Finite Group Databasebeta

← D61×#1353 #29590308

Subgroups — D61×#1353 #29590308

Order 15616.

500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 91 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#400×D61C211yesmaximal, characteristic
2#343×D61C211yesmaximal, characteristic
3#324×D61C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic, complemented
5#21443846C211yesmaximal, characteristic, complemented
6#21443845C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×C4⋊C4×D61C411yescharacteristic
10C2×C4⋊C4×D61C2211yescharacteristic
11C22⋊C8×D61—21no—
12#16839704—21no—
13#16839703—21no—
14#16839702C411yescharacteristic
15#16839701C2211yescharacteristic
16#16839700C411yescharacteristic
17#95×D61—21no—
18#95×D61—21no—
19#95×D61C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#400C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C4×D61—21no—
28C22×C4×D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758189—41no—
34M16×D61—24no—
35M16×D61—42no—
36C2×C8×D61—41no—
37C2×C8×D61—41no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196C2×C411yescharacteristic
42C2×#11758196D411yescharacteristic
43C4⋊C4×D61—41no—
44C4⋊C4×D61—41no—
45C4⋊C4×D61—41no—
46C4⋊C4×D61—41no—
47C22⋊#92418—21no—
48#14519689—41no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—22no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×C4×D61—42no—
86C2×C4×D61—44no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—42no—
90C2×C4×D61SD1612yes—
91C2×C4×D61Q1612yes—
92M16×C61—22no—
93M16×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100#11758196—41no—
101#11758196—41no—
102#11758196—42no—
103#11758194—22no—
104#11758194—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107#11758189—44no—
108C8×D61—44no—
109C8×D61—82no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—22no—
112C22×D61—22no—
113C22×D61#9911yescharacteristic
114C22×D61#9911yescharacteristic
115C22×D61#10312yes—
116C22×D61#10412yes—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—42no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61C2×SD1611yescharacteristic
129C2×C4×C61C2×Q1611yescharacteristic
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—42no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#10312yes—
142C4×D61—22no—
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—42no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—81no—
150C4×D61—84no—
151C4×D61—82no—
152C4×D61—82no—
153C8×C61—42no—
154C8×C61—81no—
155#92418—42no—
156#92418—81no—
157C2×#1353—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61C2×#9911yescharacteristic
161C22×C61C2×#10311yescharacteristic
162C22×C61C2×#10411yescharacteristic
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—24no—
166C2×D61—24no—
167C2×D61#32812yes—
168C2×D61#32812yes—
169C2×D61#35212yes—
170C2×D61#35512yes—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—81no—
176C4×C61—81no—
177Dic61—22no—
178Dic61—41no—
179Dic61—41no—
180Dic61—81no—
181Dic61—81no—
182C2×#400—611no—
183C2×#343—611no—
184C2×#324—611no—
185#1353—611no—
186#1353—611no—
187#1353—611no—
188#1353D6111yescharacteristic, direct product factor
189C2×C61—21no—
190C2×C61—21no—
191C2×C61C2×#32811yescharacteristic
192C2×C61C2×#35211yescharacteristic
193C2×C61C2×#35511yescharacteristic
194D61—22no—
195D61#135314yesdirect product factor
196C22×M16—1221no—
197C22×C4⋊C4—611no—
198C22×C4⋊C4—611no—
199C2×C22⋊C8—1221no—
200#400—611no—
201#400—611no—
202#400—611no—
203#400—1221no—
204#400—1221no—
205#400C2×D6111yescharacteristic
206C2×#95—611no—
207C2×#95—1221no—
208C2×#95—1221no—
209#343—611no—
210#343—1221no—
211#343C2×D6111yescharacteristic
212#324—611no—
213#324—1221no—
214#324C2×D6111yescharacteristic
215C61C2×#135311yescharacteristic, complemented, Sylow
216C23×C4—611no—
217C23×C4—611no—
218C23×C4—611no—
219C23×C4—1221no—
220C23×C4—1221no—
221C2×M16—21no—
222C2×M16—1224no—
223C2×M16—1221no—
224C2×M16—2441no—
225C2×M16—2442no—
226C22×C8—2441no—
227C22×C8—2441no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—2441no—
234C2×C4⋊C4—2441no—
235C2×C4⋊C4—2441no—
236C2×C4⋊C4—2441no—
237C2×C4⋊C4C4×D6111yescharacteristic
238C2×C4⋊C4C22×D6111yescharacteristic
239C22⋊C8—21no—
240C22⋊C8—1221no—
241C22⋊C8—2441no—
242#95—21no—
243#95—21no—
244#95—611no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95C4×D6111yescharacteristic
253C24—611no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—611no—
257C22×C4—612no—
258C22×C4—612no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1222no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4—2442no—
273C22×C4—2444no—
274C22×C4—2442no—
275C22×C4—2442no—
276C22×C4—2442no—
277C22×C4—2442no—
278C22×C4C2×C4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281M16—22no—
282M16—41no—
283M16—1222no—
284M16—2444no—
285M16—2441no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—4882no—
289C2×C8—2444no—
290C2×C8—2441no—
291C2×C8—2441no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2442no—
299C23—611no—
300C23—611no—
301C23—612no—
302C23—612no—
303C23—1222no—
304C23—1222no—
305C23C22⋊C4×D6111yescharacteristic
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—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—612no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—4881no—
327C2×C4—4882no—
328C2×C4—4884no—
329C2×C4—4882no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2442no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4SD16×D6111yescharacteristic
341C2×C4Q16×D6111yescharacteristic
342C8—42no—
343C8—81no—
344C8—4881no—
345C8—2442no—
346C22—21no—
347C22—21no—
348C22—612no—
349C22—612no—
350C22—612no—
351C22—612no—
352C22—1224no—
353C22—1224no—
354C22—1221no—
355C22—1221no—
356C22#99×D6111yescharacteristic
357C22#103×D6111yescharacteristic
358C22#104×D6111yescharacteristic
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—81no—
364C4—81no—
365C4—1222no—
366C4—4881no—
367C4—4881no—
368C4—2441no—
369C4—2441no—
370C2—21no—
371C2—21no—
372C2—614no—
373C2—1222no—
374C2#328×D6111yescharacteristic
375C2#352×D6111yescharacteristic
376C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1353C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1353D61
hypocenterC61C2×#1353
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
4. #21443847C2semidirect
5. #21443846C2semidirect
6. #21443845C2semidirect
7. C61×#1353C2semidirect
188. #1353D61direct (N × H)
195. D61#1353direct (N × H)
215. C61C2×#1353semidirect

Maximal subgroups

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

subgroupindex
#400×D612
#343×D612
#324×D612
#214438472
#214438462
#214438452
C61×#13532
C2×#135361