Finite Group Databasebeta

← #29836443

Subgroups — #29836443

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456475C211yesmaximal, characteristic
2#21456474C211yesmaximal, characteristic
3#21447985C211yesmaximal, characteristic, complemented
4#21447984C211yesmaximal, characteristic, complemented
5#21447983C211yesmaximal, characteristic, complemented
6#21447981C211yesmaximal, characteristic, complemented
7#21447926C211yesmaximal, characteristic
8#21447924C211yesmaximal, characteristic
9#21447909C211yesmaximal, characteristic
10#21447907C211yesmaximal, characteristic
11#21447867C211yesmaximal, characteristic, complemented
12#21447867C211yesmaximal, characteristic, complemented
13#21447866C211yesmaximal, characteristic, complemented
14#21447576C211yesmaximal, characteristic
15C61×#2209C211yesmaximal, characteristic, complemented
16#16840373—21no—
17#16840370—21no—
18C2×#14519723C2211yescharacteristic
19C2×#14519723C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22#16840164C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840140C2211yescharacteristic
25#16840130—21no—
26#16840129—21no—
27#16840019—21no—
28#16840017—21no—
29#16840004C2211yescharacteristic
30#16840000C2211yescharacteristic
31#16840000C2211yescharacteristic
32#16840000C2211yescharacteristic
33#16839869—21no—
34#16839867—21no—
35C4×Dic244C2211yescharacteristic
36Q16×Dic61C2211yescharacteristic
37Q16×Dic61C2211yescharacteristic
38#16839716C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43C4⋊#11758185C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
48#16839566C2211yescharacteristic
49#16839566C2211yescharacteristic
50#16839566C2211yescharacteristic
51#16839566C2211yescharacteristic
52C2×Q32×C61C2211yescharacteristic
53C2×Q32×C61C2211yescharacteristic
54C61×#494C2211yescharacteristic
55C4×Q16×C61C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758202—21no—
61C2×#11758189D411yescharacteristic
62C2×C8×D61C2311yescharacteristic
63#14519775—21no—
64#14519772—41no—
65#14519772—41no—
66#14519772—41no—
67#14519771—41no—
68#14519769—21no—
69#14519769—41no—
70#14519768—21no—
71#14519767—41no—
72#14519767—41no—
73#14519767—41no—
74#14519757—21no—
75#14519753—21no—
76#14519753—21no—
77#14519753—21no—
78Q8×Dic61—21no—
79Q8×Dic61—21no—
80C4×Dic122—21no—
81#14519734D411yescharacteristic
82#14519723—41no—
83#14519723—41no—
84#14519716—41no—
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87C16×D61—41no—
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519709—21no—
92#14519708—21no—
93#14519702—21no—
94#14519701—21no—
95#14519701—21no—
96#14519701—21no—
97#14519701—21no—
98#14519701—21no—
99#14519700—21no—
100#14519688D411yescharacteristic
101#14519687D411yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×Q16×C61—21no—
104C2×Q16×C61C2311yescharacteristic
105C2×Q16×C61C2311yescharacteristic
106C2×Q16×C61C2311yescharacteristic
107C4⋊Q8×C61—21no—
108C4×Q8×C61—21no—
109Q32×C61—41no—
110Q32×C61—41no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#103×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×Q8×C61—21no—
119C2×C4×D61C2×D411yescharacteristic
120C2×Dic122—21no—
121Q16×C61—21no—
122Q16×C61—21no—
123Q16×C61—21no—
124Q16×C61—21no—
125Q16×C61—21no—
126Q16×C61—21no—
127Q16×C61—42no—
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2411yescharacteristic
130C4⋊C4×C61—21no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C42×C61—41no—
135C42×C61C2×D411yescharacteristic
136#11758202—42no—
137#11758198—41no—
138#11758198—41no—
139#11758198—41no—
140#11758198—41no—
141#11758198D811yescharacteristic
142#11758198D811yescharacteristic
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
148C4⋊Dic61—41no—
149C4⋊Dic61—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196D811yescharacteristic
160#11758196D811yescharacteristic
161C4×Dic61—41no—
162C4×Dic61—41no—
163C4×Dic61—41no—
164C4×Dic61C2×D411yescharacteristic
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167Dic244—21no—
168Dic244—21no—
169#11758189—41no—
170C8×D61—21no—
171C8×D61—21no—
172C16×C61—21no—
173C16×C61—21no—
174#11758185—21no—
175#11758185—21no—
176C22×D61C2×D811yescharacteristic
177Q8×C61—41no—
178Q8×C61—41no—
179Q8×C61—41no—
180Q8×C61—41no—
181Q8×C61—41no—
182Q8×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61C2×D811yescharacteristic
195C2×Dic61C2×D811yescharacteristic
196C2×Dic61C2×D811yescharacteristic
197C4×D61—21no—
198C4×D61—21no—
199Dic122—41no—
200Dic122—41no—
201C8×C61—21no—
202C8×C61H(5,𝔽2)11yescharacteristic
203C8×C612−1+411yescharacteristic
204#92418—21no—
205#92418—21no—
206#33827—611nomaximal, Sylow
207C22×C61C22×D811yescharacteristic
208C2×D61—21no—
209C2×D61—21no—
210C2×D61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61#53711yescharacteristic
