Finite Group Databasebeta

← #29663181

Subgroups — #29663181

Order 15616.

650 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456949C211yesmaximal, characteristic
2#21456942C211yesmaximal, characteristic
3C2×#16840113C211yesmaximal, characteristic, complemented
4#21454532C211yesmaximal, characteristic
5#21445395C214yesmaximal, complemented
6#21445271C214yesmaximal, complemented
7#21444499C211yesmaximal, characteristic, complemented
8#21444490C211yesmaximal, characteristic, complemented
9C61×#1564C211yesmaximal, characteristic, complemented
10C2×#14519783—21no—
11#16840312C2211yescharacteristic
12C2×#14519777C2211yescharacteristic
13C2×#14519777C2211yescharacteristic
14#16840167—21no—
15#16840160—21no—
16#16840113—21no—
17#16840113—21no—
18#16840113C2212yes—
19#16840113C2212yes—
20#16840109—21no—
21#16840109—21no—
22#16840081—22no—
23#16840076—22no—
24#16840053C2214yes—
25#16840043C2214yes—
26#16839841—21no—
27#16839841C2212yes—
28C8×D244—21no—
29C8×D244C2212yes—
30#16839786C2211yescharacteristic
31C2×#14519702—21no—
32C2×#14519702—21no—
33#16839728—21no—
34#16839510C2214yes—
35#16839507C2214yes—
36C61×#431C2211yescharacteristic
37C61×#431C2211yescharacteristic
38C2×C4×C8×C61C2211yescharacteristic
39C61×#335C2212yes—
40C61×#334C2212yes—
41C2×#11758222—21no—
42C22×Dic122—21no—
43C22×Dic122—21no—
44#14519783—44no—
45C2×#11758194—21no—
46C2×#11758189—22no—
47C2×C8×D61—22no—
48#14519777—21no—
49#14519777—21no—
50#14519777—21no—
51#14519777—21no—
52#14519777—21no—
53#14519777—21no—
54#14519777D411yescharacteristic
55#14519777C2312yes—
56#14519777C2312yes—
57#14519774D411yescharacteristic
58#14519765—21no—
59#14519751—21no—
60#14519751D412yes—
61C4×D244—21no—
62C4×D244C2312yes—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67#14519711—24no—
68#14519709—24no—
69C4⋊#92418—21no—
70C4⋊#92418C2312yes—
71#14519702—22no—
72#14519702—22no—
73#14519702—22no—
74#14519702—22no—
75#14519699—24no—
76#14519699—24no—
77#14519689—22no—
78#14519689—22no—
79C22×C8×C61D411yescharacteristic
80C22×C8×C61D411yescharacteristic
81C2×C42×C61C2311yescharacteristic
82C4⋊C8×C61C2312yes—
83C4⋊C8×C61C2312yes—
84C22⋊C8×C61—21no—
85C22⋊C8×C61—21no—
86C4×C8×C61—21no—
87C4×C8×C61—21no—
88C4×C8×C61D411yescharacteristic
89C4×C8×C61D411yescharacteristic
90C4×C8×C61C2311yescharacteristic
91C4×C8×C61C2311yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C2×C22⋊D61—22no—
96C22×Dic61—41no—
97C22×Dic61—41no—
98#11758222—42no—
99#11758222—42no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244C2×D412yes—
103C2×C4×D61—22no—
104C2×Dic122—21no—
105C2×Dic122—22no—
106C2×Dic122—22no—
107C2×Dic122—42no—
108C2×Dic122—42no—
109C2×Dic122—41no—
110C2×Dic122—41no—
111C2×Dic122—82no—
112C2×C8×C61—22no—
113C2×C8×C61—22no—
114C2×C8×C61—22no—
115C2×C8×C61—22no—
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123C42×C61C2411yescharacteristic
124#11758198—22no—
125#11758198—22no—
126C4⋊Dic61—21no—
127C4⋊Dic61—22no—
128C4⋊Dic61—22no—
