Finite Group Databasebeta

← #29835156

Subgroups — #29835156

Order 15616.

534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456479C211yesmaximal, characteristic, complemented
2#21454689C211yesmaximal, characteristic
3#21448023C211yesmaximal, characteristic, complemented
4#21448018C211yesmaximal, characteristic, complemented
5#21447980C211yesmaximal, characteristic, complemented
6#21447870C211yesmaximal, characteristic, complemented
7#21447864C211yesmaximal, characteristic, complemented
8#21447760C211yesmaximal, characteristic
9#21447760C211yesmaximal, characteristic
10#21447689C211yesmaximal, characteristic, complemented
11#21447680C211yesmaximal, characteristic, complemented
12#21447677C211yesmaximal, characteristic, complemented
13#21447674C211yesmaximal, characteristic, complemented
14#21447625C211yesmaximal, characteristic, complemented
15C61×#2228C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17#16840375—21no—
18#16840241—21no—
19C2×Dic488C2211yescharacteristic
20C2×Dic488C2211yescharacteristic
21C2×#14519721C2211yescharacteristic
22C2×#14519721C2211yescharacteristic
23#16840142C2211yescharacteristic
24#16840132—21no—
25#16840021—21no—
26#16840004C2211yescharacteristic
27#16840004C2211yescharacteristic
28#16839868—21no—
29#16839862—21no—
30#16839859—21no—
31C4×Dic244C2211yescharacteristic
32#16839856C2211yescharacteristic
33#16839856C2211yescharacteristic
34#16839856C2211yescharacteristic
35D8×Dic61C2211yescharacteristic
36#107×D61C2211yescharacteristic
37#16839760—21no—
38#16839716C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839587C2211yescharacteristic
41C4⋊#11758185C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839565C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839541C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×D8×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758224—21no—
60#14519796—22no—
61#14519796—22no—
62C2×Dic244—21no—
63C2×Dic244C2311yescharacteristic
64C2×Dic244C2311yescharacteristic
65C2×Dic244C2311yescharacteristic
66C2×#11758200—21no—
67C2×#11758189D411yescharacteristic
68C2×C8×D61C2311yescharacteristic
69#14519777—21no—
70#14519772—41no—
71#14519772—41no—
72#14519768—41no—
73#14519768—41no—
74#14519757—21no—
75#14519757—21no—
76C4×Dic122—21no—
77#14519742—21no—
78#14519742—21no—
79#14519742—21no—
80D4×Dic61—21no—
81C4×C22⋊D61—41no—
82#14519737—41no—
83#14519734D411yescharacteristic
84#14519733—41no—
85C2×#11758196—41no—
86C4⋊C4×D61—21no—
87Dic488—22no—
88Dic488—22no—
89#14519721—22no—
90#14519721—22no—
91C2×#11758185C2311yescharacteristic
92C2×#11758185C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519710—21no—
95#14519702—21no—
96#14519700—21no—
97#14519700—21no—
98#14519700—21no—
99#14519700—21no—
100#14519700—21no—
101#14519698—21no—
102#14519688D411yescharacteristic
103#14519687D411yescharacteristic
104C8×Dic61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106#125×C61—21no—
107C4×D4×C61—21no—
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#106×C61—21no—
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×D4×C61—21no—
117C22×C4×C61—41no—
118C2×C22⋊D61—41no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121#11758224—24no—
122#11758224—42no—
123C2×C4×D61—41no—
124C2×C4×D61C2×D411yescharacteristic
125C2×Dic122—21no—
126C2×Dic122—21no—
127C2×Dic122—21no—
128D8×C61—21no—
129D8×C61#4112yes—
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2411yescharacteristic
