Finite Group Databasebeta

← #29665383

Subgroups — #29665383

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456957C211yesmaximal, characteristic
2#21455941C211yesmaximal, characteristic
3#21455858C211yesmaximal, characteristic, complemented
4#21445263C212yesmaximal, complemented
5#21445235C212yesmaximal, complemented
6#21445223C212yesmaximal, complemented
7#21445201C212yesmaximal, complemented
8#21444599C211yesmaximal, characteristic, complemented
9#21444527C211yesmaximal, characteristic, complemented
10#21444479C211yesmaximal, characteristic
11C61×#2982C211yesmaximal, characteristic, complemented
12#16840319C2211yescharacteristic
13#16840312C2211yescharacteristic
14#16840167C2211yescharacteristic
15#16840160C2211yescharacteristic
16#16840109C2211yescharacteristic
17#16840109C2211yescharacteristic
18#16840097—21no—
19#16840087—22no—
20#16840075—21no—
21#16840063—22no—
22#16840057C2212yes—
23#16840057C2212yes—
24#16839972C2212yes—
25#16839962C2212yes—
26#16839918—21no—
27#16839901—21no—
28#16839860—22no—
29C4×#11758202—22no—
30#16839819C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839515C2212yes—
33#16839513C2212yes—
34#16839510C2212yes—
35#16839510C2212yes—
36#16839507C2212yes—
37#16839505C2212yes—
38C2×C4×Q8×C61C2211yescharacteristic
39C8×Q8×C61—22no—
40C8×Q8×C61C2212yes—
41C8×Q8×C61C2212yes—
42C61×#431—22no—
43C61×#431C2211yescharacteristic
44C61×#431C2211yescharacteristic
45C2×#11758222—21no—
46C2×#11758202—22no—
47C2×#11758201—22no—
48#14519777C2311yescharacteristic
49#14519777C2311yescharacteristic
50#14519777C2311yescharacteristic
51#14519774C2311yescharacteristic
52#14519769—21no—
53#14519765—21no—
54#14519756—21no—
55#14519756—21no—
56#14519751—21no—
57#14519751—21no—
58C4×Dic122—21no—
59C4×Dic122—21no—
60C4×D244—21no—
61C4×D244—21no—
62#14519736—21no—
63#14519711—22no—
64#14519710—22no—
65#14519710—22no—
66#14519709—22no—
67C4⋊#92418C2312yes—
68C4⋊#92418C2312yes—
69#14519701—22no—
70#14519701—22no—
71#14519700—22no—
72#14519699—22no—
73#14519699—22no—
74#14519697—22no—
75C22⋊#92418—21no—
76C22⋊#92418—21no—
77#14519688—21no—
78C4×#92418—21no—
79C22×Q8×C61D411yescharacteristic
80C4×Q8×C61—21no—
81C4×Q8×C61—21no—
82C4×Q8×C61D412yes—
83C4×Q8×C61C2312yes—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61D411yescharacteristic
86C2×C42×C61—21no—
87C2×C42×C61C2311yescharacteristic
88C4⋊C8×C61—22no—
89C4⋊C8×C61—22no—
90C4⋊C8×C61D412yes—
91C4⋊C8×C61C2312yes—
92C22⋊C8×C61—21no—
93C22⋊C8×C61D412yes—
94C4×C8×C61—22no—
95C4×C8×C61—22no—
96C4×C8×C61—21no—
97C4×C8×C61C2311yescharacteristic
98C4×C8×C61C2311yescharacteristic
99C2×Q8×C61—24no—
100C2×Q8×C61—21no—
101C2×Q8×C61C2×D412yes—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C2×C22⋊D61—41no—
108#11758222—82no—
109C2×D244—21no—
110C2×D244—21no—
111C2×D244—21no—
112C2×C4×D61—41no—
113C2×Dic122—21no—
114C2×Dic122—21no—
115C2×Dic122—21no—
116C2×C8×C61—22no—
117C2×C8×C61C2×D412yes—
118C2×C8×C61C2×D412yes—
119C4⋊C4×C61—22no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—22no—
122C4⋊C4×C61C2×D412yes—
123C42×C61—22no—
124C42×C61—22no—
125C42×C61C2×D411yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61#4111yescharacteristic
128C42×C61C2411yescharacteristic
129C22⋊Dic61—41no—
130#11758202—44no—
131#11758201—44no—
132#11758198—41no—
133#11758198—41no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61—21no—
138C4⋊Dic61—21no—
139C4⋊Dic61—21no—
140#11758196—41no—
141#11758196—41no—
142C4×Dic61—41no—
143C2×#92418—22no—
144C2×#92418—22no—
145C23×C61#12111yescharacteristic
146C22×D61—41no—
147Q8×C61—24no—
148Q8×C61—22no—
149Q8×C61#13514yes—
150C2×C4×C61—24no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—22no—
155C2×C4×C61—41no—
156C2×C4×C61—81no—
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61C22×D411yescharacteristic
161C2×C4×C61C22×D411yescharacteristic
162C2×C4×C61C2×#4111yescharacteristic
163C22⋊D61—82no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167D244—42no—
168D244—42no—
169D244—81no—
170C4×D61—82no—
171Dic122—42no—
172Dic122—81no—
173Dic122—81no—
174C8×C61—22no—
175C8×C61—22no—
176C8×C61—42no—
177#92418—42no—
178#92418—42no—
179#19406—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61C2×#12111yescharacteristic
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—21no—
188C4×C61—24no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—42no—
193C4×C61C2×#13512yes—
194C4×C61#57812yes—
195Dic61—81no—
196Dic61—81no—
197Dic61—81no—
198#3228—611no—
