Finite Group Databasebeta

← #29591126

Subgroups — #29591126

Order 15616.

390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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#467×D61C211yesmaximal, characteristic
2#21447428C211yesmaximal, characteristic
3#21445856C211yesmaximal, characteristic
4#21443838C211yesmaximal, characteristic, complemented
5#21443837C211yesmaximal, characteristic, complemented
6#21443836C211yesmaximal, characteristic, complemented
7C61×#1350C211yesmaximal, characteristic, complemented
8C2×Q16×D61C411yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C22⋊Q8×D61—21no—
11C2×#14519716—21no—
12#16840004C411yescharacteristic
13#16840003C2211yescharacteristic
14#16840002—21no—
15#16840001—21no—
16#16840000C411yescharacteristic
17C2×#14519712—21no—
18#107×D61C411yescharacteristic
19#103×D61—21no—
20#16839725—21no—
21C22⋊#11758185C2211yescharacteristic
22#16839541—21no—
23#16839527C2211yescharacteristic
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#341C2211yescharacteristic
27C2×Q8×D61—21no—
28C22×C4×D61D411yescharacteristic
29C2×Dic244C2×C411yescharacteristic
30C2×#11758202—21no—
31Q16×D61—42no—
32C2×#11758194—21no—
33C22×#92418D411yescharacteristic
34C2×C8×D61—42no—
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61C2×C411yescharacteristic
37C2×C8×D61D411yescharacteristic
38C2×C8×D61D411yescharacteristic
39#14519757—21no—
40#14519756—21no—
41#14519755—41no—
42#14519754—41no—
43#14519753—21no—
44C4⋊C4×D61—21no—
45C4⋊C4×D61—41no—
46C22⋊C4×D61—41no—
47#14519716—42no—
48C2×#11758185—21no—
49#14519712—42no—
50#14519711C2×C411yescharacteristic
51#14519710—21no—
52#14519702—21no—
53#14519701—21no—
54#14519700—21no—
55#14519689—41no—
56#14519689—41no—
57C2×Q16×C61C2×C411yescharacteristic
58C2×M16×C61—21no—
59C22×C8×C61C2311yescharacteristic
60C22⋊Q8×C61—21no—
61C2×C16×C61—21no—
62#107×C61C2×C411yescharacteristic
63#103×C61—21no—
64C23×D61SD1611yescharacteristic
65C2×Q8×C61—21no—
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61SD1611yescharacteristic
68Q8×D61—42no—
69Q8×D61—42no—
70C2×C4×D61—41no—
71C2×C4×D61—41no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×C4×D61C22⋊C411yescharacteristic
75C2×C4×D61C22⋊C411yescharacteristic
76C2×C4×D61D811yescharacteristic
77C2×C4×D61D811yescharacteristic
78C2×Dic122—21no—
79C2×Dic122—41no—
80Q16×C61—41no—
81M16×C61—41no—
82M16×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61C22×C411yescharacteristic
86C2×C8×C61C2×D411yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊Dic61—41no—
91#11758202—42no—
92#11758198—41no—
93#11758198—41no—
94C4⋊Dic61—21no—
95C4⋊Dic61—41no—
96#11758196—41no—
97#11758196—41no—
98#11758196—41no—
99#11758194—41no—
100#11758194—41no—
101C2×#92418—22no—
102C2×#92418—41no—
103C2×#92418C22⋊C411yescharacteristic
104C2×#92418C22⋊C411yescharacteristic
105Dic244—41no—
106C8×D61—22no—
107C8×D61—22no—
108C8×D61—41no—
109C8×D61—41no—
110C16×C61—41no—
111#11758185—41no—
112C23×C61C2×SD1611yescharacteristic
113C22×D61—22no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61#10211yescharacteristic
117C22×D61#10211yescharacteristic
118Q8×C61—41no—
119Q8×C61—41no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61C2×C22⋊C411yescharacteristic
125C2×C4×C61C2×D811yescharacteristic
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61#10211yescharacteristic
130C2×Dic61#10211yescharacteristic
131C4×D61—21no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—41no—
136C4×D61—41no—
137C4×D61—82no—
138C4×D61—82no—
139Dic122—41no—
140Dic122—41no—
141Dic122—82no—
142C8×C61—21no—
143C8×C61—21no—
144C8×C61—81no—
145#92418—21no—
146#92418—81no—
147#92418#9912yes—
148#11896—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61C2×#10211yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—44no—
159C2×D61#36212yes—
160C4×C61—21no—
161C4×C61—81no—
162C4×C61—81no—
