Finite Group Databasebeta

← #29665357

Subgroups — #29665357

Order 15616.

644 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456949C211yesmaximal, characteristic
2C2×#16840058C211yesmaximal, characteristic, complemented
3#21455293C211yesmaximal, characteristic
4#21454899C211yesmaximal, characteristic, complemented
5#21445236C214yesmaximal, complemented
6#21445202C214yesmaximal, complemented
7#21444501C211yesmaximal, characteristic, complemented
8#21444469C211yesmaximal, characteristic
9C61×#1570C211yesmaximal, characteristic, complemented
10C2×#14519810—21no—
11#16840312C2211yescharacteristic
12C2×#14519777C2211yescharacteristic
13C2×C4×Dic122C2211yescharacteristic
14#16840160C2212yes—
15#16840109C2212yes—
16#16840081—22no—
17#16840058—22no—
18#16840058C2214yes—
19#16840053—22no—
20#16839985—22no—
21#16839973C2212yes—
22#16839963C2212yes—
23C8×Dic122C2214yes—
24#16839886—22no—
25#16839815C2211yescharacteristic
26#16839812—22no—
27C2×#14519711—21no—
28#16839764—21no—
29C2×#14519702—21no—
30#16839510C2214yes—
31#16839509C2212yes—
32#16839505C2212yes—
33C61×#431C2211yescharacteristic
34C61×#423C2211yescharacteristic
35C2×C4⋊C8×C61C2211yescharacteristic
36C61×#334C2214yes—
37C2×#11758222—21no—
38C22×Dic122—21no—
39C22×Dic122D411yescharacteristic
40#14519810—44no—
41C2×Dic244—22no—
42C2×#11758190—22no—
43#14519777—21no—
44#14519777—21no—
45#14519777—21no—
46#14519777C2311yescharacteristic
47#14519777C2312yes—
48#14519774C2311yescharacteristic
49#14519765—21no—
50#14519751—21no—
51#14519751—21no—
52C4×Dic122—21no—
53C4×Dic122—21no—
54C4×Dic122D412yes—
55C4×Dic122C2312yes—
56C4×D244—21no—
57C4×D244—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61D411yescharacteristic
61C2×#11758196—21no—
62C2×C4×Dic61—21no—
63#14519711—24no—
64#14519709—24no—
65C4⋊#92418C2312yes—
66#14519706—24no—
67#14519702—24no—
68#14519702—22no—
69#14519699—24no—
70#14519699—22no—
71C22⋊#92418—21no—
72C4×#92418—21no—
73C8×Dic61—24no—
74C2×M16×C61—21no—
75C22×C8×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61D412yes—
80C4⋊C8×C61C2312yes—
81C4⋊C8×C61C2312yes—
82C22⋊C8×C61D412yes—
83C4×C8×C61C2312yes—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—41no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—41no—
91#11758222—42no—
92#11758222—42no—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×C4×D61—41no—
97C2×Dic122—21no—
98C2×Dic122—22no—
99C2×Dic122—21no—
100C2×Dic122—22no—
101C2×Dic122—41no—
102C2×Dic122—82no—
103C2×Dic122SD1614yes—
104C2×Dic122C2×D412yes—
105M16×C61—42no—
106C2×C8×C61—22no—
107C2×C8×C61—22no—
108C2×C8×C61—42no—
109C2×C8×C61C2×D414yes—
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113C42×C61C2411yescharacteristic
114#11758198—41no—
115#11758198—41no—
116C4⋊Dic61—21no—
117C4⋊Dic61—22no—
118C4⋊Dic61—22no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61C2×D412yes—
124#11758196—22no—
125#11758196—22no—
126C4×Dic61—22no—
127C4×Dic61—22no—
128C2×#92418—22no—
129Dic244—44no—
130#11758190—44no—
131C23×C61#12111yescharacteristic
132C22×D61—41no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61C2×SD1612yes—
139C2×C4×C61#13512yes—
140C2×C4×C61C22×D411yescharacteristic
141C2×C4×C61C22×D411yescharacteristic
142C2×C4×C61C2×#4111yescharacteristic
143C22⋊D61—82no—
144C2×Dic61—22no—
145C2×Dic61—24no—
146C2×Dic61—22no—
147C2×Dic61—42no—
148C2×Dic61—41no—
149C2×Dic61—81no—
150C2×Dic61—82no—
151D244—41no—
152D244—41no—
153D244—42no—
154D244—81no—
155C4×D61—82no—
156Dic122—22no—
157Dic122—24no—
158Dic122—41no—
159Dic122—41no—
160Dic122—82no—
161Dic122—82no—
162Dic122C2×SD1614yes—
163C8×C61—24no—
164C8×C61—42no—
165C8×C61—42no—
166#92418—42no—
167#19403—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61#46512yes—
171C22×C61C2×#12111yescharacteristic
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61#46512yes—
179C4×C61C22×SD1611yescharacteristic
180C4×C61C2×#13511yescharacteristic
181C4×C61#57812yes—
182Dic61—24no—
183Dic61—42no—
184Dic61—81no—
185Dic61—82no—
186#3227—611no—
187C2×#477—611no—
188#3037—611no—
189#2982—611no—
190#1678—614no—
191#1672—614no—
192#1570D6111yescharacteristic, complemented
