Finite Group Databasebeta

← #29583742

Subgroups — #29583742

Order 15616.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#21455626C211yesmaximal, characteristic
2#21445812C211yesmaximal, characteristic
3#21444510C211yesmaximal, characteristic
4#21444275C211yesmaximal, characteristic
5C2×#16839494C211yesmaximal, characteristic
6#21443693C211yesmaximal, characteristic
7C61×#1567C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16840070—22no—
11#16840058—21no—
12#16840048—21no—
13#16839804—21no—
14#16839786C2211yescharacteristic
15C2×C4⋊#92418C2211yescharacteristic
16#16839772—21no—
17C2×#14519695—21no—
18#16839530—21no—
19#16839510—21no—
20#16839507—21no—
21#16839494—21no—
22#16839494—21no—
23#16839494—21no—
24#16839494—21no—
25C61×#423C2211yescharacteristic
26C61×#423C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C61×#335—22no—
29C22×Dic122D411yescharacteristic
30C2×#11758194—21no—
31C22×#92418—21no—
32#14519777D411yescharacteristic
33#14519777D411yescharacteristic
34#14519769—21no—
35#14519756—21no—
36#14519756—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43#14519736—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×C4×Dic61—21no—
47#14519711—22no—
48#14519709—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53#14519702—22no—
54#14519702—22no—
55#14519695—42no—
56C2×M16×C61—21no—
57C2×M16×C61—21no—
58C22×C8×C61—21no—
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61D412yes—
64C4×C8×C61—21no—
65C4×C8×C61D411yescharacteristic
66C4×C8×C61D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61#4111yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122—21no—
79C2×Dic122Q1612yes—
80M16×C61—41no—
81M16×C61—41no—
82M16×C61—41no—
83M16×C61—41no—
84C2×C8×C61—21no—
85C2×C8×C61—22no—
86C2×C8×C61—21no—
87C2×C8×C61—42no—
88C2×C8×C61—41no—
89C42×C61C2×D411yescharacteristic
90C42×C61C2×D411yescharacteristic
91C42×C61C2×D411yescharacteristic
92C42×C61#4111yescharacteristic
93C22⋊Dic61—41no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100#11758196—41no—
101#11758196—41no—
102#11758196—41no—
103#11758196—41no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107#11758194—41no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—81no—
112C23×C61#12311yescharacteristic
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61#12011yescharacteristic
117C2×C4×C61#12111yescharacteristic
118C2×C4×C61#12111yescharacteristic
119C2×C4×C61#12111yescharacteristic
120C2×C4×C61#12311yescharacteristic
121C2×C4×C61#12411yescharacteristic
122C2×C4×C61C2×Q1611yescharacteristic
123C2×C4×C61#13511yescharacteristic
124C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C61#13711yescharacteristic
126C2×Dic61—22no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—81no—
133Dic122—22no—
134Dic122—22no—
135Dic122—41no—
136Dic122—41no—
137Dic122—41no—
138Dic122—41no—
139Dic122—81no—
140C8×C61—22no—
141C8×C61—41no—
142C8×C61—42no—
143C8×C61—81no—
144#92418—81no—
145#92418—81no—
146#10463—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61#39411yescharacteristic
150C22×C61#48411yescharacteristic
151C22×C61#48511yescharacteristic
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61#44911yescharacteristic
156C4×C61#45111yescharacteristic
157C4×C61#46711yescharacteristic
158C4×C61#46811yescharacteristic
159C4×C61#47111yescharacteristic
160C4×C61#47311yescharacteristic
161Dic61—42no—
162Dic61—81no—
163Dic61—81no—
164Dic61—81no—
165#3078—611no—
166#1801—611no—
167#1567D6111yescharacteristic
168#1550—611no—
169#1493—611no—
170C2×Q8⋊C8—611no—
171#1292—611no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61#203611yescharacteristic
175C2×C61#205011yescharacteristic
