Finite Group Databasebeta

← #26135446

Subgroups — #26135446

Order 12032.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689361C211yesmaximal, characteristic
2C2×#15688951C211yesmaximal, characteristic, complemented
3C2×#15688927C211yesmaximal, characteristic, complemented
4C2×(C2×D47)⋊C16C211yesmaximal, characteristic
5#20243414C211yesmaximal, characteristic
6#20241479C211yesmaximal, characteristic, complemented
7C2×C47×#358C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×#13094000—21no—
10C22×C47⋊C16C2211yescharacteristic
11#15689361—22no—
12#15689361—22no—
13C2×#13093958C2211yescharacteristic
14C2×#13093958C2211yescharacteristic
15C2×#13093948—21no—
16#15688980—21no—
17#15688951—22no—
18#15688927—22no—
19(C2×D47)⋊C16—22no—
20#15688885—21no—
21C22×Q16×C47C2211yescharacteristic
22C22×C16×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C47×#358—22no—
25C22×C4×D47D411yescharacteristic
26C22×C47⋊C8D411yescharacteristic
27C2×C8×D47—21no—
28C2×C8×D47—21no—
29C2×C8×D47—21no—
30C2×C8×D47—21no—
31C2×C8×D47—21no—
32C2×C8×D47—21no—
33#13094000—24no—
34#13094000—42no—
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47—21no—
37C2×Dic47⋊C4—41no—
38C2×(C2×D47)⋊C4—41no—
39C2×(C2×D47)⋊C4—41no—
40C2×C47⋊C16—21no—
41C2×C47⋊C16—21no—
42C2×C47⋊C16—21no—
43#13093958—21no—
44#13093958—21no—
45#13093958—21no—
46#13093958D412yes—
47#13093948—24no—
48C47⋊#95—41no—
49C22×Q8×C47—21no—
50C2×Q16×C47—21no—
51C2×Q16×C47—21no—
52C2×Q16×C47—21no—
53C2×Q16×C47—21no—
54C2×Q16×C47—21no—
55C2×Q16×C47D412yes—
56C22×C8×C47C2311yescharacteristic
57C2×C4⋊C4×C47—21no—
58C2×C16×C47—21no—
59C2×C16×C47—21no—
60C2×C16×C47D412yes—
61#107×C47—21no—
62#107×C47—21no—
63C23×D47D811yescharacteristic
64C2×Q8×C47—22no—
65C2×Q8×C47—41no—
66C2×Q8×C47—41no—
67C2×Q8×C47—41no—
68C2×Q8×C47—41no—
69C2×Q8×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47C2×D411yescharacteristic
73C22×Dic47—41no—
74C22×Dic47—41no—
75C22×Dic47D811yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82Q16×C47—22no—
83Q16×C47—22no—
84Q16×C47—41no—
85Q16×C47—41no—
86C2×C8×C47C2×D411yescharacteristic
87C2×C8×C47C2×D411yescharacteristic
88C2×C8×C47C2×D411yescharacteristic
89C2×C8×C47#4111yescharacteristic
90C2×C8×C47#4111yescharacteristic
91C2×C8×C47#4111yescharacteristic
92C4⋊C4×C47—41no—
93C4⋊C4×C47—41no—
94(C2×D47)⋊C4—44no—
95(C2×D47)⋊C4—82no—
96C4⋊Dic47—22no—
97C4⋊Dic47—41no—
98C4⋊Dic47—41no—
99C4⋊Dic47—41no—
100Dic47⋊C4—44no—
101C2×C47⋊C8—21no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8—21no—
104C8×D47—41no—
105C8×D47—41no—
106C8×D47—41no—
107C8×D47—41no—
108C16×C47—22no—
109C47⋊C16—41no—
110C23×C47C2×D811yescharacteristic
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47SD3212yes—
118Q8×C47—42no—
119Q8×C47—42no—
120Q8×C47—81no—
121Q8×C47—81no—
122C2×C4×C47—42no—
123C2×C4×C47—81no—
124C2×C4×C47—81no—
125C2×C4×C47—81no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47#12011yescharacteristic
129C2×C4×C47#12111yescharacteristic
130C2×C4×C47#12311yescharacteristic
131C2×C4×C47#13511yescharacteristic
132C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C47#13711yescharacteristic
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—42no—
138C2×Dic47—81no—
139C2×Dic47—81no—
140C2×Dic47—81no—
141C2×Dic47—81no—
142C2×Dic47—81no—
143C4×D47—41no—
144C4×D47—41no—
145C4×D47—41no—
146C4×D47—41no—
147C8×C47#12111yescharacteristic
148C8×C47#12111yescharacteristic
149C8×C47#12311yescharacteristic
150C8×C47#12411yescharacteristic
151C47⋊C8—41no—
152#13382—471nomaximal, Sylow
153C22×C47#44711yescharacteristic
154C22×C47#46611yescharacteristic
155C22×C47#48011yescharacteristic
156C22×C47C2×SD3211yescharacteristic
157C22×C47#50811yescharacteristic
158C22×C47#51011yescharacteristic
159C22×C47#51011yescharacteristic
160C2×D47—22no—
161C2×D47—22no—
162C2×D47—22no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C4×C47—82no—
168C4×C47—161no—
169C4×C47#39411yescharacteristic
170C4×C47#45211yescharacteristic
171C4×C47#46811yescharacteristic
172C4×C47#48211yescharacteristic
173Dic47—41no—
174Dic47—82no—
175Dic47—161no—
176C2×#467—471no—
177C2×#367—471no—
178C2×#358—471no—
179C2×#358D4711yescharacteristic, complemented
180C2×C22⋊C16—471no—
181#1808—471no—
