Finite Group Databasebeta

← #29647747

Subgroups — #29647747

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459684C211yesmaximal, characteristic
2#21448784C211yesmaximal, characteristic, complemented
3#21444397C214yesmaximal, complemented
4#21444384C211yesmaximal, characteristic, complemented
5#21444380C211yesmaximal, characteristic
6#21444319C211yesmaximal, characteristic, complemented
7#21444315C211yesmaximal, characteristic
8#21444306C214yesmaximal, complemented
9C61×#2982C211yesmaximal, characteristic, complemented
10#16840497C412yescomplemented
11#16840490C412yescomplemented
12#16840485C412yescomplemented
13#16840484—22no—
14#16840472C412yescomplemented
15#16840453—22no—
16#16840359—22no—
17#16840336—21no—
18#16840319C2211yescharacteristic
19#16840312C2211yescharacteristic
20#16840296C2214yes—
21#16840243—21no—
22#16839669—21no—
23#16839648—22no—
24#16839630C2212yes—
25#16839628C2211yescharacteristic
26C4⋊C4×Dic61—21no—
27C4×C4⋊Dic61C2211yescharacteristic
28#16839608C2212yes—
29#16839500C2214yes—
30#16839500C2212yes—
31#16839500C2212yes—
32#16839497C2214yes—
33#16839497C2212yes—
34#16839497C2212yes—
35C2×C4×Q8×C61C2211yescharacteristic
36C8×Q8×C61—22no—
37C8×Q8×C61—22no—
38C61×#431C2211yescharacteristic
39C61×#431C2211yescharacteristic
40C61×#431C2214yes—
41C2×#11758222—21no—
42#14519777C2×C411yescharacteristic
43#14519777C2×C411yescharacteristic
44#14519777C2×C411yescharacteristic
45#14519775—22no—
46#14519774C2×C411yescharacteristic
47#14519772—24no—
48#14519771—24no—
49#14519769—21no—
50#14519769C2×C414yes—
51#14519767—24no—
52#14519766—22no—
53#14519765—21no—
54#14519765C2×C414yes—
55#14519762—24no—
56#14519760—24no—
57#14519756—21no—
58#14519756C2312yes—
59#14519755—24no—
60#14519753—22no—
61#14519753—22no—
62#14519751—21no—
63#14519751C2312yes—
64C4×Dic122—21no—
65C4×Dic122C2×C414yes—
66C4×Dic122C2×C412yes—
67#14519742—22no—
68C4×D244—21no—
69C4×D244C2×C412yes—
70C4×D244C2×C414yes—
71#14519739—22no—
72C4×C22⋊D61—24no—
73#14519736—21no—
74#14519735—22no—
75#14519734—24no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C4⋊C4×D61—22no—
79C2×C4×Dic61—22no—
80C2×C4×Dic61—21no—
81#14519684—22no—
82#14519684—22no—
83#14519684—21no—
84#14519684—22no—
85#14519684C2311yescharacteristic
86#14519684C2312yes—
87#14519684C2311yescharacteristic
88C22×Q8×C61D411yescharacteristic
89C4×Q8×C61C2×C412yes—
90C4×Q8×C61C2×C412yes—
91C4×Q8×C61D412yes—
92C4×Q8×C61D412yes—
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C4⋊C4×C61D412yes—
95C2×C42×C61C2312yes—
96C2×C42×C61C2311yescharacteristic
97C4⋊C8×C61—24no—
98C4⋊C8×C61—21no—
99C4⋊C8×C61—21no—
100C22⋊C8×C61C2312yes—
101C22⋊C8×C61C2312yes—
102C4×C8×C61—24no—
103C4×C8×C61—21no—
104C4×C8×C61—21no—
105C2×Q8×C61—22no—
106C2×Q8×C61—22no—
107C2×Q8×C61C22⋊C412yes—
108C2×Q8×C61C22⋊C412yes—
109C22×C4×C61C2×D412yes—
110C22×C4×C61C2×D412yes—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2411yescharacteristic
114C2×C22⋊D61—22no—
115C22×Dic61—21no—
116C22×Dic61—22no—
117C22×Dic61—21no—
118#11758222—42no—
119#11758222—42no—
120C2×D244—21no—
121C2×D244—21no—
122C2×D244C22×C412yes—
123C2×C4×D61—22no—
124C2×C4×D61—24no—
125C2×Dic122—21no—
126C2×Dic122—21no—
127C2×Dic122C22×C412yes—
128C2×C8×C61—22no—
129C2×C8×C61—22no—
130C4⋊C4×C61C22⋊C412yes—
131C4⋊C4×C61C22⋊C412yes—
132C4⋊C4×C61C22⋊C414yes—
133C4⋊C4×C61C22⋊C414yes—
134C42×C61C22×C411yescharacteristic
135C42×C61C22×C414yes—
136C42×C61C22×C411yescharacteristic
137C42×C61C2×D414yes—
138C42×C61C2×D411yescharacteristic
139C42×C61C2×D411yescharacteristic
140C22⋊Dic61—22no—
