Finite Group Databasebeta

← #29836455

Subgroups — #29836455

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456459C211yesmaximal, characteristic, complemented
2#21456451C211yesmaximal, characteristic, complemented
3#21447965C211yesmaximal, characteristic, complemented
4#21447964C211yesmaximal, characteristic, complemented
5#21447960C211yesmaximal, characteristic, complemented
6#21447959C211yesmaximal, characteristic, complemented
7#21447925C211yesmaximal, characteristic, complemented
8#21447920C211yesmaximal, characteristic
9#21447915C211yesmaximal, characteristic, complemented
10#21447884C211yesmaximal, characteristic, complemented
11#21447879C211yesmaximal, characteristic, complemented
12#21447876C211yesmaximal, characteristic, complemented
13#21447873C211yesmaximal, characteristic, complemented
14#21447577C211yesmaximal, characteristic, complemented
15C61×#2217C211yesmaximal, characteristic, complemented
16#16840385—21no—
17#16840379—21no—
18C2×#14519723C2211yescharacteristic
19C2×#14519722C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21C2×#14519717C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840166C2211yescharacteristic
24#16840147C2211yescharacteristic
25#16840145C2211yescharacteristic
26#16840123—21no—
27#16840120—21no—
28#16840010—21no—
29#16840006—21no—
30#16840003C2211yescharacteristic
31#16839998C2211yescharacteristic
32#16839865—21no—
33#16839859—21no—
34Q16×Dic61C2211yescharacteristic
35#16839856C2211yescharacteristic
36D8×Dic61C2211yescharacteristic
37#16839844C2211yescharacteristic
38#16839717C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839589C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839580C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839566C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839563C2211yescharacteristic
51#16839562C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C22×C16×C61C2211yescharacteristic
54C61×#467C2211yescharacteristic
55C61×#466C2211yescharacteristic
56C61×#367C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758200—21no—
61C2×#11758201—21no—
62C2×D488C2311yescharacteristic
63C2×#11758194D411yescharacteristic
64#14519776—21no—
65#14519776—21no—
66#14519772—41no—
67#14519770—41no—
68#14519766—21no—
69#14519764—21no—
70#14519764—41no—
71#14519763—41no—
72#14519759—41no—
73#14519758—41no—
74#14519757—41no—
75#14519756—21no—
76#14519754—41no—
77#14519751—21no—
78Q8×Dic61—21no—
79#14519742—21no—
80D4×Dic61—21no—
81#14519739—21no—
82#14519736D411yescharacteristic
83#14519723—41no—
84#14519722—41no—
85#14519718—41no—
86#14519717—41no—
87C2×#11758185C2311yescharacteristic
88C2×#11758185C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519710—21no—
92#14519710—21no—
93#14519702—21no—
94#14519701—21no—
95#14519700—21no—
96#14519699—21no—
97#14519698—21no—
98#14519697—21no—
99#14519687D411yescharacteristic
100#14519687D411yescharacteristic
101C8×Dic61C2311yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×Q16×C61C2311yescharacteristic
104C2×D8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22⋊Q8×C61—21no—
107#121×C61—21no—
108SD32×C61—41no—
109C2×C16×C61—41no—
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#103×C61—21no—
115#102×C61—21no—
116C2×Q8×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—41no—
119C22×C4×C61C2×D411yescharacteristic
120C2×C22⋊D61—41no—
121C22×Dic61—41no—
122C2×D244—21no—
123C2×C4×D61—41no—
124C2×Dic122—21no—
125C2×Dic122—41no—
126C2×Dic122—41no—
127Q16×C61—21no—
128Q16×C61—21no—
129D8×C61—21no—
130D8×C61—21no—
