Finite Group Databasebeta

← #30622376

Subgroups — #30622376

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462613C211yesmaximal, characteristic, complemented
2#21462519C211yesmaximal, characteristic
3#21462004C211yesmaximal, characteristic, complemented
4#21461933C211yesmaximal, characteristic, complemented
5#21461914C212yesmaximal
6#21461903C212yesmaximal
7#21461886C212yesmaximal, complemented
8#21461627C212yesmaximal, complemented
9#21461606C211yesmaximal, characteristic, complemented
10C4×#14519842C211yesmaximal, characteristic
11#21455602C211yesmaximal, characteristic
12#16840814—22no—
13#16840813—21no—
14Q8×#92420—21no—
15#16840787—22no—
16#16840784—21no—
17#16840781—21no—
18C2×#14519848C2212yes—
19#16840769C2212yes—
20#16840766C2211yescharacteristic
21D61⋊(C4⋊C8)C2211yescharacteristic
22C2×#14519842C2211yescharacteristic
23C2×#14519842C2211yescharacteristic
24#16840737C2212yes—
25#16840727C2212yes—
26#16840727C2212yes—
27C4×#11758213C2211yescharacteristic
28C2×#14519831C2212yes—
29C42×#6923C2211yescharacteristic
30#16840638C2212yes—
31#16840632C2211yescharacteristic
32#16840632C2211yescharacteristic
33#16840632C2212yes—
34#16840632C2212yes—
35(C2×#6923)⋊C8C2212yes—
36#16840317C2211yescharacteristic
37C4×#11758226C2211yescharacteristic
38#16840067C412yescomplemented
39#16840061C412yescomplemented
40#16840057C411yescharacteristic, complemented
41#16840053C411yescharacteristic, complemented
42#16840039C411yescharacteristic, complemented
43#16839797C2212yes—
44C4⋊C8×D61C2211yescharacteristic
45#16839757C2212yes—
46C61×#475C411yescharacteristic, complemented
47C2×#11758213C2311yescharacteristic
48C2×#11758213C2312yes—
49C2×#11758213C2311yescharacteristic
50C2×D61⋊C8C2312yes—
51C2×C4×#6923—21no—
52C2×C4×#6923—21no—
53C2×C4×#6923C2311yescharacteristic
54C2×C4×#6923C2311yescharacteristic
55#14519848—24no—
56#14519844—22no—
57#14519844D412yes—
58C4⋊#92420—22no—
59C4⋊#92420—21no—
60C4⋊#92420—21no—
61C4⋊#92420D411yescharacteristic
62C4⋊#92420D411yescharacteristic
63#14519842—22no—
64#14519842—22no—
65#14519834—22no—
66#14519834—22no—
67#14519832—22no—
68#14519832—22no—
69#14519832—21no—
70#14519831—24no—
71C4×#92420—22no—
72C4×#92420—22no—
73C4×#92420—21no—
74C2×#11758226C2311yescharacteristic
75C2×C8×D61C2312yes—
76#14519777C2×C411yescharacteristic
77#14519768C2×C412yes—
78#14519757—21no—
79#14519753—21no—
80Q8×Dic61—21no—
81Q8×Dic61C2×C411yescharacteristic
82#14519742—21no—
83C4×D244—21no—
84C4×D244C2×C411yescharacteristic
85#14519739—21no—
86#14519739C2×C411yescharacteristic
87#14519735—21no—
88#14519735C2311yescharacteristic
89#14519735C2312yes—
90C42×D61—21no—
91C42×D61C2311yescharacteristic
92#14519710C2×C412yes—
93#14519710C2×C412yes—
94#14519709C2×C412yes—
95C4⋊#92418C2×C411yescharacteristic
96#14519706C2×C412yes—
97#14519701C2×C412yes—
98#14519699C2×C412yes—
99#14519697C2×C412yes—
100C4⋊Q8×C61C2×C411yescharacteristic
101C4×Q8×C61C2×C411yescharacteristic
102#106×C61C2×C412yes—
103C4⋊C8×C61C2×C411yescharacteristic
104#103×C61C2×C412yes—
105C22×#6923—21no—
106C22×#6923—21no—
107C2×Q8×C61—21no—
108C2×Q8×C61C22×C411yescharacteristic
109#11758226—21no—
110#11758226—21no—
111#11758226—21no—
112#11758226—21no—
113C2×D244—21no—
114C2×D244C22×C411yescharacteristic
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×C4×D61#4111yescharacteristic
119C2×C4×D61#4111yescharacteristic
120C2×C4×D61C2411yescharacteristic
121C2×Dic122—21no—
122C2×#92420—21no—
123C2×#92420—22no—
124C2×#92420—21no—
125C2×#92420C2×D412yes—
126C2×#92420C2×D412yes—
127C4×#6923—21no—
128C4×#6923—21no—
129C4×#6923—21no—
130C4×#6923—42no—
131C4×#6923—42no—
132C4×#6923#4112yes—
133#11758213—21no—