141#11758198—24no—
142#11758198—24no—
143#11758198—22no—
144#11758198—24no—
145#11758198—22no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—42no—
151C4⋊Dic61—42no—
152C4⋊Dic61C22×C412yes—
153C4⋊Dic61C22×C412yes—
154#11758196—24no—
155#11758196—24no—
156#11758196—24no—
157#11758196—22no—
158#11758196—22no—
159C4×Dic61—24no—
160C4×Dic61—22no—
161C4×Dic61—44no—
162C4×Dic61—42no—
163C23×C61C22×D411yescharacteristic
164C22×D61—22no—
165Q8×C61—24no—
166Q8×C61—24no—
167C2×C4×C61—22no—
168C2×C4×C61—22no—
169C2×C4×C61—42no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61C2×C22⋊C414yes—
173C2×C4×C61C2×C22⋊C411yescharacteristic
174C2×C4×C61C2×C22⋊C414yes—
175C2×C4×C61C2×C22⋊C411yescharacteristic
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×C4×C61C2×C22⋊C411yescharacteristic
178C2×C4×C61#13512yes—
179C2×C4×C61#13512yes—
180C2×C4×C61C23×C411yescharacteristic
181C2×C4×C61C22×D411yescharacteristic
182C22⋊D61—42no—
183C22⋊D61—42no—
184C2×Dic61—22no—
185C2×Dic61—22no—
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—42no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—42no—
194C2×Dic61—41no—
195C2×Dic61—42no—
196D244—42no—
197D244—42no—
198D244—81no—
199C4×D61—44no—
200C4×D61—84no—
201Dic122—42no—
202Dic122—42no—
203Dic122—81no—
204C8×C61—42no—
205C8×C61—42no—
206#17616—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61C22×C22⋊C411yescharacteristic
210C22×C61C2×#13511yescharacteristic
211C22×C61C2×#13511yescharacteristic
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—24no—
218C4×C61—21no—
219C4×C61—24no—
220C4×C61—21no—
221C4×C61#41612yes—
222C4×C61#41612yes—
223Dic61—42no—
224Dic61—42no—
225Dic61—42no—
226Dic61—42no—
227Dic61—81no—
228Dic61—82no—
229#3507—611no—
230#2982D6111yescharacteristic, complemented
231#2356—611no—
232#1521—614no—
233#1518—611no—
234#1517—611no—
235#1503—611no—
236#1502—611no—
237#1500—614no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61#288411yescharacteristic
241C2×C61C2×#41611yescharacteristic
242C2×C61#290111yescharacteristic
243D61—82no—
244#559—612no—
245#557—612no—
246#556—612no—
247#556—1222no—
248#554—612no—
249#552—1222no—
250#539—1222no—
251#536—1221no—
252#533—611no—
253#532—611no—
254#529—614no—
255#520—1221no—
256C2×C4×Q8C2×D6111yescharacteristic
257C8×Q8—22no—
258C8×Q8—22no—
259#431C2×D6114yes—
260#431C2×D6111yescharacteristic
261#431C2×D6111yescharacteristic
262#391—1221no—
263#387—1222no—
264#383—612no—
265#382—611no—
266C4×C4⋊C4—611no—
267C4×C4⋊C4—1221no—
268#376—612no—
269#328—612no—
270#328—614no—
271#328—612no—
272#327—612no—
273#327—614no—
274#327—612no—
275C61#1761611yescharacteristic, complemented, Sylow
276C2×#41—1221no—
277C22×Q8D24411yescharacteristic
278C4⋊Q8—611no—
279C4⋊Q8—611no—
280C4⋊Q8—611no—
281C4⋊Q8—1222no—
282#127—611no—
283#126—1224no—
284#126—1224no—
285#125—614no—
286#125—1224no—
287#125—1221no—
288#124—614no—
289#124—1222no—
290#124—1221no—
291#123—1224no—
292#123—1224no—
293C22⋊Q8—612no—
294C22⋊Q8—1222no—
295C22⋊Q8—1222no—
296C22⋊Q8—1221no—
297C22⋊Q8—1224no—
298#121—612no—
299#121—1221no—
300C4×Q8—614no—
301C4×Q8—612no—
302C4×Q8—1222no—
303C4×Q8—1221no—
304C4×Q8C4×D6112yes—
305C4×Q8C4×D6112yes—
306C4×Q8C22⋊D6112yes—
307C4×Q8C22⋊D6112yes—
308C4×D4—614no—
309C4×D4—612no—
310C4×D4—1224no—
311C4×D4—1222no—
312C4×D4—1221no—
313#117—1221no—
314#117—1222no—
315#117—1224no—
316C2×C4⋊C4—1222no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4D24411yescharacteristic
320C2×C4⋊C4D24412yes—
321C2×C42—1222no—
322C2×C42—1221no—
323C2×C42C22×D6112yes—
324C2×C42C22×D6111yescharacteristic
