C2×Q8×C47—41no—
69C2×Q8×C47C4⋊C411yescharacteristic
70C2×Q8×C47C4⋊C411yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×Q811yescharacteristic
75C22×C4×C47#4111yescharacteristic
76C2×C8×C47—21no—
77C2×C8×C47—21no—
78C2×C8×C47—21no—
79C2×C8×C47—21no—
80C2×C8×C47—42no—
81C2×C8×C47—41no—
82C2×C8×C47—41no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47—21no—
85C4⋊C4×C47—21no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47C4⋊C411yescharacteristic
89C4⋊C4×C47C4⋊C411yescharacteristic
90C42×C47—21no—
91C42×C47—21no—
92C42×C47—21no—
93C42×C47—21no—
94C42×C47C22×C411yescharacteristic
95C42×C47C2×D411yescharacteristic
96C42×C47C2×D411yescharacteristic
97C42×C47#4111yescharacteristic
98#10625329—21no—
99#10625329—21no—
100#10625329—21no—
101#10625329—41no—
102#10625329—41no—
103#10625329—41no—
104#10625329—41no—
105#10625329Q1612yes—
106C2×C47⋊C8—21no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—22no—
109C2×C47⋊C8—41no—
110C2×C47⋊C8—41no—
111C23×C47C22⋊Q811yescharacteristic
112Q8×C47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—42no—
116Q8×C47#10812yescomplemented
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—41no—
124C2×C4×C47—42no—
125C2×C4×C47—81no—
126C2×C4×C47C2×C4⋊C411yescharacteristic
127C2×C4×C47C4×D411yescharacteristic
128C2×C4×C47C4×D411yescharacteristic
129C2×C4×C47#12011yescharacteristic
130C2×C4×C47C22⋊Q811yescharacteristic
131C2×C4×C47#12311yescharacteristic
132C2×C4×C47C2×Q1611yescharacteristic
133C2×C4×C47#13511yescharacteristic
134C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C47#13711yescharacteristic
136C8×C47—22no—
137C8×C47—41no—
138C8×C47—41no—
139C8×C47—41no—
140C47⋊C8—22no—
141C47⋊C8—41no—
142C47⋊C8—42no—
143C47⋊C8—81no—
144C47⋊C8—81no—
145#8907—471nomaximal, Sylow
146C22×C47—21no—
147C22×C47—21no—
148C22×C47#38511yescharacteristic
149C22×C47#47711yescharacteristic
150C22×C47#47911yescharacteristic
151C4×C47—21no—
152C4×C47—22no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C2×#10811yescharacteristic
159C4×C47#43011yescharacteristic
160C4×C47C4×Q1611yescharacteristic
161C4×C47#44011yescharacteristic
162C4×C47#44911yescharacteristic
163C4×C47#45111yescharacteristic
164Q8×M16—471no—
165#1950—471no—
166#1567—471no—
167#1487—471no—
168C2×Q8⋊C8D4711yescharacteristic
169#1301—471no—
170#1278—471no—
171C2×C47—21no—
172C2×C47—21no—
173C2×C47#185511yescharacteristic
174C2×C47#186111yescharacteristic
175C2×C47#186311yescharacteristic
176C2×C4×Q8C2×D4711yescharacteristic
177#446—942no—
178#446—941no—
179C8×Q8—941no—
180#431—471no—
181C2×#108—941no—
182#423—471no—
183#423—471no—
184#423—941no—
185C2×C4⋊C8C2×D4711yescharacteristic
186C4×M16—471no—
187C4×M16—941no—
188C2×C4×C8C2×D4711yescharacteristic
189#341—941no—
190#335—942no—
191Q8⋊C8—941no—
192Q8⋊C8—941no—
193Q8⋊C8Dic4711yescharacteristic
194Q8⋊C8Dic4711yescharacteristic
195Q8⋊C8Dic4711yescharacteristic
196Q8⋊C8Dic4711yescharacteristic
197C47#890711yescharacteristic, complemented, Sylow
198C22×Q8Dic9411yescharacteristic
199C2×M16—471no—
200C2×M16—471no—
201C2×M16—941no—
202C2×M16—941no—
203C22×C8—21no—
