Finite Group Databasebeta

← #29577876

Subgroups — #29577876

Order 15616.

454 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 105 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#21454902C211yesmaximal, characteristic
2#21451186C211yesmaximal, characteristic
3#21445812C211yesmaximal, characteristic
4#21444249C211yesmaximal, characteristic
5#21444247C211yesmaximal, characteristic
6#21443677C211yesmaximal, characteristic
7C61×#1286C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16839892—22no—
11#16839889—22no—
12#16839816—22no—
13#16839815C2211yescharacteristic
14#16839786C2211yescharacteristic
15C2×#14519695—21no—
16#16839702C412yes—
17#16839683C412yes—
18#16839667—21no—
19#16839661—21no—
20#16839647—22no—
21#16839530—21no—
22#16839494—22no—
23#16839492—22no—
24C61×#431C2211yescharacteristic
25C61×#423C2211yescharacteristic
26C61×#382C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×Dic122D411yescharacteristic
29C2×#11758194—21no—
30C4×Dic122—21no—
31C4×Dic122—21no—
32C4×Dic122—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C2×C4⋊Dic61—22no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196C2×C412yes—
43C2×C4×Dic61—21no—
44C2×C4×Dic61D412yes—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519706—24no—
49#14519695—42no—
50C22⋊#92418—21no—
51#14519687—24no—
52C4×#92418D412yes—
53#14519684—22no—
54#14519684—22no—
55#14519684—22no—
56C2×M16×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C4×C8×C61D412yes—
64#95×C61—21no—
65#95×C61C2×C412yes—
66C22×C4×C61—22no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C412yes—
73C22×Dic61C22⋊C412yes—
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122—21no—
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×Dic122—42no—
83M16×C61—41no—
84M16×C61—41no—
85C2×C8×C61—22no—
86C2×C8×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C42×C61C2×D411yescharacteristic
90C42×C61C2×D411yescharacteristic
91C42×C61#4111yescharacteristic
92C42×C61#4111yescharacteristic
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—44no—
98#11758196—22no—
99#11758196—22no—
100#11758196—41no—
101#11758196—41no—
102C4×Dic61—22no—
103C4×Dic61—22no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106#11758194—41no—
107#11758194—41no—
108C2×#92418—22no—
109C2×#92418—41no—
110C23×C61C2×C22⋊C411yescharacteristic
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61C4×D411yescharacteristic
117C2×C4×C61C4×D411yescharacteristic
118C2×C4×C61#12011yescharacteristic
119C2×C4×C61#12111yescharacteristic
120C2×C4×C61#12111yescharacteristic
121C2×C4×C61#12311yescharacteristic
122C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C61#13711yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—41no—
136Dic122—22no—
137Dic122—22no—
138Dic122—41no—
139Dic122—41no—
140Dic122—41no—
141Dic122—41no—
142Dic122—41no—
143Dic122—41no—
144C8×C61—42no—
145C8×C61—81no—
146#92418—42no—
147#92418—81no—
148#9488—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61#38611yescharacteristic
152C22×C61#41711yescharacteristic
153C22×C61#41911yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—82no—
159C4×C61#46811yescharacteristic
160C4×C61#46811yescharacteristic
161C4×C61#47011yescharacteristic
162C4×C61#47011yescharacteristic
163Dic61—42no—
164Dic61—42no—
165Dic61—42no—
166Dic61—81no—
167#2983—611no—
168#2581—611no—
169#1801—611no—
170#1487—611no—
171#1487—611no—
172#1286—611no—
173#1286D6111yescharacteristic
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#189111yescharacteristic
177C2×C61#189411yescharacteristic
178C2×C61#191211yescharacteristic
179C2×C4×Q8—611no—
