Finite Group Databasebeta

← #29663572

Subgroups — #29663572

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457126C211yesmaximal, characteristic
2#21456741C211yesmaximal, characteristic, complemented
3#21456213C211yesmaximal, characteristic, complemented
4#21445380C212yesmaximal, complemented
5#21445366C212yesmaximal, complemented
6#21445256C212yesmaximal, complemented
7#21445242C212yesmaximal, complemented
8#21444571C211yesmaximal, characteristic, complemented
9#21444469C211yesmaximal, characteristic, complemented
10C2×#16839507C211yesmaximal, characteristic, complemented
11C61×#2935C211yesmaximal, characteristic, complemented
12#16840312C2211yescharacteristic
13C2×#14519777C2211yescharacteristic
14#16840134—21no—
15#16840122—22no—
16#16840114—21no—
17#16840113C2212yes—
18#16840109C2212yes—
19#16840042C2212yes—
20#16840039—21no—
21#16839996—22no—
22#16839967C2212yes—
23#16839967C2212yes—
24#16839957C2212yes—
25#16839954—21no—
26#16839900—22no—
27#16839815C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29#16839764—21no—
30#16839764—21no—
31#16839515C2212yes—
32#16839513C2212yes—
33#16839509C2211yescharacteristic
34#16839509C2211yescharacteristic
35#16839507C2212yes—
36#16839507C2212yes—
37#16839505C2211yescharacteristic
38#16839505C2211yescharacteristic
39C2×#131×C61—21no—
40C61×#532C2211yescharacteristic
41C61×#436C2212yes—
42C61×#435—22no—
43C8×D4×C61C2212yes—
44C2×C4⋊C8×C61C2211yescharacteristic
45C61×#408—21no—
46C4×M16×C61C2211yescharacteristic
47C2×#11758222—21no—
48C22×Dic122—21no—
49C2×#11758200—22no—
50C2×#11758200—22no—
51C2×#11758199—22no—
52C22×#92418—21no—
53#14519777—21no—
54#14519777—21no—
55#14519777—21no—
56#14519777C2312yes—
57#14519777C2311yescharacteristic
58#14519774C2311yescharacteristic
59#14519765—21no—
60#14519751—21no—
61#14519751—21no—
62C4×D244—21no—
63C4×D244—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66#14519710—22no—
67C4⋊#92418—21no—
68C4⋊#92418C2312yes—
69C4⋊#92418C2311yescharacteristic
70C4⋊#92418C2311yescharacteristic
71#14519702—22no—
72#14519702—22no—
73#14519700—22no—
74#14519700—22no—
75#14519699—22no—
76#14519699—22no—
77#14519698—22no—
78#14519697—22no—
79C22⋊#92418—21no—
80C4×#92418—21no—
81C2×#41×C61—21no—
82#131×C61—44no—
83C2×M16×C61—22no—
84C2×M16×C61D411yescharacteristic
85C2×M16×C61D411yescharacteristic
86C22×C8×C61—21no—
87C22×C8×C61—22no—
88C4⋊Q8×C61D411yescharacteristic
89#127×C61D411yescharacteristic
90#124×C61—21no—
91#121×C61—21no—
92#121×C61D412yes—
93C4×D4×C61—21no—
94C4×D4×C61C2312yes—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2311yescharacteristic
98C4⋊C8×C61C2311yescharacteristic
99C22⋊C8×C61—22no—
100C22⋊C8×C61—22no—
101#97×C61D412yes—
102C4×C8×C61C2312yes—
103#41×C61—42no—
104#41×C61—42no—
105C2×Q8×C61—21no—
106C2×D4×C61—22no—
107C2×D4×C61—21no—
108C2×D4×C61—21no—
109C2×D4×C61C2×D412yes—
110C22×C4×C61—22no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C2×C22⋊D61—41no—
115C22×Dic61—41no—
116#11758222—42no—
117#11758222—42no—
118C2×D244—21no—
119C2×D244—21no—
120C2×D244—21no—
121C2×C4×D61—41no—
122C2×Dic122—22no—
123C2×Dic122—21no—
124C2×Dic122—41no—
125C2×Dic122—81no—
126C2×Dic122—81no—
127M16×C61—22no—
128M16×C61—22no—
129M16×C61—44no—
130C2×C8×C61—21no—
131C2×C8×C61—21no—
132C2×C8×C61—44no—
133C2×C8×C61—42no—
134C2×C8×C61C2×D412yes—
135C2×C8×C61C2×D412yes—
136C4⋊C4×C61—21no—
137C4⋊C4×C61C2×D412yes—
138C22⋊C4×C61—22no—
139C22⋊C4×C61—22no—
