Finite Group Databasebeta

← #29837594

Subgroups — #29837594

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#21458187C211yesmaximal, characteristic
2#21458183C211yesmaximal, characteristic
3#21448097C211yesmaximal, characteristic, complemented
4#21448030C211yesmaximal, characteristic, complemented
5#21448027C211yesmaximal, characteristic, complemented
6#21448023C211yesmaximal, characteristic, complemented
7#21448021C211yesmaximal, characteristic, complemented
8#21447986C211yesmaximal, characteristic, complemented
9#21447982C211yesmaximal, characteristic, complemented
10#21447928C211yesmaximal, characteristic, complemented
11#21447927C211yesmaximal, characteristic, complemented
12#21447677C211yesmaximal, characteristic, complemented
13#21447649C211yesmaximal, characteristic
14#21447604C211yesmaximal, characteristic, complemented
15C61×#2159C211yesmaximal, characteristic, complemented
16#16840451—21no—
17#16840447—21no—
18C2×Dic488C2211yescharacteristic
19C2×#14519716C2211yescharacteristic
20#16840163C2211yescharacteristic
21#16840163C2211yescharacteristic
22#16840105—21no—
23#16840103—21no—
24#16840094—21no—
25#16840092—21no—
26#16840072—21no—
27#16840068—21no—
28#16840004C2211yescharacteristic
29#16840004C2211yescharacteristic
30#16840003C2211yescharacteristic
31#16840003C2211yescharacteristic
32#16839856C2211yescharacteristic
33#16839856C2211yescharacteristic
34C8×C22⋊D61C2211yescharacteristic
35#16839799C2211yescharacteristic
36#107×D61C2211yescharacteristic
37#16839590C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839587C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839565C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×M32×C61C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C61×#367C2211yescharacteristic
56C61×#367C2211yescharacteristic
57C61×#366C2211yescharacteristic
58C61×#366C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×Dic244C2311yescharacteristic
61C2×C8×D61C2311yescharacteristic
62#14519772—41no—
63#14519770—41no—
64#14519769—41no—
65#14519768—21no—
66#14519768—21no—
67#14519767—41no—
68#14519760—41no—
69#14519759—41no—
70#14519757—21no—
71#14519757—21no—
72#14519756—21no—
73#14519756—21no—
74#14519742—21no—
75#14519742—21no—
76C4×C22⋊D61D411yescharacteristic
77#14519736—41no—
78#14519735—21no—
79#14519734—41no—
80C4⋊C4×D61—21no—
81Dic488—22no—
82#14519716—22no—
83C2×#11758185C2311yescharacteristic
84C2×#11758185C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519710—21no—
88#14519708—21no—
89#14519708—21no—
90#14519708—21no—
91#14519706D411yescharacteristic
92#14519702—21no—
93#14519702—21no—
94#14519700—21no—
95#14519700—21no—
96#14519700—21no—
97#14519700—21no—
98C22⋊#92418D411yescharacteristic
99#14519689D411yescharacteristic
100C8×Dic61C2311yescharacteristic
101C22×C8×C61C2311yescharacteristic
102#117×C61—21no—
103C2×C4⋊C4×C61—21no—
104M32×C61—22no—
105C2×C16×C61C2311yescharacteristic
106C2×C16×C61C2311yescharacteristic
107#107×C61—21no—
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#106×C61—21no—
113C22×C4×C61—41no—
114C22×C4×C61C2×D411yescharacteristic
115C2×C22⋊D61D811yescharacteristic
116C2×C4×D61—41no—
117C2×C4×D61C2×D411yescharacteristic
118C2×Dic122—21no—
119C2×Dic122—21no—
120C2×C8×C61—21no—
121C2×C8×C61—21no—
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2411yescharacteristic
124C4⋊C4×C61—21no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—41no—
129C22⋊C4×C61—41no—
130C42×C61—41no—
131C22⋊Dic61—41no—
132C22⋊Dic61—41no—
133C22⋊Dic61D811yescharacteristic
134#11758198—41no—
135#11758198—41no—
136#11758198—41no—
137#11758198D811yescharacteristic
138C4⋊Dic61—21no—
139C4⋊Dic61—21no—
140C4⋊Dic61—41no—
141C4⋊Dic61—41no—
142C4⋊Dic61—41no—
143C4⋊Dic61—41no—
144#11758196—41no—
145#11758196—41no—
146#11758196—41no—
147#11758196—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196D811yescharacteristic
152C4×Dic61—41no—
153C4×Dic61—41no—
154C4×Dic61—41no—
155C4×Dic61C2×D411yescharacteristic
156C2×#92418C2×D411yescharacteristic
157C2×#92418C2×D411yescharacteristic
158Dic244—21no—
159Dic244—21no—
160Dic244—21no—
161Dic244—21no—
162C8×D61—21no—
163C8×D61—21no—
164C16×C61—21no—
165C16×C61#4112yes—
166#11758185—21no—
167#11758185—21no—
168C23×C61C2×D811yescharacteristic
169C22×D61C2×D811yescharacteristic
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—82no—
177C2×C4×C61C2×D811yescharacteristic
178C2×C4×C61C22×D411yescharacteristic
179C22⋊D61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61C2×D811yescharacteristic
185C2×Dic61C2×D811yescharacteristic
186C2×Dic61C2×D811yescharacteristic
187C4×D61—21no—
188C4×D61—21no—
189C4×D61—82no—
190Dic122—41no—
191Dic122—41no—
