Finite Group Databasebeta

← #26135621

Subgroups — #26135621

Order 12032.

566 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689498C211yesmaximal, characteristic
2C2×#15688925C211yesmaximal, characteristic, complemented
3C2×#15688924C211yesmaximal, characteristic, complemented
4C2×#15688923C211yesmaximal, characteristic, complemented
5#20244122C211yesmaximal, characteristic, complemented
6#20241465C211yesmaximal, characteristic, complemented
7C2×C47×#357C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C22×#10625334—21no—
10C2×#13094020—21no—
11C22×C47⋊C16C2211yescharacteristic
12#15689498—22no—
13#15689498—22no—
14C2×#13093958C2211yescharacteristic
15C2×C8×Dic47C2211yescharacteristic
16#15689022—21no—
17#15688925—22no—
18#15688924—22no—
19#15688923—22no—
20#15688885—21no—
21C22×D8×C47C2211yescharacteristic
22C22×C16×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C47×#357—22no—
25C22×D188—21no—
26C22×C22⋊D47—41no—
27C22×C22⋊D47—41no—
28C2×D376—21no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376—21no—
33C2×D376D412yes—
34C2×#10625334—24no—
35C2×#10625334—42no—
36C2×#10625334—42no—
37C22×C47⋊C8D411yescharacteristic
38#13094020—24no—
39#13094020—42no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—41no—
42C2×C4×Dic47D411yescharacteristic
43C2×C47⋊C16—21no—
44C2×C47⋊C16—21no—
45C2×C47⋊C16—21no—
46#13093958—21no—
47#13093958—21no—
48C8×Dic47—21no—
49C8×Dic47—21no—
50C47⋊#95—41no—
51C22×D4×C47—21no—
52C2×D8×C47—21no—
53C2×D8×C47—21no—
54C2×D8×C47—21no—
55C2×D8×C47—21no—
56C2×D8×C47—21no—
57C2×D8×C47D412yes—
58C22×C8×C47C2311yescharacteristic
59C2×C4⋊C4×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47—21no—
63#107×C47—21no—
64#107×C47D412yescomplemented
65C24×C47—41no—
66C23×D47—41no—
67C2×D4×C47—22no—
68C2×D4×C47—41no—
69C2×D4×C47—41no—
70C2×D4×C47—41no—
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47C2×D411yescharacteristic
75C2×C22⋊D47—44no—
76C2×C22⋊D47—44no—
77C2×C22⋊D47—82no—
78C2×C22⋊D47—82no—
79C2×C22⋊D47—82no—
80C2×C22⋊D47—82no—
81C22×Dic47—41no—
82C22×Dic47D811yescharacteristic
83C22×Dic47D811yescharacteristic
84C2×D188—22no—
85C2×D188—41no—
86C2×D188—41no—
87C2×D188—41no—
88C2×D188—41no—
89C2×D188—41no—
90D8×C47—22no—
91D8×C47—22no—
92D8×C47—41no—
93D8×C47—41no—
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47#4111yescharacteristic
98C2×C8×C47#4111yescharacteristic
99C2×C8×C47#4111yescharacteristic
100C4⋊C4×C47—22no—
101C4⋊C4×C47—41no—
102#10625334—48no—
103C4⋊Dic47—41no—
104C4⋊Dic47—41no—
105C4⋊Dic47—82no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8SD1612yes—
111D376—22no—
112D376—22no—
113D376—41no—
114D376—41no—
115C16×C47—41no—
116C47⋊C16—41no—
117C23×C47—42no—
118C23×C47—81no—
119C23×C47—81no—
120C23×C47—81no—
121C23×C47—81no—
122C23×C47—81no—
123C23×C47—81no—
124C23×C47C2×D811yescharacteristic
125C22×D47—42no—
126C22×D47—81no—
127C22×D47—81no—
128C22×D47—81no—
129C22×D47—81no—
130C22×D47—81no—
131C22×D47—81no—
132D4×C47—42no—
133D4×C47—42no—
134D4×C47—81no—
135D4×C47—81no—
136C2×C4×C47—42no—