204C22×C8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8D18811yescharacteristic
208C4×Q8D18811yescharacteristic
209C4×Q8C2×Dic4711yescharacteristic
210C4×Q8C2×Dic4711yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4Dic9411yescharacteristic
213C2×C42—21no—
214C2×C42C22×D4711yescharacteristic
215#108—1882no—
216C4⋊C8—21no—
217C4⋊C8—472no—
218C4⋊C8—942no—
219C4⋊C8—942no—
220C4⋊C8—941no—
221C4⋊C8—941no—
222C4⋊C8—941no—
223C4⋊C8—941no—
224C4⋊C8C2×Dic4711yescharacteristic
225C4⋊C8C2×Dic4711yescharacteristic
226C22⋊C8—941no—
227#97—942no—
228#97—941no—
229C4×C8—21no—
230C4×C8—942no—
231C4×C8—941no—
232C4×C8—941no—
233C4×C8C2×Dic4711yescharacteristic
234C4×C8C2×Dic4711yescharacteristic
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8C4⋊Dic4711yescharacteristic
239C2×Q8C4⋊Dic4711yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic9411yescharacteristic
243C22×C4D4×D4711yescharacteristic
244C22×C4#1062535211yescharacteristic
245M16—472no—
246M16—941no—
247M16—941no—
248M16—941no—
249M16—1881no—
250M16—1881no—
251M16—1881no—
252M16—1881no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—941no—
261C2×C8—942no—
262C2×C8—941no—
263C2×C8—1881no—
264C2×C8—1881no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4C4⋊Dic4711yescharacteristic
271C4⋊C4C4⋊Dic4711yescharacteristic
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42C2×D18811yescharacteristic
277C42D4×D4711yescharacteristic
278C42#1062535211yescharacteristic
279C42C22×Dic4711yescharacteristic
280C23#1309400111yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8#1309396012yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4C2×C4⋊Dic4711yescharacteristic
296C2×C4D4×Dic4711yescharacteristic
297C2×C4D4×Dic4711yescharacteristic
298C2×C4#1309399411yescharacteristic
299C2×C4#1309400111yescharacteristic
300C2×C4#1309400811yescharacteristic
301C2×C4Q16×D4711yescharacteristic
302C2×C4#1309404711yescharacteristic
303C2×C4#1309405111yescharacteristic
304C2×C4#1309405311yescharacteristic
305C8—22no—
306C8—41no—
307C8—41no—
308C8—41no—
309C8—942no—
310C8—3761no—
311C8—3761no—
312C8—1881no—
313C8—1882no—
314C22—21no—
315C22—21no—
316C22#1568899811yescharacteristic
317C22#1568941611yescharacteristic
318C22#1568943211yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4C2×#1309396011yescharacteristic
327C4#1568917211yescharacteristic
328C4Q16×Dic4711yescharacteristic
329C4#1568922411yescharacteristic
330C4#1568927111yescharacteristic
331C4#1568928011yescharacteristic
332C2—21no—
333C2—21no—
334C2#2024359511yescharacteristic
335C2#2024363011yescharacteristic
336C2#2024364411yescharacteristic
subgroupG/H
centerC2×C4#13093994
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×Q8⋊C8C2
socleC22×C47#385
prime radicalC23×C47C22⋊Q8
cosocleC2×C42×C47C23
hypercenterC2×Q8⋊C8D47
hypocenterC47#8907
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
116. Q8×C47#108semidirect
197. C47#8907semidirect
285. Q8#13093960semidirect

Maximal subgroups

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

subgroupindex
Q8×#106253292
#202441642
#202421472
#202418172
#202412852
#202412252
C2×C47×Q8⋊C82
#890747