199#3112—611no—
200#3104—611no—
201#2982D6111yescharacteristic, complemented
202#1682—612no—
203#1678—612no—
204#1676—612no—
205#1672—612no—
206#1572—611no—
207#1554—611no—
208#1543—611no—
209C2×C61—41no—
210C2×C61#304411yescharacteristic
211C2×C61#305011yescharacteristic
212C2×C61#306811yescharacteristic
213D61—161no—
214#533—611no—
215#532—611no—
216C2×C4×Q8C2×D6111yescharacteristic
217#500—611no—
218#498—611no—
219#486—611no—
220#486—611no—
221#484—1221no—
222#482—1222no—
223#480—1221no—
224#478—1222no—
225#477—612no—
226#477—612no—
227#462—612no—
228#460—612no—
229#451—1221no—
230#448—1221no—
231C8×Q8—22no—
232C8×Q8C2×D6112yes—
233C8×Q8C2×D6112yes—
234#440—1222no—
235C4×Q16—1222no—
236#432—611no—
237#431—22no—
238#431—611no—
239#431C2×D6111yescharacteristic
240#431C2×D6111yescharacteristic
241#335—612no—
242#334—612no—
243#333—612no—
244#333—612no—
245#332—612no—
246#331—612no—
247C61#1940611yescharacteristic, complemented, Sylow
248C2×#41—1221no—
249C22×Q8D24411yescharacteristic
250C2×Q16—1222no—
251C2×SD16—1222no—
252C4⋊Q8—611no—
253C4⋊Q8—611no—
254C4⋊Q8—611no—
255#127—611no—
256#125—1221no—
257#124—1221no—
258C22⋊Q8—1221no—
259C22⋊Q8—1221no—
260#121—1221no—
261#121—1221no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—1221no—
265C4×Q8—1221no—
266C4×Q8D24412yes—
267C4×Q8C22×D6112yes—
268C4×D4—1221no—
269C4×D4—1221no—
270#117—1221no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4D24411yescharacteristic
273C2×C42—21no—
274C2×C42C22×D6111yescharacteristic
275#107—1222no—
276#107—1222no—
277#107—1222no—
278#106—1222no—
279C4⋊C8—22no—
280C4⋊C8—22no—
281C4⋊C8—612no—
282C4⋊C8—612no—
283C4⋊C8C22⋊D6112yes—
284C4⋊C8C22×D6112yes—
285#103—1222no—
286#103—1222no—
287#103—1222no—
288#102—1222no—
289#102—1222no—
290#102—1222no—
291C22⋊C8—21no—
292C22⋊C8—1221no—
293C22⋊C8—1221no—
294C22⋊C8C22⋊D6112yes—
295#97—1221no—
296C4×C8—22no—
297C4×C8—22no—
298C4×C8—21no—
299C4×C8—1221no—
300C4×C8C22×D6111yescharacteristic
301C4×C8C22×D6111yescharacteristic
302#41—4882no—
303C2×Q8—24no—
304C2×Q8—21no—
305C2×Q8—1221no—
306C2×Q8—1221no—
307C2×Q8—1221no—
308C2×Q8C2×D24412yes—
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—1221no—
312C2×D4—2441no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—2441no—
316C22×C4C2×D24411yescharacteristic
317C22×C4#1175822211yescharacteristic
318C22×C4C2×C22⋊D6111yescharacteristic
319Q16—2444no—
320SD16—2444no—
321C2×C8—22no—
322C2×C8—1222no—
323C2×C8—1222no—
324C2×C8C2×C22⋊D6112yes—
325C2×C8C2×C22⋊D6112yes—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C4⋊C4C2×D24412yes—
338C22⋊C4—2441no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C42—22no—
342C42—22no—
343C42—2441no—
344C42C2×D24411yescharacteristic
345C42#1175822211yescharacteristic
346C42C2×C22⋊D6111yescharacteristic
347C42C23×D6111yescharacteristic
348C23—2441no—
349C23#1451975111yescharacteristic
350Q8—24no—
351Q8—22no—
352Q8—4881no—
353Q8—4881no—
354Q8—2442no—
355Q8#1451979914yes—
356D4—4881no—
357D4—4882no—
358D4—2442no—
359D4—2442no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—4882no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4#1451975111yescharacteristic
372C2×C4#1451975111yescharacteristic
373C2×C4#1451975111yescharacteristic
374C2×C4C22×C22⋊D6111yescharacteristic
375C2×C4C22×D24411yescharacteristic
376C2×C4C2×#1175822211yescharacteristic
377C8—22no—
378C8—22no—
379C8—42no—
380C8—2442no—
381C8—2442no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—4881no—
386C22—4881no—
387C22—4881no—
388C22C2×#1451975111yescharacteristic
389C4—24no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—4881no—
396C4—4881no—
397C4—4881no—
398C4C2×#1451979912yes—
399C4#1684057712yes—
400C2—41no—
401C2—9761no—
402C2#2145534911yescharacteristic
403C2#2145540011yescharacteristic
404C2#2145554711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2982C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#2982D61
hypocenterC61#19406
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
3. #21455858C2semidirect
4. #21445263C2semidirect
5. #21445235C2semidirect
6. #21445223C2semidirect
7. #21445201C2semidirect
8. #21444599C2semidirect
9. #21444527C2semidirect
11. C61×#2982C2semidirect
201. #2982D61semidirect
247. C61#19406semidirect

Maximal subgroups

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

subgroupindex
#214569572
#214559412
#214558582
#214452632
#214452352
#214452232
#214452012
#214445992
#214445272
#214444792
C61×#29822
#1940661