Finite Group Databasebeta

← #29663358

Subgroups — #29663358

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456795C212yesmaximal, complemented
2#21454794C211yesmaximal, characteristic, complemented
3#21445384C212yesmaximal, complemented
4#21445377C212yesmaximal, complemented
5#21445210C211yesmaximal, characteristic, complemented
6#21445205C211yesmaximal, characteristic, complemented
7#21445176C211yesmaximal, characteristic, complemented
8#21445171C211yesmaximal, characteristic, complemented
9#21444567C211yesmaximal, characteristic, complemented
10#21444524C212yesmaximal, complemented
11C61×#3169C211yesmaximal, characteristic, complemented
12#16840296C2211yescharacteristic
13#16840144—22no—
14#16840116—22no—
15#16839969C2212yes—
16#16839964C2212yes—
17#16839959C2212yes—
18#16839954C2212yes—
19#16839924—22no—
20#16839907—22no—
21#16839892C2211yescharacteristic
22C8×Dic122C2211yescharacteristic
23#16839841C2211yescharacteristic
24#16839833—21no—
25C8×D244C2211yescharacteristic
26C8×C22⋊D61—21no—
27#16839821—21no—
28#16839819C2211yescharacteristic
29#16839815C2212yes—
30#16839716—21no—
31#16839515C2211yescharacteristic
32#16839515C2211yescharacteristic
33#16839513C2212yes—
34#16839508C2212yes—
35#16839508C2212yes—
36#16839506C2212yes—
37#16839506C2212yes—
38C61×#532C2212yes—
39C61×#500C2211yescharacteristic
40C61×#493C2211yescharacteristic
41C61×#486C2212yes—
42C61×#466—21no—
43C61×#466—21no—
44C4×D8×C61—21no—
45C4×D8×C61—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758202—22no—
48C2×#11758200—22no—
49C2×#11758201—22no—
50C2×#11758199—22no—
51C2×#11758189—21no—
52C2×C8×D61—21no—
53#14519771—21no—
54#14519769D411yescharacteristic
55#14519765D411yescharacteristic
56#14519760—21no—
57#14519756D411yescharacteristic
58#14519751D411yescharacteristic
59C4×Dic122C2311yescharacteristic
60C4×D244C2311yescharacteristic
61C4×C22⋊D61—21no—
62#14519734—21no—
63C4⋊#92418C2312yes—
64C4⋊#92418C2312yes—
65C4⋊#92418C2311yescharacteristic
66C4⋊#92418C2311yescharacteristic
67#14519706—21no—
68#14519706—21no—
69#14519701—22no—
70#14519701—22no—
71#14519698—22no—
72#14519698—22no—
73C22⋊#92418—22no—
74C22⋊#92418—21no—
75#14519689—21no—
76#14519689—21no—
77#14519688—21no—
78#14519687—21no—
79C4×#92418—22no—
80C8×Dic61—21no—
81C2×#41×C61—22no—
82C2×D8×C61—21no—
83C2×D8×C61—21no—
84C22×C8×C61D411yescharacteristic
85C22×C8×C61D411yescharacteristic
86C4⋊Q8×C61C2312yes—
87#127×C61C2312yes—
88#124×C61—22no—
89#121×C61—22no—
90#121×C61—22no—
91C4×D4×C61—22no—
92C4×D4×C61—22no—
93C2×C42×C61C2311yescharacteristic
94#107×C61—21no—
95#107×C61—21no—
96#102×C61—22no—
97#102×C61—22no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102#41×C61—82no—
103#41×C61—82no—
104C2×Q8×C61—22no—
105C2×D4×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61—22no—
108C2×D4×C61—42no—
109C22×C4×C61—42no—
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C2×C22⋊D61—21no—
114C2×D244C2×D411yescharacteristic
115C2×C4×D61—21no—
116C2×Dic122C2×D411yescharacteristic
117D8×C61—42no—
118D8×C61—42no—
119C2×C8×C61—22no—
120C2×C8×C61—41no—
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C4⋊C4×C61—22no—
126C4⋊C4×C61—22no—
127C22⋊C4×C61—42no—
128C22⋊C4×C61—42no—
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61#4111yescharacteristic
132C42×C61C2411yescharacteristic
