Finite Group Databasebeta

← #29599618

Subgroups — #29599618

Order 15616.

410 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519723C211yesmaximal, characteristic
2C2×#16839580C211yesmaximal, characteristic
3C2×#16839567C211yesmaximal, characteristic
4#21446681C211yesmaximal, characteristic
5#21446678C211yesmaximal, characteristic
6#21443910C211yesmaximal, characteristic
7C2×C61×#358C211yesmaximal, characteristic
8C22×Dic244C2211yescharacteristic
9C2×#14519723—22no—
10C2×#14519723—22no—
11C2×#14519723—22no—
12C22×#11758185C2211yescharacteristic
13C2×#14519711C2211yescharacteristic
14C2×#14519701—21no—
15C2×#14519700—21no—
16C2×C8×Dic61C2211yescharacteristic
17#16839669—21no—
18#16839667—21no—
19#16839580—22no—
20#16839567—22no—
21C22×Q16×C61C2211yescharacteristic
22C22×C16×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#358—22no—
25C22×Dic122—21no—
26C2×Dic244—21no—
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×Dic244—21no—
30C2×Dic244—21no—
31C2×Dic244D412yes—
32C22×#92418D411yescharacteristic
33C2×C4⋊Dic61—21no—
34C2×C4×Dic61D411yescharacteristic
35#14519723—28no—
36C2×#11758185—21no—
37C2×#11758185—21no—
38C2×#11758185D412yes—
39#14519711—21no—
40#14519711—21no—
41#14519701—42no—
42#14519700—42no—
43C8×Dic61—21no—
44C8×Dic61—21no—
45#14519684—41no—
46#14519684—41no—
47#14519684—41no—
48#14519684—41no—
49C22×Q8×C61—21no—
50C2×Q16×C61—21no—
51C2×Q16×C61—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61D412yes—
56C22×C8×C61C2311yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61#107×C61—21no—
62#107×C61—21no—
63C2×Q8×C61—22no—
64C2×Q8×C61—41no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61D811yescharacteristic
75C22×Dic61D811yescharacteristic
76C2×Dic122—22no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82Q16×C61—22no—
83Q16×C61—22no—
84Q16×C61—41no—
85Q16×C61—41no—
86C2×C8×C61C2×D411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61#4111yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C2×#92418—21no—
99C2×#92418—21no—
100C2×#92418—21no—
101Dic244—22no—
102Dic244—22no—
103Dic244—41no—
104Dic244—41no—
105C16×C61—41no—
106#11758185—22no—
107C23×C61C2×D811yescharacteristic
108Q8×C61—42no—
109Q8×C61—42no—
110Q8×C61—81no—
111Q8×C61—81no—
112C2×C4×C61—42no—
113C2×C4×C61—81no—
114C2×C4×C61—81no—
115C2×C4×C61—81no—
116C2×C4×C61—81no—
117C2×C4×C61—81no—
118C2×C4×C61#12111yescharacteristic
119C2×C4×C61#12111yescharacteristic
120C2×C4×C61#12111yescharacteristic
121C2×C4×C61#13511yescharacteristic
122C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—42no—
130C2×Dic61—81no—
131C2×Dic61—81no—
132C2×Dic61—81no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61Q3212yescomplemented
136Dic122—42no—
137Dic122—42no—
138Dic122—81no—
139Dic122—81no—
140C8×C61#12011yescharacteristic
141C8×C61#12311yescharacteristic
142C8×C61#12311yescharacteristic
143C8×C61#12411yescharacteristic
144#92418—41no—
145#13450—611nomaximal, Sylow
146C22×C61#45911yescharacteristic
147C22×C61#45911yescharacteristic
148C22×C61#46611yescharacteristic
149C22×C61C2×Q3211yescharacteristic
150C22×C61#50811yescharacteristic
151C22×C61#51011yescharacteristic
152C22×C61#51011yescharacteristic
153C4×C61—82no—
154C4×C61—161no—
155C4×C61#39411yescharacteristic
156C4×C61#46311yescharacteristic
157C4×C61#46311yescharacteristic
158C4×C61#46911yescharacteristic
159Dic61—22no—
160Dic61—41no—
161Dic61—82no—
162Dic61—161no—
163C22×Q32—611no—
164C2×C4⋊C16—611no—
165C2×#358—611no—
166C2×#358D6111yescharacteristic
167#1969—611no—
168#1969—611no—
169#1380—611no—
170C2×C61#205411yescharacteristic
171C2×C61#220911yescharacteristic
172C2×C61#220911yescharacteristic
173C2×C61#221111yescharacteristic