134#11758213—21no—
135#11758213—22no—
136#11758213—21no—
137#11758213—22no—
138#11758213#4112yes—
139D61⋊C8—22no—
140D61⋊C8—22no—
141C2×C8×C61C22×C412yes—
142C4⋊C4×C61—21no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61C22×C412yes—
145C4⋊C4×C61C22×C411yescharacteristic
146C42×C61—21no—
147C42×C61C22×C411yescharacteristic
148#11758198—21no—
149#11758198—22no—
150#11758198—21no—
151#11758198—21no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—22no—
155C4⋊Dic61C22×C412yes—
156C4⋊Dic61C22×C411yescharacteristic
157#11758196—22no—
158C4×Dic61—21no—
159C4×Dic61—21no—
160C4×Dic61—22no—
161C4×Dic61C22×C411yescharacteristic
162C4×Dic61C2×D411yescharacteristic
163C4×Dic61C2×D411yescharacteristic
164C2×#92418C22×C412yes—
165C8×D61—22no—
166C8×D61—22no—
167C22×D61—21no—
168C22×D61C2×#4111yescharacteristic
169C2×#6923—22no—
170C2×#6923—22no—
171C2×#6923—41no—
172C2×#6923—41no—
173C2×#6923—41no—
174C2×#6923—41no—
175Q8×C61—21no—
176Q8×C61—21no—
177Q8×C61—42no—
178C2×C4×C61—22no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61C4×D411yescharacteristic
182C2×C4×C61C4×D411yescharacteristic
183C2×C4×C61C23×C411yescharacteristic
184C2×Dic61—21no—
185C2×Dic61—22no—
186C2×Dic61C4×D411yescharacteristic
187C2×Dic61C4×D411yescharacteristic
188C2×Dic61C22×D411yescharacteristic
189D244—21no—
190D244—21no—
191D244—41no—
192D244—41no—
193C4×D61—22no—
194C4×D61—41no—
195C4×D61—42no—
196C4×D61—41no—
197C4×D61—41no—
198C4×D61—81no—
199C4×D61C2×#4111yescharacteristic
200C4×D61C2×#4111yescharacteristic
201C4×D612−1+411yescharacteristic
202C4×D612−1+411yescharacteristic
203Dic122—81no—
204#92420—22no—
205#92420—22no—
206#92420—22no—
207#92420—41no—
208#92420—42no—
209C8×C61—22no—
210#92418—22no—
211#23081—611nomaximal, Sylow
212C22×C61C2×C4×D411yescharacteristic
213C2×D61—21no—
214C2×D61—21no—
215C2×D61—41no—
216C2×D61—41no—
217C2×D61—41no—
218C2×D61#55211yescharacteristic
219C2×D61#55611yescharacteristic
220#6923—42no—
221#6923—42no—
222C4×C61—21no—
223C4×C61—41no—
224C4×C61—42no—
225C4×C61—41no—
226C4×C61#44412yes—
227C4×C61C4×#4111yescharacteristic
228C4×C61#51911yescharacteristic
229Dic61—21no—
230Dic61—21no—
231Dic61—41no—
232Dic61—42no—
233Dic61#54711yescharacteristic
234Dic61#54811yescharacteristic
235#3076—611no—
236#2962—611no—
237#2925—611no—
238#1994—611no—
239#1950—611no—
240#1938—612no—
241#1929—612no—
242#1922—612no—
243#1773—612no—
244#1767—611no—
245C4×#104—611no—
246C2×C61#236211yescharacteristic
247C2×C61C2×#44411yescharacteristic
248C2×C61#295611yescharacteristic
249D61—21no—
250D61—21no—
251D61—81no—
252#533—611no—
253C4×#41—611no—
254#479—612no—
255#478—612no—
256#477—611no—
257#476—611no—
258#475#692311yescharacteristic, complemented
259#474—611no—
260#446—1221no—
261#446—1222no—
262C8×Q8—1221no—
263#433—1222no—
264#432—1221no—
265#431—1221no—
266C2×#108—612no—
267#427—612no—
268#424—612no—
269#423—611no—
270C2×C4⋊C8—611no—
271C2×C4⋊C8—611no—
272C2×#104—611no—
273C2×#104—611no—
274#416—612no—
275#408—612no—
276#405—612no—
277#405—612no—
278C4×M16—611no—
279C2×#97—612no—
280C43—611no—
281#341—612no—
282#339—611no—
283#339—612no—
284#339—612no—
285#339—611no—
286#336—612no—
287C61#2308111yescharacteristic, complemented, Sylow
288C2×#41—611no—
289C2×M16—611no—
290C2×M16—612no—
291C2×M16—611no—
292C22×C8—612no—
293C22×C8—612no—
294C4⋊Q8—611no—
295C4⋊Q8C2×#692311yescharacteristic
296#125—612no—
297C22⋊Q8—1221no—
298C22⋊Q8—1221no—
299C4×Q8—611no—
300C4×Q8—1221no—
301C4×Q8—1221no—
302C4×Q8C2×#692311yescharacteristic
303C4×D4—611no—
304C4×D4—611no—
305C4×D4—1221no—
306C4×D4—1221no—
307#117—611no—
308#117—612no—
309#117—1221no—
310C2×C42—611no—
311C2×C42—611no—