176C2×C61#205211yescharacteristic
177#533—611no—
178C2×C4×Q8—611no—
179#479—1222no—
180#477—1221no—
181#475—1221no—
182#428—1221no—
183#423—611no—
184#423C2×D6111yescharacteristic
185#423C2×D6111yescharacteristic
186C2×C4⋊C8—611no—
187#419—1221no—
188C2×#101—1221no—
189C2×C4×C8C2×D6111yescharacteristic
190#343—1221no—
191#335—22no—
192#333—1221no—
193#332—1221no—
194Q8⋊C8—1221no—
195Q8⋊C8—1221no—
196Q8⋊C8—1221no—
197Q8⋊C8—1221no—
198C61#1046311yescharacteristic, complemented, Sylow
199C22×Q8—611no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—1221no—
203C22×C8—21no—
204C22×C8—1221no—
205C4⋊Q8—611no—
206C4⋊Q8—611no—
207#125—1221no—
208C22⋊Q8—1221no—
209C22⋊Q8—1221no—
210C4×Q8—1221no—
211C4×Q8—1221no—
212C4×Q8—1221no—
213C4×Q8—1221no—
214C4×Q8—1221no—
215C4×Q8—1221no—
216#117—1221no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—1221no—
219C2×C42—1221no—
220C2×C42C22×D6111yescharacteristic
221#107—1222no—
222#106—1222no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—1221no—
227C4⋊C8—1221no—
228C4⋊C8—1221no—
229C4⋊C8—1221no—
230C4⋊C8C22⋊D6112yes—
231#103—1222no—
232#103—1222no—
233#101—2442no—
234C4×C8—21no—
235C4×C8D24411yescharacteristic
236C4×C8D24411yescharacteristic
237C2×Q8—612no—
238C2×Q8—1221no—
239C2×Q8—1221no—
240C2×Q8—1221no—
241C2×Q8—1221no—
242C2×Q8—1221no—
243C2×Q8—1221no—
244C2×Q8—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4#1175822211yescharacteristic
248C22×C4D4×D6111yescharacteristic
249C22×C4#1175822611yescharacteristic
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—2441no—
255M16—2441no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—4881no—
262C2×C8—2441no—
263C2×C8—2441no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C22⋊C4—2441no—
275C42—2441no—
276C42—2441no—
277C42—2441no—
278C42C2×D24411yescharacteristic
279C42D4×D6111yescharacteristic
280C42#1175822611yescharacteristic
281C42C2×C22⋊D6111yescharacteristic
282C23#1451976211yescharacteristic
283Q8—1222no—
284Q8—1222no—
285Q8—4881no—
286Q8—2441no—
287Q8—2441no—
288Q8—2441no—
289Q8—2441no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—1222no—
294C2×C4—4881no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4#1451974511yescharacteristic
301C2×C4#1451975111yescharacteristic
302C2×C4#1451975211yescharacteristic
303C2×C4#1451975211yescharacteristic
304C2×C4#1451976211yescharacteristic
305C2×C4#1451976611yescharacteristic
306C2×C4Q16×D6111yescharacteristic
307C2×C4#1451979611yescharacteristic
308C2×C4#1451980111yescharacteristic
309C2×C4#1451980911yescharacteristic
310C8—22no—
311C8—41no—
312C8—42no—
313C8—81no—
314C8—4881no—
315C8—4881no—
316C22—21no—
317C22—21no—
318C22#1683967911yescharacteristic
319C22#1684009911yescharacteristic
320C22#1684010511yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—4881no—
325C4—4881no—
326C4—4881no—
327C4—2442no—
328C4#1683990411yescharacteristic
329C4#1683991611yescharacteristic
330C4#1684000411yescharacteristic
331C4#1684000911yescharacteristic
332C4#1684002611yescharacteristic
333C4#1684003811yescharacteristic
334C2—21no—
335C2—21no—
336C2#2144702411yescharacteristic
337C2#2144710611yescharacteristic
338C2#2144712011yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1567C2
socleC22×C61#394
prime radicalC23×C61#123
hypercenter#1567D61
hypocenterC61#10463
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1567

Complements

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

NH ≅ G/Ntype
198. C61#10463semidirect

Maximal subgroups

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

subgroupindex
#214556262
#214458122
#214445102
#214442752
C2×#168394942
#214436932
C61×#15672
#1046361