Finite Group Databasebeta

← #29834873

Subgroups — #29834873

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454419C211yesmaximal, characteristic, complemented
2#21448024C212yesmaximal, complemented
3#21448019C212yesmaximal, complemented
4#21448007C212yesmaximal, complemented
5#21447997C212yesmaximal, complemented
6#21447605C211yesmaximal, characteristic, complemented
7C2×#16839587C211yesmaximal, characteristic, complemented
8#21447531C211yesmaximal, characteristic, complemented
9#21447526C211yesmaximal, characteristic, complemented
10#21447433C211yesmaximal, characteristic, complemented
11C61×#3061C211yesmaximal, characteristic
12#16840245—21no—
13C2×#14519717C2211yescharacteristic
14C22×#11758185C2211yescharacteristic
15#16839804—21no—
16#16839804—22no—
17#16839800C2212yes—
18#16839800C2211yescharacteristic
19C2×#14519711C2212yes—
20C2×#14519711C2211yescharacteristic
21#16839589C2212yes—
22#16839587C2212yes—
23#16839587C2212yes—
24#16839587C2212yes—
25#16839566C2211yescharacteristic
26#16839566C2212yes—
27#16839566C2211yescharacteristic
28#16839563C2211yescharacteristic
29#16839563C2212yes—
30#16839563C2211yescharacteristic
31C22⋊#11758185C2212yes—
32C22⋊#11758185C2212yes—
33C2×#135×C61C2211yescharacteristic
34C2×#131×C61C2211yescharacteristic
35C61×#537—21no—
36C61×#468—22no—
37C61×#467C2212yes—
38C61×#466C2212yes—
39C2×#107×C61C2211yescharacteristic
40C61×#417—21no—
41Q8×Dic61—41no—
42D4×Dic61—42no—
43D4×Dic61—41no—
44#14519736—22no—
45#14519736—21no—
46C2×C4⋊Dic61—22no—
47C2×C4⋊Dic61—21no—
48#14519717—22no—
49C2×#11758185—22no—
50C2×#11758185C2311yescharacteristic
51C2×#11758185C2311yescharacteristic
52C2×#11758185C2312yes—
53#14519711—22no—
54#14519711—21no—
55#14519711C2311yescharacteristic
56#14519711C2312yes—
57#14519711C2311yescharacteristic
58#14519709—22no—
59#14519709—21no—
60C2×#41×C61—21no—
61C2×#41×C61D411yescharacteristic
62#135×C61—22no—
63#135×C61—22no—
64C2×Q16×C61C2311yescharacteristic
65C2×SD16×C61—21no—
66C2×D8×C61C2311yescharacteristic
67#131×C61—22no—
68#131×C61—22no—
69C2×M16×C61D411yescharacteristic
70C2×M16×C61D412yes—
71C22×C8×C61C2312yes—
72C22×C8×C61C2311yescharacteristic
73C22⋊Q8×C61—22no—
74C22⋊Q8×C61—41no—
75#121×C61—22no—
76#121×C61—41no—
77#121×C61—42no—
78C2×C4⋊C4×C61—21no—
79#107×C61—21no—
80#107×C61C2312yes—
81#103×C61—22no—
82#102×C61—22no—
83#41×C61—22no—
84#41×C61—22no—
85#41×C61—42no—
86#41×C61—42no—
87C2×Q8×C61—21no—
88C2×Q8×C61D811yescharacteristic
89C2×D4×C61—21no—
90C2×D4×C61—41no—
91C2×D4×C61—42no—
92C2×D4×C61D812yes—
93C2×D4×C61D811yescharacteristic
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61C2×D412yes—
97C22×C4×C61C2×D411yescharacteristic
98C22×Dic61—42no—
99C22×Dic61—41no—
100Q16×C61—21no—
101Q16×C61—21no—
102SD16×C61—42no—
103D8×C61—21no—
104D8×C61—21no—
105M16×C61—22no—
106M16×C61—24no—
107C2×C8×C61—22no—
108C2×C8×C61—22no—
109C2×C8×C61C2×D412yes—
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61#4112yes—