131C2×C8×C61—21no—
132C2×C8×C61—21no—
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2411yescharacteristic
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊Dic61—41no—
141C22⋊Dic61—41no—
142C22⋊Dic61—41no—
143C22⋊Dic61—41no—
144C22⋊Dic61D811yescharacteristic
145C22⋊Dic61D811yescharacteristic
146#11758201—42no—
147#11758200—42no—
148#11758198—41no—
149#11758198—41no—
150#11758198—41no—
151#11758198—41no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—41no—
155C4⋊Dic61D811yescharacteristic
156C4⋊Dic61D811yescharacteristic
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61—41no—
162C4×Dic61—41no—
163C4×Dic61C2×D411yescharacteristic
164C4×Dic61C2×D411yescharacteristic
165#11758194—41no—
166C2×#92418C2×D411yescharacteristic
167C2×#92418C2×D411yescharacteristic
168Dic244—21no—
169Dic244—21no—
170D488—21no—
171D488—21no—
172C16×C61—21no—
173C16×C61—21no—
174#11758185—21no—
175#11758185—21no—
176C23×C61—41no—
177C23×C61C2×D811yescharacteristic
178C22×D61—41no—
179Q8×C61—41no—
180Q8×C61—41no—
181D4×C61—41no—
182D4×C61—41no—
183D4×C61—161no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C22⋊D61—161no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—161no—
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199C2×Dic61C2×D811yescharacteristic
200D244—41no—
201D244—41no—
202C4×D61—161no—
203Dic122—41no—
204Dic122—41no—
205Dic122—161no—
206Dic122—161no—
207C8×C61—21no—
208C8×C61H(5,𝔽2)11yescharacteristic
209C8×C612−1+411yescharacteristic
210#92418—21no—
211#92418—21no—
212#33829—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61C22×D811yescharacteristic
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—21no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61#53711yescharacteristic
228C4×C61#57511yescharacteristic
229Dic61—21no—
230Dic61—21no—
231Dic61—21no—
232Dic61—21no—
233Dic61—81no—
234Dic61—81no—
235Dic61—81no—
236#3175—611no—
237#3175—611no—
238#2226—611no—
239#2226—611no—
240#2225—611no—
241#2225—611no—
242#2219—611no—
243#2218—611no—
244#2217—611no—
245#2217D6111yescharacteristic, complemented
246#2211—611no—
247#2211—611no—
248#2210—611no—
249#2210—611no—
250#2151—611no—
251C2×C61—41no—
252C2×C61—161no—
253C2×C61#324511yescharacteristic
254C2×C61#341611yescharacteristic
255C2×C61#341611yescharacteristic
256D61—161no—
257#542—1221no—
258#542—1221no—
259C2×Q32—611no—
260C2×SD32—611no—
261C2×SD32C2×D6111yescharacteristic
262C2×D16—611no—
263C2×M32—611no—
264C22×C16C2×D6111yescharacteristic
265#500—611no—
266#500—611no—
267#495—611no—
268#495—611no—
269#489—1221no—
270#489—1221no—
271#468—1221no—
272#468—1221no—
273#467—611no—
274#467C2×D6111yescharacteristic
275#466—611no—
276#466C2×D6111yescharacteristic
277#440—1221no—
278#440—1221no—
279C4×Q16—611no—
280C4×Q16—611no—
281C4×D8—611no—
282C4×D8—611no—
283#405—611no—
284#367—611no—
285#367—611no—
286#367—611no—
287#367C2×D6111yescharacteristic
288C4⋊C16—611no—
289C4⋊C16—611no—
290C4⋊C16—611no—
291C4⋊C16—611no—
292#358—611no—
293#358—611no—
294#358—611no—
295#358C2×D6111yescharacteristic
296#357—611no—
297#357—611no—
298#357—611no—
299#357C2×D6111yescharacteristic
300C61#3382911yescharacteristic, complemented, Sylow
301C2×Q16—611no—
302C2×Q16C22×D6111yescharacteristic
303C2×SD16—1221no—
304C2×SD16—1221no—
305C2×D8—611no—
306C2×D8C22×D6111yescharacteristic
307C2×M16—611no—
308C22×C8C22×D6111yescharacteristic
309C4⋊Q8—1221no—
310C4⋊Q8—1221no—
311#126—2441no—
312#126—2441no—
313#124—1221no—
314#124—1221no—
315#124—2441no—
316#124—2441no—
317#123—2441no—
318#123—2441no—
