Finite Group Databasebeta

← #29835154

Subgroups — #29835154

Order 15616.

534 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#21456471C211yesmaximal, characteristic, complemented
2#21454693C211yesmaximal, characteristic
3#21448021C211yesmaximal, characteristic, complemented
4#21447986C211yesmaximal, characteristic, complemented
5#21447975C211yesmaximal, characteristic, complemented
6#21447868C211yesmaximal, characteristic, complemented
7#21447863C211yesmaximal, characteristic, complemented
8#21447761C211yesmaximal, characteristic
9#21447757C211yesmaximal, characteristic
10#21447689C211yesmaximal, characteristic, complemented
11#21447686C211yesmaximal, characteristic, complemented
12#21447675C211yesmaximal, characteristic, complemented
13#21447670C211yesmaximal, characteristic, complemented
14#21447623C211yesmaximal, characteristic, complemented
15C61×#2235C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17#16840372—21no—
18#16840243—21no—
19C2×Dic488C2211yescharacteristic
20C2×#14519723C2211yescharacteristic
21C2×#14519722C2211yescharacteristic
22C2×#14519720C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840140C2211yescharacteristic
25#16840129—21no—
26#16840018—21no—
27#16840003C2211yescharacteristic
28#16839866—21no—
29#16839861—21no—
30#16839861—21no—
31Q16×Dic61C2211yescharacteristic
32#16839856C2211yescharacteristic
33#16839856C2211yescharacteristic
34#16839856C2211yescharacteristic
35#16839844C2211yescharacteristic
36#16839844C2211yescharacteristic
37#16839761—21no—
38#16839717C2211yescharacteristic
39#16839587C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839565C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839562C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#367C2211yescharacteristic
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
67C2×#11758194D411yescharacteristic
68#14519775—21no—
69#14519770—41no—
70#14519770—41no—
71#14519768—21no—
72#14519768—41no—
73#14519767—41no—
74#14519756—21no—
75Q8×Dic61—21no—
76#14519742—21no—
77#14519742—21no—
78#14519742—21no—
79#14519739—21no—
80#14519739—21no—
81C4×C22⋊D61—41no—
82C4×C22⋊D61—41no—
83#14519736D411yescharacteristic
84#14519735—41no—
85C4⋊C4×D61—41no—
86Dic488—22no—
87#14519723—22no—
88#14519722—22no—
89#14519720—22no—
90C2×#11758185C2311yescharacteristic
91C2×#11758185C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519708—21no—
94#14519702—21no—
95#14519701—21no—
96#14519700—21no—
97#14519700—21no—
98#14519700—21no—
99#14519697—21no—
100#14519697—21no—
101#14519687D411yescharacteristic
102#14519687D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C8×Dic61C2311yescharacteristic
105C2×Q16×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22⋊Q8×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61—21no—
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#107×C61C2311yescharacteristic
115#103×C61—21no—
116C2×Q8×C61—21no—
117C22×C4×C61—41no—
118C22×C4×C61C2×D411yescharacteristic
119C2×C22⋊D61—41no—
120#11758222—24no—
121#11758222—42no—
122C2×D244—21no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×Dic122—21no—
127C2×Dic122—21no—
128Q16×C61—21no—
129Q16×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—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊Dic61—41no—
141C22⋊Dic61D811yescharacteristic
142C22⋊Dic61D811yescharacteristic
143#11758202—42no—
144#11758198—41no—
145#11758198—41no—
146C4⋊Dic61—21no—
147C4⋊Dic61—41no—
148C4⋊Dic61—41no—
149C4⋊Dic61D811yescharacteristic
150C4⋊Dic61D811yescharacteristic
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—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—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×C61—161no—
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C22⋊D61—44no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61C2×D811yescharacteristic
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199D244—22no—
200D244—41no—
201C4×D61—44no—
202C4×D61—161no—
203C4×D61—161no—
204Dic122—22no—
205Dic122—41no—
206Dic122—41no—
207Dic122—41no—
208C8×C61—21no—
209C8×C61C2×#4111yescharacteristic
210C8×C61C2×#4111yescharacteristic
211#92418—21no—
212#92418—21no—
213#33680—611nomaximal, Sylow
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61C22×D811yescharacteristic
218C2×D61—42no—
219C2×D61—81no—
220C2×D61—81no—
221C4×C61—21no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61#52511yescharacteristic
227C4×C61#57511yescharacteristic
228Dic61—21no—
229Dic61—21no—
230Dic61—21no—
231Dic61—21no—
232Dic61—42no—
233Dic61—81no—
234Dic61—81no—
235#3177—611no—
236#2951—611no—
237#2236—611no—
238#2235D6111yescharacteristic, complemented
239#2229—611no—
240#2228—611no—
