Finite Group Databasebeta

← #29835161

Subgroups — #29835161

Order 15616.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456451C211yesmaximal, characteristic
2#21454686C211yesmaximal, characteristic, complemented
3#21448027C211yesmaximal, characteristic, complemented
4#21447970C211yesmaximal, characteristic, complemented
5#21447960C211yesmaximal, characteristic, complemented
6#21447880C211yesmaximal, characteristic, complemented
7#21447880C211yesmaximal, characteristic, complemented
8#21447755C211yesmaximal, characteristic, complemented
9#21447735C211yesmaximal, characteristic
10#21447689C211yesmaximal, characteristic, complemented
11#21447680C211yesmaximal, characteristic, complemented
12#21447677C211yesmaximal, characteristic, complemented
13#21447674C211yesmaximal, characteristic, complemented
14#21447623C211yesmaximal, characteristic, complemented
15C61×#2234C211yesmaximal, characteristic
16C22×Dic244C2211yescharacteristic
17#16840379—21no—
18#16840239—21no—
19C2×Dic488C2211yescharacteristic
20C2×Dic488C2211yescharacteristic
21C2×#14519721C2211yescharacteristic
22C2×#14519721C2211yescharacteristic
23#16840166C2211yescharacteristic
24#16840145C2211yescharacteristic
25#16840120—21no—
26#16840006—21no—
27#16840003C2211yescharacteristic
28#16839868—21no—
29#16839868—21no—
30#16839859—21no—
31#16839856C2211yescharacteristic
32#16839856C2211yescharacteristic
33#16839856C2211yescharacteristic
34#16839856C2211yescharacteristic
35#16839856C2211yescharacteristic
36D8×Dic61C2211yescharacteristic
37#16839770—21no—
38#16839717C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839565C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#466C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C22×Dic122—21no—
60C2×Dic244—21no—
61C2×Dic244—22no—
62C2×Dic244—22no—
63C2×Dic244C2311yescharacteristic
64C2×Dic244C2311yescharacteristic
65C2×Dic244C2311yescharacteristic
66C2×#11758200—21no—
67C2×#11758194D411yescharacteristic
68#14519776—21no—
69#14519770—41no—
70#14519764—21no—
71#14519764—41no—
72#14519758—41no—
73#14519756—21no—
74#14519754—41no—
75C4×Dic122—41no—
76C4×Dic122—41no—
77#14519742—21no—
78#14519742—21no—
79#14519742—21no—
80#14519742—21no—
81#14519742—21no—
82D4×Dic61—21no—
83#14519736D411yescharacteristic
84#14519733—41no—
85#14519733—41no—
86Dic488—22no—
87Dic488—22no—
88#14519721—22no—
89#14519721—22no—
90C2×#11758185C2311yescharacteristic
91C2×#11758185C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519702—21no—
95#14519700—21no—
96#14519700—21no—
97#14519700—21no—
98#14519700—21no—
99#14519700—21no—
100#14519698—21no—
101#14519687D411yescharacteristic
102#14519687D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C8×Dic61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107#121×C61—21no—
108#117×C61—21no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#106×C61—21no—
115#102×C61—21no—
116C2×D4×C61—21no—
117C2×D4×C61—41no—
118C22×C4×C61C2×D411yescharacteristic
119C22×Dic61—41no—
120C22×Dic61—41no—
121C2×Dic122—24no—
122C2×Dic122—21no—
123C2×Dic122—21no—
124C2×Dic122—21no—
125C2×Dic122—42no—
126C2×Dic122—41no—
127C2×Dic122—41no—
128D8×C61—21no—
129D8×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61—21no—
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2411yescharacteristic