319C22⋊Q8—21no—
320C22⋊Q8—1221no—
321C22⋊Q8—2441no—
322C22⋊Q8—2441no—
323#121—21no—
324#121—1221no—
325C4×Q8—1221no—
326C4×Q8—1221no—
327C4×D4—1221no—
328C4×D4—1221no—
329#117—611no—
330Q32—2441no—
331SD32—41no—
332SD32—2441no—
333D16—2441no—
334M32—2441no—
335C2×C16—41no—
336C2×C16—611no—
337C2×C16—611no—
338C2×C16C22×D6111yescharacteristic
339C2×C16C22×D6111yescharacteristic
340#107—611no—
341#107—611no—
342#107—1221no—
343#107—1221no—
344#107C22×D6111yescharacteristic
345#107C22×D6111yescharacteristic
346#103—21no—
347#103—1221no—
348#103—1221no—
349#103—1221no—
350#102—21no—
351#102—1221no—
352#102—1221no—
353#102—1221no—
354#97—611no—
355#97—611no—
356C4×C8—611no—
357C4×C8—611no—
358C2×Q8—21no—
359C2×Q8—1221no—
360C2×Q8—2441no—
361C2×Q8—2441no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4—1221no—
365C2×D4—2441no—
366C22×C4—2441no—
367C22×C4—2441no—
368C22×C4D4×D6111yescharacteristic
369Q16—21no—
370Q16—21no—
371Q16—1221no—
372Q16—1221no—
373SD16—2442no—
374SD16—2442no—
375D8—21no—
376D8—21no—
377D8—1221no—
378D8—1221no—
379M16—2441no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—611no—
383C2×C8—611no—
384C2×C8D4×D6111yescharacteristic
385C2×C8C23×D6111yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—611no—
390C4⋊C4—611no—
391C4⋊C4—1221no—
392C4⋊C4—1221no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—611no—
401C22⋊C4—611no—
402C22⋊C4—2441no—
403C22⋊C4—2441no—
404C22⋊C4—2441no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C42—611no—
411C42—611no—
412C42—2441no—
413C42—2441no—
414C16—21no—
415C16—21no—
416C16—1221no—
417C16—1221no—
418C23—41no—
419C23—2441no—
420C23D8×D6111yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—9761no—
424Q8—9761no—
425Q8—2441no—
426Q8—2441no—
427D4—41no—
428D4—41no—
429D4—161no—
430D4—9761no—
431D4—2441no—
432D4—2441no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—611no—
441C2×C4—611no—
442C2×C4—9761no—
443C2×C4—9761no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4D8×D6111yescharacteristic
448C2×C4C2×D4×D6111yescharacteristic
449C8—21no—
450C8—1221no—
451C8—1221no—
452C8#1451982211yescharacteristic
453C8#1451982411yescharacteristic
454C22—21no—
455C22—21no—
456C22—21no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—4881no—
461C22—4881no—
462C22—4881no—
463C22C2×D8×D6111yescharacteristic
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—1221no—
469C4—1221no—
470C4—1221no—
471C4—1221no—
472C4—4881no—
473C4—4881no—
474C4—4881no—
475C4#1684033911yescharacteristic
476C4#1684055911yescharacteristic
477C2—41no—
478C2—161no—
479C2—9761no—
480C2#2145712511yescharacteristic
481C2#2145896111yescharacteristic
482C2#2145896211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2217C2
socleC22×C61C22×D8
prime radical#21447920C2
hypercenter#2217D61
hypocenterC61#33829
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #21456459C2semidirect
2. #21456451C2semidirect
3. #21447965C2semidirect
4. #21447964C2semidirect
5. #21447960C2semidirect
6. #21447959C2semidirect
7. #21447925C2semidirect
9. #21447915C2semidirect
10. #21447884C2semidirect
11. #21447879C2semidirect
12. #21447876C2semidirect
13. #21447873C2semidirect
14. #21447577C2semidirect
15. C61×#2217C2semidirect
245. #2217D61semidirect
300. C61#33829semidirect

Maximal subgroups

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

subgroupindex
#214564592
#214564512
#214479652
#214479642
#214479602
#214479592
#214479252
#214479202
#214479152
#214478842
#214478792
#214478762
#214478732
#214475772
C61×#22172
#3382961