Finite Group Databasebeta

← #29837595

Subgroups — #29837595

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458189C211yesmaximal, characteristic
2#21458186C211yesmaximal, characteristic
3#21448095C211yesmaximal, characteristic, complemented
4#21448030C211yesmaximal, characteristic, complemented
5#21448025C211yesmaximal, characteristic, complemented
6#21448023C211yesmaximal, characteristic, complemented
7#21448020C211yesmaximal, characteristic, complemented
8#21447984C211yesmaximal, characteristic, complemented
9#21447926C211yesmaximal, characteristic, complemented
10#21447926C211yesmaximal, characteristic, complemented
11C4×#14519723C211yesmaximal, characteristic, complemented
12#21447650C211yesmaximal, characteristic
13#21447606C211yesmaximal, characteristic, complemented
14#21447604C211yesmaximal, characteristic, complemented
15C61×#2229C211yesmaximal, characteristic, complemented
16#16840453—21no—
17#16840450—21no—
18C2×#14519723C2211yescharacteristic
19C2×#14519716C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21#16840164C2211yescharacteristic
22#16840106—21no—
23#16840101—21no—
24#16840094—21no—
25#16840091—21no—
26#16840069—21no—
27#16840066—21no—
28#16840004C2211yescharacteristic
29#16840004C2211yescharacteristic
30#16840000C2211yescharacteristic
31#16840000C2211yescharacteristic
32C4×Dic244C2211yescharacteristic
33C8×D244C2211yescharacteristic
34#16839799C2211yescharacteristic
35#16839799C2211yescharacteristic
36#107×D61C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43#16839587C2211yescharacteristic
44#16839587C2211yescharacteristic
45#16839567C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839566C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51C4×#11758185C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×C8×D61C2311yescharacteristic
61C2×C8×D61C2311yescharacteristic
62#14519772—41no—
63#14519771—41no—
64#14519769—21no—
65#14519768—41no—
66#14519767—41no—
67#14519762—41no—
68#14519762—41no—
69#14519757—21no—
70#14519757—21no—
71#14519753—21no—
72#14519753—21no—
73C4×Dic122—21no—
74C4×D244D411yescharacteristic
75#14519735—21no—
76#14519735—21no—
77#14519735—41no—
78#14519734—41no—
79C4⋊C4×D61—21no—
80C4⋊C4×D61—21no—
81#14519723—22no—
82#14519716—22no—
83#14519716—22no—
84C2×#11758185C2311yescharacteristic
85C2×#11758185C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519710—21no—
90#14519710—21no—
91#14519709—21no—
92#14519708—21no—
93#14519708—21no—
94C4⋊#92418D411yescharacteristic
95#14519702—21no—
96#14519701—21no—
97#14519701—21no—
98#14519700—21no—
99#14519700—21no—
100#14519689D411yescharacteristic
101#14519689D411yescharacteristic
102C2×Q16×C61C2311yescharacteristic
103#125×C61—21no—
104C4×Q8×C61—21no—
105C2×C16×C61C2311yescharacteristic
106C2×C16×C61C2311yescharacteristic
107#107×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#106×C61—21no—
111#103×C61—21no—
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—21no—
114C2×D244D811yescharacteristic
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61C2×D411yescharacteristic
118C2×C4×D61C2×D411yescharacteristic
119C2×Dic122—21no—
120Q16×C61—21no—
121Q16×C61—21no—
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2411yescharacteristic
124C4⋊C4×C61—21no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—41no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C42×C61—41no—
