Finite Group Databasebeta

← #30597588

Subgroups — #30597588

Order 15616.

574 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊#92420C211yesmaximal, characteristic, complemented
2#21461534C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal
4#21460655C212yesmaximal, complemented
5#21448277C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C4×#92420—21no—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12#16840610C418yescomplemented
13C2×#14519739C2211yescharacteristic
14C2×#14519735—21no—
15#16839664C411yescharacteristic
16#16839663C411yescharacteristic
17#16839661C411yescharacteristic
18#16839654—21no—
19#16839652—21no—
20C4⋊C4×Dic61C2211yescharacteristic
21#16839609—21no—
22C42×Dic61C2211yescharacteristic
23C61×#389C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26C4⋊#92420—22no—
27C4⋊#92420C2×C414yes—
28C4×#92420—22no—
29C4×#92420—42no—
30C4×#92420C2×C414yes—
31C22×D244C2×C411yescharacteristic
32C22×C4×D61—21no—
33#14519739—22no—
34#14519739C2×C414yes—
35#14519735—42no—
36#14519735—42no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
51#14519684—21no—
52#14519684—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57#95×C61—21no—
58C23×D61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×D244—22no—
70C2×D244—22no—
71C2×D244—21no—
72C2×D244C4212yes—
73C2×C4×D61—24no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—42no—
77C2×#92420—24no—
78C2×#92420—24no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—42no—
86C4⋊C4×C61C4212yes—
87C42×C61—22no—
88#11758198—24no—
89#11758198—42no—
90#11758198—42no—
91#11758198—42no—
92#11758198—42no—
93C4⋊Dic61—22no—
94C4⋊Dic61—42no—
95C4×Dic61—22no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101C4×Dic61D812yes—
102C4×Dic61SD1612yes—
103C4×Dic61C22×C412yes—
104C4×Dic61#4112yes—
105C23×C61C2×C22⋊C411yescharacteristic
106C22×D61—22no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61#10212yes—
125C2×C4×C61C2×C4211yescharacteristic
126C2×C4×C61#11711yescharacteristic
127C2×C4×C61#13112yes—
128C2×C4×C61#13112yes—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61#10212yes—
140C2×Dic61C4×D412yes—
141C2×Dic61C4×D412yes—
142C2×Dic61C2×D811yescharacteristic
143C2×Dic61C2×SD1611yescharacteristic
144C2×Dic61#13512yes—
145D244—24no—
146D244—42no—
147C4×D61—44no—
148C4×D61—44no—
149#92420—44no—
150#92420—44no—
151#8183—611nomaximal, Sylow
152C22×C61C4×C22⋊C411yescharacteristic
153C22×C61#40811yescharacteristic
154C22×C61#40811yescharacteristic
155C22×C61C2×#10211yescharacteristic
156C22×C61#41611yescharacteristic
157C22×C61#42111yescharacteristic
158C22×C61#42111yescharacteristic
159C2×D61—42no—
160C2×D61—42no—
161C2×D61—42no—
162C2×D61—81no—
163C2×D61—81no—
164C2×D61—81no—
165C2×D61—81no—
166C4×C61—22no—
167C4×C61—41no—
168C4×C61—42no—
169C4×C61—81no—
170C4×C61#40512yes—
171C4×C61#43312yes—
172Dic61—22no—
173Dic61—22no—
174Dic61—41no—
175Dic61—81no—
176Dic61C4×D812yes—
177Dic61C4×SD1612yes—
178#2293—611no—
179C4×C4⋊C8—611no—
180#1744—611no—
181C2×D4⋊C8—612no—
182#1279—612no—
183C2×C61#148011yescharacteristic
184C2×C61#148011yescharacteristic
185C2×C61#148211yescharacteristic
186C2×C61#148211yescharacteristic
187C2×C61#175011yescharacteristic
188C2×C61#175911yescharacteristic
189C2×C61C4×#10211yescharacteristic
190D61—82no—
191C2×C4×D4—611no—
192C2×#117—1221no—
193C2×C4⋊C8—612no—
194C2×C4×C8—612no—
