Finite Group Databasebeta

← #29834692

Subgroups — #29834692

Order 15616.

542 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840163C211yesmaximal, characteristic, complemented
2#21454590C211yesmaximal, characteristic
3#21447986C212yesmaximal, complemented
4#21447982C212yesmaximal, complemented
5#21447979C212yesmaximal, complemented
6#21447975C212yesmaximal, complemented
7#21447608C211yesmaximal, characteristic, complemented
8#21447574C211yesmaximal, characteristic, complemented
9#21447532C211yesmaximal, characteristic
10#21447529C211yesmaximal, characteristic
11C61×#2159C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C2×#14519768—21no—
14#16840230—21no—
15C2×#14519717C2211yescharacteristic
16#16840163—21no—
17#16840163—21no—
18#16840163C2212yes—
19#16840163C2212yes—
20#16839856C2211yescharacteristic
21#16839856C2211yescharacteristic
22#16839849—21no—
23#16839849—21no—
24#16839844C2211yescharacteristic
25#16839844C2211yescharacteristic
26C2×#14519711C2211yescharacteristic
27C2×#14519708—21no—
28#16839756—21no—
29C2×C8×Dic61C2211yescharacteristic
30#16839589C2212yes—
31#16839587C2212yes—
32#16839580C2212yes—
33#16839580C2212yes—
34#16839567C2212yes—
35#16839565C2212yes—
36#16839564C2212yes—
37#16839562C2212yes—
38C2×M32×C61C2211yescharacteristic
39C61×#427C2211yescharacteristic
40C2×#107×C61C2211yescharacteristic
41C61×#367C2212yes—
42C61×#366C2212yes—
43C2×#11758222—21no—
44#14519799—22no—
45#14519799Q814yes—
46C2×Dic244C2311yescharacteristic
47C2×#11758190—21no—
48C2×D488C2311yescharacteristic
49C22×#92418D411yescharacteristic
50#14519768—22no—
51#14519768—22no—
52#14519768—41no—
53#14519768—41no—
54#14519742—21no—
55#14519742—21no—
56#14519739—21no—
57#14519739—21no—
58#14519737—41no—
59#14519737—41no—
60#14519734—41no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—41no—
63C2×#11758196—41no—
64C2×C4×Dic61D411yescharacteristic
65C42×D61—41no—
66#14519717—22no—
67C2×#11758185C2312yes—
68#14519711—21no—
69#14519711C2312yes—
70#14519708—22no—
71#14519708—22no—
72#14519700—21no—
73#14519700—21no—
74#14519697—21no—
75#14519697—21no—
76C8×Dic61D411yescharacteristic
77C8×Dic61D411yescharacteristic
78C8×Dic61C2311yescharacteristic
79C8×Dic61C2311yescharacteristic
80C22×C8×C61C2311yescharacteristic
81#117×C61—21no—
82C2×C4⋊C4×C61—21no—
83M32×C61—22no—
84C2×C16×C61C2312yes—
85#107×C61—21no—
86#107×C61C2311yescharacteristic
87#107×C61C2312yes—
88#107×C61C2311yescharacteristic
89#106×C61—21no—
90C22×C4×C61—41no—
91C22×C4×C61C2×D411yescharacteristic
92C2×C22⋊D61—41no—
93C22×Dic61—41no—
94C22×Dic61D811yescharacteristic
95C22×Dic61D811yescharacteristic
96#11758222—24no—
97#11758222—42no—
98C2×D244—21no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×Dic122—21no—
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61C2×Q812yes—
105C2×C8×C61#4112yes—
106C2×C8×C61C2411yescharacteristic
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C42×C61—41no—
113#11758198—41no—
114#11758198—41no—
115C4⋊Dic61—22no—
116C4⋊Dic61—41no—
117C4⋊Dic61—42no—
118C4⋊Dic61—42no—
119#11758196—42no—
120#11758196—42no—
121#11758196—41no—
122#11758196—41no—
123C4×Dic61—41no—
124C4×Dic61—41no—
125C4×Dic61D811yescharacteristic
126C4×Dic61D811yescharacteristic
127C4×Dic61C2×D411yescharacteristic
128C4×Dic61C2×D411yescharacteristic
129C2×#92418—22no—
130C2×#92418C2×D411yescharacteristic
131C2×#92418C2×D411yescharacteristic
132Dic244—21no—
133Dic244C2×Q812yes—
134D488—21no—
135D488C2×Q812yes—
136#11758190—24no—
137C16×C61—22no—
138#11758185—22no—
139C23×C61C2×D811yescharacteristic
140C22×D61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—42no—
144C2×C4×C61—82no—
145C2×C4×C61C22⋊Q812yes—
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61#13712yes—
148C2×C4×C61C22×D411yescharacteristic
149C22⋊D61—44no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61—82no—
155C2×Dic61C2×D811yescharacteristic
156C2×Dic61C2×D811yescharacteristic
157C2×Dic61C2×D811yescharacteristic
158C2×Dic61C2×D811yescharacteristic
159D244—22no—
160D244—41no—
161C4×D61—44no—
162C4×D61—82no—
163C4×D61—82no—
164Dic122—22no—
165Dic122—41no—
166C8×C61C22⋊Q812yes—
167C8×C61C22×Q811yescharacteristic
168C8×C61C2×#4111yescharacteristic
169#92418—21no—
170#92418—21no—
171#33630—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#47412yes—
175C22×C61C22×D811yescharacteristic
176C2×D61—42no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—81no—
180C4×C61—81no—
181C4×C61—82no—
182C4×C61#47412yes—
