Finite Group Databasebeta

← #29835003

Subgroups — #29835003

Order 15616.

552 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#21456400C211yesmaximal, characteristic, complemented
2#21454590C211yesmaximal, characteristic
3#21448027C211yesmaximal, characteristic, complemented
4#21447960C211yesmaximal, characteristic, complemented
5#21447955C211yesmaximal, characteristic, complemented
6#21447868C211yesmaximal, characteristic, complemented
7#21447863C211yesmaximal, characteristic, complemented
8#21447761C211yesmaximal, characteristic
9#21447757C211yesmaximal, characteristic
10#21447677C211yesmaximal, characteristic, complemented
11#21447675C211yesmaximal, characteristic, complemented
12#21447670C211yesmaximal, characteristic, complemented
13#21447668C211yesmaximal, characteristic, complemented
14#21447615C211yesmaximal, characteristic, complemented
15C61×#2237C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17#16840314—21no—
18#16840230—21no—
19C2×Dic488C2211yescharacteristic
20C2×#14519723C2211yescharacteristic
21C2×#14519722C2211yescharacteristic
22C2×#14519720C2211yescharacteristic
23#16840166C2211yescharacteristic
24#16840140C2211yescharacteristic
25#16840111—21no—
26#16840003C2211yescharacteristic
27#16840001—21no—
28Q16×Dic61C2211yescharacteristic
29#16839856C2211yescharacteristic
30#16839856C2211yescharacteristic
31#16839856C2211yescharacteristic
32#16839854—21no—
33#16839849—21no—
34#16839849—21no—
35#16839844C2211yescharacteristic
36#16839844C2211yescharacteristic
37#16839756—21no—
38C2×C8×Dic61C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839565C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839562C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50C16×Dic61C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758222—21no—
60#14519799—22no—
61#14519799—22no—
62C2×Dic244C2311yescharacteristic
63C2×Dic244C2311yescharacteristic
64C2×#11758202—21no—
65C2×#11758190—21no—
66C2×D488C2311yescharacteristic
67C22×#92418D411yescharacteristic
68#14519776—21no—
69#14519775—21no—
70#14519767—41no—
71#14519756—21no—
72#14519754—41no—
73Q8×Dic61—21no—
74#14519742—21no—
75#14519742—21no—
76#14519742—21no—
77#14519742—41no—
78#14519739—21no—
79#14519739—21no—
80#14519737—41no—
81#14519737—41no—
82#14519734—41no—
83#14519733—41no—
84C2×C4×Dic61D411yescharacteristic
85C42×D61—41no—
86Dic488—22no—
87#14519723—22no—
88#14519722—22no—
89#14519720—22no—
90C2×#11758185C2311yescharacteristic
91C2×#11758185C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519702—21no—
95#14519701—21no—
96#14519700—21no—
97#14519700—21no—
98#14519700—21no—
99#14519697—21no—
100#14519697—21no—
101C8×Dic61D411yescharacteristic
102C8×Dic61D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C8×Dic61C2311yescharacteristic
105C2×Q16×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22⋊Q8×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#103×C61—21no—
116C2×Q8×C61—21no—
117C22×C4×C61C2×D411yescharacteristic
118C2×C22⋊D61—41no—
119C22×Dic61D811yescharacteristic
120C22×Dic61D811yescharacteristic
121#11758222—24no—
122#11758222—42no—
123C2×D244—21no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×Dic122—21no—
128C2×Dic122—21no—
129C2×Dic122—41no—
130Q16×C61—21no—
131Q16×C61—21no—
132C2×C8×C61—21no—
133C2×C8×C61—21no—
134C2×C8×C61C2×D411yescharacteristic
135C2×C8×C61C2411yescharacteristic
136C4⋊C4×C61—21no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—41no—