325C4⋊C8—24no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C22⋊C8C22×D6112yes—
329C22⋊C8C22×D6112yes—
330C4×C8—24no—
331C4×C8—21no—
332C4×C8—21no—
333#95—611no—
334#95—612no—
335#95—611no—
336#95—1222no—
337#95—1222no—
338#95—1221no—
339#95—1222no—
340#41—2442no—
341#41—2442no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—612no—
345C2×Q8—1221no—
346C2×Q8—1221no—
347C2×Q8#1175819812yes—
348C2×Q8#1175819812yes—
349C2×D4—612no—
350C2×D4—1222no—
351C2×D4—1221no—
352C2×D4—1221no—
353C22×C4—1221no—
354C22×C4—1224no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4—1221no—
358C22×C4C2×D24412yes—
359C22×C4C2×D24412yes—
360C22×C4C2×D24411yescharacteristic
361C22×C4C2×D24411yescharacteristic
362C22×C4C23×D6111yescharacteristic
363C2×C8—22no—
364C2×C8—22no—
365C4⋊C4—612no—
366C4⋊C4—612no—
367C4⋊C4—1222no—
368C4⋊C4—1221no—
369C4⋊C4—1224no—
370C4⋊C4—1224no—
371C4⋊C4—1222no—
372C4⋊C4—1224no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C4⋊C4—2442no—
377C4⋊C4—2442no—
378C4⋊C4#1175819812yes—
379C4⋊C4#1175819812yes—
380C4⋊C4#1175819814yes—
381C4⋊C4#1175819814yes—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—1224no—
385C22⋊C4—1224no—
386C22⋊C4—1222no—
387C22⋊C4—1224no—
388C42—1224no—
389C42—1222no—
390C42—2444no—
391C42—2442no—
392C42C2×C4×D6111yescharacteristic
393C42C2×C4×D6114yes—
394C42C2×C4×D6111yescharacteristic
395C42C2×C22⋊D6114yes—
396C42C2×C22⋊D6111yescharacteristic
397C42C2×C22⋊D6111yescharacteristic
398C23—1222no—
399C23C22×D24411yescharacteristic
400Q8—24no—
401Q8—24no—
402Q8—4881no—
403Q8—2442no—
404Q8—2442no—
405D4—4881no—
406D4—2442no—
407D4—2442no—
408D4—2442no—
409D4—2442no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—1222no—
416C2×C4—1222no—
417C2×C4—1222no—
418C2×C4—1222no—
419C2×C4—4884no—
420C2×C4—2442no—
421C2×C4—2441no—
422C2×C4—2442no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2442no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2444no—
429C2×C4C2×#1175819814yes—
430C2×C4C2×#1175819814yes—
431C2×C4C2×#1175819811yescharacteristic
432C2×C4C2×#1175819811yescharacteristic
433C2×C4C2×#1175819811yescharacteristic
434C2×C4C2×#1175819811yescharacteristic
435C2×C4#1451979912yes—
436C2×C4#1451979912yes—
437C2×C4C22×C4×D6111yescharacteristic
438C2×C4C22×C22⋊D6111yescharacteristic
439C8—42no—
440C8—42no—
441C22—21no—
442C22—21no—
443C22—2442no—
444C22—2442no—
445C22—2442no—
446C22C22×#1175819811yescharacteristic
447C22C2×#1451979911yescharacteristic
448C22C2×#1451979911yescharacteristic
449C4—24no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—24no—
455C4—4882no—
456C4—4881no—
457C4—2442no—
458C4—2442no—
459C4—2442no—
460C4—2442no—
461C4#1683975912yes—
462C4#1683975912yes—
463C2—21no—
464C2—21no—
465C2—4882no—
466C2#2145428211yescharacteristic
467C2C2×#1683975911yescharacteristic
468C2#2145436411yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2982C2
socleC22×C61C22×C22⋊C4
prime radical#16840312C22
cosocleC22×C4×C61C24
hypercenter#2982D61
hypocenterC61#17616
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #21448784C2semidirect
3. #21444397C2semidirect
4. #21444384C2semidirect
6. #21444319C2semidirect
8. #21444306C2semidirect
9. C61×#2982C2semidirect
10. #16840497C4semidirect
11. #16840490C4semidirect
12. #16840485C4semidirect
14. #16840472C4semidirect
230. #2982D61semidirect
275. C61#17616semidirect

Maximal subgroups

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

subgroupindex
#214596842
#214487842
#214443972
#214443842
#214443802
#214443192
#214443152
#214443062
C61×#29822
#1761661