133C22⋊Dic61—21no—
134#11758202—82no—
135#11758201—82no—
136#11758200—82no—
137#11758199—82no—
138#11758198—21no—
139#11758198—21no—
140#11758198—21no—
141#11758198—21no—
142C4⋊Dic61C2×D411yescharacteristic
143C4⋊Dic61C2×D411yescharacteristic
144#11758196—21no—
145#11758196—21no—
146#11758196—21no—
147#11758196—21no—
148C4×Dic61—21no—
149C2×#92418—21no—
150C2×#92418—22no—
151C2×#92418—22no—
152C2×#92418—21no—
153#11758189—42no—
154C8×D61—42no—
155C23×C61—42no—
156C23×C61#12111yescharacteristic
157C22×D61—21no—
158Q8×C61—42no—
159Q8×C61—42no—
160D4×C61—42no—
161D4×C61—42no—
162D4×C61—42no—
163D4×C61—42no—
164D4×C61—82no—
165D4×C61—84no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—41no—
171C2×C4×C61—42no—
172C2×C4×C61—84no—
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61C22×D411yescharacteristic
177C2×C4×C61C22×D411yescharacteristic
178C2×C4×C61C2×#4111yescharacteristic
179C22⋊D61—42no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183D244—21no—
184D244—21no—
185C4×D61—41no—
186C4×D61—41no—
187Dic122—21no—
188Dic122—21no—
189C8×C61—21no—
190C8×C61—21no—
191C8×C61—21no—
192C8×C61#13512yes—
193#92418—41no—
194#92418—41no—
195#92418—42no—
196#92418—42no—
197#19219—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—82no—
202C22×C61—82no—
203C22×C61—82no—
204C22×C61C2×#12111yescharacteristic
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—82no—
213C4×C61C2×#13511yescharacteristic
214C4×C61#57511yescharacteristic
215C4×C61#57611yescharacteristic
216C4×C61#57611yescharacteristic
217Dic61—41no—
218Dic61—41no—
219Dic61—41no—
220#3212—612no—
221#3169D6111yescharacteristic, complemented
222#2966—611no—
223#1702—612no—
224#1701—612no—
225#1674—611no—
226#1673—611no—
227#1668—611no—
228#1667—611no—
229#1564—611no—
230#1553—612no—
231C2×C61—41no—
232C2×C61—162no—
233C2×C61#303511yescharacteristic
234C2×C61#305811yescharacteristic
235C2×C61#306711yescharacteristic
236D61—81no—
237#532C2×D6112yes—
238#529—611no—
239#500C2×D6111yescharacteristic
240#495—1222no—
241#493C2×D6111yescharacteristic
242#488—1222no—
243#486C2×D6112yes—
244#466—21no—
245#466—21no—
246#462—612no—
247#461—612no—
248#460—612no—
249#459—612no—
250#452—1222no—
251#449—1222no—
252#446—611no—
253C8×Q8—611no—
254C4×D8—21no—
255C4×D8—21no—
256#436—611no—
257#435—1221no—
258C8×D4—611no—
259C8×D4—1221no—
260#433—1221no—
261#432—611no—
262#431—612no—
263#405—1221no—
264C2×C4×C8C2×D6111yescharacteristic
265#335—611no—
266#335—611no—
267#334—612no—
268#332—612no—
269#332—612no—
270#331—612no—
271#331—612no—
272C61#1921911yescharacteristic, complemented, Sylow
273C2×#41—22no—
274C2×Q16—1222no—
275C2×SD16—1222no—
276C2×SD16—1222no—
277C2×D8—21no—
278C2×D8—21no—
279C2×D8—1222no—
280C2×M16—1221no—
281C22×C8—1221no—
282C22×C8C22⋊D6111yescharacteristic
283C22×C8C22⋊D6111yescharacteristic
284C4⋊Q8C22×D6112yes—
285#127C22×D6112yes—
286#126—1221no—
287#125—611no—
288#124—22no—
289#124—611no—
290#123—1221no—
291C22⋊Q8—611no—
292#121—22no—
293#121—22no—
294#121—611no—
295C4×Q8—611no—
296C4×D4—22no—
297C4×D4—22no—
298C4×D4—611no—
299C4×D4—1221no—
300#117—1221no—
301C2×C42C22×D6111yescharacteristic
302#107—21no—
303#107—21no—
304C4⋊C8—611no—
305C4⋊C8—611no—
306C4⋊C8—612no—
307C4⋊C8—612no—
308C4⋊C8—1221no—
309C4⋊C8—1221no—
310#103—1222no—
311#103—1222no—
312#102—22no—