163C4×C61C2×#9911yescharacteristic
164C4×C61#42111yescharacteristic
165Dic61—21no—
166Dic61—21no—
167Dic61—81no—
168Dic61—81no—
169C2×#467—611no—
170#2112—611no—
171#1810—611no—
172#1350—611no—
173#1350—611no—
174#1350—611no—
175#1350D6111yescharacteristic, complemented
176C2×C61—41no—
177C2×C61#151911yescharacteristic
178C2×C61#214311yescharacteristic
179C2×C61C2×#36211yescharacteristic
180D61—22no—
181D61—41no—
182C22×Q16—611no—
183C23×C8—611no—
184C2×C22⋊Q8—1221no—
185C2×M32—1221no—
186#467—611no—
187#467—611no—
188#467—611no—
189#467—1221no—
190#467—1221no—
191#467C2×D6111yescharacteristic
192C2×#108—1221no—
193C2×#107—611no—
194C2×#103—1221no—
195#407—1221no—
196C22⋊C16—611no—
197C22⋊C16—1221no—
198C22⋊C16C2×D6111yescharacteristic
199#341—611no—
200#341C2×D6111yescharacteristic
201C61#1189611yescharacteristic, complemented, Sylow
202C22×Q8—1221no—
203C23×C4—611no—
204C2×Q16—611no—
205C2×Q16—1221no—
206C2×Q16—2442no—
207C2×Q16C4×D6111yescharacteristic
208C2×M16—21no—
209C2×M16—1221no—
210C22×C8—611no—
211C22×C8—611no—
212C22×C8—611no—
213C22×C8—611no—
214C22×C8—611no—
215C22×C8—2442no—
216C22×C8C22×D6111yescharacteristic
217C22⋊Q8—21no—
218C22⋊Q8—1221no—
219C22⋊Q8—1221no—
220C22⋊Q8—1221no—
221C22⋊Q8—2441no—
222C22⋊Q8—2441no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—2441no—
225C2×C22⋊C4—2441no—
226M32—2442no—
227C2×C16—21no—
228C2×C16—1221no—
229#108—2442no—
230#107—611no—
231#107—1221no—
232#107C4×D6111yescharacteristic
233#103—21no—
234#103—1221no—
235#103—1221no—
236#103—1221no—
237C22⋊C8—2441no—
238C22⋊C8—2441no—
239C24—611no—
240C2×Q8—21no—
241C2×Q8—1221no—
242C2×Q8—2441no—
243C2×Q8—2442no—
244C2×Q8—2442no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—2441no—
251C22×C4—2441no—
252C22×C4—2441no—
253C22×C4—2441no—
254C22×C4D4×D6111yescharacteristic
255Q16—41no—
256Q16—2441no—
257Q16—2442no—
258M16—41no—
259M16—41no—
260M16—2441no—
261M16—2441no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—1222no—
267C2×C8—1222no—
268C2×C8—1222no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8—2441no—
272C2×C8C2×C4×D6111yescharacteristic
273C2×C8D4×D6111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—1221no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C22⋊C4—41no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C16—41no—
286C16—2441no—
287C23—611no—
288C23—611no—
289C23—1222no—
290C23—2441no—
291C23—2441no—
292C23SD16×D6111yescharacteristic
293Q8—41no—
294Q8—41no—
295Q8—4882no—
296Q8—2441no—
297Q8—2441no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—4882no—
309C2×C4—4882no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4C22⋊C4×D6111yescharacteristic
316C2×C4D8×D6111yescharacteristic
317C8—21no—
318C8—21no—
319C8—81no—
320C8—612no—
321C8—1221no—
322C8—4881no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—612no—
327C22—1221no—
328C22—1221no—
329C22—1221no—
330C22—1221no—
331C22—1221no—
332C22—2444no—
333C22#102×D6111yescharacteristic
334C4—21no—
335C4—81no—
336C4—81no—
337C4—1221no—
338C4—1221no—
339C4—4881no—
340C4—4881no—
341C4#99×D6111yescharacteristic
342C4#1683977711yescharacteristic
343C2—41no—
344C2—1222no—
345C2—2441no—
346C2#2144438511yescharacteristic
347C2#2144754511yescharacteristic
348C2#362×D6111yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1350C2
socleC22×C61C2×#102
prime radicalC23×D61SD16
cosocleC22×C8×C61C23
hypercenter#1350D61
hypocenterC61#11896
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1350

Complements

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

NH ≅ G/Ntype
4. #21443838C2semidirect
5. #21443837C2semidirect
6. #21443836C2semidirect
7. C61×#1350C2semidirect
175. #1350D61semidirect
201. C61#11896semidirect

Maximal subgroups

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

subgroupindex
#467×D612
#214474282
#214458562
#214438382
#214438372
#214438362
C61×#13502
#1189661