Finite Group Databasebeta

← #11774062

Subgroups — #11774062

Order 1152.

521 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64079C211yesmaximal, characteristic
2C3×#4926C211yesmaximal, characteristic
3C3×#4925C211yesmaximal, characteristic
4#10589148C214yesmaximal
5#70831—31nomaximal
6#70787—31nomaximal
7C2×C32×C42C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C411yescharacteristic
9C2×C4⋊(C3⋊Dic3)C411yescharacteristic
10C2×#3750C412yes—
11C2×#3750C2212yes—
12#64079—21no—
13#64079—21no—
14#64079—21no—
15#64079—21no—
16C3×#830C2212yes—
17C3×#830C2212yes—
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)—21no—
20C3×#803—21no—
21C3×C4×C3⋊C8—21no—
22C2×#870—31no—
23C2×#870—31no—
24C2×#870—61no—
25C3×#432—31no—
26C3×#431—31no—
27#4926D311yescharacteristic
28#4925D311yescharacteristic
29#4469—34no—
30#4469—34no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3C2×C412yes—
35C22×C3⋊Dic3C2×C412yes—
36C32×C42D411yescharacteristic
37C32×C42D411yescharacteristic
38C32×C42D411yescharacteristic
39C32×C42D411yescharacteristic
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44#3750—22no—
45#3750—22no—
46#3750—22no—
47#3750—22no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50#1470—91noSylow
51C2×C3×C42—21no—
52C2×C3×C42C2×D311yescharacteristic
53C2×C3×C42C2×D311yescharacteristic
54C2×C4⋊Dic3—31no—
55C2×C4⋊Dic3—31no—
56C2×C4⋊Dic3—31no—
57C2×C4⋊Dic3—31no—
58C2×C4⋊Dic3—61no—
59C2×C4⋊Dic3—61no—
60C2×Dic3⋊C4—32no—
61C2×Dic3⋊C4—32no—
62C2×Dic3⋊C4—32no—
63C2×Dic3⋊C4—32no—
64C2×Dic3⋊C4—62no—
65C2×Dic3⋊C4—62no—
66#870—62no—
67#870—62no—
68#870—62no—
69#870—62no—
70#870—61no—
71#870—61no—
72#870—61no—
73#870—61no—
74#870—61no—
75#870—61no—
76#870—61no—
77#870—61no—
78C3×C4⋊C8—61no—
79C3×C4⋊C8—61no—
80C3×C22⋊C8—32no—
81C3×C22⋊C8—32no—
82C3×#97—61no—
83C3×C4×C8—61no—
84#830C2×D312yes—
85#830C2×D312yes—
86C4⋊(C3⋊C8)—21no—
87C4⋊(C3⋊C8)—21no—
88#803—21no—
89C4×C3⋊C8—21no—
90C23×C32C22×C411yescharacteristic
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4—41no—
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—42no—
104C3×C3⋊C8—42no—
105C3×C3⋊C8—42no—
106C2×#125—91no—
107#432—31no—
108#431—31no—
109#324—94no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4C4×D311yescharacteristic
114C22×C3×C4C4×D311yescharacteristic
115C22×C3×C4C4×D311yescharacteristic
116C22×C3×C4C4×D311yescharacteristic
117C22×C3×C4C22×D311yescharacteristic
118C22×C3×C4C22×D311yescharacteristic
119C22×Dic3—32no—
120C22×Dic3—32no—
121C22×Dic3—32no—
122C22×Dic3—32no—
123C22×Dic3—62no—
124C22×Dic3—62no—
125C2×C3×C8—62no—
126C2×C3×C8—62no—
127C3×C42—21no—
128C3×C42—21no—
129C3×C42—21no—
130C3×C42—21no—
131C3×C42D1211yescharacteristic
132C3×C42D1211yescharacteristic
133C3×C42D1211yescharacteristic
134C3×C42D1211yescharacteristic
135C3×C42#6711yescharacteristic
136C3×C42#6711yescharacteristic
137C3×C42#6711yescharacteristic
138C3×C42#6711yescharacteristic
139C4⋊Dic3—62no—
140C4⋊Dic3—62no—
141C4⋊Dic3—62no—
142C4⋊Dic3—62no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151Dic3⋊C4—64no—
152Dic3⋊C4—64no—
153Dic3⋊C4—64no—
154Dic3⋊C4—64no—
155Dic3⋊C4—62no—
156Dic3⋊C4—62no—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159Dic3⋊C4—62no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163C2×C3⋊C8—22no—
164C2×C3⋊C8—22no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32C2×C22⋊C411yescharacteristic
168C22×C32#13112yes—
169C32×C4—21no—
170C32×C4—21no—
171C32×C4—21no—
172C32×C4—21no—
173C32×C4—21no—
174C32×C4#10112yes—
175C3⋊Dic3—42no—