140C22⋊C4×C61—41no—
141C22⋊C4×C61—41no—
142C42×C61—41no—
143C22⋊Dic61—41no—
144#11758202—42no—
145#11758198—41no—
146#11758198—41no—
147C4⋊Dic61—21no—
148C4⋊Dic61—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156C4×Dic61—41no—
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160C4×Dic61D811yescharacteristic
161C4×Dic61D811yescharacteristic
162C4×Dic61C2×D411yescharacteristic
163C4×Dic61C2×D411yescharacteristic
164C2×#92418—41no—
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167Dic244—21no—
168Dic244—21no—
169Dic244—21no—
170Dic244#4112yes—
171D488—21no—
172D488#4112yes—
173#11758190—24no—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61C2×D811yescharacteristic
179C22×D61—41no—
180Q8×C61—41no—
181Q8×C61—41no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C22⋊D61—44no—
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199C2×Dic61C2×D811yescharacteristic
200D244—22no—
201D244—41no—
202C4×D61—44no—
203C4×D61—82no—
204C4×D61—82no—
205Dic122—22no—
206Dic122—41no—
207Dic122—41no—
208Dic122—41no—
209Dic122—82no—
210C8×C61—21no—
211C8×C61C2×#4111yescharacteristic
212C8×C61C2×#4111yescharacteristic
213#92418—21no—
214#92418—21no—
215#33667—611nomaximal, Sylow
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61C22×D811yescharacteristic
220C2×D61—42no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—21no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61—81no—
228C4×C61#52511yescharacteristic
229C4×C61#57511yescharacteristic
230Dic61—21no—
231Dic61—21no—
232Dic61—42no—
233Dic61—81no—
234Dic61—81no—
235Dic61#50812yes—
236Dic61#51012yes—
237#3170—611no—
238C4×#135—611no—
239#2237—611no—
240#2237D6111yescharacteristic, complemented
241#2225—611no—
242#2224—611no—
243#2209—611no—
244#2208—611no—
245#2189—611no—
246#2189—611no—
247C4×Q32—611no—
248C4×Q32—611no—
249C4×SD32—611no—
250C4×SD32—611no—
251#2162—611no—
252C2×C61—41no—
253C2×C61#310011yescharacteristic
254C2×C61C2×#50811yescharacteristic
255C2×C61C2×#51011yescharacteristic
256D61—82no—
257C2×#135—611no—
258#533—1221no—
259C4×#41—1221no—
260C2×Q32—611no—
261C2×Q32—611no—
262C2×SD32—611no—
263C2×SD32—611no—
264#500—611no—
265#494—611no—
266#487—1221no—
267#467—611no—
268#467—1221no—
269#467C2×D6111yescharacteristic
270C4×Q16—611no—
271C4×Q16—611no—
272C4×Q16—611no—
273C4×Q16—611no—
274C4×Q16—1221no—
275C4×SD16—1221no—
276C4×SD16—1221no—
277C4×D8—611no—
278C4×D8—611no—
279#427C2×D6111yescharacteristic
280#416—1221no—
281C2×C4×C8—611no—
282#367—611no—
283#367C2×D6111yescharacteristic
284#366—611no—
285#366C2×D6111yescharacteristic
286C4⋊C16—611no—
287C4⋊C16—611no—
288#358—611no—
289#358—611no—
290#358—611no—
291#358—611no—
292#358C2×D6111yescharacteristic
293#358C2×D6111yescharacteristic
294#357—611no—
295#357—611no—
296C22⋊C16—611no—
297C22⋊C16C2×D6111yescharacteristic
298C4×C16—611no—
299C4×C16—611no—
300C61#3366711yescharacteristic, complemented, Sylow
301C2×#41—1221no—
302#135—1222no—
303#135—1222no—
304C2×Q16—611no—
305C2×Q16—611no—
306C2×Q16—1221no—
307C2×Q16C22×D6111yescharacteristic
308C2×SD16—1221no—
309C2×D8—611no—
310C22×C8—611no—
311C22×C8C22×D6111yescharacteristic
312C4⋊Q8—1221no—
313C4⋊Q8—1221no—
314#125—2441no—
315C22⋊Q8—21no—
316C22⋊Q8—1221no—
317C22⋊Q8—2441no—
318C4×Q8—1221no—
319C4×Q8—1221no—
320C4×Q8—1221no—
321C4×Q8—1221no—
322C4×Q8—2441no—
323C4×D4—1221no—
324C4×D4—1221no—
325C4×D4—2441no—
326C4×D4—2441no—
327#117—21no—
328#117—2441no—
