Finite Group Databasebeta

← #26110626

Subgroups — #26110626

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
1M16×Dic94C211yesmaximal, characteristic
2#20242143C211yesmaximal, characteristic
3#20241816C211yesmaximal, characteristic
4C2×#15688853C211yesmaximal, characteristic
5#20241285C211yesmaximal, characteristic
6#20241226C211yesmaximal, characteristic
7C47×#1950C211yesmaximal, characteristic
8C2×C4×Dic94C2211yescharacteristic
9#15689253—21no—
10#15689251—22no—
11C8×Dic94—21no—
12#15689176C2211yescharacteristic
13#15689147C2211yescharacteristic
14#15689146—21no—
15M16×Dic47—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17#15688873—22no—
18#15688853—21no—
19#15688853—21no—
20#15688853C411yescharacteristic
21#15688853C411yescharacteristic
22#15688853C411yescharacteristic
23#15688853C411yescharacteristic
24C2×#108×C47—21no—
25C47×#423C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C4×M16×C47C2211yescharacteristic
28C47×#341—21no—
29C22×Dic94Q811yescharacteristic
30C2×#10625329—21no—
31C22×C47⋊C8—21no—
32C4×Dic94—21no—
33C4×Dic94—21no—
34C4×Dic94C2×C411yescharacteristic
35C4×Dic94C2×C411yescharacteristic
36C4×Dic94D411yescharacteristic
37C4×Dic94D411yescharacteristic
38C2×C4⋊Dic47Q811yescharacteristic
39C2×Dic47⋊C4—21no—
40C2×C4×Dic47—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)D412yes—
44Dic47⋊C8—22no—
45Dic47⋊C8—22no—
46C22⋊(C47⋊C8)—21no—
47#13093934—22no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8—21no—
50C4×C47⋊C8C2×C411yescharacteristic
51C4×C47⋊C8C2×C411yescharacteristic
52C8×Dic47—22no—
53C2×M16×C47—21no—
54C2×M16×C47D411yescharacteristic
55C2×M16×C47D411yescharacteristic
56C22×C8×C47—21no—
57C2×C42×C47C2311yescharacteristic
58#108×C47—42no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47C2×C411yescharacteristic
63C4⋊C8×C47C2×C411yescharacteristic
64#97×C47—21no—
65C4×C8×C47—21no—
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×Q811yescharacteristic
68C22×C4×C47#4111yescharacteristic
69C22×Dic47—21no—
70C22×Dic47—21no—
71C2×Dic94—22no—
72C2×Dic94—21no—
73C2×Dic94—41no—
74C2×Dic94C4⋊C411yescharacteristic
75C2×Dic94C4⋊C411yescharacteristic
76M16×C47—21no—
77M16×C47—21no—
78M16×C47—21no—
79M16×C47—41no—
80M16×C47—41no—
81M16×C47SD1612yes—
82C2×C8×C47—21no—
83C2×C8×C47—21no—
84C2×C8×C47—21no—
85C2×C8×C47—21no—
86C2×C8×C47—41no—
87C2×C8×C47—41no—
88C2×C8×C47—41no—
89C42×C47C22×C411yescharacteristic
90C42×C47C2×D411yescharacteristic
91C42×C47C2×D411yescharacteristic
92C42×C47#4111yescharacteristic
93C4⋊Dic47—21no—
94C4⋊Dic47C4⋊C411yescharacteristic
95C4⋊Dic47C4⋊C411yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104#10625329—41no—
105#10625329—41no—
106C2×C47⋊C8—21no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—22no—
109C2×C47⋊C8—42no—
110C2×C47⋊C8—41no—
111C23×C47C22⋊Q811yescharacteristic
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—41no—
115C2×C4×C47C2×C4⋊C411yescharacteristic
116C2×C4×C47C4×D411yescharacteristic
117C2×C4×C47C4×D411yescharacteristic
118C2×C4×C47#12011yescharacteristic
119C2×C4×C47C22⋊Q811yescharacteristic
120C2×C4×C47#12311yescharacteristic
121C2×C4×C47C2×SD1611yescharacteristic
122C2×C4×C47#13511yescharacteristic
123C2×C4×C47#13711yescharacteristic
124C2×C4×C47#13711yescharacteristic
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—42no—
130C2×Dic47—81no—
131Dic94—21no—
132Dic94—21no—
133Dic94—21no—
134Dic94—42no—
135Dic94#10812yescomplemented
136C8×C47—22no—
137C8×C47—41no—
138C8×C47—41no—
139C8×C47—41no—
140C8×C47—81no—
141C47⋊C8—22no—
142C47⋊C8—41no—
143C47⋊C8—42no—
144C47⋊C8—81no—
145#8909—471nomaximal, Sylow
146C22×C47—21no—
147C22×C47—21no—
148C22×C47#38511yescharacteristic
149C22×C47#47511yescharacteristic
150C22×C47#47911yescharacteristic
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47C2×#10811yescharacteristic
155C4×C47#43011yescharacteristic
156C4×C47C4×SD1611yescharacteristic
157C4×C47#44111yescharacteristic