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C42×C61—41no—
140C22⋊Dic61—41no—
141C22⋊Dic61—41no—
142C22⋊Dic61—41no—
143C22⋊Dic61—41no—
144C22⋊Dic61D811yescharacteristic
145C22⋊Dic61D811yescharacteristic
146#11758200—42no—
147C4⋊Dic61—21no—
148C4⋊Dic61D811yescharacteristic
149C4⋊Dic61D811yescharacteristic
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160C4×Dic61—41no—
161C4×Dic61—41no—
162C4×Dic61C2×D411yescharacteristic
163C4×Dic61C2×D411yescharacteristic
164#11758194—41no—
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167Dic244—24no—
168Dic244—21no—
169Dic244—21no—
170Dic244—21no—
171Dic244—21no—
172Dic244#4112yes—
173Dic244#4112yes—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61—41no—
179C23×C61C2×D811yescharacteristic
180D4×C61—41no—
181D4×C61—41no—
182D4×C61—161no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×Dic61—44no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—161no—
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199C2×Dic61C2×D811yescharacteristic
200Dic122—22no—
201Dic122—22no—
202Dic122—44no—
203Dic122—41no—
204Dic122—41no—
205Dic122—41no—
206Dic122—41no—
207Dic122—161no—
208C8×C61—21no—
209C8×C61C2×#4111yescharacteristic
210C8×C61C2×#4111yescharacteristic
211#92418—21no—
212#92418—21no—
213#33681—611nomaximal, Sylow
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61C22×D811yescharacteristic
221C4×C61—21no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61#52511yescharacteristic
226C4×C61#57511yescharacteristic
227Dic61—21no—
228Dic61—21no—
229Dic61—21no—
230Dic61—21no—
231Dic61—42no—
232Dic61—42no—
233Dic61—81no—
234Dic61—81no—
235#3175—611no—
236#2950—611no—
237#2237—611no—
238#2234D6111yescharacteristic
239#2227—611no—
240#2225—611no—
241#2211—611no—
242#2211—611no—
243#2188—611no—
244#2185—611no—
245#2176—611no—
246#2175—611no—
247C4×Q32—611no—
248C4×SD32—611no—
249#2164—611no—
250C2×C61—41no—
251C2×C61—161no—
252C2×C61#310011yescharacteristic
253C2×C61#341611yescharacteristic
254C2×C61#341711yescharacteristic
255C22×Q16—611no—
256#542—1221no—
257#519—1221no—
258C2×Q32—611no—
259C2×Q32—611no—
260C2×SD32—611no—
261C2×SD32—611no—
262#500—611no—
263#495—611no—
264#489—1221no—
265#468—1221no—
266#467—611no—
267#466C2×D6111yescharacteristic
268#441—1221no—
269#441—1221no—
270#440—1221no—
271C4×Q16—611no—
272C4×Q16—611no—
273C4×Q16—611no—
274C4×Q16—611no—
275C4×Q16—611no—
276C4×D8—611no—
277#427C2×D6111yescharacteristic
278#419—1221no—
279#405—611no—
280#367—611no—
281#367C2×D6111yescharacteristic
282#366—611no—
283#366C2×D6111yescharacteristic
284C4⋊C16—611no—
285C4⋊C16—611no—
286#358—611no—
287#358—611no—
288#358—611no—
289#358—611no—
290#358—611no—
291#358—611no—
292#357C2×D6111yescharacteristic
293#357C2×D6111yescharacteristic
294C22⋊C16—611no—
295C22⋊C16C2×D6111yescharacteristic
296#346—611no—
297C4×C16—611no—
298C61#3368111yescharacteristic, complemented, Sylow
299C22×Q8—1221no—
300C2×Q16—611no—
301C2×Q16—611no—
302C2×Q16—611no—
303C2×Q16—1222no—
304C2×Q16—1222no—
305C2×Q16—1221no—
306C2×SD16—1221no—
307C2×D8C22×D6111yescharacteristic
308C2×M16—611no—
309C22×C8C22×D6111yescharacteristic
310C4⋊Q8—1221no—
311#126—2441no—
312#124—1221no—
313#124—2441no—
314#123—2441no—
315C22⋊Q8—1221no—
316C22⋊Q8—2441no—
317#121—21no—
318C4×Q8—1221no—
319C4×Q8—1221no—
320C4×Q8—1221no—
321C4×Q8—1221no—
322C4×Q8—1221no—