329#117—2441no—
330C2×C42—611no—
331C2×C42—2441no—
332Q32—1222no—
333Q32—1222no—
334SD32—1222no—
335SD32—1222no—
336C2×C16—611no—
337C2×C16—611no—
338C2×C16C22×D6111yescharacteristic
339C2×C16C22×D6111yescharacteristic
340#107—611no—
341#107—1221no—
342#107C22×D6111yescharacteristic
343#107C22×D6111yescharacteristic
344#107C22×D6111yescharacteristic
345#106—21no—
346#103—21no—
347#103—1221no—
348#103—1221no—
349#103—1221no—
350#103—1221no—
351#103—1221no—
352#102—1221no—
353#102—1221no—
354C4×C8—611no—
355C4×C8—611no—
356C4×C8—611no—
357C4×C8—611no—
358#41—1224no—
359#41—2442no—
360C2×Q8—21no—
361C2×Q8—1221no—
362C2×Q8—1221no—
363C2×Q8—2441no—
364C2×D4—1221no—
365C2×D4—2441no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—2441no—
369C22×C4—2441no—
370C22×C4—2441no—
371C22×C4D4×D6111yescharacteristic
372Q16—21no—
373Q16—21no—
374Q16—612no—
375Q16—1221no—
376Q16—1221no—
377Q16—1221no—
378Q16—2442no—
379SD16—1224no—
380D8—612no—
381D8—1221no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—611no—
385C2×C8—611no—
386C2×C8—2441no—
387C2×C8D4×D6111yescharacteristic
388C2×C8C23×D6111yescharacteristic
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—1221no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C4⋊C4—2441no—
399C4⋊C4—2441no—
400C4⋊C4—2441no—
401C4⋊C4—2441no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—2441no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C42—41no—
408C42—611no—
409C42—611no—
410C42—611no—
411C42—611no—
412C42—2441no—
413C42—2441no—
414C42—2441no—
415C42—2441no—
416C16—21no—
417C16—21no—
418C16—1221no—
419C16—1221no—
420C23—2441no—
421C23D8×D6111yescharacteristic
422Q8—41no—
423Q8—41no—
424Q8—1222no—
425Q8—4882no—
426Q8—2441no—
427Q8—2441no—
428Q8—2441no—
429D4—1222no—
430D4—2444no—
431D4—2441no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—611no—
441C2×C4—611no—
442C2×C4—1222no—
443C2×C4—1222no—
444C2×C4—4882no—
445C2×C4—4882no—
446C2×C4—2444no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4D8×D6111yescharacteristic
451C2×C4C2×D4×D6111yescharacteristic
452C8—21no—
453C8—1221no—
454C8—1221no—
455C8#41×D6111yescharacteristic
456C8#41×D6111yescharacteristic
457C22—21no—
458C22—21no—
459C22—21no—
460C22—4881no—
461C22—4881no—
462C22—2442no—
463C22C2×D8×D6111yescharacteristic
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—612no—
470C4—612no—
471C4—1221no—
472C4—1221no—
473C4—4881no—
474C4—4881no—
475C4—2442no—
476C4#1684027011yescharacteristic
477C4#1684056111yescharacteristic
478C2—41no—
479C2—4882no—
480C2#2145581611yescharacteristic
481C2#508×D6111yescharacteristic
482C2#510×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2237C2
socleC22×C61C22×D8
prime radicalC2×#14519799C22
hypercenter#2237D61
hypocenterC61#33667
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
1. #21456400C2semidirect
3. #21448027C2semidirect
4. #21447960C2semidirect
5. #21447955C2semidirect
6. #21447868C2semidirect
7. #21447863C2semidirect
10. #21447677C2semidirect
11. #21447675C2semidirect
12. #21447670C2semidirect
13. #21447668C2semidirect
14. #21447615C2semidirect
15. C61×#2237C2semidirect
240. #2237D61semidirect
300. C61#33667semidirect

Maximal subgroups

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

subgroupindex
#214564002
#214545902
#214480272
#214479602
#214479552
#214478682
#214478632
#214477612
#214477572
#214476772
#214476752
#214476702
#214476682
#214476152
C61×#22372
#3366761