137C2×C4×C47—81no—
138C2×C4×C47—81no—
139C2×C4×C47#12011yescharacteristic
140C2×C4×C47#12111yescharacteristic
141C2×C4×C47#12411yescharacteristic
142C2×C4×C47C2×SD1611yescharacteristic
143C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
145C22⋊D47—88no—
146C22⋊D47—88no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—81no—
152C2×Dic47—81no—
153C2×Dic47—81no—
154C2×Dic47D1612yes—
155C2×Dic47SD3212yes—
156D188—42no—
157D188—42no—
158D188—81no—
159D188—81no—
160C8×C47#12111yescharacteristic
161C8×C47#12111yescharacteristic
162C8×C47#12311yescharacteristic
163C8×C47#12311yescharacteristic
164C47⋊C8—22no—
165#13407—471nomaximal, Sylow
166C22×C47—82no—
167C22×C47—82no—
168C22×C47—82no—
169C22×C47—161no—
170C22×C47—161no—
171C22×C47—161no—
172C22×C47—161no—
173C22×C47#44711yescharacteristic
174C22×C47#45911yescharacteristic
175C22×C47#48611yescharacteristic
176C22×C47C2×D1611yescharacteristic
177C22×C47C2×SD3211yescharacteristic
178C22×C47#50911yescharacteristic
179C22×C47#50911yescharacteristic
180C2×D47—82no—
181C2×D47—82no—
182C2×D47—82no—
183C2×D47—161no—
184C2×D47—161no—
185C2×D47—161no—
186C2×D47—161no—
187C4×C47—82no—
188C4×C47#39411yescharacteristic
189C4×C47#45011yescharacteristic
190C4×C47#46011yescharacteristic
191C4×C47#49011yescharacteristic
192Dic47—22no—
193Dic47—22no—
194Dic47—161no—
195C2×#493—471no—
196C2×#357—471no—
197C2×#357—471no—
198C2×#357—471no—
199C2×#357D4711yescharacteristic, complemented
200#1942—471no—
201#1374—471no—
202C2×C47—162no—
203C2×C47#204111yescharacteristic
204C2×C47#218411yescharacteristic
205C2×C47#218711yescharacteristic
206C2×C47#220611yescharacteristic
207C2×C47#220711yescharacteristic
208C2×C47#224011yescharacteristic
209C2×C47#224411yescharacteristic
210D47—162no—
211C22×D8—471no—
212C22×D8—941no—
213C22×D8C2×D4711yescharacteristic
214C2×#127—941no—
215C22×C16—471no—
216C22×C16C2×D4711yescharacteristic
217#493—942no—
218#493—942no—
219C2×#107—471no—
220C2×#107C2×D4711yescharacteristic
221C2×C4×C8—471no—
222#389—941no—
223#357—22no—
224#357—942no—
225#357—942no—
226#357—942no—
227#340—941no—
228C47#1340711yescharacteristic, complemented, Sylow
229C22×D4—21no—
230C22×D4—941no—
231C22×D4—1881no—
232C22×D4—1881no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—472no—
239C2×D8—944no—
240C2×D8—941no—
241C2×D8—941no—
242C2×D8—941no—
243C2×D8—941no—
244C2×D8—941no—
245C2×D8—1882no—
246C2×D8—1882no—
247C2×D8D18812yes—
248C22×C8—471no—
249C22×C8C22×D4711yescharacteristic
250#127—944no—
251#127—1882no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—941no—
254C2×C4⋊C4—1881no—
255C2×C42—471no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16—941no—
260C2×C16—941no—
261C2×C16—941no—
262#107—21no—
263#107—941no—
264#107—941no—
265#107C22⋊D4712yescomplemented
266C4×C8—941no—
267C4×C8—941no—
268#95—1881no—
269C24—41no—
270C24—1881no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—942no—
278C2×D4—3762no—
279C2×D4—3762no—
280C2×D4—3762no—
281C2×D4—3762no—
282C2×D4—1884no—
283C2×D4—1884no—
284C2×D4—1881no—
285C2×D4—1881no—
