Finite Group Databasebeta

← #26133154

Subgroups — #26133154

Order 12032.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689539C211yesmaximal, characteristic, complemented
2C2×#15689241C211yesmaximal, characteristic
3C2×#15688906C211yesmaximal, characteristic, complemented
4C2×#15688906C211yesmaximal, characteristic, complemented
5#20245001C211yesmaximal, characteristic, complemented
6#20241470C211yesmaximal, characteristic, complemented
7C47×#1374C211yesmaximal, characteristic, complemented
8C2×#13094046C411yescharacteristic
9C2×#13094030C2211yescharacteristic
10C2×#13094030C2211yescharacteristic
11#15689539—22no—
12#15689539—22no—
13C2×#13093964C2211yescharacteristic
14C2×#13093964C2211yescharacteristic
15C2×#13093963—21no—
16C2×C16×D47—21no—
17#15689241—22no—
18#15689241—22no—
19C2×#13093960C411yescharacteristic
20C2×#13093952C411yescharacteristic
21C2×#13093952C411yescharacteristic
22#15688906—22no—
23#15688906—22no—
24(C2×D47)⋊C16—21no—
25(C2×D47)⋊C16—21no—
26C22×C16×C47C2211yescharacteristic
27C22×C16×C47C2211yescharacteristic
28C2×C4×C8×C47C2211yescharacteristic
29C2×#10625350C2×C411yescharacteristic
30C2×#10625350C2×C411yescharacteristic
31#13094046—22no—
32#13094046—22no—
33C2×Dic188C811yescharacteristic
34C2×#10625325C811yescharacteristic
35C2×#10625325C811yescharacteristic
36C2×D376C811yescharacteristic
37#13094030—21no—
38#13094030—21no—
39#13094030—21no—
40#13094030—21no—
41#13094030—21no—
42#13094030—21no—
43#13094030D412yes—
44#13094030D412yes—
45C2×#10625329C2×C411yescharacteristic
46C2×#10625329C2×C411yescharacteristic
47C2×#10625324—21no—
48C2×#10625324—21no—
49C2×C8×D47—21no—
50C2×C8×D47—21no—
51#13093964—21no—
52#13093964—21no—
53#13093964—21no—
54#13093964D412yes—
55#13093963—24no—
56C2×C47⋊C16—21no—
57C2×C47⋊C16—21no—
58C16×D47—24no—
59#13093960—22no—
60#13093952—22no—
61#13093952—22no—
62C22×C8×C47C2×C411yescharacteristic
63C22×C8×C47C2311yescharacteristic
64C2×C42×C47C2×C411yescharacteristic
65C2×C16×C47—21no—
66C2×C16×C47—21no—
67C2×C16×C47—21no—
68C2×C16×C47—21no—
69C2×C16×C47—21no—
70C2×C16×C47D411yescharacteristic
71C2×C16×C47D411yescharacteristic
72C4×C8×C47—21no—
73C4×C8×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47C22×C411yescharacteristic
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78#10625350—21no—
79#10625350—21no—
80#10625350—21no—
81#10625350—21no—
82#10625350—21no—
83#10625350—21no—
84#10625350C22⋊C412yes—
85#10625350M1612yes—
86C2×D188C2×C811yescharacteristic
87C2×D188C2×C811yescharacteristic
88C2×C4×D47—21no—
89C2×C4×D47—21no—
90C2×Dic94C2×C811yescharacteristic
91C2×Dic94C2×C811yescharacteristic
92C2×C8×C47—21no—
93C2×C8×C47—21no—
94C2×C8×C47C2×C811yescharacteristic
95C2×C8×C47C2×C811yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47C2×D411yescharacteristic
98C2×C8×C47C2×D411yescharacteristic
99C2×C8×C47C2×D411yescharacteristic
100C2×C8×C47#4111yescharacteristic
101C2×C8×C47#4111yescharacteristic
102C42×C47—21no—
103C42×C47—21no—
104#10625329—21no—
105#10625329—21no—