183C4×C61C2×C22⋊Q811yescharacteristic
184C4×C61C2×#13711yescharacteristic
185Dic61—21no—
186Dic61—21no—
187Dic61—21no—
188Dic61—21no—
189Dic61—42no—
190Dic61—82no—
191C2×#499—611no—
192C4×#135—611no—
193#2229—612no—
194#2229—612no—
195#2228—612no—
196#2228—612no—
197#2159—611no—
198#2159D6111yescharacteristic, complemented
199#2150—611no—
200#2139—611no—
201#2139—611no—
202C2×C61—22no—
203C2×C61C2×#47411yescharacteristic
204C2×C61#341411yescharacteristic
205C2×C61#341411yescharacteristic
206D61—82no—
207C2×#135—611no—
208C2×#125—1221no—
209C4×#41—1221no—
210C2×M32—611no—
211C2×M32C2×D6111yescharacteristic
212#499—612no—
213#499—612no—
214#499—1221no—
215#499—1221no—
216C4×Q16—611no—
217C4×Q16—611no—
218C4×SD16—1221no—
219C4×SD16—1221no—
220C4×D8—611no—
221C4×D8—611no—
222#427C2×D6111yescharacteristic
223C2×#107—611no—
224C2×#107C2×D6111yescharacteristic
225C2×#106—1221no—
226#416—1221no—
227C2×C4×C8—611no—
228#367—612no—
229#367C2×D6112yes—
230#366—612no—
231#366C2×D6112yes—
232C4⋊C16—612no—
233C4⋊C16—612no—
234#358—612no—
235#358—612no—
236#357—612no—
237#357—612no—
238C61#3363011yescharacteristic, complemented, Sylow
239C2×#41—1221no—
240#135—614no—
241#135—1222no—
242C2×Q16—611no—
243C2×SD16—1221no—
244C2×D8—611no—
245C22×C8—611no—
246C22×C8C22×D6111yescharacteristic
247#125—1222no—
248#125—1222no—
249#125—2441no—
250#125—2441no—
251C4×Q8—1221no—
252C4×Q8—1221no—
253C4×D4—1221no—
254C4×D4—1221no—
255C4×D4—2441no—
256C4×D4—2441no—
257#117—21no—
258#117—2441no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—2441no—
262C2×C4⋊C4—2441no—
263C2×C42—611no—
264C2×C42—2441no—
265M32—22no—
266M32—1222no—
267C2×C16—612no—
268C2×C16C22×D6112yes—
269#107—21no—
270#107—612no—
271#107—1221no—
272#107C22×D6112yes—
273#107C22×D6111yescharacteristic
274#107C22×D6111yescharacteristic
275#106—21no—
276#106—1222no—
277#106—1222no—
278#103—1221no—
279#103—1221no—
280#102—1221no—
281#102—1221no—
282C4×C8—611no—
283C4×C8—611no—
284C4×C8—611no—
285C4×C8—611no—
286#41—1224no—
287#41—2442no—
288C2×Q8—1221no—
289C2×D4—1221no—
290C2×D4—2441no—
291C22×C4—41no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4D4×D6111yescharacteristic
299Q16—612no—
300Q16—1221no—
301SD16—1224no—
302D8—612no—
303D8—1221no—
304C2×C8—611no—
305C2×C8—611no—
306C2×C8—1222no—
307C2×C8#1175822212yes—
308C2×C8D4×D6111yescharacteristic
309C2×C8Q8×D6112yes—
310C2×C8C23×D6111yescharacteristic
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—1222no—
316C4⋊C4—2442no—
317C4⋊C4—2442no—
318C4⋊C4—2442no—
319C4⋊C4—2442no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C22⋊C4—41no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C42—41no—
327C42—611no—
328C42—611no—
329C42—611no—
330C42—611no—
331C42—2441no—
332C42—2441no—
333C16—22no—
334C16—1222no—
335C23—2441no—
336C23D8×D6111yescharacteristic
337Q8—1222no—
338Q8—2441no—
339D4—1222no—
340D4—2444no—
341D4—2441no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—4882no—
351C2×C4—4882no—
352C2×C4—4882no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2442no—
356C2×C4—2441no—
357C2×C4—2444no—
358C2×C4#1451975512yes—
359C2×C4D8×D6111yescharacteristic
360C2×C4#1451980912yes—
361C2×C4C2×D4×D6111yescharacteristic
362C8—1221no—
363C8—1221no—
364C8#1451975512yes—
365C8C2×Q8×D6111yescharacteristic
366C8C2×#1175822211yescharacteristic
367C22—21no—
368C22—21no—
369C22—4881no—
370C22—4881no—
371C22—2442no—
372C22#1684004112yes—
373C22C2×D8×D6111yescharacteristic
374C4—82no—
375C4—81no—
376C4—81no—
377C4—1221no—
378C4—1221no—
379C4—1221no—
380C4—1221no—
381C4—4882no—
382C4—2442no—
383C4#1684004112yes—
384C4C2×#1451975511yescharacteristic
385C4C2×#1451980911yescharacteristic
386C2—22no—
387C2—4882no—
388C2C2×#1684004111yescharacteristic
389C2#2145895111yescharacteristic
390C2#2145895411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2159C2
socleC22×C61C22×D8
prime radicalC2×#14519799C22
hypercenter#2159D61
hypocenterC61#33630
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
1. C2×#16840163C2semidirect
3. #21447986C2semidirect
4. #21447982C2semidirect
5. #21447979C2semidirect
6. #21447975C2semidirect
7. #21447608C2semidirect
8. #21447574C2semidirect
11. C61×#2159C2semidirect
198. #2159D61semidirect
238. C61#33630semidirect

Maximal subgroups

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

subgroupindex
C2×#168401632
#214545902
#214479862
#214479822
#214479792
#214479752
#214476082
#214475742
#214475322
#214475292
C61×#21592
#3363061