129C4⋊Dic61—22no—
130C4⋊Dic61—22no—
131C4⋊Dic61—41no—
132C4⋊Dic61—41no—
133C4⋊Dic61—41no—
134C4⋊Dic61—41no—
135C4⋊Dic61C2×D412yes—
136#11758194—42no—
137C2×#92418—22no—
138#11758189—44no—
139C8×D61—44no—
140C23×C61#12111yescharacteristic
141C22×D61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#13512yes—
148C2×C4×C61AGL(1,ℤ/8)12yes—
149C2×C4×C61C22×D411yescharacteristic
150C2×C4×C61C22×D411yescharacteristic
151C2×C4×C61C2×#4111yescharacteristic
152C22⋊D61—44no—
153C2×Dic61—22no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—82no—
157C2×Dic61—82no—
158D244—24no—
159D244—42no—
160D244—42no—
161C4×D61—42no—
162C4×D61—42no—
163Dic122—42no—
164Dic122—42no—
165Dic122—42no—
166Dic122—82no—
167Dic122—82no—
168Dic122—82no—
169C8×C61—21no—
170C8×C61—21no—
171C8×C61—21no—
172C8×C61—21no—
173C8×C61—42no—
174C8×C61—42no—
175#92418—42no—
176#19199—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61#46312yes—
180C22×C61C2×#12111yescharacteristic
181C2×D61—42no—
182C2×D61—42no—
183C2×D61—42no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61#46312yes—
187C4×C61#47112yes—
188C4×C61C2×#13511yescharacteristic
189C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
190C4×C61#57812yes—
191Dic61—42no—
192Dic61—82no—
193Dic61—82no—
194#3227—611no—
195#3226—611no—
196C2×#487—611no—
197#2931—611no—
198#1703—614no—
199#1683—614no—
200#1564D6111yescharacteristic, complemented
201#1548—611no—
202#1546—611no—
203C2×C61—22no—
204C2×C61C2×#46311yescharacteristic
205C2×C61#305911yescharacteristic
206C2×C61C2×#47111yescharacteristic
207D61—82no—
208C2×#131—1221no—
209#532—611no—
210C2×C4⋊Q8—611no—
211C2×C4⋊Q8—611no—
212#500—1221no—
213#498—1221no—
214#487—612no—
215#487—612no—
216#487—1221no—
217#487—1221no—
218#486—1221no—
219#486—1221no—
220#481—1222no—
221#480—1222no—
222#476—614no—
223#474—614no—
224#436—612no—
225#436—1221no—
226C8×D4—612no—
227C8×D4—1221no—
228#431C2×D6111yescharacteristic
229#431C2×D6111yescharacteristic
230#423—611no—
231C2×#103—1221no—
232C2×#103—1221no—
233#408—1221no—
234C2×C4×C8C2×D6111yescharacteristic
235#335C2×D6112yes—
236#334C2×D6112yes—
237#333—614no—
238#332—614no—
239C61#1919911yescharacteristic, complemented, Sylow
240C2×#41—1221no—
241C22×Q8—1221no—
242C22×Q8—1221no—
243#131—2444no—
244C2×M16—1221no—
245C2×M16—1222no—
246C22×C8—1222no—
247C22×C8D24411yescharacteristic
248C22×C8D24411yescharacteristic
249C4⋊Q8—611no—
250C4⋊Q8—612no—
251C4⋊Q8—612no—
252C4⋊Q8—1221no—
253C4⋊Q8—1221no—
254C4⋊Q8—1221no—
255C4⋊Q8—1221no—
256C4⋊Q8—1221no—
257C4⋊Q8—1221no—
258#127—611no—
259#124—1221no—
260#121—612no—
261#121—1221no—
262C4×D4—612no—
263C4×D4—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—1221no—
268C2×C42C22×D6111yescharacteristic
269#107—1224no—
270#106—1224no—
271C4⋊C8—612no—
272C4⋊C8—1221no—
273C4⋊C8C22×D6112yes—
274C4⋊C8C22×D6112yes—
275#103—1222no—
276#103—1222no—
277#103—1222no—
278#103—1222no—
279#102—1224no—
280#102—1224no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—1222no—
