Finite Group Databasebeta

← #29663952

Subgroups — #29663952

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455975C212yesmaximal
2C8×#11758222C211yesmaximal, characteristic
3#21445220C211yesmaximal, characteristic, complemented
4#21445215C211yesmaximal, characteristic, complemented
5#21445210C211yesmaximal, characteristic, complemented
6#21445205C211yesmaximal, characteristic, complemented
7#21445198C212yesmaximal, complemented
8#21445191C212yesmaximal, complemented
9#21444582C211yesmaximal, characteristic, complemented
10#21444529C212yesmaximal, complemented
11C61×#3160C211yesmaximal, characteristic, complemented
12C4×#11758222C2211yescharacteristic
13#16840100—22no—
14#16840054C2212yes—
15#16840049C2212yes—
16#16839969C2212yes—
17#16839964C2212yes—
18#16839922—22no—
19C8×Dic122C2211yescharacteristic
20C8×Dic122C2211yescharacteristic
21#16839867—22no—
22#16839860—22no—
23C8×D244C2211yescharacteristic
24C8×D244C2211yescharacteristic
25C8×C22⋊D61—21no—
26C8×C22⋊D61—21no—
27#16839819C2212yes—
28#16839815C2211yescharacteristic
29#16839813—21no—
30C4×C8×D61—21no—
31#16839515C2211yescharacteristic
32#16839515C2211yescharacteristic
33#16839513C2212yes—
34#16839511C2212yes—
35#16839511C2212yes—
36#16839508C2212yes—
37#16839508C2212yes—
38C61×#533C2212yes—
39C61×#500C2211yescharacteristic
40C61×#500C2211yescharacteristic
41C61×#499—21no—
42C61×#499—21no—
43C61×#498C2212yes—
44C61×#427—21no—
45C61×#427—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758222D411yescharacteristic
48C2×#11758202—22no—
49C2×#11758201—22no—
50C2×C8×D61—21no—
51C2×C8×D61—21no—
52C4×Dic122D411yescharacteristic
53C4×Dic122C2311yescharacteristic
54C4×D244D411yescharacteristic
55C4×D244C2311yescharacteristic
56C4×C22⋊D61—21no—
57C4×C22⋊D61—21no—
58#14519736D411yescharacteristic
59#14519734—21no—
60C42×D61—21no—
61#14519710—22no—
62#14519708—22no—
63C4⋊#92418C2312yes—
64C4⋊#92418C2312yes—
65C4⋊#92418C2311yescharacteristic
66C4⋊#92418C2311yescharacteristic
67#14519706—21no—
68#14519706—21no—
69#14519701—22no—
70#14519701—22no—
71#14519700—22no—
72#14519697—22no—
73C22⋊#92418—21no—
74C22⋊#92418—22no—
75#14519689—21no—
76#14519689—21no—
77#14519688—22no—
78C4×#92418—21no—
79C8×Dic61—21no—
80C8×Dic61—21no—
81C22×C8×C61D411yescharacteristic
82C22×C8×C61D411yescharacteristic
83C4⋊Q8×C61C2312yes—
84C4⋊Q8×C61C2312yes—
85#125×C61—22no—
86C22⋊Q8×C61—22no—
87C22⋊Q8×C61—22no—
88C4×Q8×C61—22no—
89C4×Q8×C61—22no—
90#117×C61—22no—
91C2×C42×C61C2311yescharacteristic
92#107×C61—21no—
93#107×C61—21no—
94#107×C61—21no—
95#107×C61—21no—
96#106×C61—22no—
97#106×C61—22no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C2×C22⋊D61—21no—
108#11758222—22no—
109#11758222—22no—
110C2×D244C2×D411yescharacteristic
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×Dic122C2×D411yescharacteristic
115C2×C8×C61—22no—
116C2×C8×C61—22no—
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2×D411yescharacteristic
121C4⋊C4×C61—22no—
122C4⋊C4×C61—22no—
123C4⋊C4×C61—22no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—42no—
126C4⋊C4×C61—42no—
127C22⋊C4×C61—42no—
128C42×C61—42no—
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61#4111yescharacteristic