106#10625329—21no—
107#10625329C22⋊C412yes—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110Dic188—22no—
111D376—22no—
112#10625325—22no—
113#10625325—22no—
114#10625324—22no—
115#10625324—22no—
116#10625324—41no—
117#10625324—41no—
118C8×D47—22no—
119C8×D47—22no—
120C8×D47—41no—
121C8×D47—41no—
122C16×C47—21no—
123C16×C47—21no—
124C16×C47—41no—
125C47⋊C16—22no—
126C47⋊C16—41no—
127C23×C47#13111yescharacteristic
128C22×D47—21no—
129C22×D47—21no—
130C2×C4×C47—22no—
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—22no—
140C22⋊D47—22no—
141C22⋊D47—41no—
142C22⋊D47—41no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145D188—21no—
146D188—21no—
147D188—21no—
148D188C22⋊C812yes—
149C4×D47—22no—
150C4×D47—22no—
151C4×D47—41no—
152C4×D47—41no—
153Dic94—21no—
154Dic94—21no—
155Dic94—21no—
156Dic94C22⋊C812yes—
157C8×C47—21no—
158C8×C47—21no—
159C8×C47#12011yescharacteristic
160C8×C47#12111yescharacteristic
161C8×C47#12111yescharacteristic
162C8×C47#12311yescharacteristic
163C47⋊C8—22no—
164C47⋊C8—41no—
165#12980—471nomaximal, Sylow
166C22×C47—21no—
167C22×C47—21no—
168C22×C47#40811yescharacteristic
169C22×C47C8×D411yescharacteristic
170C22×C47#43511yescharacteristic
171C2×D47—22no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C4×C47—42no—
178C4×C47#38611yescharacteristic
179C4×C47C2×C22⋊C811yescharacteristic
180C4×C47C8×D411yescharacteristic
181C4×C47#43511yescharacteristic
182Dic47—22no—
183Dic47—41no—
184C2×#504—471no—
185C2×#443—471no—
186C2×#350—471no—
187C2×#350—471no—
188#2113—471no—
189#1376—471no—
190#1374D4711yescharacteristic, complemented
191C2×C47—21no—
192C2×C47—21no—
193C2×C47#186911yescharacteristic
194C2×C47#217011yescharacteristic
195C2×C47#217111yescharacteristic
196D47—42no—
197D47—81no—
198C2×#135—471no—
199C2×#131—471no—
200C2×#131—471no—
201#504—942no—
202#504—942no—
203C2×M32—471no—
204C2×M32—471no—
205C2×M32—941no—
206C22×C16—941no—
207C22×C16C2×D4711yescharacteristic
208C22×C16C2×D4711yescharacteristic
209#443—942no—
210#443—942no—
211C2×#108—471no—
212C2×#104—471no—
213C2×#104—471no—
214C2×C4×C8C2×D4711yescharacteristic
215#350—942no—
216#350—942no—
217C22⋊C16—941no—
218C22⋊C16—941no—
219C47#1298011yescharacteristic, complemented, Sylow
220C2×#41—471no—
221C2×#41—471no—
222#135—942no—
223#135—942no—
224C2×Q16—471no—
225C2×SD16—471no—
226C2×SD16—471no—
227C2×D8—471no—
228#131—472no—
229#131—472no—
230#131—941no—
231#131—941no—
232#131—941no—
233#131—941no—
234#131—941no—
235#131—941no—
236C2×M16—471no—
237C2×M16—471no—
238C2×M16—941no—
239C2×M16—941no—
240C22×C8—941no—
241C22×C8—941no—
242C22×C8C4×D4711yescharacteristic
243C22×C8C22×D4711yescharacteristic
244C2×C42C4×D4711yescharacteristic
245M32—472no—
246M32—944no—
247M32—941no—
248M32—941no—
249M32—941no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—21no—
253C2×C16—21no—
254C2×C16—21no—
255C2×C16—944no—
256C2×C16—941no—
257C2×C16—941no—
258C2×C16D18811yescharacteristic
259C2×C16D18811yescharacteristic
260#108—942no—
261#104—942no—
262#104—942no—