112C2×C8×C61#4112yes—
113C2×C8×C61C2411yescharacteristic
114C4⋊C4×C61—22no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—42no—
117C22⋊C4×C61—42no—
118C22⋊C4×C61—42no—
119C22⋊Dic61—42no—
120C22⋊Dic61—41no—
121C4⋊Dic61—21no—
122C4⋊Dic61—22no—
123C4⋊Dic61—21no—
124C4⋊Dic61—42no—
125C4⋊Dic61—41no—
126C4×Dic61—42no—
127C4×Dic61—41no—
128#11758185—21no—
129#11758185—21no—
130#11758185—22no—
131C23×C61—41no—
132C23×C61C2×D812yes—
133C23×C61C2×D811yescharacteristic
134Q8×C61—22no—
135Q8×C61—41no—
136Q8×C61—41no—
137D4×C61—24no—
138D4×C61—22no—
139D4×C61—41no—
140D4×C61—41no—
141D4×C61—82no—
142D4×C61—162no—
143C2×C4×C61—22no—
144C2×C4×C61—22no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—82no—
148C2×C4×C61—161no—
149C2×C4×C61#12312yes—
150C2×C4×C61C2×D812yes—
151C2×C4×C61C2×D811yescharacteristic
152C2×C4×C61#13712yes—
153C2×C4×C61C22×D411yescharacteristic
154C2×Dic61—41no—
155C2×Dic61—42no—
156C2×Dic61—41no—
157C2×Dic61—161no—
158C2×Dic61—162no—
159C8×C61—22no—
160C8×C61#12312yes—
161C8×C61C2×#4111yescharacteristic
162C8×C61C2×#4111yescharacteristic
163#33652—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61#48012yes—
173C22×C61C22×D811yescharacteristic
174C4×C61—22no—
175C4×C61—81no—
176C4×C61—82no—
177C4×C61#48012yes—
178C4×C61C2×#12311yescharacteristic
179C4×C61C2×#13711yescharacteristic
180Dic61—82no—
181Dic61—81no—
182Dic61—81no—
183#3061D6111yescharacteristic
184#2913—611no—
185#2237—612no—
186#2236—612no—
187#2234—612no—
188#2232—612no—
189#2159—611no—
190C2×#366—611no—
191#2139—611no—
192#2138—611no—
193#2113—611no—
194C2×C61—22no—
195C2×C61—42no—
196C2×C61—161no—
197C2×C61C2×#48011yescharacteristic
198C2×C61#341511yescharacteristic
199C2×C61#341711yescharacteristic
200C2×#135C2×D6111yescharacteristic
201C2×#131C2×D6111yescharacteristic
202#537—21no—
203#520—1221no—
204C2×M32—611no—
205C22×C16—611no—
206#468—22no—
207#467C2×D6112yes—
208#466C2×D6112yes—
209#428—1221no—
210#428—1222no—
211#427—611no—
212#427—612no—
213C2×#107—611no—
214C2×#107—612no—
215C2×#107C2×D6111yescharacteristic
216#417—21no—
217#367—612no—
218#366—612no—
219#366—612no—
220#366—612no—
221#358—611no—
222#358—611no—
223#358—612no—
224#357—611no—
225#357—611no—
226#357—612no—
227C22⋊C16—612no—
228C22⋊C16—612no—
229C61#3365211yescharacteristic, complemented, Sylow
230C2×#41—21no—
231C2×#41C22⋊D6111yescharacteristic
232#135—22no—
233#135—22no—
234C2×Q16C22×D6111yescharacteristic
235C2×SD16—21no—
236C2×D8C22×D6111yescharacteristic
237#131—22no—
238#131—22no—
239C2×M16C22⋊D6111yescharacteristic
240C2×M16C22⋊D6112yes—
241C22×C8C22×D6112yes—
242C22×C8C22×D6111yescharacteristic
243C22⋊Q8—22no—
244C22⋊Q8—41no—
245#121—22no—
246#121—41no—
247#121—42no—
248C4×Q8—2441no—
249C4×D4—2442no—
250C4×D4—2441no—
251#117—1222no—
252#117—1221no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—1222no—
255C2×C4⋊C4—1221no—
256M32—1222no—
257C2×C16—611no—
258C2×C16—611no—
259C2×C16—612no—