241#2209—611no—
242#2208—611no—
243#2189—611no—
244#2189—611no—
245#2176—611no—
246#2175—611no—
247C4×Q32—611no—
248C4×SD32—611no—
249#2164—611no—
250C2×C61—41no—
251C2×C61#310011yescharacteristic
252C2×C61#341611yescharacteristic
253C2×C61#341711yescharacteristic
254D61—82no—
255C2×#135—611no—
256#541—1221no—
257#520—1221no—
258C2×Q32—611no—
259C2×Q32—611no—
260C2×SD32—611no—
261C2×SD32—611no—
262#499—611no—
263#494—611no—
264#491—1221no—
265#470—1221no—
266#467—611no—
267#467C2×D6111yescharacteristic
268#441—1221no—
269#440—1221no—
270#440—1221no—
271C4×Q16—611no—
272C4×Q16—611no—
273C4×Q16—611no—
274C4×Q16—611no—
275C4×D8—611no—
276C4×D8—611no—
277C2×#107C2×D6111yescharacteristic
278#417—1221no—
279#405—611no—
280#367C2×D6111yescharacteristic
281#367C2×D6111yescharacteristic
282#366—611no—
283#366—611no—
284C4⋊C16—611no—
285C4⋊C16—611no—
286#358—611no—
287#358—611no—
288#358—611no—
289#358—611no—
290#358C2×D6111yescharacteristic
291#358C2×D6111yescharacteristic
292#357—611no—
293#357—611no—
294C22⋊C16—611no—
295C22⋊C16C2×D6111yescharacteristic
296#346—611no—
297C4×C16—611no—
298C61#3368011yescharacteristic, complemented, Sylow
299C2×#41—1221no—
300#135—1222no—
301#135—1222no—
302C2×Q16—611no—
303C2×Q16—611no—
304C2×Q16—1221no—
305C2×Q16C22×D6111yescharacteristic
306C2×SD16—1221no—
307C2×D8—611no—
308C2×M16—611no—
309C22×C8C22×D6111yescharacteristic
310C4⋊Q8—1221no—
311#126—2441no—
312#126—2441no—
313#125—1221no—
314#125—2441no—
315#125—2441no—
316C22⋊Q8—21no—
317C22⋊Q8—1221no—
318C4×Q8—1221no—
319C4×Q8—1221no—
320C4×Q8—1221no—
321C4×Q8—1221no—
322C4×D4—1221no—
323C4×D4—1221no—
324C4×D4—2441no—
325C4×D4—2441no—
326#117—611no—
327#117—2441no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—2441no—
330Q32—1222no—
331Q32—1222no—
332SD32—1222no—
333SD32—1222no—
334C2×C16—611no—
335C2×C16—611no—
336C2×C16C22×D6111yescharacteristic
337C2×C16C22×D6111yescharacteristic
338#107—21no—
339#107—611no—
340#107C22×D6111yescharacteristic
341#107C22×D6111yescharacteristic
342#107C22×D6111yescharacteristic
343#106—1221no—
344#103—21no—
345#103—1221no—
346#103—1221no—
347#103—1221no—
348#103—1221no—
349#103—1221no—
350#102—1221no—
351#102—1221no—
352#97—611no—
353#97—611no—
354C4×C8—611no—
355C4×C8—611no—
356#41—1224no—
357#41—2442no—
358C2×Q8—21no—
359C2×Q8—1221no—
360C2×Q8—1221no—
361C2×D4—1221no—
362C2×D4—2441no—
363C22×C4—41no—
364C22×C4—2441no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4D4×D6111yescharacteristic
368Q16—21no—
369Q16—21no—
370Q16—612no—
371Q16—1221no—
372Q16—1221no—
373Q16—1221no—
374Q16—2442no—
375SD16—1224no—
376D8—612no—
377D8—1221no—
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—41no—
389C4⋊C4—41no—
390C4⋊C4—611no—
391C4⋊C4—611no—
392C4⋊C4—1221no—
393C4⋊C4—2441no—
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—611no—
404C22⋊C4—611no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C42—611no—
409C42—611no—
410C42—2441no—
411C42—2441no—
412C42—2441no—
413C42—2441no—
414C16—21no—
415C16—21no—
416C16—1221no—
417C16—1221no—
418C23—2441no—
419C23D8×D6111yescharacteristic
420Q8—41no—
421Q8—41no—
422Q8—1222no—
423Q8—2441no—
424Q8—2441no—
425Q8—2441no—
426D4—1222no—
427D4—2444no—
428D4—2441no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—161no—
436C2×C4—611no—
437C2×C4—611no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—9761no—
441C2×C4—9761no—
442C2×C4—2444no—
443C2×C4—2441no—
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—4881no—
457C22—4881no—
458C22—2442no—
459C22C2×D8×D6111yescharacteristic
460C4—21no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—1221no—
466C4—1221no—
467C4—1221no—
468C4—1221no—
469C4—4881no—
470C4—4881no—
471C4—2442no—
472C4#1684027011yescharacteristic
473C4#1684056111yescharacteristic
474C2—41no—
475C2—4882no—
476C2#2145581611yescharacteristic
477C2#2145896111yescharacteristic
478C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2235C2
socleC22×C61C22×D8
prime radicalC2×#14519799C22
hypercenter#2235D61
hypocenterC61#33680
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
1. #21456471C2semidirect
3. #21448021C2semidirect
4. #21447986C2semidirect
5. #21447975C2semidirect
6. #21447868C2semidirect
7. #21447863C2semidirect
10. #21447689C2semidirect
11. #21447686C2semidirect
12. #21447675C2semidirect
13. #21447670C2semidirect
14. #21447623C2semidirect
15. C61×#2235C2semidirect
238. #2235D61semidirect
298. C61#33680semidirect

Maximal subgroups

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

subgroupindex
#214564712
#214546932
#214480212
#214479862
#214479752
#214478682
#214478632
#214477612
#214477572
#214476892
#214476862
#214476752
#214476702
#214476232
C61×#22352
#3368061