174C2×C61#221111yescharacteristic
175C2×C61#221611yescharacteristic
176C2×C61#221911yescharacteristic
177C22×Q16—611no—
178C22×Q16C2×D6111yescharacteristic
179C2×Q32—1222no—
180C2×Q32—1222no—
181C2×Q32—1222no—
182C22×C16—611no—
183C22×C16C2×D6111yescharacteristic
184C2×#107—611no—
185C2×#107C2×D6111yescharacteristic
186C2×#103—1221no—
187C2×#103—1221no—
188C2×C4×C8—611no—
189#391—1221no—
190#391—1221no—
191C4⋊C16—1222no—
192#358—22no—
193#358—1222no—
194C61#1345011yescharacteristic, complemented, Sylow
195C22×Q8—21no—
196C22×Q8—1221no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—612no—
203C2×Q16—1221no—
204C2×Q16—1221no—
205C2×Q16—1221no—
206C2×Q16—1221no—
207C2×Q16—1221no—
208C2×Q16C22⋊D6112yes—
209C22×C8—611no—
210C22×C8C22×D6111yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4—1221no—
213C2×C42—611no—
214Q32—1228no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—21no—
218C2×C16—612no—
219C2×C16—1221no—
220C2×C16—1221no—
221#107—21no—
222#107—21no—
223#107—1221no—
224#107—1221no—
225#103—2442no—
226#103—2442no—
227C4×C8—1221no—
228C4×C8—1221no—
229#95—2441no—
230#95—2441no—
231#95—2441no—
232#95—2441no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—1222no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C2×Q8—2441no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—2441no—
250C22×C4—2441no—
251C22×C4D4×D6111yescharacteristic
252Q16—22no—
253Q16—22no—
254Q16—41no—
255Q16—41no—
256Q16—1222no—
257Q16—1222no—
258Q16—2441no—
259Q16—2441no—
260C2×C8—1221no—
261C2×C8—1221no—
262C2×C8—1221no—
263C2×C8#1175822211yescharacteristic
264C2×C8#1175822211yescharacteristic
265C2×C8D4×D6111yescharacteristic
266C2×C8D4×D6111yescharacteristic
267C2×C8#1175822411yescharacteristic
268C2×C8C2×C22⋊D6111yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C42—1221no—
274C42—1221no—
275C16—41no—
276C16—1222no—
277C23D8×D6111yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282Q8—4881no—
283Q8—4881no—
284Q8—2442no—
285Q8—2442no—
286C2×C4—42no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—612no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—4881no—
299C2×C4—4881no—
300C2×C4—4881no—
301C2×C4—4881no—
302C2×C4—4881no—
303C2×C4—2442no—
304C2×C4#1451974911yescharacteristic
305C2×C4#1451975011yescharacteristic
306C2×C4#1451975011yescharacteristic
307C2×C4#1451979811yescharacteristic
308C2×C4#1451980111yescharacteristic
309C2×C4#1451980411yescharacteristic
310C8—2441no—
311C8#1451974511yescharacteristic
312C8#1451975911yescharacteristic
313C8#1451976011yescharacteristic
314C8#1451976311yescharacteristic
315C22#1683995511yescharacteristic
316C22#1683995611yescharacteristic
317C22#1683999711yescharacteristic
318C22Q32×D6111yescharacteristic
319C22#1684019311yescharacteristic
320C22#1684020111yescharacteristic
321C22#1684020411yescharacteristic
322C4—82no—
323C4—161no—
324C4—1222no—
325C4—9761no—
326C4—4882no—
327C4—2441no—
328C4#1683967711yescharacteristic
329C4#1683997611yescharacteristic
330C4#1683997911yescharacteristic
331C4#1684001411yescharacteristic
332C2#2144712811yescharacteristic
333C2#2144786711yescharacteristic
334C2#2144786811yescharacteristic
335C2#2144787911yescharacteristic
336C2#2144788411yescharacteristic
337C2#2144790911yescharacteristic
338C2#2144792611yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#358C2
socle, prime radicalC23×C61C2×D8
hypercenterC2×#358D61
hypocenterC61#13450
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
135. C2×Dic61Q32semidirect
194. C61#13450semidirect

Maximal subgroups

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

subgroupindex
C22×#145197232
C2×#168395802
C2×#168395672
#214466812
#214466782
#214439102
C2×C61×#3582
#1345061