312C2×C42—611no—
313C2×C42—1221no—
314C2×C42—1221no—
315C2×C42—1221no—
316#108—1224no—
317#107—612no—
318#107—612no—
319#106—612no—
320#106C2×#692312yes—
321C4⋊C8—611no—
322C4⋊C8—611no—
323C4⋊C8—612no—
324C4⋊C8—612no—
325C4⋊C8—611no—
326C4⋊C8—1221no—
327C4⋊C8—1221no—
328C4⋊C8—1222no—
329C4⋊C8—1222no—
330C4⋊C8C2×#692311yescharacteristic
331#104—1222no—
332#104—1222no—
333#103—612no—
334#103C2×#692312yes—
335#102—612no—
336#102—612no—
337C22⋊C8—1222no—
338C22⋊C8—1222no—
339#97—1224no—
340#97—1221no—
341#97—1222no—
342#97—1222no—
343C4×C8—1221no—
344C4×C8—1222no—
345C4×C8—1222no—
346#41—1221no—
347#41—1221no—
348#41—1221no—
349#41—1221no—
350C2×Q8—21no—
351C2×Q8—1221no—
352C2×Q8C22×#692311yescharacteristic
353C2×D4—611no—
354C2×D4—1221no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—1221no—
359C22×C4—1221no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—1221no—
363M16—612no—
364M16—1221no—
365M16—1221no—
366M16—1222no—
367M16—1221no—
368M16—1222no—
369C2×C8—612no—
370C2×C8—612no—
371C2×C8—612no—
372C2×C8—1222no—
373C2×C8—1222no—
374C2×C8—1221no—
375C2×C8—1222no—
376C2×C8—1222no—
377C2×C8—1222no—
378C2×C8—1221no—
379C2×C8C22×#692312yes—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—612no—
383C4⋊C4—611no—
384C4⋊C4—1222no—
385C4⋊C4—1221no—
386C4⋊C4—1222no—
387C4⋊C4—1221no—
388C4⋊C4C22×#692312yes—
389C4⋊C4C22×#692311yescharacteristic
390C22⋊C4—1221no—
391C22⋊C4—1221no—
392C22⋊C4—1222no—
393C22⋊C4—1221no—
394C42—21no—
395C42—611no—
396C42—611no—
397C42—611no—
398C42—612no—
399C42—1221no—
400C42—1222no—
401C42—1221no—
402C42—1221no—
403C42—1221no—
404C42—1221no—
405C42—2442no—
406C42—2442no—
407C42C22×#692311yescharacteristic
408C23—611no—
409C23—1221no—
410Q8—21no—
411Q8—21no—
412Q8—42no—
413Q8—4881no—
414D4—1221no—
415D4—1221no—
416D4—2441no—
417D4—2441no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—611no—
422C2×C4—611no—
423C2×C4—611no—
424C2×C4—611no—
425C2×C4—611no—
426C2×C4—611no—
427C2×C4—611no—
428C2×C4—1222no—
429C2×C4—1222no—
430C2×C4—1222no—
431C2×C4—1221no—
432C2×C4—1222no—
433C2×C4—4881no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2442no—
442C2×C4D4×#692311yescharacteristic
443C2×C4D4×#692311yescharacteristic
444C2×C4C23×#692311yescharacteristic
445C8—22no—
446C8—1222no—
447C8—1222no—
448C8—1222no—
449C8—1222no—
450C8—2441no—
451C8—2442no—
452C22—611no—
453C22—611no—
454C22—1221no—
455C22—1221no—
456C22—2441no—
457C22—2441no—
458C22—2441no—
459C22C2×D4×#692311yescharacteristic
460C4—21no—
461C4—42no—
462C4—41no—
463C4—41no—
464C4—611no—
465C4—611no—
466C4—1221no—
467C4—1221no—
468C4—2442no—
469C4—2442no—
470C4—2441no—
471C4—2442no—
472C4#1684080712yes—
473C4#41×#692311yescharacteristic
474C4#1684083011yescharacteristic
475C2—1221no—
476C2—1221no—
477C2—4881no—
478C2#2146234511yescharacteristic
479C2C2×#1684080711yescharacteristic
480C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#475C4
socleC22×C61C2×C4×D4
prime radicalC2×#11758226C23
cosocleC2×C4×D61C24
hypercenter#475#6923
hypocenterC61#23081
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #21462613C2semidirect
3. #21462004C2semidirect
4. #21461933C2semidirect
7. #21461886C2semidirect
8. #21461627C2semidirect
9. #21461606C2semidirect
38. #16840067C4semidirect
39. #16840061C4semidirect
40. #16840057C4semidirect
41. #16840053C4semidirect
42. #16840039C4semidirect
46. C61×#475C4semidirect
258. #475#6923semidirect
287. C61#23081semidirect

Maximal subgroups

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

subgroupindex
#214626132
#214625192
#214620042
#214619332
#214619142
#214619032
#214618862
#214616272
#214616062
C4×#145198422
#214556022
#2308161