131C42×C61C2×D411yescharacteristic
132#11758198—41no—
133#11758198—41no—
134#11758198—41no—
135#11758198—41no—
136#11758198—41no—
137#11758198—41no—
138#11758198D811yescharacteristic
139#11758198D811yescharacteristic
140C4⋊Dic61—21no—
141C4⋊Dic61—21no—
142C4⋊Dic61—21no—
143C4⋊Dic61—41no—
144C4⋊Dic61—41no—
145C4⋊Dic61D811yescharacteristic
146#11758196—41no—
147#11758196—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153C4×Dic61—41no—
154C4×Dic61—41no—
155C4×Dic61—41no—
156C2×#92418C2×D411yescharacteristic
157C2×#92418C2×D411yescharacteristic
158Dic244—21no—
159Dic244—21no—
160C8×D61—21no—
161C8×D61—21no—
162C8×D61—21no—
163C8×D61—21no—
164C16×C61—21no—
165C16×C61—21no—
166#11758185—21no—
167#11758185#4112yes—
168C22×D61C2×D811yescharacteristic
169C22×D61C2×D811yescharacteristic
170Q8×C61—41no—
171Q8×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61C2×D811yescharacteristic
177C2×C4×C61C2×D811yescharacteristic
178C2×C4×C61C22×D411yescharacteristic
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61C2×D811yescharacteristic
184C2×Dic61C2×D811yescharacteristic
185D244—41no—
186C4×D61—21no—
187C4×D61—21no—
188C4×D61—21no—
189C4×D61—21no—
190C4×D61—82no—
191C4×D61—82no—
192Dic122—41no—
193Dic122—41no—
194C8×C61—21no—
195C8×C61C2×#4111yescharacteristic
196C8×C612−1+411yescharacteristic
197#92418—21no—
198#92418—21no—
199#33919—611nomaximal, Sylow
200C22×C61C22×D811yescharacteristic
201C2×D61—21no—
202C2×D61—21no—
203C2×D61—21no—
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—81no—
210C4×C61—81no—
211C4×C61—81no—
212C4×C61—81no—
213C4×C61#54711yescharacteristic
214C4×C61#57811yescharacteristic
215Dic61—21no—
216Dic61—21no—
217Dic61—81no—
218Dic61—81no—
219Dic61—81no—
220Dic61—81no—
221#3336—611no—
222#3336—611no—
223#2253—611no—
224#2237—611no—
225#2237—611no—
226#2236—611no—
227#2236—611no—
228#2229—611no—
229#2229D6111yescharacteristic, complemented
230#2219—611no—
231#2219—611no—
232C4×Q32—611no—
233#2169—611no—
234#2159—611no—
235#2159—611no—
236C2×C61#333411yescharacteristic
237C2×C61#341411yescharacteristic
238C2×C61#341711yescharacteristic
239D61—41no—
240D61—41no—
241#552—1221no—
242#552—1221no—
243C2×Q32—611no—
244C2×M32—611no—
245C2×M32—611no—
246#499—611no—
247#499C2×D6111yescharacteristic
248#485—1221no—
249#485—1221no—
250#483—1221no—
251#483—1221no—
252#479—1221no—
253#479—1221no—
254#467—611no—
255#467—611no—
256#467—611no—
257#467—611no—
258C4×Q16—611no—
259C4×Q16C2×D6111yescharacteristic
260C8×D4—611no—
261#427—611no—
262#427—611no—
263C2×#107—611no—
264C2×#107—611no—
265#367—611no—
266#367—611no—
267#367—611no—
268#367C2×D6111yescharacteristic
269#366—611no—
270#366—611no—
271#366—611no—
272#366—611no—
273#366C2×D6111yescharacteristic
274C4⋊C16C2×D6111yescharacteristic
275#358—611no—
276#358—611no—
277#358—611no—
278#358—611no—
279#358C2×D6111yescharacteristic
280#358C2×D6111yescharacteristic
281C22⋊C16—611no—
282C22⋊C16—611no—
283C4×C16—611no—
284C61#3391911yescharacteristic, complemented, Sylow
285C2×Q16—611no—
286C2×Q16C22×D6111yescharacteristic
287C22×C8—611no—
288C22×C8—611no—
289#126—2441no—
290#126—2441no—
291#125—21no—
292#125—1221no—
293#125—2441no—
294#125—2441no—
295#123—2441no—
296#123—2441no—
297C22⋊Q8—1221no—
298C22⋊Q8—1221no—
299C22⋊Q8—1221no—
300C22⋊Q8—1221no—
301C4×Q8—21no—