140C42×C61C2×D411yescharacteristic
141C42×C61C2×D411yescharacteristic
142C42×C61#4111yescharacteristic
143C42×C61C2411yescharacteristic
144#11758200—82no—
145#11758200—82no—
146#11758199—82no—
147#11758198—41no—
148#11758198—41no—
149C4⋊Dic61—21no—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—21no—
153C4⋊Dic61—41no—
154C4⋊Dic61—41no—
155C2×#92418—21no—
156C2×#92418—21no—
157C2×#92418—22no—
158C2×#92418—81no—
159C23×C61—22no—
160C23×C61#12111yescharacteristic
161C22×D61—41no—
162Q8×C61—42no—
163D4×C61—22no—
164D4×C61—22no—
165D4×C61—44no—
166D4×C61—42no—
167D4×C61—81no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—22no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#13512yes—
178C2×C4×C61AGL(1,ℤ/8)12yes—
179C2×C4×C61C22×D411yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C2×C4×C61C2×#4111yescharacteristic
182C22⋊D61—82no—
183C2×Dic61—42no—
184C2×Dic61—41no—
185C2×Dic61—82no—
186D244—41no—
187D244—41no—
188D244—41no—
189D244—41no—
190D244—81no—
191C4×D61—82no—
192Dic122—41no—
193Dic122—41no—
194Dic122—42no—
195Dic122—42no—
196Dic122—82no—
197C8×C61—22no—
198C8×C61—22no—
199C8×C61—41no—
200C8×C61—41no—
201#92418—42no—
202#92418—41no—
203#92418—41no—
204#19237—611nomaximal, Sylow
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—42no—
208C22×C61—42no—
209C22×C61—42no—
210C22×C61#46312yes—
211C22×C61C2×#12111yescharacteristic
212C2×D61—81no—
213C2×D61—81no—
214C2×D61—81no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—42no—
219C4×C61#46312yes—
220C4×C61C2×#13511yescharacteristic
221C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
222C4×C61#57611yescharacteristic
223C4×C61#57711yescharacteristic
224Dic61—81no—
225Dic61—82no—
226#3245—611no—
227#3206—611no—
228#3141—611no—
229#2935D6111yescharacteristic, complemented
230#1701—612no—
231#1699—612no—
232#1681—612no—
233#1679—612no—
234#1565—611no—
235#1540—611no—
236C2×#332—611no—
237C2×C61—22no—
238C2×C61—82no—
239C2×C61C2×#46311yescharacteristic
240C2×C61#306211yescharacteristic
241C2×C61#306911yescharacteristic
242D61—161no—
243C2×#131—21no—
244#532—611no—
245#532C2×D6111yescharacteristic
246C2×C4⋊Q8—611no—
247#492—1221no—
248#489—1222no—
249#487—612no—
250#487—1221no—
251#486—612no—
252#474—612no—
253#474—1221no—
254#466—1222no—
255#461—612no—
256#461—612no—
257#459—612no—
258#459—1221no—
259#448—1222no—
260#436C2×D6112yes—
261#435—22no—
262C8×D4C2×D6112yes—
263#431—611no—
264C2×C4⋊C8—611no—
265C2×C4⋊C8C2×D6111yescharacteristic
266#417—1221no—
267#417—1221no—
268#408—21no—
269C4×M16C2×D6111yescharacteristic
270#335—612no—
271#334—612no—
272#332—612no—
273#332—612no—
274#332—611no—
275#332—611no—
276#331—611no—
277#331—611no—
278C61#1923711yescharacteristic, complemented, Sylow
279C2×#41—21no—
280C2×#41—1221no—
281C22×Q8—1221no—
282C2×SD16—1222no—
283C2×SD16—1222no—
284C2×D8—1222no—
285#131—44no—
286C2×M16—22no—
287C2×M16C22⋊D6111yescharacteristic
288C2×M16C22⋊D6111yescharacteristic
289C22×C8—21no—
290C22×C8—22no—
291C22×C8—1221no—
292C4⋊Q8—612no—
293C4⋊Q8—611no—
294C4⋊Q8—1221no—
295C4⋊Q8—1221no—
296C4⋊Q8—1221no—
297C4⋊Q8D24411yescharacteristic
298#127—611no—
299#127D24411yescharacteristic
300#124—21no—
301#124—1221no—
302#121—21no—
303#121—1221no—
304#121—1221no—
305#121D24412yes—
306C4×D4—21no—
307C4×D4—1221no—
308C4×D4—1221no—
309C4×D4C22×D6112yes—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4—1221no—
312C2×C42C22×D6111yescharacteristic
313#107—1222no—
314C4⋊C8—21no—