218C4×C61#57511yescharacteristic
219Dic61—21no—
220Dic61—21no—
221Dic61—21no—
222Dic61—81no—
223Dic61—81no—
224Dic61—81no—
225Dic61—81no—
226#3177—611no—
227#3177—611no—
228#2229—611no—
229#2229—611no—
230#2229—611no—
231#2229—611no—
232#2219—611no—
233#2219—611no—
234#2216—611no—
235#2216—611no—
236#2209—611no—
237#2209—611no—
238#2209—611no—
239#2209D6111yescharacteristic, complemented
240#2151—611no—
241C2×C61#324511yescharacteristic
242C2×C61#341711yescharacteristic
243C2×C61#341711yescharacteristic
244D61—41no—
245#541—1221no—
246#541—1221no—
247C2×Q32—611no—
248C2×Q32—611no—
249C2×Q32C2×D6111yescharacteristic
250C2×Q32C2×D6111yescharacteristic
251C2×M32—611no—
252C22×C16—611no—
253#499—611no—
254#499—611no—
255#494—611no—
256#494C2×D6111yescharacteristic
257#491—1221no—
258#491—1221no—
259#470—1221no—
260#470—1221no—
261#467—611no—
262#467—611no—
263#467—611no—
264#467—611no—
265#441—1221no—
266#441—1221no—
267C4×Q16—611no—
268C4×Q16—611no—
269C4×Q16—611no—
270C4×Q16C2×D6111yescharacteristic
271#405—611no—
272#367—611no—
273#367—611no—
274#366—611no—
275#366—611no—
276C4⋊C16—611no—
277C4⋊C16—611no—
278C4⋊C16—611no—
279C4⋊C16C2×D6111yescharacteristic
280#358—611no—
281#358—611no—
282#358—611no—
283#358—611no—
284#358—611no—
285#358—611no—
286#358C2×D6111yescharacteristic
287#358C2×D6111yescharacteristic
288C61#3382711yescharacteristic, complemented, Sylow
289C2×Q16—21no—
290C2×Q16—611no—
291C2×Q16—1221no—
292C2×Q16C22×D6111yescharacteristic
293C2×Q16C22×D6111yescharacteristic
294C2×Q16C22×D6111yescharacteristic
295C2×M16—611no—
296C22×C8—611no—
297C4⋊Q8—21no—
298C4⋊Q8—1221no—
299#126—2441no—
300#126—2441no—
301#126—2441no—
302#126—2441no—
303#125—1221no—
304#125—1221no—
305#125—2441no—
306#125—2441no—
307#125—2441no—
308#125—2441no—
309C22⋊Q8—1221no—
310C22⋊Q8—1221no—
311C22⋊Q8—1221no—
312C22⋊Q8—1221no—
313C4×Q8—21no—
314C4×Q8—1221no—
315C4×Q8—1221no—
316C4×Q8—1221no—
317#117—611no—
318Q32—41no—
319Q32—41no—
320Q32—2441no—
321Q32—2441no—
322M32—2441no—
323C2×C16—611no—
324C2×C16—611no—
325C2×C16—2441no—
326C2×C16C22×D6111yescharacteristic
327C2×C16C22×D6111yescharacteristic
328#107—611no—
329#107—611no—
330#107—611no—
331#107C22×D6111yescharacteristic
332#106—1221no—
333#106—1221no—
334#103—21no—
335#103—1221no—
336#103—1221no—
337#103—1221no—
338#103—1221no—
339#103—1221no—
340#103—1221no—
341#103—1221no—
342#97—611no—
343#97—611no—
344C4×C8—611no—
345C4×C8C22×D6111yescharacteristic
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—1221no—
350C22×C4—611no—
351Q16—21no—
352Q16—21no—
353Q16—21no—
354Q16—21no—
355Q16—21no—
356Q16—21no—
357Q16—42no—
358Q16—1221no—
359Q16—1221no—
360Q16—2442no—
361M16—2441no—
362C2×C8—611no—
363C2×C8—611no—
364C2×C8—1221no—
365C2×C8—1221no—
366C2×C8D4×D6111yescharacteristic
367C2×C8C23×D6111yescharacteristic
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—611no—
373C4⋊C4—611no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C22⋊C4—611no—
391C22⋊C4—611no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C42—41no—
397C42—611no—
398C42—2441no—
399C42—2441no—
400C42—2441no—
401C42D4×D6111yescharacteristic
402C16—21no—
403C16—21no—
404C16—1221no—
405C16—1221no—
406C23—611no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—41no—
411Q8—41no—
412Q8—41no—
413Q8—2441no—
414Q8—2441no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4D8×D6111yescharacteristic
429C2×C4D8×D6111yescharacteristic
430C2×C4C2×D4×D6111yescharacteristic
431C8—21no—
432C8—1221no—
433C8—1221no—
434C8#1451982211yescharacteristic
435C8#1451982411yescharacteristic
436C22—1221no—
437C22—1221no—
438C22—1221no—
439C22C2×D8×D6111yescharacteristic
440C4—21no—
441C4—21no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4—81no—
446C4—1221no—
447C4—1221no—
448C4—1221no—
449C4—4881no—
450C4—4881no—
451C4—4881no—
452C4—4881no—
453C4#1684034111yescharacteristic
454C4#1684055811yescharacteristic
455C2—2441no—
456C2#2145712711yescharacteristic
457C2#2145896811yescharacteristic
458C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2209C2
socleC22×C61C22×D8
prime radicalC22×D61C2×D8
hypercenter#2209D61
hypocenterC61#33827
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
3. #21447985C2semidirect
4. #21447984C2semidirect
5. #21447983C2semidirect
6. #21447981C2semidirect
11. #21447867C2semidirect
12. #21447867C2semidirect
13. #21447866C2semidirect
15. C61×#2209C2semidirect
239. #2209D61semidirect
288. C61#33827semidirect

Maximal subgroups

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

subgroupindex
#214564752
#214564742
#214479852
#214479842
#214479832
#214479812
#214479262
#214479242
#214479092
#214479072
#214478672
#214478662
#214475762
C61×#22092
#3382761