176C3⋊Dic3—42no—
177#125—181no—
178#125—181no—
179#125—181no—
180#125—181no—
181C2×C4⋊C4—92no—
182C2×C4⋊C4—91no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4—92no—
185C2×C42D3211yescharacteristic
186C4⋊C8—61no—
187C4⋊C8—61no—
188C22⋊C8—32no—
189C22⋊C8—32no—
190#97—61no—
191C4×C8—61no—
192C23×C3—21no—
193C23×C3C2×C4×D311yescharacteristic
194C23×C3C2×C4×D311yescharacteristic
195C2×C3×C4—24no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—42no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—42no—
210C2×C3×C4(C2×D3)⋊C411yescharacteristic
211C2×C3×C4(C2×D3)⋊C411yescharacteristic
212C2×C3×C4(C2×D3)⋊C411yescharacteristic
213C2×C3×C4(C2×D3)⋊C411yescharacteristic
214C2×C3×C4(C2×D3)⋊C411yescharacteristic
215C2×C3×C4(C2×D3)⋊C411yescharacteristic
216C2×C3×C4(C2×D3)⋊C411yescharacteristic
217C2×C3×C4(C2×D3)⋊C411yescharacteristic
218C2×C3×C4C2×D1211yescharacteristic
219C2×C3×C4C2×D1211yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—124no—
231C2×Dic3—124no—
232C2×Dic3—122no—
233C2×Dic3—122no—
234C3×C8—122no—
235C3×C8—122no—
236C3⋊C8—42no—
237C3⋊C8—42no—
238C2×C32—22no—
239C2×C32#40811yescharacteristic
240C2×C32#41011yescharacteristic
241C2×C32C2×#10111yescharacteristic
242C22×C4—92no—
243C22×C4—92no—
244C22×C4#62411yescharacteristic
245C22×C4#62411yescharacteristic
246C22×C4C2×D3211yescharacteristic
247C2×C8—62no—
248C2×C8—62no—
249C4⋊C4—182no—
250C4⋊C4—182no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—182no—
256C4⋊C4—182no—
257C42#62611yescharacteristic
258C42#62611yescharacteristic
259C42#62611yescharacteristic
260C42#62611yescharacteristic
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—22no—
268C22×C3—21no—
269C22×C3#90112yes—
270C22×C3#90712yes—
271C22×C3C2×(C2×D3)⋊C411yescharacteristic
272C22×C3C2×(C2×D3)⋊C411yescharacteristic
273C3×C4—22no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—22no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4#82412yes—
290C3×C4#82412yes—
291Dic3—124no—
292Dic3—124no—
293Dic3—122no—
294Dic3—122no—
295Dic3—122no—
296Dic3—122no—
297C32#147011yescharacteristic, complemented, Sylow
298C23C2×#62411yescharacteristic
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—184no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—362no—
306C2×C4#372211yescharacteristic
307C2×C4#372211yescharacteristic
308C2×C4#372211yescharacteristic
309C2×C4#372211yescharacteristic
310C2×C4C2×#62611yescharacteristic
311C2×C4C2×#62611yescharacteristic
312C8—122no—
313C8—122no—
314C2×C3—24no—
315C2×C3—22no—
316C2×C3—22no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3#500611yescharacteristic
321C2×C3#500611yescharacteristic
322C2×C3#511011yescharacteristic
323C2×C3#512911yescharacteristic
324C2×C3C2×#82411yescharacteristic
325C2×C3C2×#82411yescharacteristic
326C22—21no—
327C22—21no—
328C22#6381712yes—
329C22C2×#372211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—362no—
336C4—362no—
337C4#6356112yes—
338C3—21no—
339C3#7078711yescharacteristic, complemented
340C3#7083111yescharacteristic, complemented
341C2—22no—
342C2#1059107311yescharacteristic
343C2C2×#6356111yescharacteristic
344C2#1059123211yescharacteristic
subgroupG/H
centerC22C2×#3722
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1470
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
297. C32#1470semidirect
339. C3#70787semidirect
340. C3#70831semidirect

Maximal subgroups

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

subgroupindex
C2×#640792
C3×#49262
C3×#49252
#105891482
#708313
#707873