Finite Group Databasebeta

← #26133330

Subgroups — #26133330

Order 12032.

476 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689240C211yesmaximal, characteristic, complemented
2C2×#15688930C211yesmaximal, characteristic, complemented
3C2×#15688930C211yesmaximal, characteristic, complemented
4#20244277C211yesmaximal, characteristic, complemented
5#20241482C211yesmaximal, characteristic, complemented
6#20241465C211yesmaximal, characteristic, complemented
7C2×C47×#508C211yesmaximal, characteristic
8C2×#13094031—21no—
9C22×C47⋊C16C2211yescharacteristic
10#15689240—22no—
11#15689240—22no—
12C2×#13093960C2211yescharacteristic
13C2×#13093960C2211yescharacteristic
14C2×#13093951—21no—
15C2×#13093951—21no—
16#15689090—21no—
17C2×C8×Dic47C2211yescharacteristic
18#15688930—22no—
19#15688930—22no—
20C2×#135×C47C2211yescharacteristic
21C2×#135×C47C2211yescharacteristic
22C47×#508—22no—
23C47×#508—22no—
24C2×Q32×C47C411yescharacteristic, complemented
25C2×SD32×C47C411yescharacteristic, complemented
26C2×SD32×C47C411yescharacteristic, complemented
27C2×D16×C47C411yescharacteristic, complemented
28C22×C16×C47C2211yescharacteristic
29#13094031—24no—
30#13094031—42no—
31C2×#10625329—21no—
32C2×#10625329—21no—
33C2×#10625329—41no—
34C22×C47⋊C8—41no—
35C22×C47⋊C8D411yescharacteristic
36C2×C4×Dic47D411yescharacteristic
37C2×C47⋊C16—21no—
38C2×C47⋊C16—21no—
39C2×C47⋊C16—21no—
40#13093960—21no—
41#13093960—21no—
42#13093960—21no—
43#13093960D412yes—
44#13093951—24no—
45#13093951—42no—
46C22⋊(C47⋊C8)—41no—
47C22⋊(C47⋊C8)—41no—
48C8×Dic47—21no—
49C8×Dic47—21no—
50C2×#41×C47—21no—
51C2×#41×C47—21no—
52#135×C47—21no—
53#135×C47—21no—
54#135×C47—21no—
55#135×C47—21no—
56#135×C47—21no—
57#135×C47—21no—
58#135×C47D412yes—
59#135×C47D412yes—
60C2×Q16×C47C2×C411yescharacteristic
61C2×Q16×C47C2×C411yescharacteristic
62C2×SD16×C47—21no—
63C2×SD16×C47—21no—
64C2×D8×C47C2×C411yescharacteristic
65C2×D8×C47C2×C411yescharacteristic
66C22×C8×C47C2311yescharacteristic
67Q32×C47—22no—
68SD32×C47—22no—
69SD32×C47—22no—
70D16×C47—22no—
71C2×C16×C47—21no—
72C2×C16×C47—21no—
73C2×C16×C47C2×C411yescharacteristic
74C2×C16×C47C2×C411yescharacteristic
75#41×C47—22no—
76#41×C47—22no—
77#41×C47—41no—
78#41×C47—41no—
79#41×C47—41no—
80#41×C47—41no—
81#41×C47—41no—
82#41×C47—41no—
83C2×Q8×C47—21no—
84C2×Q8×C47—21no—
85C2×D4×C47—21no—
86C2×D4×C47—21no—
87C2×D4×C47—41no—
88C2×D4×C47—41no—
89C22×C4×C47—41no—
90C22×C4×C47—41no—
91C22×C4×C47C2×D411yescharacteristic
92C22×Dic47—21no—
93Q16×C47—21no—
94Q16×C47—21no—
95Q16×C47—21no—
96Q16×C47C22⋊C412yes—
97SD16×C47—22no—
98SD16×C47—22no—
99SD16×C47—41no—
100SD16×C47—41no—
101D8×C47—21no—
102D8×C47—21no—
103D8×C47—21no—
104D8×C47C22⋊C412yes—
105C2×C8×C47C22×C411yescharacteristic
106C2×C8×C47C2×D411yescharacteristic
107C2×C8×C47C2×D411yescharacteristic
108C2×C8×C47C2×D411yescharacteristic
109C2×C8×C47#4111yescharacteristic
110C2×C8×C47#4111yescharacteristic
111C4×Dic47—21no—
112C4×Dic47—21no—
113#10625329—22no—
114#10625329—44no—
115#10625329—41no—
116#10625329—41no—
117#10625329—41no—