132C42×C61C2411yescharacteristic
133C22⋊Dic61—21no—
134#11758202—44no—
135#11758201—44no—
136#11758198—21no—
137#11758198—21no—
138C4⋊Dic61C2×D411yescharacteristic
139C4⋊Dic61C2×D411yescharacteristic
140#11758196—21no—
141#11758196—21no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144C4×Dic61—21no—
145C2×#92418—21no—
146C2×#92418—21no—
147C2×#92418—22no—
148C2×#92418—22no—
149C8×D61—42no—
150C8×D61—42no—
151C23×C61#12111yescharacteristic
152C22×D61—21no—
153Q8×C61—42no—
154Q8×C61—42no—
155Q8×C61—82no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61C22×D411yescharacteristic
167C2×C4×C61C22×D411yescharacteristic
168C2×C4×C61C2×#4111yescharacteristic
169C22⋊D61—24no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173D244—21no—
174D244#13512yes—
175C4×D61—24no—
176C4×D61—42no—
177C4×D61—41no—
178C4×D61—41no—
179Dic122—21no—
180Dic122#13512yes—
181C8×C61—21no—
182C8×C61—21no—
183C8×C61#13712yes—
184C8×C61#13712yes—
185#92418—42no—
186#92418—42no—
187#92418—41no—
188#92418—41no—
189#19273—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61C2×#12111yescharacteristic
194C2×D61—22no—
195C2×D61—41no—
196C2×D61—41no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—82no—
202C4×C61—82no—
203C4×C61C2×#13511yescharacteristic
204C4×C61C2×#13511yescharacteristic
205C4×C61C2×#13711yescharacteristic
206C4×C61C2×#13711yescharacteristic
207Dic61—22no—
208Dic61—41no—
209Dic61—41no—
210#3160D6111yescharacteristic, complemented
211#3116—612no—
212C8×#41—611no—
213#1676—611no—
214#1675—611no—
215#1674—611no—
216#1673—611no—
217#1672—612no—
218#1671—612no—
219#1568—611no—
220#1554—612no—
221C2×C61—41no—
222C2×C61#303911yescharacteristic
223C2×C61#305011yescharacteristic
224C2×C61#306711yescharacteristic
225D61—42no—
226#533C2×D6112yes—
227C4×#41—611no—
228#500C2×D6111yescharacteristic
229#500C2×D6111yescharacteristic
230#499—21no—
231#499—21no—
232#498C2×D6112yes—
233#485—1222no—
234#477—612no—
235#476—612no—
236#462—612no—
237#461—612no—
238#452—1222no—
239C8×Q8—611no—
240C8×Q8—611no—
241#441—1222no—
242#440—1222no—
243C8×D4—611no—
244C8×D4—611no—
245C8×D4—1221no—
246C8×D4—1221no—
247#432—612no—
248#431—611no—
249#431—1221no—
250#427—21no—
251#427—21no—
252C2×C4×C8—1221no—
253C2×C4×C8C2×D6111yescharacteristic
254#335—611no—
255#335—611no—
256#334—612no—
257#333—612no—
258#333—612no—
259#332—612no—
260#332—612no—
261C61#1927311yescharacteristic, complemented, Sylow
262C2×#41—611no—
263C2×Q16—1222no—
264C2×SD16—1222no—
265C22×C8—1221no—
266C22×C8—1221no—
267C22×C8C22⋊D6111yescharacteristic
268C22×C8C22⋊D6111yescharacteristic
269C4⋊Q8C22×D6112yes—
270C4⋊Q8C22×D6112yes—
271#125—22no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C4×Q8—22no—
275C4×Q8—22no—
276C4×Q8—611no—
277C4×Q8—611no—
278C4×D4—611no—
279C4×D4—611no—
280C4×D4—1221no—
281C4×D4—1221no—
282#117—22no—
283#117—611no—
284#117—1221no—
285C2×C42—1221no—
286C2×C42C22×D6111yescharacteristic
287#107—21no—
288#107—21no—
289#107—21no—
290#107—21no—
291#107—1222no—
292#106—22no—
293#106—22no—
294#106—1222no—
295C4⋊C8—611no—
296C4⋊C8—611no—
297C4⋊C8—612no—
298C4⋊C8—612no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301#103—1222no—
