Finite Group Databasebeta

← #29835233

Subgroups — #29835233

Order 15616.

520 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456471C211yesmaximal, characteristic
2#21454686C211yesmaximal, characteristic
3#21448027C211yesmaximal, characteristic
4#21447986C211yesmaximal, characteristic, complemented
5#21447982C211yesmaximal, characteristic, complemented
6#21447868C211yesmaximal, characteristic, complemented
7#21447868C211yesmaximal, characteristic, complemented
8#21447755C211yesmaximal, characteristic
9#21447752C211yesmaximal, characteristic
10#21447689C211yesmaximal, characteristic, complemented
11#21447687C211yesmaximal, characteristic, complemented
12#21447677C211yesmaximal, characteristic, complemented
13#21447675C211yesmaximal, characteristic, complemented
14#21447623C211yesmaximal, characteristic
15C61×#2237C211yesmaximal, characteristic
16C22×Dic244C2211yescharacteristic
17#16840372—21no—
18#16840239—21no—
19C2×Dic488C2211yescharacteristic
20C2×Dic488C2211yescharacteristic
21C2×#14519723C2211yescharacteristic
22C2×#14519723C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840140C2211yescharacteristic
25#16840129—21no—
26#16840018—21no—
27#16840003C2211yescharacteristic
28#16839868—21no—
29#16839868—21no—
30#16839866—21no—
31Q16×Dic61C2211yescharacteristic
32#16839856C2211yescharacteristic
33#16839856C2211yescharacteristic
34#16839856C2211yescharacteristic
35#16839856C2211yescharacteristic
36#16839856C2211yescharacteristic
37#16839770—21no—
38#16839717C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839565C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C22×Dic122—21no—
60C2×Dic244—21no—
61C2×Dic244—22no—
62C2×Dic244—22no—
63C2×Dic244C2311yescharacteristic
64C2×Dic244C2311yescharacteristic
65C2×Dic244C2311yescharacteristic
66C2×#11758202—21no—
67C2×#11758194D411yescharacteristic
68#14519775—21no—
69#14519770—41no—
70#14519770—41no—
71#14519768—21no—
72#14519768—41no—
73#14519767—41no—
74#14519756—21no—
75Q8×Dic61—21no—
76C4×Dic122—41no—
77C4×Dic122—41no—
78#14519742—21no—
79#14519742—21no—
80#14519742—21no—
81#14519742—21no—
82#14519742—21no—
83#14519736D411yescharacteristic
84#14519733—41no—
85#14519733—41no—
86Dic488—22no—
87Dic488—22no—
88#14519723—22no—
89#14519723—22no—
90C2×#11758185C2311yescharacteristic
91C2×#11758185C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519708—21no—
94#14519702—21no—
95#14519701—21no—
96#14519700—21no—
97#14519700—21no—
98#14519700—21no—
99#14519700—21no—
100#14519700—21no—
101#14519687D411yescharacteristic
102#14519687D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C8×Dic61C2311yescharacteristic
105C2×Q16×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22⋊Q8×C61—21no—
108#117×C61—21no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#106×C61—21no—
115#103×C61—21no—
116C2×Q8×C61—21no—
117C22×C4×C61C2×D411yescharacteristic
118C22×Dic61—41no—
119C2×Dic122—24no—
120C2×Dic122—21no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122—42no—
124C2×Dic122—41no—
125Q16×C61—21no—
126Q16×C61—21no—
127C2×C8×C61—21no—
128C2×C8×C61—21no—
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2411yescharacteristic
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C42×C61—41no—