118C2×C47⋊C8—21no—
119C2×C47⋊C8—21no—
120C2×C47⋊C8—44no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8D811yescharacteristic
124C2×C47⋊C8D811yescharacteristic
125C16×C47—21no—
126C16×C47—21no—
127C47⋊C16—41no—
128C23×C47—41no—
129C23×C47—41no—
130C23×C47#13511yescharacteristic
131Q8×C47—22no—
132Q8×C47—41no—
133Q8×C47—41no—
134Q8×C47—41no—
135D4×C47—22no—
136D4×C47—42no—
137D4×C47—42no—
138D4×C47—41no—
139D4×C47—41no—
140D4×C47—41no—
141D4×C47—81no—
142D4×C47—81no—
143C2×C4×C47—41no—
144C2×C4×C47—42no—
145C2×C4×C47—42no—
146C2×C4×C47—41no—
147C2×C4×C47—81no—
148C2×C4×C47—81no—
149C2×C4×C47C4×D411yescharacteristic
150C2×C4×C47#12011yescharacteristic
151C2×C4×C47#12111yescharacteristic
152C2×C4×C47C2×D811yescharacteristic
153C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
155C2×Dic47—22no—
156C2×Dic47—41no—
157C2×Dic47—41no—
158C8×C47C2×C22⋊C411yescharacteristic
159C8×C47C4×D411yescharacteristic
160C8×C47#12111yescharacteristic
161C8×C47#12311yescharacteristic
162C47⋊C8—21no—
163C47⋊C8—21no—
164C47⋊C8—42no—
165C47⋊C8—81no—
166#13011—471nomaximal, Sylow
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—42no—
170C22×C47—81no—
171C22×C47—81no—
172C22×C47—81no—
173C22×C47—81no—
174C22×C47—81no—
175C22×C47C4×D811yescharacteristic
176C22×C47#44911yescharacteristic
177C22×C47#46311yescharacteristic
178C4×C47—42no—
179C4×C47—81no—
180C4×C47#38611yescharacteristic
181C4×C47#44211yescharacteristic
182C4×C47#44711yescharacteristic
183C4×C47#45911yescharacteristic
184Dic47—42no—
185C2×#508D4711yescharacteristic
186C2×#443—471no—
187C2×#359—471no—
188C2×#359—471no—
189#1974—471no—
190#1381—471no—
191#1374—471no—
192C2×C47—21no—
193C2×C47—21no—
194C2×C47—82no—
195C2×C47—161no—
196C2×C47#187911yescharacteristic
197C2×C47#217811yescharacteristic
198C2×C47#217911yescharacteristic
199C2×#135C2×D4711yescharacteristic
200C2×#135C2×D4711yescharacteristic
201C2×#131—941no—
202#508—22no—
203#508—22no—
204C2×Q32Dic4711yescharacteristic, complemented
205C2×SD32Dic4711yescharacteristic, complemented
206C2×SD32Dic4711yescharacteristic, complemented
207C2×D16Dic4711yescharacteristic, complemented
208C22×C16—471no—
209C22×C16C2×D4711yescharacteristic
210#443—942no—
211#443—942no—
212C2×#108—471no—
213C2×#108—471no—
214C2×#104—941no—
215C2×#104—941no—
216#408—941no—
217C2×C4×C8—471no—
218#359—942no—
219#359—942no—
220C47#1301111yescharacteristic, complemented, Sylow
221C2×#41—21no—
222C2×#41—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135—21no—
228#135—21no—
229#135C22⋊D4712yes—
230#135C22⋊D4712yes—
231C2×Q16C2×Dic4711yescharacteristic
232C2×Q16C2×Dic4711yescharacteristic
233C2×SD16—21no—
234C2×SD16—21no—
235C2×D8C2×Dic4711yescharacteristic
236C2×D8C2×Dic4711yescharacteristic
237#131—944no—
238#131—1882no—
239C2×M16—941no—
240C2×M16—941no—
241C2×M16—1881no—
242C22×C8—471no—
243C22×C8—1881no—
244C22×C8C22×D4711yescharacteristic
245C2×C42—471no—
246Q32—22no—
247SD32—22no—
248SD32—22no—
249D16—22no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—941no—
253C2×C16—941no—
254C2×C16—941no—
