Finite Group Databasebeta

← #29665364

Subgroups — #29665364

Order 15616.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456940C211yesmaximal, characteristic
2#21455293C211yesmaximal, characteristic
3C2×#16839969C211yesmaximal, characteristic, complemented
4#21454899C211yesmaximal, characteristic, complemented
5#21445266C214yesmaximal, complemented
6#21445212C214yesmaximal, complemented
7#21444595C211yesmaximal, characteristic, complemented
8#21444466C211yesmaximal, characteristic
9C61×#1546C211yesmaximal, characteristic, complemented
10C2×#14519810—21no—
11C22×#11758202—21no—
12#16840312C2211yescharacteristic
13C2×C4×Dic122C2211yescharacteristic
14#16840165C2212yes—
15#16840110C2212yes—
16#16840075—22no—
17#16840039—22no—
18#16839985—22no—
19#16839973C2212yes—
20#16839969—22no—
21#16839969C2214yes—
22#16839963C2212yes—
23C8×Dic122—22no—
24#16839886C2214yes—
25#16839815C2211yescharacteristic
26#16839812—22no—
27C2×C4⋊#92418C2211yescharacteristic
28#16839764—21no—
29C2×#14519701—21no—
30#16839514C2214yes—
31#16839507C2212yes—
32#16839505C2212yes—
33C2×C4⋊Q8×C61C2211yescharacteristic
34C61×#431C2211yescharacteristic
35C61×#423C2211yescharacteristic
36C61×#332C2214yes—
37C2×#11758222—21no—
38C22×Dic122D411yescharacteristic
39#14519810—44no—
40C2×Dic244—22no—
41C2×#11758202—24no—
42C2×#11758202—44no—
43C2×#11758190—22no—
44C22×#92418—21no—
45#14519777C2311yescharacteristic
46#14519774C2311yescharacteristic
47#14519765—21no—
48#14519751—21no—
49#14519751—21no—
50C4×Dic122—21no—
51C4×Dic122—21no—
52C4×Dic122D412yes—
53C4×Dic122C2312yes—
54C4×D244—21no—
55C4×D244—21no—
56C2×C4⋊Dic61D411yescharacteristic
57C2×#11758196—21no—
58C2×C4×Dic61—21no—
59#14519710—24no—
60C4⋊#92418—21no—
61C4⋊#92418D412yes—
62C4⋊#92418C2312yes—
63#14519706—24no—
64#14519702—22no—
65#14519701—24no—
66#14519699—22no—
67#14519697—24no—
68C22⋊#92418D412yes—
69C4×#92418C2312yes—
70C8×Dic61—24no—
71C22×Q8×C61—21no—
72C2×M16×C61—21no—
73C4⋊Q8×C61—21no—
74C4⋊Q8×C61—21no—
75C4⋊Q8×C61—21no—
76C4⋊Q8×C61C2312yes—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61—21no—
79C2×C42×C61C2311yescharacteristic
80C4⋊C8×C61—21no—
81C4⋊C8×C61C2312yes—
82C4⋊C8×C61C2312yes—
83C22⋊C8×C61—21no—
84C4×C8×C61—21no—
85C2×Q8×C61—22no—
86C2×Q8×C61—41no—
87C2×Q8×C61—42no—
88C2×Q8×C61—42no—
89C22×C4×C61—41no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C2×C22⋊D61—41no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96#11758222—42no—
97#11758222—42no—
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×C4×D61—41no—
102C2×Dic122—21no—
103C2×Dic122—22no—
104C2×Dic122—21no—
105C2×Dic122D814yes—
106C2×Dic122C2×D412yes—
107M16×C61—42no—
108C2×C8×C61—22no—
109C2×C8×C61—22no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—22no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117C42×C61C2411yescharacteristic
118#11758202—48no—
119#11758198—41no—
120#11758198—41no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61C2×D412yes—
125#11758196—22no—
126#11758196—22no—
127C4×Dic61—22no—
128C4×Dic61—22no—
129C2×#92418—22no—
130C2×#92418—42no—
131C2×#92418C2×D414yes—
132Dic244—44no—
133#11758190—44no—
134C23×C61#12111yescharacteristic
135C22×D61—41no—
136Q8×C61—42no—
137Q8×C61—42no—
138Q8×C61—82no—
139C2×C4×C61—22no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—82no—
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61C2×D812yes—
147C2×C4×C61#13512yes—
148C2×C4×C61C22×D411yescharacteristic
149C2×C4×C61C22×D411yescharacteristic
150C2×C4×C61C2×#4111yescharacteristic
151C22⋊D61—82no—
152C2×Dic61—22no—
153C2×Dic61—24no—
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—81no—
157D244—41no—
158D244—41no—
159D244—42no—
160D244—81no—
161C4×D61—82no—
162Dic122—22no—
163Dic122—24no—
164Dic122—41no—
165Dic122—41no—
166Dic122C2×D814yes—
167C8×C61—42no—
168C8×C61—42no—
169#92418—24no—
170#92418—42no—
171#19404—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#46612yes—
175C22×C61C2×#12111yescharacteristic
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—82no—
183C4×C61#46612yes—
184C4×C61C22×D811yescharacteristic
185C4×C61C2×#13511yescharacteristic
186C4×C61#57812yes—
187Dic61—24no—
188Dic61—42no—
189Dic61—81no—
190#3226—611no—
191#3037—611no—
192C2×#462—611no—
193#2982—611no—
194#1682—614no—
