Finite Group Databasebeta

← #30595569

Subgroups — #30595569

Order 15616.

594 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461546C211yesmaximal, characteristic
2#21461546C211yesmaximal, characteristic
3#21460638C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#389×D61C211yesmaximal, characteristic
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×#14519832—21no—
9C2×#14519832—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×C4⋊C4×D61—21no—
13C2×C4⋊C4×D61C411yescharacteristic
14C2×C4⋊C4×D61C411yescharacteristic
15C2×C42×D61C2211yescharacteristic
16#16839661C2211yescharacteristic
17#16839660C411yescharacteristic
18#16839659—21no—
19#16839658C2211yescharacteristic
20#16839657—21no—
21#95×D61—21no—
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26#14519834—24no—
27#14519832—42no—
28#14519832—42no—
29C22×C4×D61—21no—
30C22×C4×D61—21no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C4⋊C4×D61—22no—
42C4⋊C4×D61—22no—
43C4⋊C4×D61—44no—
44C4⋊C4×D61—42no—
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48C42×D61—42no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56#95×C61—21no—
57C23×D61C22⋊C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×C4×D61—22no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—22no—
72C2×C4×D61—24no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C2×#92420—24no—
85C2×#92420—24no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—42no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61M1612yes—
94C42×C61—41no—
95C4⋊Dic61—21no—
96C4⋊Dic61—42no—
97C4⋊Dic61—41no—
98C4⋊Dic61M1612yes—
99#11758196—24no—
100#11758196—42no—
101#11758196—42no—
102#11758196—42no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—41no—
106C23×C61C2×C22⋊C411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61#10112yes—
112C22×D61#10412yes—
113C22×D61#10412yes—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—22no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61C2×M1611yescharacteristic
129C2×C4×C61C2×M1611yescharacteristic
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—22no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#9912yes—
143C2×Dic61AGL(1,ℤ/8)12yes—
144C2×Dic61#13712yes—
145C4×D61—24no—
146C4×D61—24no—
147C4×D61—44no—
148C4×D61—44no—
149C4×D61—48no—
150C4×D61—84no—
151#92420—44no—
152#92420—44no—
153#7627—611nomaximal, Sylow
154C22×C61#40711yescharacteristic
155C22×C61C2×#9911yescharacteristic
156C22×C61C2×#10111yescharacteristic
157C22×C61#41811yescharacteristic
158C22×C61#41911yescharacteristic
159C22×C61C2×#10411yescharacteristic
160C22×C61C2×#10411yescharacteristic
161C2×D61—22no—
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—22no—
167C2×D61#33014yes—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—42no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—81no—
174Dic61—22no—
175Dic61—22no—
176Dic61—22no—
177Dic61—42no—
178Dic61—81no—
179C2×#389—611no—
180#1749—611no—
181#1749—611no—
182#1271—612no—
183#1271—612no—
184C2×C61#146311yescharacteristic
185C2×C61#149011yescharacteristic
186C2×C61#149111yescharacteristic
187C2×C61#150711yescharacteristic
188C2×C61#150811yescharacteristic
189C2×C61C2×#33011yescharacteristic
190C2×C61#155611yescharacteristic
191D61—24no—
192C22×C4⋊C4—611no—
193C22×C4⋊C4—611no—
194C22×C4⋊C4—1221no—
195C22×C42—611no—
196C2×C22⋊C8—1221no—
197C2×C22⋊C8—1221no—
198C2×#97—1221no—
199C2×#97—1221no—
200#389—611no—
201#389—611no—
202#389—611no—
203#389—1221no—
204#389—1221no—
205#389#692311yescharacteristic
206C2×#95—1221no—
207#336—612no—
208#336—612no—
209C61#762711yescharacteristic, complemented, Sylow
210C23×C4—611no—
211C23×C4—611no—
212C23×C4—611no—
213C23×C4—1221no—
214C23×C4—1221no—
215C22×C8—1222no—
216C22×C8—1222no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1222no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1222no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—2444no—
228C2×C4⋊C4—2442no—
229C2×C4⋊C4C2×#692311yescharacteristic
230C2×C4⋊C4C2×#692311yescharacteristic
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—2442no—
235C2×C42C2×#692311yescharacteristic
236C22⋊C8—1224no—
237C22⋊C8—1224no—
238#97—2442no—
239#97—2442no—
240#95—21no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244C24—611no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—1222no—
255C22×C4—1222no—
256C22×C4—1224no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2442no—
264C22×C4—2442no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4—2442no—
268C22×C4C22⋊#692311yescharacteristic
269C22×C4C22⋊#692311yescharacteristic
270C22×C4C22×#692311yescharacteristic
271C2×C8—1224no—
272C2×C8—1224no—
273C2×C8—2442no—
274C2×C8—2442no—
275C2×C8—2442no—
276C2×C8—2442no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—612no—
281C4⋊C4—1224no—
282C4⋊C4—1221no—
283C4⋊C4—2441no—
284C4⋊C4—2442no—
285C4⋊C4—2442no—
286C4⋊C4—2442no—
287C4⋊C4—2442no—
288C4⋊C4#1175821312yes—
289C42—41no—
290C42—1222no—
291C42—1222no—
292C42—2441no—
293C23—612no—
294C23—612no—
295C23—612no—
296C23—1221no—
297C23—1221no—
298C23—1221no—
299C23—1221no—
300C23C2×C22⋊#692311yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—612no—
318C2×C4—1224no—
319C2×C4—1224no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1222no—
327C2×C4—4884no—
328C2×C4—2444no—
329C2×C4—2444no—
330C2×C4—2448no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4D61⋊M1611yescharacteristic
337C2×C4C2×#1175821311yescharacteristic
338C8—2444no—
339C8—2444no—
340C22—614no—
341C22—1222no—
342C22—1222no—
343C22—1222no—
344C22—1222no—
345C22—1222no—
346C22—1222no—
347C22#1684073311yescharacteristic
348C22D61⋊#9911yescharacteristic
349C22D61⋊#10111yescharacteristic
350C22#1684075411yescharacteristic
351C22#1684075511yescharacteristic
352C22D61⋊#10411yescharacteristic
353C22D61⋊#10411yescharacteristic
354C4—21no—
355C4—21no—
356C4—42no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—1222no—
361C4—1222no—
362C4—1222no—
363C4—4881no—
364C4—2442no—
365C2—1224no—
366C2#2146106811yescharacteristic
367C2#2146115911yescharacteristic
368C2#2146116211yescharacteristic
369C2#2146121411yescharacteristic
370C2#2146121711yescharacteristic
371C2D61⋊#33011yescharacteristic
372C2#2146134911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7627
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #21460638C2semidirect
4. #21460637C2semidirect
209. C61#7627semidirect

Maximal subgroups

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

subgroupindex
#214615462
#214606382
#214606372
#389×D612
#762761