Finite Group Databasebeta

← #29663377

Subgroups — #29663377

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457000C212yesmaximal
2#21456405C211yesmaximal, characteristic, complemented
3#21454794C211yesmaximal, characteristic
4#21445402C212yesmaximal, complemented
5#21445395C212yesmaximal, complemented
6#21445224C211yesmaximal, characteristic, complemented
7#21445219C211yesmaximal, characteristic, complemented
8#21445190C211yesmaximal, characteristic, complemented
9#21445185C211yesmaximal, characteristic, complemented
10#21444527C212yesmaximal, complemented
11C61×#1564C211yesmaximal, characteristic, complemented
12#16840319C2212yes—
13#16840296C2211yescharacteristic
14#16840167C2211yescharacteristic
15#16840164—22no—
16#16840142C2211yescharacteristic
17#16840117—22no—
18#16840113C2212yes—
19#16840104—22no—
20#16840087—22no—
21#16840058C2212yes—
22#16840053C2212yes—
23#16840048C2212yes—
24#16840043C2212yes—
25#16840003—21no—
26#16840003—21no—
27#16839892C2211yescharacteristic
28C8×Dic122C2211yescharacteristic
29C4×Dic244—21no—
30C4×Dic244—21no—
31#16839841C2211yescharacteristic
32#16839833—21no—
33C8×D244C2211yescharacteristic
34C8×C22⋊D61—21no—
35#16839821—21no—
36#16839819C2211yescharacteristic
37#16839716—21no—
38#16839510C2212yes—
39#16839510C2212yes—
40#16839507C2212yes—
41#16839507C2212yes—
42C61×#431C2212yes—
43C2×C4×C8×C61C2211yescharacteristic
44C61×#335C2211yescharacteristic
45C61×#335C2211yescharacteristic
46C61×#334C2212yes—
47C2×Dic244—21no—
48C2×Dic244—21no—
49C2×#11758189—21no—
50C2×C8×D61—21no—
51#14519777C2312yes—
52#14519777C2312yes—
53#14519771—21no—
54#14519769—22no—
55#14519769D411yescharacteristic
56#14519765D411yescharacteristic
57#14519760—21no—
58#14519756—22no—
59#14519756—22no—
60#14519756D411yescharacteristic
61#14519751D411yescharacteristic
62C4×Dic122—22no—
63C4×Dic122—22no—
64C4×Dic122C2311yescharacteristic
65C4×D244C2311yescharacteristic
66C4×C22⋊D61—21no—
67#14519736—22no—
68#14519734—21no—
69#14519711—21no—
70#14519711—21no—
71#14519711—22no—
72#14519711—22no—
73#14519709—22no—
74#14519709—22no—
75C4⋊#92418C2311yescharacteristic
76C4⋊#92418C2311yescharacteristic
77#14519706—21no—
78#14519706—21no—
79#14519702—22no—
80#14519702—22no—
81#14519702—22no—
82#14519702—22no—
83#14519699—22no—
84#14519699—22no—
85C22⋊#92418—21no—
86#14519689—21no—
87#14519689—21no—
88#14519688—21no—
89#14519687—21no—
90C8×Dic61—21no—
91C22×C8×C61D411yescharacteristic
92C22×C8×C61D411yescharacteristic
93C2×C42×C61C2311yescharacteristic
94C4⋊C8×C61C2312yes—
95C4⋊C8×C61C2312yes—
96C22⋊C8×C61—22no—
97C4×C8×C61—22no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61#4111yescharacteristic
105C2×C22⋊D61—21no—
106C2×D244C2×D411yescharacteristic
107C2×C4×D61—21no—
108C2×Dic122—22no—
109C2×Dic122—22no—
110C2×Dic122C2×D411yescharacteristic
111C2×C8×C61—22no—
112C2×C8×C61—22no—
113C2×C8×C61—22no—
114C2×C8×C61—41no—
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122C42×C61C2411yescharacteristic
123C22⋊Dic61—21no—
124C22⋊Dic61—42no—
125#11758198—21no—
126#11758198—21no—
127#11758198—21no—
128#11758198—21no—
129C4⋊Dic61—22no—