180C2×C4×Q8—611no—
181#446—1222no—
182#446—1222no—
183#432—1222no—
184#431—611no—
185#431C2×D6111yescharacteristic
186#423—611no—
187#423C2×D6111yescharacteristic
188C2×#101—1221no—
189#400—612no—
190#395—612no—
191#391—1221no—
192#389—1221no—
193#387—1222no—
194#382C2×D6111yescharacteristic
195#343—1221no—
196Q8⋊C8—1222no—
197Q8⋊C8—1222no—
198C61#948811yescharacteristic, complemented, Sylow
199C22×Q8—611no—
200C22×Q8—611no—
201C2×M16—21no—
202C2×M16—1221no—
203C4×Q8—1221no—
204C4×Q8—1221no—
205C4×Q8—1221no—
206C4×Q8—1221no—
207C4×Q8—1221no—
208C4×Q8—1221no—
209C4×Q8—1221no—
210C4×Q8—1221no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—612no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1222no—
216C2×C4⋊C4—1221no—
217C2×C42—612no—
218C2×C42—1221no—
219C2×C42C22×D6111yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—1224no—
224C4⋊C8—1221no—
225C4⋊C8—1221no—
226C4⋊C8—1221no—
227#101—2442no—
228C22⋊C8—21no—
229C22⋊C8—1221no—
230#97—1224no—
231C4×C8—612no—
232C4×C8D24412yes—
233#95—21no—
234#95—1222no—
235#95—1222no—
236#95—1222no—
237#95C4×D6112yes—
238C2×Q8—1221no—
239C2×Q8—1221no—
240C2×Q8—1221no—
241C2×Q8—1221no—
242C2×Q8—1221no—
243C2×Q8—1221no—
244C2×Q8—1221no—
245C2×Q8—1221no—
246C2×Q8—2442no—
247C22×C4—22no—
248C22×C4—612no—
249C22×C4—612no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4C2×C4×D6111yescharacteristic
253C22×C4D4×D6111yescharacteristic
254C22×C4D4×D6111yescharacteristic
255M16—41no—
256M16—41no—
257M16—2441no—
258M16—2441no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—1222no—
262C2×C8—2441no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1222no—
266C4⋊C4—1222no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—2444no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C42—1222no—
275C42—1222no—
276C42—2441no—
277C42—2441no—
278C42C2×D24411yescharacteristic
279C42#1175822211yescharacteristic
280C42D4×D6111yescharacteristic
281C42#1175822611yescharacteristic
282C23C22⋊C4×D6111yescharacteristic
283Q8—1222no—
284Q8—1222no—
285Q8—2441no—
286Q8—2441no—
287Q8—2441no—
288Q8—2441no—
289Q8—2441no—
290Q8—2441no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—1222no—
297C2×C4—1222no—
298C2×C4—1222no—
299C2×C4—1222no—
300C2×C4—1222no—
301C2×C4—2442no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2442no—
306C2×C4#1451973911yescharacteristic
307C2×C4C4×D24411yescharacteristic
308C2×C4#1451974711yescharacteristic
309C2×C4#1451975011yescharacteristic
310C2×C4#1451975211yescharacteristic
311C2×C4#1451976211yescharacteristic
312C2×C4#1451980111yescharacteristic
313C2×C4#1451980611yescharacteristic
314C2×C4#1451980611yescharacteristic
315C2×C4#1451980911yescharacteristic
316C8—42no—
317C8—81no—
318C8—4881no—
319C8—2442no—
320C22—21no—
321C22—21no—
322C22#1683964011yescharacteristic
323C22#1683976011yescharacteristic
324C22#1683976911yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—82no—
330C4—4881no—
331C4—2442no—
332C4—2442no—
333C4—2442no—
334C4#1684000711yescharacteristic
335C4#1684000911yescharacteristic
336C4#1684001911yescharacteristic
337C4#1684002111yescharacteristic
338C2—21no—
339C2—21no—
340C2#2144623611yescharacteristic
341C2#2144625111yescharacteristic
342C2#2144635511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1286C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1286D61
hypocenterC61#9488
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
198. C61#9488semidirect

Maximal subgroups

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

subgroupindex
#214549022
#214511862
#214458122
#214442492
#214442472
#214436772
C61×#12862
#948861