302#103—1222no—
303#103—1222no—
304#102—1222no—
305C22⋊C8—1222no—
306C22⋊C8—1221no—
307C22⋊C8—1221no—
308C22⋊C8—1221no—
309#97—1222no—
310C4×C8—1221no—
311C4×C8—1221no—
312C4×C8—1221no—
313C4×C8C22⋊D6111yescharacteristic
314C4×C8C22⋊D6111yescharacteristic
315C4×C8C22×D6111yescharacteristic
316C4×C8C22×D6111yescharacteristic
317#41—1222no—
318#41—1222no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8—611no—
322C2×D4—611no—
323C2×D4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4D4×D6111yescharacteristic
328C22×C4#1175822411yescharacteristic
329C22×C4C2×C22⋊D6111yescharacteristic
330Q16—2444no—
331SD16—2444no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—1222no—
335C2×C8—1222no—
336C2×C8—1221no—
337C2×C8—1221no—
338C2×C8—2442no—
339C2×C8—2442no—
340C2×C8C2×C22⋊D6111yescharacteristic
341C2×C8C2×C22⋊D6111yescharacteristic
342C2×C8C2×C22⋊D6111yescharacteristic
343C2×C8C2×C22⋊D6111yescharacteristic
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—611no—
351C4⋊C4—611no—
352C4⋊C4—1221no—
353C4⋊C4—1221no—
354C22⋊C4—42no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C42—42no—
359C42—1221no—
360C42—1221no—
361C42—1221no—
362C42D4×D6111yescharacteristic
363C42#1175822411yescharacteristic
364C42C2×C22⋊D6111yescharacteristic
365C42C23×D6111yescharacteristic
366C23—1221no—
367C23#1451974811yescharacteristic
368Q8—42no—
369Q8—42no—
370Q8—82no—
371Q8—612no—
372Q8—1221no—
373D4—612no—
374D4—1224no—
375D4—1221no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—1224no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4#1451974811yescharacteristic
391C2×C4#1451974811yescharacteristic
392C2×C4#1451974811yescharacteristic
393C2×C4C2×D4×D6111yescharacteristic
394C2×C4C22×C22⋊D6111yescharacteristic
395C2×C4C2×#1175822411yescharacteristic
396C8—21no—
397C8—21no—
398C8—2442no—
399C8—2442no—
400C8—2441no—
401C8—2441no—
402C8#1451980812yes—
403C8#1451980812yes—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—1222no—
408C22—2441no—
409C22—2441no—
410C22C2×#1451974811yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—82no—
416C4—82no—
417C4—1222no—
418C4—2441no—
419C4—2441no—
420C4#135×D6111yescharacteristic
421C4#135×D6111yescharacteristic
422C4C2×#1451980811yescharacteristic
423C4C2×#1451980811yescharacteristic
424C2—41no—
425C2—2442no—
426C2#2145530211yescharacteristic
427C2#2145539611yescharacteristic
428C2#2145553511yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3160C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#3160D61
hypocenterC61#19273
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3160

Complements

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

NH ≅ G/Ntype
3. #21445220C2semidirect
4. #21445215C2semidirect
5. #21445210C2semidirect
6. #21445205C2semidirect
7. #21445198C2semidirect
8. #21445191C2semidirect
9. #21444582C2semidirect
10. #21444529C2semidirect
11. C61×#3160C2semidirect
210. #3160D61semidirect
261. C61#19273semidirect

Maximal subgroups

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

subgroupindex
#214559752
C8×#117582222
#214452202
#214452152
#214452102
#214452052
#214451982
#214451912
#214445822
#214445292
C61×#31602
#1927361