193#1548—611no—
194#1540—611no—
195C2×C61—22no—
196C2×C61#304411yescharacteristic
197C2×C61C2×#46511yescharacteristic
198C2×C61#306811yescharacteristic
199D61—161no—
200C2×#137—1221no—
201#532—611no—
202C2×C4⋊Q8—611no—
203C2×C4×Q8—611no—
204#498—612no—
205#486—612no—
206#481—1222no—
207#477—614no—
208#477—1222no—
209#476—1222no—
210#464—1222no—
211#462—612no—
212#460—612no—
213C8×Q8—614no—
214C8×Q8—1222no—
215#431—611no—
216#431—1222no—
217#431C2×D6111yescharacteristic
218C2×#107—1221no—
219#423C2×D6111yescharacteristic
220C2×C4⋊C8C2×D6111yescharacteristic
221#417—1221no—
222C2×#103—1221no—
223#334C2×D6114yes—
224#333—614no—
225#332—612no—
226#331—612no—
227C61#1940311yescharacteristic, complemented, Sylow
228C2×#41—1221no—
229C22×Q8—611no—
230C22×Q8—1221no—
231#137—2444no—
232C2×Q16—1222no—
233C2×SD16—1222no—
234C2×M16—21no—
235C22×C8—21no—
236C4⋊Q8—612no—
237C4⋊Q8—611no—
238C4⋊Q8—1221no—
239C4⋊Q8—1221no—
240C4⋊Q8—1221no—
241#127—611no—
242#124—1221no—
243#121—1221no—
244#121—1221no—
245C4×Q8—612no—
246C4×Q8—612no—
247C4×Q8—1221no—
248C4×Q8—1221no—
249C4×D4—1221no—
250C4×D4—1221no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C42—1221no—
256C2×C42C22×D6111yescharacteristic
257#107—1224no—
258#106—1224no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—612no—
262C4⋊C8—1224no—
263C4⋊C8D24412yes—
264C4⋊C8C22×D6112yes—
265C4⋊C8C22×D6112yes—
266#103—1222no—
267#103—1224no—
268#102—1222no—
269#102—1224no—
270C22⋊C8—1221no—
271C22⋊C8D24412yes—
272C4×C8—1224no—
273C4×C8—1221no—
274C4×C8C22×D6112yes—
275#41—2442no—
276#41—2442no—
277C2×Q8—612no—
278C2×Q8—614no—
279C2×Q8—1221no—
280C2×Q8—1222no—
281C2×Q8—1221no—
282C2×Q8—1222no—
283C2×Q8—4882no—
284C2×Q8—2441no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—2441no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4C2×D24411yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C22×C4#1175822611yescharacteristic
296Q16—2444no—
297SD16—2444no—
298M16—42no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—1222no—
303C2×C8C2×D24414yes—
304C4⋊C4—612no—
305C4⋊C4—1222no—
306C4⋊C4—1221no—
307C4⋊C4—1222no—
308C4⋊C4—1222no—
309C4⋊C4—1222no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C42—1222no—
317C42—1222no—
318C42C2×D24411yescharacteristic
319C42D4×D6111yescharacteristic
320C42#1175822611yescharacteristic
321C42C23×D6111yescharacteristic
322C23—2441no—
323C23#1451975211yescharacteristic
324Q8—614no—
325Q8—1224no—
326Q8—1222no—
327Q8—4882no—
328Q8—4882no—
329Q8—2441no—
330Q8—2441no—
331D4—4881no—
332D4—4882no—
333D4—2441no—
334D4—2441no—
335D4—2442no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—1224no—
339C2×C4—1222no—
340C2×C4—1222no—
341C2×C4—4882no—
342C2×C4—4882no—
343C2×C4—4881no—
344C2×C4—2441no—
345C2×C4—2442no—
346C2×C4#1451975211yescharacteristic
347C2×C4#1451975211yescharacteristic
348C2×C4#1451975211yescharacteristic
349C2×C4SD16×D6112yes—
350C2×C4#1451979812yes—
351C2×C4C2×D4×D6111yescharacteristic
352C2×C4C22×D24411yescharacteristic
353C2×C4C2×#1175822611yescharacteristic
354C8—24no—
355C8—42no—
356C8—42no—
357C8—2442no—
358C22—21no—
359C22—21no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22#1683999212yes—
364C22C2×#1451975211yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—1224no—
369C4—4881no—
370C4—4882no—
371C4—2442no—
372C4#1683999212yes—
373C4C2×SD16×D6111yescharacteristic
374C4C2×#1451979811yescharacteristic
375C4#1684057912yes—
376C2—22no—
377C2—9761no—
378C2#2145535011yescharacteristic
379C2C2×#1683999211yescharacteristic
380C2#2145554811yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1570C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1570D61
hypocenterC61#19403
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
2. C2×#16840058C2semidirect
4. #21454899C2semidirect
5. #21445236C2semidirect
6. #21445202C2semidirect
7. #21444501C2semidirect
9. C61×#1570C2semidirect
192. #1570D61semidirect
227. C61#19403semidirect

Maximal subgroups

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

subgroupindex
#214569492
C2×#168400582
#214552932
#214548992
#214452362
#214452022
#214445012
#214444692
C61×#15702
#1940361