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C42×C61C2×D411yescharacteristic
139C22⋊Dic61—41no—
140#11758200—24no—
141#11758198—41no—
142#11758198—41no—
143#11758198D811yescharacteristic
144#11758198D811yescharacteristic
145C4⋊Dic61—21no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
148C4⋊Dic61—41no—
149C4⋊Dic61—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196D811yescharacteristic
156#11758196D811yescharacteristic
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61C2×D411yescharacteristic
162C2×#92418C2×D411yescharacteristic
163C2×#92418C2×D411yescharacteristic
164Dic244—21no—
165Dic244—21no—
166Dic244—21no—
167Dic244—21no—
168Dic244—21no—
169Dic244—42no—
170Dic244#4112yes—
171#11758189—41no—
172C8×D61—21no—
173C8×D61—21no—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61—41no—
179C22×D61C2×D811yescharacteristic
180D4×C61—22no—
181D4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—161no—
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C22⋊D61—44no—
190C2×Dic61—44no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—161no—
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199C4×D61—21no—
200C4×D61—21no—
201C4×D61—161no—
202Dic122—22no—
203Dic122—41no—
204Dic122—41no—
205Dic122—41no—
206Dic122—41no—
207Dic122—41no—
208C8×C61—21no—
209C8×C61C2×#4111yescharacteristic
210C8×C61C2×#4111yescharacteristic
211#92418—21no—
212#92418—21no—
213#33680—611nomaximal, Sylow
214C22×C61—42no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61C22×D811yescharacteristic
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—21no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61#52511yescharacteristic
227C4×C61#57511yescharacteristic
228Dic61—21no—
229Dic61—21no—
230Dic61—21no—
231Dic61—42no—
232Dic61—81no—
233Dic61—81no—
234Dic61—81no—
235#3177—611no—
236#2951—611no—
237#2236—611no—
238#2235—611no—
239#2229—611no—
240#2228D6111yescharacteristic, complemented
241#2209—611no—
242#2208—611no—
243#2189—611no—
244#2189—611no—
245#2176—611no—
246#2175—611no—
247C4×Q32—611no—
248C4×SD32—611no—
249#2164—611no—
250C2×C61—82no—
251C2×C61#310011yescharacteristic
252C2×C61#341611yescharacteristic
253C2×C61#341711yescharacteristic
254D61—41no—
255C2×#135—611no—
256#541—1221no—
257#520—1221no—
258C2×Q32—611no—
259C2×Q32—611no—
260C2×SD32—611no—
261C2×SD32—611no—
262#499C2×D6111yescharacteristic
263#494—611no—
264#491—1221no—
265#470—1221no—
266#467—611no—
267#467—611no—
268#441—1221no—
269#440—1221no—
270#440—1221no—
271C4×Q16—611no—
272C4×Q16—611no—
273C4×Q16—611no—
274C4×Q16—611no—
275C4×D8—611no—
276C4×D8C2×D6111yescharacteristic
277C2×#107—611no—
278#417—1221no—
279#405—611no—
280#367—611no—
281#367C2×D6111yescharacteristic
282#366—611no—
283#366C2×D6111yescharacteristic
284C4⋊C16—611no—
285C4⋊C16C2×D6111yescharacteristic
286#358—611no—
287#358—611no—
288#358—611no—
289#358—611no—
290#358—611no—
291#358—611no—
292#357C2×D6111yescharacteristic
293#357C2×D6111yescharacteristic
294C22⋊C16—611no—
295C22⋊C16—611no—
296#346—611no—
297C4×C16—611no—
298C61#3368011yescharacteristic, complemented, Sylow
299C2×#41—1221no—
300#135—1222no—
301#135—1222no—
302C2×Q16—611no—
303C2×Q16—611no—
304C2×Q16—611no—
305C2×Q16—1221no—
306C2×SD16—1221no—
307C2×D8C22×D6111yescharacteristic
308C2×M16—611no—
309C22×C8—611no—
310C4⋊Q8—1221no—
311#126—2441no—
312#126—2441no—
313#125—21no—
314#125—2441no—
315#125—2441no—
316C22⋊Q8—1221no—
317C22⋊Q8—1221no—
318C4×Q8—1221no—
319C4×Q8—1221no—
320C4×Q8—1221no—
321C4×Q8—1221no—
322C4×D4—21no—
