Finite Group Databasebeta

← #30595773

Subgroups — #30595773

Order 15616.

562 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C4×C22⋊#92420C211yesmaximal, characteristic
2#21461482C211yesmaximal, characteristic
3#21460638C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#21454169C211yesmaximal, characteristic
6C22×#11758217—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×#14519754—21no—
14C22×C4×Dic61C2211yescharacteristic
15#16839666—21no—
16#16839661C2211yescharacteristic
17#16839659—21no—
18#16839658C2211yescharacteristic
19#16839631C411yescharacteristic
20#16839622C411yescharacteristic
21#16839620—21no—
22C61×#380C411yescharacteristic
23C2×#11758217—24no—
24C2×#11758217—42no—
25C2×#11758217—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28C22⋊#92420—24no—
29C4×#92420—42no—
30C22×Dic122—21no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519776—42no—
34#14519754—42no—
35#14519754—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C4×Dic61—42no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
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—22no—
59C22×C4×C61—22no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—41no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—22no—
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61D812yes—
75C22×Dic61SD1612yes—
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×Dic122—42no—
79C2×Dic122—42no—
80C2×Dic122—42no—
81#11758217—48no—
82C2×#92420—24no—
83C2×#92420—24no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—42no—
91C22⋊Dic61—42no—
92C4⋊Dic61—22no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—42no—
97#11758196—42no—
98#11758196—42no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61—22no—
102C4×Dic61—22no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61#10212yes—
112C23×C61C2×C22⋊C411yescharacteristic
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—44no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61#10112yes—
125C2×C4×C61#13112yes—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—24no—
133C2×Dic61—24no—
134C2×Dic61—44no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#9912yes—
142C2×Dic61#10212yes—
143C2×Dic61#10412yes—
144C2×Dic61#10412yes—
145C2×Dic61C2×D811yescharacteristic
146C2×Dic61C2×SD1611yescharacteristic
147C2×Dic61#13712yes—
148Dic122—84no—
149#92420—44no—
150#92420—44no—
151#7685—611nomaximal, Sylow
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61#40811yescharacteristic
160C22×C61C2×#9911yescharacteristic
161C22×C61C2×#10111yescharacteristic
162C22×C61C2×#10211yescharacteristic
163C22×C61#41911yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C22×C61C2×#10411yescharacteristic
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—81no—
169C4×C61—81no—
170Dic61—21no—
171Dic61—21no—
172Dic61—22no—
173Dic61—22no—
174Dic61—81no—
175Dic61—81no—
176Dic61#32714yes—
177#2857—611no—
178C4×C22⋊C8—611no—
179#1728—611no—
180#1271—612no—
181#1271—612no—
182C2×C61—42no—
183C2×C61#147211yescharacteristic
184C2×C61#148511yescharacteristic
185C2×C61#149211yescharacteristic
186C2×C61C2×#32711yescharacteristic
187C2×C61#150811yescharacteristic
188C2×C61#152611yescharacteristic
189C2×C61#154611yescharacteristic
190C22×M16—1221no—
191C2×C4⋊Q8—611no—
192C2×C22⋊Q8—1221no—
193C22×C42—611no—
194C2×C22⋊C8—1221no—
195C2×C4×C8—1221no—
196#391—1221no—
197#389—611no—
198#389—611no—
199#389—1221no—
200#384—611no—
201#380—611no—
202#380—1221no—
203#380#692311yescharacteristic
204#336—612no—
205#336—612no—
206#336—1221no—
207C61#768511yescharacteristic, complemented, Sylow
208C22×Q8—1221no—
209C23×C4—611no—
210C23×C4—611no—
211C23×C4C2×#692311yescharacteristic
212C2×M16—1224no—
213C2×M16—2442no—
214C2×M16—2442no—
215C22×C8—1222no—
216C22×C8—1222no—
217C4⋊Q8—2442no—
218C22⋊Q8—2442no—
219C22⋊Q8—2442no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4C2×#692311yescharacteristic
228C2×C4⋊C4C2×#692311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—1221no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—2442no—
236C22⋊C8—1224no—
237C4×C8—2442no—
238#95—21no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242C24C22⋊#692311yescharacteristic
243C2×Q8—2442no—
244C2×Q8—2442no—
245C2×Q8—2442no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—611no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—2441no—
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22×#692311yescharacteristic
266M16—2448no—
267C2×C8—1224no—
268C2×C8—1224no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—1222no—
276C4⋊C4—2441no—
277C4⋊C4—2442no—
278C4⋊C4—2442no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2442no—
284C22⋊C4—42no—
285C22⋊C4—2442no—
286C42—1222no—
287C42—1222no—
288C42—2441no—
289C42—2441no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#1451983912yes—
297C23C2×C22⋊#692311yescharacteristic
298Q8—4884no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—44no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—612no—
311C2×C4—612no—
312C2×C4—612no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—612no—
317C2×C4—1224no—
318C2×C4—1224no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—2444no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451983812yes—
333C2×C4#1451986412yes—
334C8—2444no—
335C8—2444no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22#1684073511yescharacteristic
344C22D61⋊#9911yescharacteristic
345C22C2×#1451983811yescharacteristic
346C22C2×#1451983911yescharacteristic
347C22#1684075511yescharacteristic
348C22D61⋊#10411yescharacteristic
349C22D61⋊#10411yescharacteristic
350C4—22no—
351C4—22no—
352C4—81no—
353C4—81no—
354C4—614no—
355C4—1221no—
356C4—1221no—
357C4—1222no—
358C4—1222no—
359C4—4881no—
360C4—4881no—
361C2—42no—
362C2#2146109811yescharacteristic
363C2#2146114111yescharacteristic
364C2#2146116411yescharacteristic
365C2D61⋊#32711yescharacteristic
366C2#2146121711yescharacteristic
367C2#2146127611yescharacteristic
368C2#2146132811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#7685
LCSG ▷ C22×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. #21460638C2semidirect
4. #21460637C2semidirect
207. C61#7685semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#924202
#214614822
#214606382
#214606372
#214541692
#768561