263C4×C8—21no—
264C4×C8—21no—
265#41—472no—
266#41—472no—
267#41—941no—
268#41—941no—
269#41—941no—
270#41—941no—
271#41—941no—
272#41—941no—
273C2×Q8—471no—
274C2×Q8—471no—
275C2×D4—471no—
276C2×D4—471no—
277C2×D4—941no—
278C2×D4—941no—
279C22×C4—21no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4C2×C4×D4711yescharacteristic
283Q16—942no—
284SD16—942no—
285SD16—942no—
286D8—942no—
287M16—472no—
288M16—941no—
289M16—942no—
290M16—942no—
291M16—941no—
292M16—941no—
293M16—1881no—
294M16—1881no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—941no—
298C2×C8—942no—
299C2×C8—942no—
300C2×C8—941no—
301C2×C8—1881no—
302C2×C8—1881no—
303C2×C8C8×D4711yescharacteristic
304C2×C8C8×D4711yescharacteristic
305C2×C8C2×D18811yescharacteristic
306C2×C8#1062535011yescharacteristic
307C2×C8D4×D4711yescharacteristic
308C2×C8D4×D4711yescharacteristic
309C2×C8D4×D4711yescharacteristic
310C2×C8#1062535411yescharacteristic
311C42—21no—
312C42—21no—
313C16—21no—
314C16—21no—
315C16—41no—
316C16—942no—
317C16—1881no—
318C23—941no—
319C23—941no—
320C23#1309403011yescharacteristic
321Q8—472no—
322Q8—941no—
323Q8—941no—
324Q8—941no—
325D4—472no—
326D4—942no—
327D4—942no—
328D4—941no—
329D4—941no—
330D4—941no—
331D4—1881no—
332D4—1881no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—941no—
337C2×C4—942no—
338C2×C4—942no—
339C2×C4—941no—
340C2×C4—1881no—
341C2×C4—1881no—
342C2×C4C22⋊C4×D4711yescharacteristic
343C2×C4#1309398611yescharacteristic
344C2×C4C4×D18811yescharacteristic
345C2×C4C2×C8×D4711yescharacteristic
346C2×C4M16×D4711yescharacteristic
347C2×C4#1309403211yescharacteristic
348C8—21no—
349C8—21no—
350C8—942no—
351C8—1881no—
352C8#1309399411yescharacteristic
353C8#1309399711yescharacteristic
354C8#1309399911yescharacteristic
355C8#1309400911yescharacteristic
356C22—21no—
357C22—21no—
358C22—942no—
359C22—1881no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22—1881no—
364C22#1568908811yescharacteristic
365C22C8×D18811yescharacteristic
366C22#1568919311yescharacteristic
367C4—42no—
368C4—942no—
369C4—1881no—
370C4#1568900111yescharacteristic
371C4C22⋊C8×D4711yescharacteristic
372C4#1568918811yescharacteristic
373C4#1568919611yescharacteristic
374C2—21no—
375C2—21no—
376C2—3761no—
377C2—1882no—
378C2#2024367911yescharacteristic
379C2#2024522611yescharacteristic
380C2#2024523111yescharacteristic
subgroupG/H
centerC2×C8C2×D188
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#1374C2
socleC22×C47C8×D4
prime radicalC2×#13094046C4
cosocleC22×C8×C47C23
hypercenter#1374D47
hypocenterC47#12980
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ #1374

Complements

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

NH ≅ G/Ntype
1. C2×#15689539C2semidirect
3. C2×#15688906C2semidirect
4. C2×#15688906C2semidirect
5. #20245001C2semidirect
6. #20241470C2semidirect
7. C47×#1374C2semidirect
190. #1374D47semidirect
219. C47#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#156895392
C2×#156892412
C2×#156889062
#202450012
#202414702
C47×#13742
#1298047