284C22⋊C8—1222no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8D24411yescharacteristic
288C4×C8D24411yescharacteristic
289C4×C8C22×D6111yescharacteristic
290C4×C8C22×D6111yescharacteristic
291#41—2442no—
292#41—2442no—
293C2×Q8—1221no—
294C2×Q8—1222no—
295C2×Q8—1222no—
296C2×Q8—4882no—
297C2×Q8—2442no—
298C2×Q8—2442no—
299C2×Q8—2441no—
300C2×Q8—2441no—
301C2×D4—612no—
302C2×D4—1222no—
303C2×D4—1221no—
304C2×D4—1221no—
305C22×C4—1222no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4C2×D24411yescharacteristic
309C22×C4D4×D6111yescharacteristic
310C22×C4#1175822611yescharacteristic
311M16—2444no—
312M16—2442no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—1222no—
318C2×C8—2444no—
319C2×C8C2×D24411yescharacteristic
320C2×C8C2×D24411yescharacteristic
321C2×C8C2×D24411yescharacteristic
322C2×C8C2×D24411yescharacteristic
323C4⋊C4—612no—
324C4⋊C4—1221no—
325C4⋊C4—1222no—
326C4⋊C4—1222no—
327C4⋊C4—1222no—
328C4⋊C4—1222no—
329C4⋊C4—2441no—
330C4⋊C4—2441no—
331C4⋊C4—2441no—
332C4⋊C4—2441no—
333C22⋊C4—1222no—
334C22⋊C4—1222no—
335C42C2×D24411yescharacteristic
336C42D4×D6111yescharacteristic
337C42#1175822611yescharacteristic
338C42C23×D6111yescharacteristic
339C23—1222no—
340C23#1451975211yescharacteristic
341Q8—4882no—
342Q8—4882no—
343Q8—4882no—
344Q8—2442no—
345Q8—2442no—
346Q8—2442no—
347D4—1224no—
348D4—2444no—
349D4—2442no—
350D4—2442no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—1222no—
354C2×C4—4882no—
355C2×C4—4882no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4#1451975211yescharacteristic
361C2×C4#1451975211yescharacteristic
362C2×C4#1451975211yescharacteristic
363C2×C4#1451979912yes—
364C2×C4#1451980512yes—
365C2×C4C2×D4×D6111yescharacteristic
366C2×C4C22×D24411yescharacteristic
367C2×C4C2×#1175822611yescharacteristic
368C8—21no—
369C8—21no—
370C8—21no—
371C8—21no—
372C8—42no—
373C8—42no—
374C8—2442no—
375C22—21no—
376C22—21no—
377C22—2442no—
378C22—2442no—
379C22—2442no—
380C22#1683997812yes—
381C22C2×#1451975211yescharacteristic
382C4—21no—
383C4—21no—
384C4—4882no—
385C4—4882no—
386C4—2442no—
387C4#1683997812yes—
388C4#1684002612yes—
389C4C2×#1451979911yescharacteristic
390C4C2×#1451980511yescharacteristic
391C4#1684057612yes—
392C2—22no—
393C2—4882no—
394C2C2×#1683997811yescharacteristic
395C2#2145547511yescharacteristic
396C2C2×#1684002611yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1564C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1564D61
hypocenterC61#19199
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
3. C2×#16840113C2semidirect
5. #21445395C2semidirect
6. #21445271C2semidirect
7. #21444499C2semidirect
8. #21444490C2semidirect
9. C61×#1564C2semidirect
200. #1564D61semidirect
239. C61#19199semidirect

Maximal subgroups

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

subgroupindex
#214569492
#214569422
C2×#168401132
#214545322
#214453952
#214452712
#214444992
#214444902
C61×#15642
#1919961