260C2×C16—1222no—
261#107—21no—
262#107—611no—
263#107—612no—
264#107—611no—
265#107—1222no—
266#107—1221no—
267#107C22×D6112yes—
268#106—1222no—
269#106—1221no—
270#103—22no—
271#102—22no—
272#41—22no—
273#41—22no—
274#41—42no—
275#41—42no—
276C2×Q8—21no—
277C2×Q8#1175819911yescharacteristic
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—42no—
281C2×D4#1175819912yes—
282C2×D4#1175819911yescharacteristic
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—2442no—
286C22×C4—2441no—
287C22×C4C2×C22⋊D6112yes—
288C22×C4C2×C22⋊D6111yescharacteristic
289Q16—21no—
290Q16—21no—
291SD16—42no—
292D8—21no—
293D8—21no—
294M16—22no—
295M16—24no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8#1175822412yes—
299C2×C8#1175822412yes—
300C2×C8C2×C22⋊D6112yes—
301C2×C8C2×C22⋊D6111yescharacteristic
302C2×C8C23×D6111yescharacteristic
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—42no—
306C4⋊C4—1221no—
307C4⋊C4—1222no—
308C4⋊C4—1221no—
309C4⋊C4—2442no—
310C4⋊C4—2441no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—2442no—
314C22⋊C4—2441no—
315C42—2442no—
316C42—2441no—
317C16—1221no—
318C16—1221no—
319C16—1222no—
320C23—41no—
321C23C2×#1175819912yes—
322C23C2×#1175819911yescharacteristic
323Q8—22no—
324Q8—41no—
325Q8—41no—
326D4—24no—
327D4—22no—
328D4—41no—
329D4—41no—
330D4—82no—
331D4—162no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—161no—
338C2×C4—9761no—
339C2×C4—9762no—
340C2×C4—2441no—
341C2×C4—2442no—
342C2×C4—2441no—
343C2×C4#1451975812yes—
344C2×C4C2×#1175819912yes—
345C2×C4C2×#1175819911yescharacteristic
346C2×C4#1451980712yes—
347C2×C4C22×C22⋊D6111yescharacteristic
348C8—22no—
349C8#1451975812yes—
350C8C2×#1175822411yescharacteristic
351C8C2×#1175822411yescharacteristic
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1684007312yes—
361C22C22×#1175819911yescharacteristic
362C4—22no—
363C4—82no—
364C4—81no—
365C4—4882no—
366C4—4881no—
367C4—4881no—
368C4#1684007312yes—
369C4C2×#1451975811yescharacteristic
370C4C2×#1451980711yescharacteristic
371C2—22no—
372C2—42no—
373C2—161no—
374C2C2×#1684007311yescharacteristic
375C2#2145895811yescharacteristic
376C2#2145897011yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
Fitting, prime radicalC61×#3061C2
socleC22×C61C22×D8
hypercenter#3061D61
hypocenterC61#33652
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3061

Complements

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

NH ≅ G/Ntype
1. #21454419C2semidirect
2. #21448024C2semidirect
3. #21448019C2semidirect
4. #21448007C2semidirect
5. #21447997C2semidirect
6. #21447605C2semidirect
7. C2×#16839587C2semidirect
8. #21447531C2semidirect
9. #21447526C2semidirect
10. #21447433C2semidirect
229. C61#33652semidirect

Maximal subgroups

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

subgroupindex
#214544192
#214480242
#214480192
#214480072
#214479972
#214476052
C2×#168395872
#214475312
#214475262
#214474332
C61×#30612
#3365261