138C22⋊Dic61—41no—
139C22⋊Dic61D811yescharacteristic
140C22⋊Dic61D811yescharacteristic
141#11758202—42no—
142C4⋊Dic61—21no—
143C4⋊Dic61—41no—
144C4⋊Dic61—41no—
145C4⋊Dic61D811yescharacteristic
146C4⋊Dic61D811yescharacteristic
147#11758196—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156C4×Dic61—41no—
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61—41no—
162C4×Dic61C2×D411yescharacteristic
163C4×Dic61C2×D411yescharacteristic
164#11758194—41no—
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167Dic244—24no—
168Dic244—21no—
169Dic244—21no—
170Dic244—21no—
171Dic244—21no—
172Dic244#4112yes—
173Dic244#4112yes—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61C2×D811yescharacteristic
179Q8×C61—41no—
180Q8×C61—41no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C2×Dic61—44no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61C2×D811yescharacteristic
195C2×Dic61C2×D811yescharacteristic
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198Dic122—22no—
199Dic122—22no—
200Dic122—44no—
201Dic122—41no—
202Dic122—41no—
203Dic122—41no—
204Dic122—41no—
205C8×C61—21no—
206C8×C61C2×#4111yescharacteristic
207C8×C61C2×#4111yescharacteristic
208#92418—21no—
209#92418—21no—
210#33687—611nomaximal, Sylow
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61C22×D811yescharacteristic
215C4×C61—21no—
216C4×C61—81no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61—81no—
220C4×C61#52511yescharacteristic
221C4×C61#57511yescharacteristic
222Dic61—21no—
223Dic61—21no—
224Dic61—21no—
225Dic61—21no—
226Dic61—42no—
227Dic61—42no—
228Dic61—81no—
229Dic61—81no—
230#3177—611no—
231#2950—611no—
232#2237—611no—
233#2237D6111yescharacteristic
234#2229—611no—
235#2229—611no—
236#2209—611no—
237#2209—611no—
238#2188—611no—
239#2188—611no—
240#2176—611no—
241#2176—611no—
242C4×Q32—611no—
243C4×Q32—611no—
244#2164—611no—
245C2×C61—41no—
246C2×C61#310011yescharacteristic
247C2×C61#341711yescharacteristic
248C2×C61#341711yescharacteristic
249C22×Q16—611no—
250#541—1221no—
251#519—1221no—
252C2×Q32—611no—
253C2×Q32—611no—
254C2×Q32—611no—
255C2×Q32—611no—
256#499—611no—
257#494—611no—
258#491—1221no—
259#470—1221no—
260#467—611no—
261#467C2×D6111yescharacteristic
262#441—1221no—
263#441—1221no—
264#441—1221no—
265C4×Q16—611no—
266C4×Q16—611no—
267C4×Q16—611no—
268C4×Q16—611no—
269C4×Q16—611no—
270C4×Q16—611no—
271#427C2×D6111yescharacteristic
272#419—1221no—
273#405—611no—
274#367—611no—
275#367C2×D6111yescharacteristic
276#366—611no—
277#366C2×D6111yescharacteristic
278C4⋊C16—611no—
279C4⋊C16—611no—
280#358—611no—
281#358—611no—
282#358—611no—
283#358—611no—
284#358—611no—
285#358—611no—
286#358C2×D6111yescharacteristic
287#358C2×D6111yescharacteristic
288C22⋊C16—611no—
289C22⋊C16C2×D6111yescharacteristic
290#346—611no—
291C4×C16—611no—
292C61#3368711yescharacteristic, complemented, Sylow
293C22×Q8—1221no—
294C2×Q16—611no—
295C2×Q16—611no—
296C2×Q16—611no—
297C2×Q16—1222no—
298C2×Q16—1222no—
299C2×Q16—1221no—
300C2×Q16—1221no—
301C2×Q16C22×D6111yescharacteristic
302C2×M16—611no—
303C22×C8C22×D6111yescharacteristic
304C4⋊Q8—1221no—
305#126—2441no—
306#126—2441no—
307#125—1221no—
308#125—2441no—
309#125—2441no—
310C22⋊Q8—21no—
311C22⋊Q8—1221no—