130C4⋊Dic61—22no—
131C4⋊Dic61—22no—
132C4⋊Dic61—22no—
133C4⋊Dic61C2×D411yescharacteristic
134C4⋊Dic61C2×D411yescharacteristic
135#11758196—21no—
136#11758196—21no—
137#11758196—21no—
138#11758196—21no—
139#11758196—42no—
140#11758196—42no—
141C4×Dic61—21no—
142C4×Dic61—42no—
143C2×#92418—21no—
144C2×#92418—21no—
145Dic244—42no—
146Dic244—42no—
147#11758189—42no—
148C8×D61—42no—
149C23×C61#12111yescharacteristic
150C22×D61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—41no—
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61C22×D411yescharacteristic
160C2×C4×C61C22×D411yescharacteristic
161C2×C4×C61C2×#4111yescharacteristic
162C22⋊D61—42no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—42no—
167C2×Dic61—42no—
168D244—21no—
169D244—21no—
170C4×D61—41no—
171C4×D61—41no—
172Dic122—21no—
173Dic122—21no—
174Dic122—42no—
175Dic122—42no—
176Dic122—82no—
177C8×C61—21no—
178C8×C61—21no—
179C8×C61—21no—
180C8×C61—42no—
181C8×C61—42no—
182C8×C61#13512yes—
183#92418—41no—
184#92418—41no—
185#19220—611nomaximal, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61C2×#12111yescharacteristic
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61C2×#13511yescharacteristic
198C4×C61#57511yescharacteristic
199C4×C61#57811yescharacteristic
200C4×C61#57811yescharacteristic
201Dic61—41no—
202Dic61—41no—
203Dic61—41no—
204Dic61—82no—
205Dic61—82no—
206#3233—612no—
207#3170—611no—
208#2966—611no—
209#1704—612no—
210#1703—612no—
211#1676—611no—
212#1675—611no—
213#1670—611no—
214#1669—611no—
215#1564D6111yescharacteristic, complemented
216#1554—612no—
217C2×C61—41no—
218C2×C61#303511yescharacteristic
219C2×C61#305911yescharacteristic
220C2×C61#306711yescharacteristic
221D61—81no—
222#533—612no—
223#529—611no—
224#500—611no—
225#499—1222no—
226#494—611no—
227#488—1222no—
228#487—612no—
229#485—1222no—
230#482—1222no—
231#477—612no—
232#476—612no—
233#475—612no—
234#474—612no—
235#467—1221no—
236#467—1221no—
237#446—611no—
238C8×Q8—611no—
239C4×Q16—1221no—
240C4×Q16—1221no—
241#436—611no—
242#435—1221no—
243C8×D4—611no—
244C8×D4—1221no—
245#433—1221no—
246#432—611no—
247#431C2×D6112yes—
248#405—1221no—
249C2×C4×C8C2×D6111yescharacteristic
250#335C2×D6111yescharacteristic
251#335C2×D6111yescharacteristic
252#334C2×D6112yes—
253#333—612no—
254#333—612no—
255#332—612no—
256#332—612no—
257C61#1922011yescharacteristic, complemented, Sylow
258C2×Q16—1221no—
259C2×Q16—1221no—
260C2×M16—1221no—
261C22×C8—1221no—
262C22×C8D24411yescharacteristic
263C22×C8D24411yescharacteristic
264C4⋊Q8—612no—
265C4⋊Q8—612no—
266#126—1221no—
267#125—611no—
268#125—1222no—
269#124—611no—
270#123—1221no—
271C22⋊Q8—611no—
272C22⋊Q8—1222no—
273C22⋊Q8—1222no—
274#121—611no—
275C4×Q8—611no—
276C4×Q8—1222no—
277C4×Q8—1222no—
278C4×D4—611no—
279C4×D4—1221no—
280#117—1221no—
281#117—1222no—
282C2×C42C22×D6111yescharacteristic
283#107—1222no—
284#107—1222no—
285#107—1221no—
286#107—1221no—
287#106—1222no—
288#106—1222no—
289C4⋊C8—611no—
290C4⋊C8—611no—
291C4⋊C8—1221no—
292C4⋊C8—1221no—
293C4⋊C8C22×D6112yes—
294C4⋊C8C22×D6112yes—
295#103—1222no—
296#103—1222no—
