Finite Group Databasebeta

← #30595356

Subgroups — #30595356

Order 15616.

596 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊#92420C211yesmaximal, characteristic
2C2×#16840628C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460638C212yesmaximal, complemented
5#21448347C211yesmaximal, characteristic
6C23×#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519756C411yescharacteristic
13C2×#14519742C411yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15#16839667C2211yescharacteristic
16#16839658C2211yescharacteristic
17#16839644—21no—
18#16839634—21no—
19C4⋊C4×Dic61C411yescharacteristic
20#16839613—21no—
21C22⋊C4×Dic61—21no—
22C61×#380C411yescharacteristic
23C22×#92420—24no—
24C22×#92420—22no—
25C22×#92420—22no—
26C22×#92420—42no—
27C22×#92420—42no—
28C22⋊#92420—24no—
29C4×#92420—42no—
30C22×Dic122C2×C411yescharacteristic
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519756—22no—
34#14519756C814yescomplemented
35#14519742—42no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—42no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C23×C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56#95×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C2×C812yes—
64C22×C4×C61M1612yes—
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—22no—
72C22×Dic61—41no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61SD1612yes—
76C22×Dic61Q1612yes—
77C22×Dic61C2×D411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79C2×Dic122—21no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122C2×C812yescomplemented
83C2×#92420—24no—
84C2×#92420—24no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—48no—
88C2×#92420—42no—
89C2×#92420—42no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C22⋊C4×C61—42no—
93C22⋊Dic61—24no—
94C4⋊Dic61—21no—
95C4⋊Dic61C2×C812yescomplemented
96#11758196—24no—
97#11758196—42no—
98#11758196—42no—
99C4×Dic61—22no—
100C4×Dic61—22no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C4×Dic61—42no—
104C4×Dic61—42no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61C22⋊C812yes—
110C23×C61#10312yes—
111C23×C61#10412yes—
112C23×C61C2×C22⋊C411yescharacteristic
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61C22⋊C812yes—
126C2×C4×C61C22×C811yescharacteristic
127C2×C4×C61C2×M1611yescharacteristic
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—24no—
133C2×Dic61—24no—
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—44no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#9912yes—
145C2×Dic61#10312yes—
146C2×Dic61#10412yes—
147C2×Dic61C2×SD1611yescharacteristic
148C2×Dic61C2×Q1611yescharacteristic
149C2×Dic61#13512yes—
150Dic122—42no—
151Dic122—42no—
152#92420—44no—
153#92420—44no—
154#7566—611nomaximal, Sylow
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—22no—
161C22×C61Q8⋊C814yes—
162C22×C61C2×C22⋊C811yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C22×C61#41311yescharacteristic
165C22×C61C2×#10311yescharacteristic
166C22×C61#41611yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C22×C61C2×#10411yescharacteristic
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—22no—
172C4×C61—81no—
173C4×C61—81no—
174Dic61—21no—
175Dic61—21no—
176Dic61—22no—
177Dic61—42no—
178Dic61—42no—
179Dic61—41no—
180Dic61#32814yes—
181C4×C22⋊Q8—611no—
182C4×C22⋊C8—611no—
183C2×#336—611no—
184#1272—612no—
185#1271—612no—
186C2×C61—24no—
187C2×C61#145911yescharacteristic
188C2×C61C2×Q8⋊C811yescharacteristic
189C2×C61#147611yescharacteristic
190C2×C61C2×#32811yescharacteristic
191C2×C61#150111yescharacteristic
192C2×C61#152411yescharacteristic
193C2×C61#154211yescharacteristic
194C23×C8—1221no—
195C2×C22⋊Q8—611no—
196C2×C4×Q8—611no—
197C22×C42—611no—
198C2×C22⋊C8—1221no—
199C2×C4×C8—1221no—
200#391—611no—
201#389—611no—
202#387—1221no—
203#385—1221no—
204#380#692311yescharacteristic
205C4×C4⋊C4—611no—
206C4×C4⋊C4—1221no—
207C4×C22⋊C4—1221no—
208#336—612no—
209#336—612no—
210#336—1221no—
211C61#756611yescharacteristic, complemented, Sylow
212C22×Q8—611no—
213C23×C4—611no—
214C23×C4—611no—
215C23×C4C2×#692311yescharacteristic
216C22×C8—1222no—
217C22×C8—1222no—
218C22×C8—1224no—
219C22×C8—2442no—
220C22×C8—2442no—
221C22⋊Q8—614no—
222C22⋊Q8—1222no—
223C4×Q8—2442no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4C2×#692311yescharacteristic
229C2×C4⋊C4C2×#692311yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—1221no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—1221no—
237C2×C42—1221no—
238C2×C42—2442no—
239C22⋊C8—1224no—
240C4×C8—2442no—
241#95—21no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24C22⋊#692311yescharacteristic
247C2×Q8—612no—
248C2×Q8—1221no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—611no—
256C22×C4—612no—
257C22×C4—612no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—1222no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—1222no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—2441no—
268C22×C4D61⋊C812yes—
269C22×C4#1175821312yes—
270C22×C4C22⋊#692311yescharacteristic
271C22×C4C22×#692311yescharacteristic
272C2×C8—1224no—
273C2×C8—1224no—
274C2×C8—2442no—
275C2×C8—2442no—
276C2×C8—2442no—
277C2×C8—2448no—
278C2×C8—2442no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—612no—
282C4⋊C4—1224no—
283C4⋊C4—1221no—
284C4⋊C4—2442no—
285C4⋊C4—2442no—
286C22⋊C4—42no—
287C22⋊C4—1224no—
288C42—1222no—
289C42—1222no—
290C42—2441no—
291C42—2441no—
292C42—2442no—
293C42—2442no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23#1451983412yes—
299C23#1451984012yes—
300C23#1451984112yes—
301C23C2×C22⋊#692311yescharacteristic
302Q8—2442no—
303Q8—2442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—612no—
317C2×C4—612no—
318C2×C4—612no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—612no—
322C2×C4—1224no—
323C2×C4—1224no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—2444no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4#1451983412yes—
339C2×C4C2×D61⋊C811yescharacteristic
340C2×C4C2×#1175821311yescharacteristic
341C8—2444no—
342C8—2444no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22#1684061214yes—
350C22C2×#1451983411yescharacteristic
351C22D61⋊#9911yescharacteristic
352C22#1684074911yescharacteristic
353C22C2×#1451984011yescharacteristic
354C22#1684075211yescharacteristic
355C22C2×#1451984111yescharacteristic
356C22D61⋊#10411yescharacteristic
357C4—22no—
358C4—21no—
359C4—21no—
360C4—81no—
361C4—81no—
362C4—614no—
363C4—1221no—
364C4—1221no—
365C4—1222no—
366C4—2442no—
367C4—2442no—
368C4—2441no—
369C2—24no—
370C2#2146105711yescharacteristic
371C2C2×#1684061211yescharacteristic
372C2#2146111211yescharacteristic
373C2D61⋊#32811yescharacteristic
374C2#2146119511yescharacteristic
375C2#2146127011yescharacteristic
376C2#2146132111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#7566
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460638C2semidirect
34. #14519756C8semidirect
82. C2×Dic122C2×C8semidirect
95. C4⋊Dic61C2×C8semidirect
211. C61#7566semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#924202
C2×#168406282
#214606402
#214606382
#214483472
#756661