158C4×C47#44811yescharacteristic
159C4×C47#45211yescharacteristic
160Dic47—22no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Q8×M16—471no—
165#1950D4711yescharacteristic
166#1566—471no—
167#1487—471no—
168C2×Q8⋊C8—471no—
169#1301—471no—
170#1278—471no—
171C2×C47—21no—
172C2×C47—21no—
173C2×C47#185511yescharacteristic
174C2×C47#186111yescharacteristic
175C2×C47#186511yescharacteristic
176C2×C4×Q8—471no—
177#446—941no—
178#446—942no—
179C8×Q8—941no—
180#431—471no—
181C2×#108—21no—
182#423—471no—
183#423—941no—
184#423C2×D4711yescharacteristic
185C2×C4⋊C8C2×D4711yescharacteristic
186C4×M16—941no—
187C4×M16C2×D4711yescharacteristic
188C2×C4×C8—471no—
189#341—21no—
190#334—942no—
191Q8⋊C8—471no—
192Q8⋊C8—471no—
193Q8⋊C8—471no—
194Q8⋊C8—471no—
195Q8⋊C8—941no—
196Q8⋊C8—941no—
197C47#890911yescharacteristic, complemented, Sylow
198C22×Q8—471no—
199C2×M16—21no—
200C2×M16—941no—
201C2×M16C22⋊D4711yescharacteristic
202C2×M16C22⋊D4711yescharacteristic
203C22×C8—21no—
204C22×C8—941no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×Q8—471no—
209C4×Q8—941no—
210C4×Q8—941no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—941no—
213C2×C42—941no—
214C2×C42C22×D4711yescharacteristic
215#108—42no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—472no—
220C4⋊C8—942no—
221C4⋊C8—942no—
222C4⋊C8—941no—
223C4⋊C8—941no—
224C4⋊C8C4×D4711yescharacteristic
225C4⋊C8C4×D4711yescharacteristic
226C22⋊C8—941no—
227#97—21no—
228#97—942no—
229C4×C8—21no—
230C4×C8—471no—
231C4×C8—471no—
232C4×C8—942no—
233C4×C8—941no—
234C4×C8—941no—
235C2×Q8—471no—
236C2×Q8—471no—
237C2×Q8—942no—
238C2×Q8—941no—
239C2×Q8—1881no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4Q8×D4711yescharacteristic
243C22×C4#1062535411yescharacteristic
244C22×C4C2×C22⋊D4711yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—41no—
249M16—41no—
250M16—1881no—
251M16—1881no—
252M16#1062533512yes—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—941no—
261C2×C8—941no—
262C2×C8—942no—
263C2×C8—1882no—
264C2×C8—1881no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C42—941no—
273C42—941no—
274C42—941no—
275C42—941no—
276C42C2×C4×D4711yescharacteristic
277C42#1062535011yescharacteristic
278C42D4×D4711yescharacteristic
279C42D4×D4711yescharacteristic
280C23#1309400011yescharacteristic
281Q8—472no—
282Q8—941no—
283Q8—941no—
284Q8—941no—
285Q8—1882no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—3761no—
294C2×C4—1882no—
295C2×C4C4⋊C4×D4711yescharacteristic
296C2×C4C4×C22⋊D4711yescharacteristic
297C2×C4#1309398611yescharacteristic
298C2×C4#1309399211yescharacteristic
299C2×C4#1309400211yescharacteristic
300C2×C4#1309400911yescharacteristic
301C2×C4C2×#1062533511yescharacteristic
302C2×C4#1309404411yescharacteristic
303C2×C4#1309405411yescharacteristic
304C2×C4#1309405511yescharacteristic
305C8—22no—
306C8—41no—
307C8—41no—
308C8—41no—
309C8—81no—
310C8—942no—
311C8—3761no—
312C8—1881no—
313C8—1882no—
314C22—21no—
315C22—21no—
316C22#1568899411yescharacteristic
317C22#1568940511yescharacteristic
318C22#1568942711yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—942no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4#108×D4711yescharacteristic
327C4#1568917011yescharacteristic
328C4C4×#1062533511yescharacteristic
329C4#1568922811yescharacteristic
330C4#1568926111yescharacteristic
331C4#1568928311yescharacteristic
332C2—21no—
333C2—21no—
334C2#2024359111yescharacteristic
335C2#2024362511yescharacteristic
336C2#2024365511yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1950C2
socleC22×C47#385
prime radicalC23×C47C22⋊Q8
cosocleC2×C42×C47C23
hypercenter#1950D47
hypocenterC47#8909
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
135. Dic94#108semidirect
197. C47#8909semidirect

Maximal subgroups

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

subgroupindex
M16×Dic942
#202421432
#202418162
C2×#156888532
#202412852
#202412262
C47×#19502
#890947