297#103—1222no—
298#103—1222no—
299#102—1222no—
300#102—1222no—
301C22⋊C8—22no—
302C22⋊C8—1221no—
303C22⋊C8—1221no—
304C22⋊C8—1221no—
305#97—1221no—
306#97—1221no—
307C4×C8—22no—
308C4×C8—1221no—
309C4×C8D24411yescharacteristic
310C4×C8D24411yescharacteristic
311C4×C8C22×D6111yescharacteristic
312C4×C8C22×D6111yescharacteristic
313C2×Q8—611no—
314C2×Q8—1222no—
315C2×Q8—1222no—
316C2×D4—611no—
317C2×D4—1221no—
318C22×C4—1221no—
319C22×C4C2×D24411yescharacteristic
320C22×C4D4×D6111yescharacteristic
321C22×C4#1175822611yescharacteristic
322Q16—2442no—
323Q16—2442no—
324M16—2442no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—1221no—
330C2×C8—1221no—
331C2×C8—2442no—
332C2×C8C2×D24411yescharacteristic
333C2×C8C2×D24411yescharacteristic
334C2×C8C2×D24411yescharacteristic
335C2×C8C2×D24411yescharacteristic
336C4⋊C4—611no—
337C4⋊C4—611no—
338C4⋊C4—1221no—
339C4⋊C4—1221no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—1222no—
343C4⋊C4—1222no—
344C4⋊C4—1222no—
345C4⋊C4—1222no—
346C4⋊C4—2442no—
347C4⋊C4—2442no—
348C22⋊C4—1221no—
349C22⋊C4—1221no—
350C22⋊C4—1221no—
351C22⋊C4—1221no—
352C22⋊C4—1221no—
353C22⋊C4—2442no—
354C42—1221no—
355C42—2442no—
356C42C2×D24411yescharacteristic
357C42D4×D6111yescharacteristic
358C42#1175822611yescharacteristic
359C42C23×D6111yescharacteristic
360C23—1221no—
361C23#1451975211yescharacteristic
362Q8—1221no—
363Q8—1221no—
364Q8—4882no—
365Q8—2442no—
366Q8—2442no—
367D4—1221no—
368D4—1221no—
369D4—2442no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—2442no—
379C2×C4—2442no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4#1451975211yescharacteristic
383C2×C4#1451975211yescharacteristic
384C2×C4#1451975211yescharacteristic
385C2×C4C2×D4×D6111yescharacteristic
386C2×C4C22×D24411yescharacteristic
387C2×C4C2×#1175822611yescharacteristic
388C8—21no—
389C8—21no—
390C8—21no—
391C8—42no—
392C8—42no—
393C8—2441no—
394C8—2441no—
395C8#1451979912yes—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—2441no—
400C22—2441no—
401C22—2441no—
402C22C2×#1451975211yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—4882no—
408C4—4882no—
409C4—2441no—
410C4—2441no—
411C4—2441no—
412C4C2×#1451979911yescharacteristic
413C4#1684056211yescharacteristic
414C4#1684057611yescharacteristic
415C4#1684057611yescharacteristic
416C2—41no—
417C2—4881no—
418C2#2145527611yescharacteristic
419C2#2145547511yescharacteristic
420C2#2145554011yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1564C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#1564D61
hypocenterC61#19220
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
2. #21456405C2semidirect
4. #21445402C2semidirect
5. #21445395C2semidirect
6. #21445224C2semidirect
7. #21445219C2semidirect
8. #21445190C2semidirect
9. #21445185C2semidirect
10. #21444527C2semidirect
11. C61×#1564C2semidirect
215. #1564D61semidirect
257. C61#19220semidirect

Maximal subgroups

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

subgroupindex
#214570002
#214564052
#214547942
#214454022
#214453952
#214452242
#214452192
#214451902
#214451852
#214445272
C61×#15642
#1922061