315C4⋊C8—611no—
316C4⋊C8—611no—
317C4⋊C8—612no—
318C4⋊C8—1221no—
319C4⋊C8C22×D6111yescharacteristic
320C4⋊C8C22×D6111yescharacteristic
321#103—1222no—
322#103—1222no—
323#103—1222no—
324#103—1222no—
325#102—1222no—
326#102—1222no—
327#102—1222no—
328#102—1222no—
329C22⋊C8—22no—
330C22⋊C8—22no—
331C22⋊C8—1221no—
332#97C22⋊D6112yes—
333C4×C8—1221no—
334C4×C8C22×D6112yes—
335#41—42no—
336#41—42no—
337#41—2442no—
338#41—2442no—
339C2×Q8—21no—
340C2×Q8—1221no—
341C2×Q8—1222no—
342C2×Q8—4881no—
343C2×Q8—4881no—
344C2×Q8—2441no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—1221no—
349C2×D4—1221no—
350C2×D4—1221no—
351C2×D4—2441no—
352C2×D4C2×D24412yes—
353C22×C4—22no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4C2×D24411yescharacteristic
357C22×C4#1175822211yescharacteristic
358C22×C4C2×C22⋊D6111yescharacteristic
359SD16—4882no—
360SD16—4882no—
361D8—4882no—
362M16—22no—
363M16—22no—
364M16—44no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—44no—
368C2×C8—42no—
369C2×C8—1221no—
370C2×C8—1221no—
371C2×C8—1222no—
372C2×C8—4881no—
373C2×C8C2×C22⋊D6112yes—
374C2×C8C2×C22⋊D6112yes—
375C4⋊C4—21no—
376C4⋊C4—1222no—
377C4⋊C4—1221no—
378C4⋊C4—1222no—
379C4⋊C4—1221no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4C2×D24412yes—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C42C2×D24411yescharacteristic
388C42#1175822211yescharacteristic
389C42C2×C22⋊D6111yescharacteristic
390C42C23×D6111yescharacteristic
391C23—22no—
392C23—2441no—
393C23#1451975111yescharacteristic
394Q8—42no—
395Q8—4882no—
396Q8—2441no—
397Q8—2441no—
398Q8—2442no—
399Q8—2442no—
400D4—22no—
401D4—22no—
402D4—44no—
403D4—42no—
404D4—81no—
405D4—4881no—
406D4—4882no—
407D4—2441no—
408D4—2441no—
409D4—2441no—
410D4—2441no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—4882no—
418C2×C4—4882no—
419C2×C4—2441no—
420C2×C4—2442no—
421C2×C4#1451975111yescharacteristic
422C2×C4#1451975111yescharacteristic
423C2×C4#1451975111yescharacteristic
424C2×C4#1451979712yes—
425C2×C4#1451980312yes—
426C2×C4C22×C22⋊D6111yescharacteristic
427C2×C4C22×D24411yescharacteristic
428C2×C4C2×#1175822211yescharacteristic
429C8—22no—
430C8—22no—
431C8—41no—
432C8—41no—
433C8—2442no—
434C8—2441no—
435C8—2441no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—4881no—
442C22—4881no—
443C22—4881no—
444C22#1683997712yes—
445C22C2×#1451975111yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—4881no—
451C4—4882no—
452C4#1683997712yes—
453C4C2×#1451979711yescharacteristic
454C4C2×#1451980311yescharacteristic
455C4#1684056711yescharacteristic
456C4#1684057411yescharacteristic
457C2—22no—
458C2—82no—
459C2—9761no—
460C2C2×#1683997711yescharacteristic
461C2#2145549911yescharacteristic
462C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2935C2
socleC22×C61C2×#121
prime radical#21457126C2
hypercenter#2935D61
hypocenterC61#19237
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #21456741C2semidirect
3. #21456213C2semidirect
4. #21445380C2semidirect
5. #21445366C2semidirect
6. #21445256C2semidirect
7. #21445242C2semidirect
8. #21444571C2semidirect
9. #21444469C2semidirect
10. C2×#16839507C2semidirect
11. C61×#2935C2semidirect
229. #2935D61semidirect
278. C61#19237semidirect

Maximal subgroups

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

subgroupindex
#214571262
#214567412
#214562132
#214453802
#214453662
#214452562
#214452422
#214445712
#214444692
C2×#168395072
C61×#29352
#1923761