313#102—22no—
314#102—1222no—
315#102—1222no—
316C22⋊C8—1222no—
317C22⋊C8—1221no—
318C22⋊C8—1221no—
319C22⋊C8—1221no—
320#97—1221no—
321#97—1221no—
322C4×C8—1221no—
323C4×C8—1222no—
324C4×C8C22⋊D6111yescharacteristic
325C4×C8C22⋊D6111yescharacteristic
326C4×C8C22×D6111yescharacteristic
327C4×C8C22×D6111yescharacteristic
328#41—82no—
329#41—82no—
330C2×Q8—22no—
331C2×Q8—611no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—42no—
336C2×D4—611no—
337C2×D4—1221no—
338C22×C4—42no—
339C22×C4—1221no—
340C22×C4D4×D6111yescharacteristic
341C22×C4#1175822411yescharacteristic
342C22×C4C2×C22⋊D6111yescharacteristic
343Q16—4882no—
344SD16—4882no—
345SD16—4882no—
346D8—42no—
347D8—42no—
348D8—4882no—
349M16—2442no—
350C2×C8—22no—
351C2×C8—41no—
352C2×C8—1222no—
353C2×C8—1222no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8—2442no—
357C2×C8C2×C22⋊D6111yescharacteristic
358C2×C8C2×C22⋊D6111yescharacteristic
359C2×C8C2×C22⋊D6111yescharacteristic
360C2×C8C2×C22⋊D6111yescharacteristic
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—611no—
364C4⋊C4—611no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—1221no—
368C4⋊C4—1221no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C22⋊C4—1221no—
372C22⋊C4—1221no—
373C22⋊C4—1221no—
374C22⋊C4—1221no—
375C22⋊C4—1221no—
376C42—1221no—
377C42D4×D6111yescharacteristic
378C42#1175822411yescharacteristic
379C42C2×C22⋊D6111yescharacteristic
380C42C23×D6111yescharacteristic
381C23—42no—
382C23—1221no—
383C23#1451974811yescharacteristic
384Q8—42no—
385Q8—42no—
386Q8—1221no—
387Q8—1221no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—82no—
393D4—84no—
394D4—1221no—
395D4—1221no—
396D4—2442no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—84no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4#1451974811yescharacteristic
410C2×C4#1451974811yescharacteristic
411C2×C4#1451974811yescharacteristic
412C2×C4C2×D4×D6111yescharacteristic
413C2×C4C22×C22⋊D6111yescharacteristic
414C2×C4C2×#1175822411yescharacteristic
415C8—21no—
416C8—21no—
417C8—21no—
418C8—2441no—
419C8—2441no—
420C8—2442no—
421C8—2442no—
422C8#1451979712yes—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22—2441no—
430C22—2441no—
431C22—2441no—
432C22C2×#1451974811yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—82no—
438C4—2441no—
439C4—2441no—
440C4—2441no—
441C4C2×#1451979711yescharacteristic
442C4#1684056011yescharacteristic
443C4#1684056311yescharacteristic
444C4#1684056311yescharacteristic
445C2—41no—
446C2—162no—
447C2—4881no—
448C2#2145526811yescharacteristic
449C2#2145546311yescharacteristic
450C2#2145553511yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3169C2
socleC22×C61C2×#121
hypercenter#3169D61
hypocenterC61#19219
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #21456795C2semidirect
2. #21454794C2semidirect
3. #21445384C2semidirect
4. #21445377C2semidirect
5. #21445210C2semidirect
6. #21445205C2semidirect
7. #21445176C2semidirect
8. #21445171C2semidirect
9. #21444567C2semidirect
10. #21444524C2semidirect
11. C61×#3169C2semidirect
221. #3169D61semidirect
272. C61#19219semidirect

Maximal subgroups

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

subgroupindex
#214567952
#214547942
#214453842
#214453772
#214452102
#214452052
#214451762
#214451712
#214445672
#214445242
C61×#31692
#1921961