302C4×Q8—1221no—
303C4×D4—611no—
304#117—1221no—
305#117—1221no—
306#117—2441no—
307#117—2441no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310Q32—1222no—
311M32—1222no—
312M32—1222no—
313C2×C16—611no—
314C2×C16—611no—
315C2×C16C22×D6111yescharacteristic
316C2×C16C22×D6111yescharacteristic
317#107—611no—
318#107—611no—
319#107—611no—
320#107—1221no—
321#107—1221no—
322#107C22×D6111yescharacteristic
323#107C22×D6111yescharacteristic
324#107C22×D6111yescharacteristic
325#106—21no—
326#106—1221no—
327#106—1221no—
328#106—1221no—
329C4⋊C8—611no—
330#103—21no—
331#103—1221no—
332#103—1221no—
333#103—1221no—
334#103—1221no—
335#103—1221no—
336C22⋊C8—611no—
337C22⋊C8—611no—
338C4×C8C22×D6111yescharacteristic
339C2×Q8—21no—
340C2×Q8—1221no—
341C2×D4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—2441no—
345C22×C4—2441no—
346Q16—21no—
347Q16—21no—
348Q16—1221no—
349Q16—1221no—
350C2×C8—611no—
351C2×C8—611no—
352C2×C8—1221no—
353C2×C8—1221no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8D4×D6111yescharacteristic
357C2×C8C23×D6111yescharacteristic
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—611no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—1221no—
368C4⋊C4—2441no—
369C4⋊C4—2441no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C4⋊C4—2441no—
377C22⋊C4—611no—
378C22⋊C4—611no—
379C22⋊C4—2441no—
380C22⋊C4—2441no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C42—41no—
386C42—2441no—
387C42—2441no—
388C42—2441no—
389C42D4×D6111yescharacteristic
390C16—21no—
391C16—21no—
392C16—612no—
393C16—1221no—
394C23—611no—
395C23—611no—
396Q8—41no—
397Q8—41no—
398Q8—2441no—
399Q8—2441no—
400D4—2441no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—611no—
406C2×C4—611no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—4882no—
412C2×C4—4882no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4D8×D6111yescharacteristic
418C2×C4D8×D6111yescharacteristic
419C2×C4C2×D4×D6111yescharacteristic
420C8—21no—
421C8—1221no—
422C8—1221no—
423C8#41×D6111yescharacteristic
424C8#1451982511yescharacteristic
425C22—1221no—
426C22—1221no—
427C22—1221no—
428C22—1221no—
429C22—1221no—
430C22—1221no—
431C22C2×D8×D6111yescharacteristic
432C4—21no—
433C4—21no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—1221no—
439C4—1221no—
440C4—4881no—
441C4—4881no—
442C4—4881no—
443C4—4881no—
444C4#1684041411yescharacteristic
445C4#1684057811yescharacteristic
446C2—2441no—
447C2—2441no—
448C2#2145816511yescharacteristic
449C2#2145895211yescharacteristic
450C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2229C2
socleC22×C61C22×D8
prime radicalC2×D244D8
hypercenter#2229D61
hypocenterC61#33919
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
3. #21448095C2semidirect
4. #21448030C2semidirect
5. #21448025C2semidirect
6. #21448023C2semidirect
7. #21448020C2semidirect
8. #21447984C2semidirect
9. #21447926C2semidirect
10. #21447926C2semidirect
11. C4×#14519723C2semidirect
13. #21447606C2semidirect
14. #21447604C2semidirect
15. C61×#2229C2semidirect
229. #2229D61semidirect
284. C61#33919semidirect

Maximal subgroups

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

subgroupindex
#214581892
#214581862
#214480952
#214480302
#214480252
#214480232
#214480202
#214479842
#214479262
C4×#145197232
#214476502
#214476062
#214476042
C61×#22292
#3391961