312C4×Q8—1221no—
313C4×Q8—1221no—
314C4×Q8—1221no—
315C4×Q8—1221no—
316C4×Q8—1221no—
317C4×Q8—1221no—
318C4×Q8—2441no—
319C4×Q8—2441no—
320#117—21no—
321#117—611no—
322#117—2441no—
323#117—2441no—
324Q32—1222no—
325Q32—1222no—
326Q32—1222no—
327Q32—1222no—
328C2×C16—611no—
329C2×C16—611no—
330C2×C16C22×D6111yescharacteristic
331C2×C16C22×D6111yescharacteristic
332#107—611no—
333#107C22×D6111yescharacteristic
334#107C22×D6111yescharacteristic
335#107C22×D6111yescharacteristic
336#106—21no—
337#106—1221no—
338#103—21no—
339#103—1221no—
340#103—1221no—
341#103—1221no—
342#103—1221no—
343#103—1221no—
344#103—1221no—
345#103—1221no—
346#97—611no—
347#97—611no—
348C4×C8—611no—
349C4×C8—611no—
350C2×Q8—21no—
351C2×Q8—1224no—
352C2×Q8—1221no—
353C2×Q8—1221no—
354C2×Q8—1221no—
355C2×Q8—2442no—
356C2×Q8—2441no—
357C22×C4—2441no—
358C22×C4D4×D6111yescharacteristic
359Q16—21no—
360Q16—21no—
361Q16—612no—
362Q16—612no—
363Q16—1224no—
364Q16—1221no—
365Q16—1221no—
366Q16—1221no—
367Q16—1221no—
368Q16—2442no—
369M16—2441no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—611no—
373C2×C8—611no—
374C2×C8D4×D6111yescharacteristic
375C2×C8C23×D6111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—611no—
381C4⋊C4—611no—
382C4⋊C4—1221no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4—2441no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—611no—
397C22⋊C4—611no—
398C22⋊C4—2441no—
399C42—41no—
400C42—611no—
401C42—611no—
402C42—2441no—
403C42—2441no—
404C42—2441no—
405C42—2441no—
406C42—2441no—
407C42—2441no—
408C16—21no—
409C16—21no—
410C16—1221no—
411C16—1221no—
412C23D8×D6111yescharacteristic
413Q8—41no—
414Q8—41no—
415Q8—1222no—
416Q8—1222no—
417Q8—2444no—
418Q8—2441no—
419Q8—2441no—
420Q8—2441no—
421Q8—2441no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—611no—
429C2×C4—611no—
430C2×C4—611no—
431C2×C4—611no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2444no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4D8×D6111yescharacteristic
438C2×C4C2×D4×D6111yescharacteristic
439C8—21no—
440C8—1221no—
441C8—1221no—
442C8#41×D6111yescharacteristic
443C8#41×D6111yescharacteristic
444C22—21no—
445C22—21no—
446C22—21no—
447C22C2×D8×D6111yescharacteristic
448C4—21no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—1221no—
454C4—1221no—
455C4—1221no—
456C4—1221no—
457C4—4881no—
458C4—4881no—
459C4—2442no—
460C4—2442no—
461C4#1684027011yescharacteristic
462C4#1684056111yescharacteristic
463C2—41no—
464C2#2145581611yescharacteristic
465C2#2145896911yescharacteristic
466C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2237C2
socleC22×C61C22×D8
prime radicalC23×C61C2×D8
hypercenter#2237D61
hypocenterC61#33687
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
4. #21447986C2semidirect
5. #21447982C2semidirect
6. #21447868C2semidirect
7. #21447868C2semidirect
10. #21447689C2semidirect
11. #21447687C2semidirect
12. #21447677C2semidirect
13. #21447675C2semidirect
292. C61#33687semidirect

Maximal subgroups

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

subgroupindex
#214564712
#214546862
#214480272
#214479862
#214479822
#214478682
#214477552
#214477522
#214476892
#214476872
#214476772
#214476752
#214476232
C61×#22372
#3368761