255C2×C16C2×Dic4711yescharacteristic
256C2×C16C2×Dic4711yescharacteristic
257#108—472no—
258#108—941no—
259#108—941no—
260#108—941no—
261#104—944no—
262#104—1882no—
263C22⋊C8—1881no—
264C22⋊C8—1881no—
265C4×C8—941no—
266C4×C8—941no—
267#41—22no—
268#41—22no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—941no—
284C22×C4D4×D4711yescharacteristic
285Q16—21no—
286Q16—21no—
287Q16—21no—
288Q16C22⋊Dic4712yes—
289SD16—22no—
290SD16—22no—
291SD16—41no—
292SD16—41no—
293D8—21no—
294D8—21no—
295D8—21no—
296D8C22⋊Dic4712yes—
297M16—942no—
298M16—1884no—
299M16—1881no—
300M16—1881no—
301M16—1881no—
302C2×C8—471no—
303C2×C8—471no—
304C2×C8—941no—
305C2×C8—941no—
306C2×C8—1884no—
307C2×C8—1881no—
308C2×C8—1881no—
309C2×C8D4×D4711yescharacteristic
310C2×C8#1062535211yescharacteristic
311C2×C8#1062535211yescharacteristic
312C2×C8C22×Dic4711yescharacteristic
313C2×C8C2×C22⋊D4711yescharacteristic
314C2×C8C2×C22⋊D4711yescharacteristic
315C42—941no—
316C42—941no—
317C16—21no—
318C16—21no—
319C16—1881no—
320C23—41no—
321C23—41no—
322C23#1309404311yescharacteristic
323Q8—22no—
324Q8—41no—
325Q8—41no—
326Q8—41no—
327D4—22no—
328D4—42no—
329D4—42no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—81no—
334D4—81no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—942no—
342C2×C4—1881no—
343C2×C4—1881no—
344C2×C4D4×Dic4711yescharacteristic
345C2×C4#1309399211yescharacteristic
346C2×C4#1309399611yescharacteristic
347C2×C4D8×D4711yescharacteristic
348C2×C4#1309404811yescharacteristic
349C2×C4#1309404811yescharacteristic
350C8—941no—
351C8—941no—
352C8—3761no—
353C8—1882no—
354C8C2×C22⋊Dic4711yescharacteristic
355C8D4×Dic4711yescharacteristic
356C8#1309399611yescharacteristic
357C8#1309400511yescharacteristic
358C22—21no—
359C22—21no—
360C22—42no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22D8×Dic4711yescharacteristic
367C22#1568926511yescharacteristic
368C22#1568933611yescharacteristic
369C4—42no—
370C4—81no—
371C4—1882no—
372C4#1568900311yescharacteristic
373C4#1568923511yescharacteristic
374C4#1568925511yescharacteristic
375C4#1568931611yescharacteristic
376C2—21no—
377C2—21no—
378C2—82no—
379C2—161no—
380C2#2024373811yescharacteristic
381C2#2024526911yescharacteristic
382C2#2024527411yescharacteristic
subgroupG/H
centerC2×C4D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
Fitting, prime radicalC2×C47×#508C2
socleC22×C47C4×D8
cosocleC22×C8×C47C23
hypercenterC2×#508D47
hypocenterC47#13011
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#15689240C2semidirect
2. C2×#15688930C2semidirect
3. C2×#15688930C2semidirect
4. #20244277C2semidirect
5. #20241482C2semidirect
6. #20241465C2semidirect
24. C2×Q32×C47C4semidirect
25. C2×SD32×C47C4semidirect
26. C2×SD32×C47C4semidirect
27. C2×D16×C47C4semidirect
204. C2×Q32Dic47semidirect
205. C2×SD32Dic47semidirect
206. C2×SD32Dic47semidirect
207. C2×D16Dic47semidirect
220. C47#13011semidirect

Maximal subgroups

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

subgroupindex
C2×#156892402
C2×#156889302
#202442772
#202414822
#202414652
C2×C47×#5082
#1301147