195#1674—614no—
196#1571—611no—
197#1546D6111yescharacteristic, complemented
198#1540—611no—
199C2×C61—22no—
200C2×C61#304411yescharacteristic
201C2×C61C2×#46611yescharacteristic
202C2×C61#306911yescharacteristic
203D61—161no—
204C2×#137—1221no—
205C22×Q16—1221no—
206#532—611no—
207C2×C4⋊Q8C2×D6111yescharacteristic
208C2×C4×Q8—611no—
209#500—612no—
210#486—612no—
211#480—1222no—
212#474—1222no—
213#464—1222no—
214#462—614no—
215#462—612no—
216#462—1222no—
217#460—612no—
218C8×Q8—614no—
219C8×Q8—1222no—
220#431—611no—
221#431—1222no—
222#431C2×D6111yescharacteristic
223#423C2×D6111yescharacteristic
224C2×C4⋊C8—611no—
225#417—1221no—
226C2×#103—1221no—
227#335—614no—
228#332—612no—
229#332C2×D6114yes—
230#331—612no—
231C61#1940411yescharacteristic, complemented, Sylow
232C2×#41—1221no—
233C22×Q8—21no—
234C22×Q8—611no—
235#137—2444no—
236C2×Q16—1222no—
237C2×Q16—1224no—
238C2×Q16—2444no—
239C2×SD16—1222no—
240C2×M16—21no—
241C22×C8—1221no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—611no—
246C4⋊Q8C22×D6112yes—
247#127—611no—
248#124—1221no—
249#121—1221no—
250#121—1221no—
251C4×Q8—612no—
252C4×Q8—612no—
253C4×Q8—1221no—
254C4×Q8—1221no—
255C4×D4—1221no—
256C4×D4—1221no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—1221no—
261C2×C42—1221no—
262C2×C42C22×D6111yescharacteristic
263#107—1224no—
264C4⋊C8—21no—
265C4⋊C8—612no—
266C4⋊C8—612no—
267C4⋊C8—1224no—
268C4⋊C8—1221no—
269C4⋊C8C22×D6112yes—
270C4⋊C8C22×D6112yes—
271#103—1222no—
272#103—1224no—
273#102—1224no—
274#102—1222no—
275C22⋊C8—21no—
276C22⋊C8—612no—
277C4×C8—21no—
278C4×C8—612no—
279C4×C8—1224no—
280#41—2442no—
281#41—2442no—
282C2×Q8—22no—
283C2×Q8—41no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×Q8—612no—
287C2×Q8—614no—
288C2×Q8—1221no—
289C2×Q8—1222no—
290C2×Q8—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—2441no—
295C22×C4—41no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—2441no—
299C22×C4#1175822211yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4D4×D6111yescharacteristic
302Q16—2444no—
303Q16—2448no—
304SD16—2444no—
305M16—42no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—614no—
309C2×C8—1222no—
310C2×C8—2442no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—612no—
316C4⋊C4—1222no—
317C4⋊C4—1221no—
318C4⋊C4—1222no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C42—1222no—
324C42—1222no—
325C42#1175822211yescharacteristic
326C42D4×D6111yescharacteristic
327C42D4×D6111yescharacteristic
328C42C23×D6111yescharacteristic
329C23—2441no—
330C23#1451975011yescharacteristic
331Q8—42no—
332Q8—42no—
333Q8—82no—
334Q8—614no—
335Q8—1224no—
336Q8—1222no—
337Q8—2441no—
338Q8—2441no—
339D4—4881no—
340D4—4882no—
341D4—2441no—
342D4—2441no—
343D4—2442no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—1224no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—4882no—
352C2×C4—4881no—
353C2×C4—2441no—
354C2×C4#1451975011yescharacteristic
355C2×C4#1451975011yescharacteristic
356C2×C4#1451975011yescharacteristic
357C2×C4D8×D6112yes—
358C2×C4#1451979812yes—
359C2×C4C2×D4×D6111yescharacteristic
360C2×C4C2×D4×D6111yescharacteristic
361C2×C4C2×#1175822211yescharacteristic
362C8—42no—
363C8—42no—
364C8—1224no—
365C8—2442no—
366C22—21no—
367C22—21no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22#1683999712yes—
372C22C2×#1451975011yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—82no—
377C4—1224no—
378C4—4881no—
379C4—2442no—
380C4#1683999712yes—
381C4C2×D8×D6111yescharacteristic
382C4C2×#1451979811yescharacteristic
383C4#1684057812yes—
384C2—22no—
385C2—9761no—
386C2#2145534811yescharacteristic
387C2C2×#1683999711yescharacteristic
388C2#2145555511yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1546C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1546D61
hypocenterC61#19404
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C2×#16839969C2semidirect
4. #21454899C2semidirect
5. #21445266C2semidirect
6. #21445212C2semidirect
7. #21444595C2semidirect
9. C61×#1546C2semidirect
197. #1546D61semidirect
231. C61#19404semidirect

Maximal subgroups

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

subgroupindex
#214569402
#214552932
C2×#168399692
#214548992
#214452662
#214452122
#214445952
#214444662
C61×#15462
#1940461