286C2×D4—1881no—
287C2×D4—1881no—
288C2×D4—1881no—
289C22×C4—41no—
290C22×C4—471no—
291C22×C4—471no—
292C22×C4—1881no—
293C22×C4D4×D4711yescharacteristic
294D8—22no—
295D8—22no—
296D8—41no—
297D8—41no—
298D8—942no—
299D8—942no—
300D8—1888no—
301D8—1881no—
302D8—1881no—
303C2×C8—472no—
304C2×C8—941no—
305C2×C8—941no—
306C2×C8C2×D18811yescharacteristic
307C2×C8#1062535011yescharacteristic
308C2×C8D4×D4711yescharacteristic
309C2×C8#1062535211yescharacteristic
310C2×C8#1062535211yescharacteristic
311C2×C8C2×C22⋊D4711yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—3762no—
315C4⋊C4—1881no—
316C4⋊C4—1881no—
317C42—941no—
318C42—941no—
319C16—41no—
320C16—1881no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—3761no—
329C23—3761no—
330C23—3761no—
331C23—3761no—
332C23—3761no—
333C23—3761no—
334C23—1882no—
335C23D8×D4711yescharacteristic
336D4—42no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—3768no—
341D4—3768no—
342D4—3761no—
343D4—3761no—
344D4—1882no—
345D4—1882no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—472no—
350C2×C4—472no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—3761no—
356C2×C4—3761no—
357C2×C4—3761no—
358C2×C4#1309399411yescharacteristic
359C2×C4#1309399611yescharacteristic
360C2×C4#1309401011yescharacteristic
361C2×C4SD16×D4711yescharacteristic
362C2×C4#1309404811yescharacteristic
363C2×C4#1309405111yescharacteristic
364C8—942no—
365C8#1309399511yescharacteristic
366C8#1309399811yescharacteristic
367C8#1309400611yescharacteristic
368C8#1309400811yescharacteristic
369C22—82no—
370C22—82no—
371C22—82no—
372C22—161no—
373C22—161no—
374C22—161no—
375C22—161no—
376C22—3762no—
377C22—3762no—
378C22—3762no—
379C22—7521no—
380C22—7521no—
381C22—7521no—
382C22—7521no—
383C22#1568925811yescharacteristic
384C22#1568931611yescharacteristic
385C22#1568946811yescharacteristic
386C22D16×D4711yescharacteristic
387C22SD32×D4711yescharacteristic
388C22#1568955711yescharacteristic
389C22#1568956011yescharacteristic
390C4—82no—
391C4—942no—
392C4—942no—
393C4—7521no—
394C4#1568903911yescharacteristic
395C4#1568927511yescharacteristic
396C4#1568932111yescharacteristic
397C4#1568948611yescharacteristic
398C2—162no—
399C2—7522no—
400C2#2024462111yescharacteristic
401C2#2024530111yescharacteristic
402C2#2024531811yescharacteristic
403C2#2024542111yescharacteristic
404C2#2024542611yescharacteristic
405C2#2024561011yescharacteristic
406C2#2024562811yescharacteristic
subgroupG/H
centerC23D8×D47
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC2×#15689498C2
hypercenterC2×#357D47
hypocenterC47#13407
LCSG ▷ C22×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#15688925C2semidirect
3. C2×#15688924C2semidirect
4. C2×#15688923C2semidirect
5. #20244122C2semidirect
6. #20241465C2semidirect
7. C2×C47×#357C2semidirect
64. #107×C47D4semidirect
199. C2×#357D47semidirect
228. C47#13407semidirect
265. #107C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156894982
C2×#156889252
C2×#156889242
C2×#156889232
#202441222
#202414652
C2×C47×#3572
#1340747