Finite Group Databasebeta

← #30595759

Subgroups — #30595759

Order 15616.

568 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461482C211yesmaximal, characteristic
2C2×#16840628C211yesmaximal, characteristic
3#21460639C212yesmaximal, complemented
4#21460638C212yesmaximal, complemented
5#21454153C211yesmaximal, characteristic
6C22×#11758217—21no—
7C23×#92420—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C22×C4×Dic61C2211yescharacteristic
13#16839669C411yescharacteristic
14#16839669C2211yescharacteristic
15#16839658C411yescharacteristic
16#16839658C2211yescharacteristic
17#16839643—21no—
18#16839643—21no—
19#16839634—21no—
20#16839623—21no—
21#16839622C411yescharacteristic
22C2×C22⋊Q8×C61C411yescharacteristic
23C2×#11758217—24no—
24C2×#11758217—42no—
25C2×#11758217—42no—
26C22×#92420—24no—
27C22×#92420—22no—
28C22×#92420—22no—
29C22×#92420—42no—
30C22×#92420—42no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61—42no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C22×Q8×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52C22⋊Q8×C61—42no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C24×C61C22⋊C411yescharacteristic
57C2×Q8×C61—22no—
58C2×Q8×C61—41no—
59C2×Q8×C61—41no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—41no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61SD1612yes—
78C22×Dic61Q1612yes—
79C22×Dic61C2×D411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81#11758217—48no—
82C2×#92420—24no—
83C2×#92420—24no—
84C2×#92420—48no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—42no—
92C22⋊Dic61—42no—
93C4⋊Dic61—22no—
94C4⋊Dic61—41no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101C4×Dic61—41no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61#9912yes—
107C23×C61#10312yes—
108C23×C61#10412yes—
109C23×C61C2×C22⋊C411yescharacteristic
110Q8×C61—82no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—44no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61#13112yes—
124C2×Dic61—24no—
125C2×Dic61—24no—
126C2×Dic61—24no—
127C2×Dic61—24no—
128C2×Dic61—21no—
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—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#10312yes—
143C2×Dic61#10412yes—
144C2×Dic61C2×SD1611yescharacteristic
145C2×Dic61C2×Q1611yescharacteristic
146C2×Dic61AGL(1,ℤ/8)11yescharacteristic
147C2×Dic61#13711yescharacteristic
148#92420—44no—
149#92420—44no—
150#7681—611nomaximal, Sylow
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61#32814yes—
158C22×C61#40811yescharacteristic
159C22×C61C2×#9911yescharacteristic
160C22×C61#41311yescharacteristic
161C22×C61C2×#10311yescharacteristic
162C22×C61#41711yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C4×C61—22no—
166C4×C61—41no—
167C4×C61—81no—
168C4×C61—81no—
169Dic61—21no—
170Dic61—22no—
171Dic61—21no—
172Dic61—21no—
173Dic61—22no—
174Dic61—21no—
175Dic61—81no—
176Dic61—81no—
177#2855—611no—
178#1728—611no—
179C2×#336—611no—
180#1272—612no—
181#1271—612no—
182C2×C61—24no—
183C2×C61#146811yescharacteristic
184C2×C61#148311yescharacteristic
185C2×C61#149311yescharacteristic
186C2×C61C2×#32811yescharacteristic
187C2×C61#150411yescharacteristic
188C2×C61#152411yescharacteristic
189C2×C61#155011yescharacteristic
190C22×M16—1221no—
191C23×C8—1221no—
192C2×C22⋊Q8#692311yescharacteristic
193C22×C42—611no—
194#391—611no—
195#391—611no—
196#389—611no—
197#389—611no—
198#387—1221no—
199#387—1221no—
200#385—1221no—
201#381—1221no—
202#380—611no—
203#336—612no—
204#336—612no—
205#336—1221no—
206#336—1221no—
207C61#768111yescharacteristic, complemented, Sylow
208C22×Q8C2×#692311yescharacteristic
209C23×C4—611no—
210C23×C4—611no—
211C23×C4C2×#692311yescharacteristic
212C2×M16—1224no—
213C2×M16—2442no—
214C2×M16—2442no—
215C22×C8—1222no—
216C22×C8—1222no—
217C22×C8—1224no—
218C22×C8—2442no—
219C22×C8—2442no—
220C22⋊Q8—42no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4C2×#692311yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—1221no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—2442no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24C22⋊#692311yescharacteristic
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—612no—
251C22×C4—612no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—1222no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—1222no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22×#692311yescharacteristic
266M16—2448no—
267C2×C8—1224no—
268C2×C8—1224no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2448no—
272C2×C8—2442no—
273C2×C8—2442no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—1222no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2442no—
281C22⋊C4—42no—
282C22⋊C4—2442no—
283C42—2441no—
284C42—2441no—
285C42—2441no—
286C42—2441no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23#1451983512yes—
292C23#1451984012yes—
293C23#1451984212yes—
294C23C2×C22⋊#692311yescharacteristic
295Q8—82no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—44no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—612no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—612no—
314C2×C4—1224no—
315C2×C4—1224no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1224no—
325C2×C4—1224no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451986412yes—
333C8—2444no—
334C8—2444no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22#1684061614yes—
342C22#1684073511yescharacteristic
343C22C2×#1451983511yescharacteristic
344C22#1684074911yescharacteristic
345C22C2×#1451984011yescharacteristic
346C22#1684075311yescharacteristic
347C22D61⋊#10411yescharacteristic
348C22C2×#1451984211yescharacteristic
349C4—22no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—1221no—
354C4—1222no—
355C4—1221no—
356C4—1221no—
357C4—1222no—
358C4—1221no—
359C4—4881no—
360C4—4881no—
361C2—24no—
362C2#2146108411yescharacteristic
363C2#2146113611yescharacteristic
364C2#2146116711yescharacteristic
365C2C2×#1684061611yescharacteristic
366C2#2146120511yescharacteristic
367C2#2146127211yescharacteristic
368C2#2146133711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊Q8#6923
hypocenterC61#7681
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21460639C2semidirect
4. #21460638C2semidirect
207. C61#7681semidirect

Maximal subgroups

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

subgroupindex
#214614822
C2×#168406282
#214606392
#214606382
#214541532
#768161