323C4×Q8—2441no—
324C4×Q8—2441no—
325C4×D4—1221no—
326#117—21no—
327#117—611no—
328#117—2441no—
329#117—2441no—
330Q32—1222no—
331Q32—1222no—
332SD32—1222no—
333SD32—1222no—
334C2×C16—611no—
335C2×C16—611no—
336C2×C16C22×D6111yescharacteristic
337C2×C16C22×D6111yescharacteristic
338#107—611no—
339#107—1221no—
340#107C22×D6111yescharacteristic
341#107C22×D6111yescharacteristic
342#107C22×D6111yescharacteristic
343#106—21no—
344#103—1221no—
345#103—1221no—
346#103—1221no—
347#103—1221no—
348#103—1221no—
349#103—1221no—
350#102—21no—
351#102—1221no—
352#97—611no—
353#97—611no—
354C4×C8—611no—
355C4×C8—611no—
356C2×Q8—1224no—
357C2×Q8—1221no—
358C2×Q8—1221no—
359C2×Q8—1221no—
360C2×Q8—2442no—
361C2×Q8—2441no—
362C2×Q8—2441no—
363C2×D4—21no—
364C2×D4—41no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4D4×D6111yescharacteristic
368Q16—612no—
369Q16—612no—
370Q16—1224no—
371Q16—1221no—
372Q16—1221no—
373Q16—1221no—
374Q16—1221no—
375SD16—2442no—
376D8—21no—
377D8—21no—
378M16—2441no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—611no—
382C2×C8—611no—
383C2×C8D4×D6111yescharacteristic
384C2×C8C23×D6111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—611no—
389C4⋊C4—611no—
390C4⋊C4—1221no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
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—
406C42—41no—
407C42—611no—
408C42—611no—
409C42—2441no—
410C42—2441no—
411C42—2441no—
412C42—2441no—
413C42—2441no—
414C16—21no—
415C16—21no—
416C16—1221no—
417C16—1221no—
418C23—41no—
419C23D8×D6111yescharacteristic
420Q8—1222no—
421Q8—1222no—
422Q8—9761no—
423Q8—2444no—
424Q8—2441no—
425Q8—2441no—
426Q8—2441no—
427Q8—2441no—
428D4—41no—
429D4—41no—
430D4—161no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—611no—
437C2×C4—611no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—9761no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2444no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4D8×D6111yescharacteristic
447C2×C4C2×D4×D6111yescharacteristic
448C8—21no—
449C8—1221no—
450C8—1221no—
451C8#41×D6111yescharacteristic
452C8#41×D6111yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22C2×D8×D6111yescharacteristic
460C4—21no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4—1221no—
465C4—1221no—
466C4—1221no—
467C4—1221no—
468C4—4881no—
469C4—4881no—
470C4—2442no—
471C4—2442no—
472C4#1684027011yescharacteristic
473C4#1684056111yescharacteristic
474C2—41no—
475C2—161no—
476C2#2145581611yescharacteristic
477C2#2145896511yescharacteristic
478C2#2145896911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2234C2
socleC22×C61C22×D8
prime radicalC61×#466C22
hypercenter#2234D61
hypocenterC61#33681
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
2. #21454686C2semidirect
3. #21448027C2semidirect
4. #21447970C2semidirect
5. #21447960C2semidirect
6. #21447880C2semidirect
7. #21447880C2semidirect
8. #21447755C2semidirect
10. #21447689C2semidirect
11. #21447680C2semidirect
12. #21447677C2semidirect
13. #21447674C2semidirect
14. #21447623C2semidirect
298. C61#33681semidirect

Maximal subgroups

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

subgroupindex
#214564512
#214546862
#214480272
#214479702
#214479602
#214478802
#214477552
#214477352
#214476892
#214476802
#214476772
#214476742
#214476232
C61×#22342
#3368161