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×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61C22×D811yescharacteristic
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—21no—
207C4×C61—21no—
208C4×C61—81no—
209C4×C61—81no—
210C4×C61—81no—
211C4×C61—81no—
212C4×C61#54711yescharacteristic
213C4×C61#57811yescharacteristic
214Dic61—21no—
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#2229—611no—
230#2219—611no—
231#2219—611no—
232C4×Q32—611no—
233#2169—611no—
234#2159—611no—
235#2159D6111yescharacteristic, complemented
236C2×C61—41no—
237C2×C61#333411yescharacteristic
238C2×C61#341411yescharacteristic
239C2×C61#341711yescharacteristic
240D61—41no—
241#552—1221no—
242#552—1221no—
243C2×Q32—611no—
244C2×M32—611no—
245C2×M32C2×D6111yescharacteristic
246#499—611no—
247#499—611no—
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×Q16—611no—
260C8×D4—611no—
261#427—611no—
262#427C2×D6111yescharacteristic
263C2×#107—611no—
264C2×#107C2×D6111yescharacteristic
265#367—611no—
266#367—611no—
267#367C2×D6111yescharacteristic
268#367C2×D6111yescharacteristic
269#366—611no—
270#366—611no—
271#366—611no—
272#366C2×D6111yescharacteristic
273#366C2×D6111yescharacteristic
274C4⋊C16—611no—
275#358—611no—
276#358—611no—
277#358—611no—
278#358—611no—
279#358—611no—
280#358—611no—
281C22⋊C16—611no—
282C22⋊C16—611no—
283C4×C16—611no—
284C61#3391911yescharacteristic, complemented, Sylow
285C2×Q16—611no—
286C2×Q16—611no—
287C22×C8—611no—
288C22×C8C22×D6111yescharacteristic
289#126—2441no—
290#126—2441no—
291#125—1221no—
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—1221no—
302C4×Q8—1221no—
303C4×D4—611no—
304#117—21no—
305#117—1221no—
306#117—2441no—
307#117—2441no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—1221no—
310Q32—1222no—
311M32—22no—
312M32—1222no—
313C2×C16—611no—
314C2×C16—611no—
315C2×C16C22×D6111yescharacteristic
316C2×C16C22×D6111yescharacteristic
317#107—21no—
318#107—611no—
319#107—611no—
320#107—1221no—
321#107C22×D6111yescharacteristic
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—1221no—
331#103—1221no—
332#103—1221no—
333#103—1221no—
334#103—1221no—
335#103—1221no—
336C22⋊C8—611no—
337C22⋊C8—611no—
338C4×C8—611no—
339C2×Q8—1221no—
340C2×Q8—1221no—
341C2×D4—611no—
342C22×C4—41no—
343C22×C4—611no—
344C22×C4—2441no—
345C22×C4D4×D6111yescharacteristic
346Q16—1221no—
347Q16—1221no—
348Q16—1221no—
349Q16—1221no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—611no—
353C2×C8—611no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8D4×D6111yescharacteristic
357C2×C8C23×D6111yescharacteristic
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—611no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—2441no—
367C4⋊C4—2441no—
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—41no—
378C22⋊C4—611no—
379C22⋊C4—611no—
380C22⋊C4—2441no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C42—41no—
386C42—611no—
387C42—2441no—
388C42—2441no—
389C42—2441no—
390C16—21no—
391C16—1221no—
392C16—1221no—
393C16#1175822212yes—
394C23—611no—
395C23D8×D6111yescharacteristic
396Q8—2441no—
397Q8—2441no—
398Q8—2441no—
399Q8—2441no—
400D4—2441no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—82no—
408C2×C4—611no—
409C2×C4—611no—
410C2×C4—611no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—4882no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4D8×D6111yescharacteristic
419C2×C4C2×D4×D6111yescharacteristic
420C8—21no—
421C8—1221no—
422C8—1221no—
423C8C2×#1175822211yescharacteristic
424C8#1451982511yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—1221no—
429C22—1221no—
430C22—1221no—
431C22C2×D8×D6111yescharacteristic
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—1221no—
438C4—1221no—
439C4—1221no—
440C4—4881no—
441C4—4881no—
442C4—4881no—
443C4—4881no—
444C4#1684041311yescharacteristic
445C4#1684057511yescharacteristic
446C2—41no—
447C2—2441no—
448C2#2145816411yescharacteristic
449C2#2145895111yescharacteristic
450C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2159C2
socleC22×C61C22×D8
prime radicalC2×C22⋊D61D8
hypercenter#2159D61
hypocenterC61#33919
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
3. #21448097C2semidirect
4. #21448030C2semidirect
5. #21448027C2semidirect
6. #21448023C2semidirect
7. #21448021C2semidirect
8. #21447986C2semidirect
9. #21447982C2semidirect
10. #21447928C2semidirect
11. #21447927C2semidirect
12. #21447677C2semidirect
14. #21447604C2semidirect
15. C61×#2159C2semidirect
235. #2159D61semidirect
284. C61#33919semidirect

Maximal subgroups

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

subgroupindex
#214581872
#214581832
#214480972
#214480302
#214480272
#214480232
#214480212
#214479862
#214479822
#214479282
#214479272
#214476772
#214476492
#214476042
C61×#21592
#3391961