323C4×D4—1221no—
324C4×D4—2441no—
325C4×D4—2441no—
326#117—611no—
327#117—2441no—
328C2×C4⋊C4—1221no—
329C2×C4⋊C4—2441no—
330Q32—1222no—
331Q32—1222no—
332SD32—1222no—
333SD32—1222no—
334C2×C16—611no—
335C2×C16—611no—
336C2×C16C22×D6111yescharacteristic
337C2×C16C22×D6111yescharacteristic
338#107—611no—
339#107—1221no—
340#107C22×D6111yescharacteristic
341#107C22×D6111yescharacteristic
342#107C22×D6111yescharacteristic
343#106—21no—
344#103—1221no—
345#103—1221no—
346#103—1221no—
347#103—1221no—
348#103—1221no—
349#103—1221no—
350#102—21no—
351#102—1221no—
352#97—611no—
353#97—611no—
354C4×C8—611no—
355C4×C8C22×D6111yescharacteristic
356#41—1224no—
357#41—2442no—
358C2×Q8—1221no—
359C2×Q8—1221no—
360C2×Q8—1221no—
361C2×D4—21no—
362C2×D4—2441no—
363C22×C4—41no—
364C22×C4—611no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4—2441no—
368Q16—612no—
369Q16—1221no—
370Q16—1221no—
371Q16—1221no—
372Q16—1221no—
373Q16—1221no—
374Q16—2442no—
375SD16—1224no—
376D8—21no—
377D8#1175822612yes—
378M16—2441no—
379C2×C8—611no—
380C2×C8—611no—
381C2×C8—1221no—
382C2×C8—1221no—
383C2×C8D4×D6111yescharacteristic
384C2×C8C23×D6111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—611no—
391C4⋊C4—611no—
392C4⋊C4—1221no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C4⋊C4—2441no—
399C4⋊C4—2441no—
400C4⋊C4—2441no—
401C4⋊C4—2441no—
402C22⋊C4—41no—
403C22⋊C4—611no—
404C22⋊C4—611no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C42—611no—
409C42—2441no—
410C42—2441no—
411C42—2441no—
412C42—2441no—
413C42D4×D6111yescharacteristic
414C16—21no—
415C16—21no—
416C16—1221no—
417C16—1221no—
418C23—41no—
419C23—611no—
420Q8—1222no—
421Q8—2441no—
422Q8—2441no—
423Q8—2441no—
424Q8—2441no—
425Q8—2441no—
426D4—22no—
427D4—41no—
428D4—2444no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—161no—
433C2×C4—611no—
434C2×C4—611no—
435C2×C4—611no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—9761no—
439C2×C4—9761no—
440C2×C4—2444no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4D8×D6111yescharacteristic
446C2×C4D8×D6111yescharacteristic
447C2×C4C2×D4×D6111yescharacteristic
448C8—21no—
449C8—1221no—
450C8—1221no—
451C8#41×D6111yescharacteristic
452C8C2×#1175822611yescharacteristic
453C22—42no—
454C22—81no—
455C22—81no—
456C22—1221no—
457C22—1221no—
458C22—1221no—
459C22C2×D8×D6111yescharacteristic
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—1221no—
466C4—1221no—
467C4—1221no—
468C4—4881no—
469C4—4881no—
470C4—4881no—
471C4—2442no—
472C4#1684027511yescharacteristic
473C4#1684056111yescharacteristic
474C2—82no—
475C2—2441no—
476C2#2145582111yescharacteristic
477C2#2145896511yescharacteristic
478C2#2145896911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2228C2
socleC22×C61C22×D8
prime radicalC2×#14519796C22
hypercenter#2228D61
hypocenterC61#33680
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #21456479C2semidirect
3. #21448023C2semidirect
4. #21448018C2semidirect
5. #21447980C2semidirect
6. #21447870C2semidirect
7. #21447864C2semidirect
10. #21447689C2semidirect
11. #21447680C2semidirect
12. #21447677C2semidirect
13. #21447674C2semidirect
14. #21447625C2semidirect
15. C61×#2228C2semidirect
240. #2228D61semidirect
298. C61#33680semidirect

Maximal subgroups

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

subgroupindex
#214564792
#214546892
#214480232
#214480182
#214479802
#214478702
#214478642
#214477602
#214476892
#214476802
#214476772
#214476742
#214476252
C61×#22282
#3368061