195C2×C4×C8—1221no—
196#390—611no—
197#390—611no—
198#389—611no—
199#389#692311yescharacteristic
200#388—1221no—
201#388—1221no—
202C4×C4⋊C4—611no—
203C4×C22⋊C4—1221no—
204C43—611no—
205#336—1221no—
206#336—1221no—
207#336—1221no—
208D4⋊C8—618no—
209C61#818311yescharacteristic, complemented, Sylow
210C22×D4—611no—
211C23×C4—1221no—
212C22×C8—1222no—
213C22×C8—1222no—
214C4×D4—614no—
215C4×D4—1222no—
216#117—2442no—
217#117—2442no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4C2×#692311yescharacteristic
222C2×C4⋊C4C2×#692311yescharacteristic
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C42—611no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—1221no—
235C2×C42C2×#692311yescharacteristic
236C4⋊C8—614no—
237C4⋊C8—1222no—
238C4×C8—614no—
239C4×C8—1222no—
240C4×C8—2442no—
241#95—21no—
242#95—1221no—
243#95—1221no—
244C24—1221no—
245C2×D4—612no—
246C2×D4—1221no—
247C2×D4—1222no—
248C2×D4—1222no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1224no—
256C22×C4—1221no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4—2442no—
260C22×C4C22⋊#692311yescharacteristic
261C22×C4C22⋊#692311yescharacteristic
262C22×C4C22×#692311yescharacteristic
263C2×C8—1224no—
264C2×C8—1224no—
265C2×C8—2442no—
266C2×C8—2442no—
267C2×C8—2442no—
268C2×C8—2442no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—42no—
272C4⋊C4—1222no—
273C4⋊C4—2442no—
274C4⋊C4C4×#692312yes—
275C22⋊C4—1224no—
276C22⋊C4—2442no—
277C22⋊C4—2442no—
278C22⋊C4—2442no—
279C22⋊C4—2442no—
280C42—22no—
281C42—612no—
282C42—612no—
283C42—612no—
284C42—612no—
285C42—1222no—
286C42—1222no—
287C42—2441no—
288C42—2441no—
289C42—2441no—
290C42—2441no—
291C23—1222no—
292C23—2441no—
293C23—2441no—
294C23—2441no—
295C23—2441no—
296C23—2441no—
297C23—2441no—
298C23C2×C22⋊#692311yescharacteristic
299D4—1224no—
300D4—2442no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—612no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—612no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—2444no—
326C2×C4—2444no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4#1451983912yes—
331C2×C4C2×C4×#692311yescharacteristic
332C2×C4#1451985611yescharacteristic
333C2×C4#1451986412yes—
334C2×C4#1451986512yes—
335C8—2444no—
336C8—2444no—
337C22—4881no—
338C22—4881no—
339C22—4881no—
340C22—4881no—
341C22—2442no—
342C22—2442no—
343C22—2442no—
344C22C4×C22⋊#692311yescharacteristic
345C22#1684073511yescharacteristic
346C22#1684073711yescharacteristic
347C22C2×#1451983911yescharacteristic
348C22#1684075211yescharacteristic
349C22#1684075911yescharacteristic
350C22#1684076111yescharacteristic
351C4—22no—
352C4—42no—
353C4—41no—
354C4—81no—
355C4—612no—
356C4—612no—
357C4—1222no—
358C4—1222no—
359C4—4881no—
360C4—2441no—
361C4#1684072712yes—
362C4#1684078712yes—
363C2—4882no—
364C2#2146112411yescharacteristic
365C2#2146112611yescharacteristic
366C2#2146113211yescharacteristic
367C2#2146113311yescharacteristic
368C2#2146154811yescharacteristic
369C2#2146158311yescharacteristic
370C2C4×#1451983911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#8183
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊#92420C2semidirect
2. #21461534C2semidirect
4. #21460655C2semidirect
12. #16840610C4semidirect
209. C61#8183semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#924202
#214615342
C2×#168406102
#214606552
#214482772
#818361