182#1380—471no—
183C2×C47#203311yescharacteristic
184C2×C47#218511yescharacteristic
185C2×C47#218911yescharacteristic
186C2×C47#221711yescharacteristic
187C2×C47#221911yescharacteristic
188C2×C47#223511yescharacteristic
189C2×C47#223711yescharacteristic
190D47—42no—
191C22×Q16C2×D4711yescharacteristic
192C23×C8—471no—
193C2×C22⋊Q8—941no—
194C22×C16—471no—
195C22×C16C2×D4711yescharacteristic
196#467—942no—
197#467—942no—
198C2×#107—471no—
199C2×#107—471no—
200C2×#107C2×D4711yescharacteristic
201C2×#103—941no—
202#380—941no—
203#367—942no—
204#358—22no—
205#358—942no—
206C22⋊C16—942no—
207#340—941no—
208C47#1338211yescharacteristic, complemented, Sylow
209C22×Q8—21no—
210C23×C4—471no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16D18812yes—
217C22×C8—471no—
218C22×C8—941no—
219C22×C8—941no—
220C22×C8—941no—
221C22×C8—941no—
222C22×C8—941no—
223C22×C8—941no—
224C22×C8C22×D4711yescharacteristic
225C22⋊Q8—944no—
226C22⋊Q8—1882no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—941no—
229C2×C4⋊C4—941no—
230C2×C4⋊C4—1881no—
231C2×C22⋊C4—1881no—
232C2×C22⋊C4—1881no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—941no—
236C2×C16—941no—
237C2×C16—941no—
238C2×C16C22⋊D4712yes—
239#107—21no—
240#107—21no—
241#107—472no—
242#107—941no—
243#107—941no—
244#107—941no—
245#103—944no—
246#95—1881no—
247C24—471no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—471no—
257C22×C4—941no—
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4—1881no—
264C22×C4—1881no—
265C22×C4D4×D4711yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—41no—
269Q16—41no—
270C2×C8—941no—
271C2×C8—941no—
272C2×C8—941no—
273C2×C8—1881no—
274C2×C8—1881no—
275C2×C8—1881no—
276C2×C8—1881no—
277C2×C8C2×D18811yescharacteristic
278C2×C8#1062535011yescharacteristic
279C2×C8D4×D4711yescharacteristic
280C2×C8#1062535211yescharacteristic
281C2×C8#1062535211yescharacteristic
282C2×C8C2×C22⋊D4711yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—942no—
286C4⋊C4—1884no—
287C4⋊C4—1881no—
288C4⋊C4—1881no—
289C4⋊C4—1881no—
290C22⋊C4—3762no—
291C22⋊C4—1884no—
292C16—22no—
293C16—1881no—
294C23—472no—
295C23—941no—
296C23—941no—
297C23—941no—
298C23—941no—
299C23—941no—
300C23—941no—
301C23D8×D4711yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—3761no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4—3761no—
319C2×C4—3761no—
320C2×C4—1882no—
321C2×C4—1881no—
322C2×C4—1881no—
323C2×C4—1881no—
324C2×C4—1881no—
325C2×C4#1309399411yescharacteristic
326C2×C4#1309399511yescharacteristic
327C2×C4#1309400611yescharacteristic
328C2×C4#1309404311yescharacteristic
329C2×C4#1309405111yescharacteristic
330C2×C4#1309405311yescharacteristic
331C8—1881no—
332C8#1309399611yescharacteristic
333C8#1309399811yescharacteristic
334C8#1309400811yescharacteristic
335C8#1309401011yescharacteristic
336C22—942no—
337C22—942no—
338C22—942no—
339C22—1881no—
340C22—1881no—
341C22—1881no—
342C22—1881no—
343C22#1568925811yescharacteristic
344C22#1568935611yescharacteristic
345C22#1568943511yescharacteristic
346C22SD32×D4711yescharacteristic
347C22#1568955411yescharacteristic
348C22#1568956511yescharacteristic
349C22#1568956511yescharacteristic
350C4—82no—
351C4—161no—
352C4—3762no—
353C4—1881no—
354C4—7521no—
355C4#1568903911yescharacteristic
356C4#1568928611yescharacteristic
357C4#1568936611yescharacteristic
358C4#1568944511yescharacteristic
359C2—1882no—
360C2#2024456911yescharacteristic
361C2#2024530611yescharacteristic
362C2#2024533111yescharacteristic
363C2#2024548111yescharacteristic
364C2#2024549311yescharacteristic
365C2#2024558411yescharacteristic
366C2#2024559411yescharacteristic
subgroupG/H
centerC23D8×D47
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC2×C47×#358C2
socleC23×C47C2×D8
prime radicalC23×D47D8
hypercenterC2×#358D47
hypocenterC47#13382
LCSG ▷ C22×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#15688951C2semidirect
3. C2×#15688927C2semidirect
6. #20241479C2semidirect
7. C2×C47×#358C2semidirect
179. C2×#358D47semidirect
208. C47#13382semidirect

Maximal subgroups

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

subgroupindex
C2×#156893612
C2×#156889512
C2×#156889272
C2×(C2×D47)⋊C162
#202434142
#202414792
C2×C47×#3582
#1338247