Finite Group Databasebeta

← #29835145

Subgroups — #29835145

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#21454696C211yesmaximal, characteristic
2#21448019C211yesmaximal, characteristic, complemented
3#21448014C211yesmaximal, characteristic, complemented
4#21447980C211yesmaximal, characteristic, complemented
5#21447973C211yesmaximal, characteristic, complemented
6#21447866C211yesmaximal, characteristic, complemented
7#21447861C211yesmaximal, characteristic, complemented
8#21447757C211yesmaximal, characteristic
9#21447757C211yesmaximal, characteristic
10#21447688C211yesmaximal, characteristic, complemented
11#21447681C211yesmaximal, characteristic, complemented
12C4×#14519723C211yesmaximal, characteristic, complemented
13C4×#14519720C211yesmaximal, characteristic, complemented
14#21447626C211yesmaximal, characteristic, complemented
15C61×#3177C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17#16840242—21no—
18C2×#14519723C2211yescharacteristic
19C2×#14519723C2211yescharacteristic
20C2×#14519720C2211yescharacteristic
21C2×#14519720C2211yescharacteristic
22#16839864—21no—
23#16839864—21no—
24C4×Dic244C2211yescharacteristic
25C4×Dic244C2211yescharacteristic
26C4×D488C2211yescharacteristic
27C4×D488C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29#16839764—21no—
30#16839589C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839587C2211yescharacteristic
33#16839587C2211yescharacteristic
34C4⋊#11758185C2211yescharacteristic
35C4⋊#11758185C2211yescharacteristic
36#16839566C2211yescharacteristic
37#16839566C2211yescharacteristic
38#16839566C2211yescharacteristic
39#16839566C2211yescharacteristic
40#16839565C2211yescharacteristic
41#16839565C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44C22⋊#11758185C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46#16839538C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C61×#541—21no—
49C61×#499C2211yescharacteristic
50C61×#494C2211yescharacteristic
51C61×#491—21no—
52C61×#470—21no—
53C61×#467C2211yescharacteristic
54C61×#467C2211yescharacteristic
55C61×#441—21no—
56C4×Q16×C61C2211yescharacteristic
57C4×Q16×C61C2211yescharacteristic
58C61×#405C2211yescharacteristic
59C2×#11758222—21no—
60#14519799—22no—
61#14519799—22no—
62C2×Dic244C2311yescharacteristic
63C2×#11758190—21no—
64C2×D488C2311yescharacteristic
65C4×Dic122—21no—
66C4×Dic122—21no—
67C4×D244—21no—
68C4×D244—21no—
69#14519737—41no—
70#14519737—41no—
71#14519735—41no—
72C2×C4⋊Dic61—21no—
73C4⋊C4×D61—41no—
74#14519723—22no—
75#14519723—22no—
76#14519720—22no—
77#14519720—22no—
78C2×#11758185C2311yescharacteristic
79C2×#11758185C2311yescharacteristic
80C2×#11758185C2311yescharacteristic
81C2×#11758185C2311yescharacteristic
82#14519711—21no—
83#14519711C2311yescharacteristic
84#14519711C2311yescharacteristic
85#14519702—21no—
86#14519702—21no—
87#14519699—21no—
88#14519699—21no—
89C2×Q16×C61—21no—
90C2×Q16×C61C2311yescharacteristic
91C2×Q16×C61C2311yescharacteristic
92C2×M16×C61D411yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C4⋊Q8×C61—21no—
95#126×C61—41no—
96#126×C61—41no—
97#125×C61—21no—
98#125×C61—41no—
99#125×C61—41no—
100C22⋊Q8×C61—21no—
101C22⋊Q8×C61—21no—
102C4×Q8×C61—21no—
103C4×Q8×C61—21no—
104#117×C61D411yescharacteristic
105#107×C61C2311yescharacteristic
106#107×C61C2311yescharacteristic
107#106×C61—21no—
108#103×C61—21no—
109#103×C61—21no—
110#103×C61—21no—
111#103×C61—21no—
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C22×C4×C61C2×D411yescharacteristic
119C2×C22⋊D61—41no—
120C22×Dic61—41no—
121#11758222—24no—
122#11758222—42no—
123C2×D244—21no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×Dic122—21no—
128Q16×C61—21no—
129Q16×C61—21no—
130Q16×C61—21no—
131Q16×C61—21no—
132Q16×C61—42no—
133M16×C61—41no—
134C2×C8×C61—21no—
135C2×C8×C61—21no—
136C2×C8×C61C2×D411yescharacteristic
137C2×C8×C61C2×D411yescharacteristic
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2411yescharacteristic
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—41no—
143C4⋊C4×C61—41no—
144C4⋊C4×C61—41no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61—41no—
147C4⋊C4×C61—41no—
148C4⋊C4×C61—41no—
149C4⋊C4×C61—41no—
150C4⋊C4×C61D811yescharacteristic
151C4⋊C4×C61D811yescharacteristic
152C22⋊C4×C61—41no—
153C22⋊C4×C61—41no—
154C22⋊C4×C61D811yescharacteristic
155C22⋊C4×C61D811yescharacteristic
156C42×C61—41no—
157C42×C61—41no—
158C42×C61C2×D411yescharacteristic
159C42×C61C2×D411yescharacteristic
160#11758198—41no—
161#11758198—41no—
162C4⋊Dic61—21no—
163C4⋊Dic61—21no—
164C4⋊Dic61—41no—
165#11758196—41no—
166#11758196—41no—
167C4×Dic61—41no—
168C4×Dic61—41no—
169Dic244—21no—
170Dic244#4112yes—
171D488—21no—
172D488#4112yes—
173#11758190—24no—
174#11758185—21no—
175#11758185—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61C2×D811yescharacteristic
179C22×D61—41no—
180Q8×C61—41no—
181Q8×C61—41no—
182Q8×C61—41no—
183Q8×C61—41no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61C2×D811yescharacteristic
191C2×C4×C61C2×D811yescharacteristic
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C22⋊D61—44no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—161no—
201D244—22no—
202D244—41no—
203C4×D61—44no—
204C4×D61—161no—
205C4×D61—161no—
206Dic122—22no—
207Dic122—41no—
208C8×C61—21no—
209C8×C61—21no—
210C8×C61—21no—
211C8×C61C2×#4111yescharacteristic
212C8×C61C2×#4111yescharacteristic
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—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—81no—
227C4×C61—81no—
228C4×C61—81no—
229C4×C61—81no—
230C4×C61#52511yescharacteristic
231C4×C61#57511yescharacteristic
232Dic61—42no—
233Dic61—81no—
234Dic61—81no—
235#3177D6111yescharacteristic, complemented
236#2951—611no—
237#2236—611no—
238#2235—611no—
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—21no—
257#520—1221no—
258C2×Q32—611no—
259C2×Q32—611no—
260C2×SD32—611no—
261C2×SD32—611no—
262#499C2×D6111yescharacteristic
263#494C2×D6111yescharacteristic
264#491—21no—
265#470—21no—
266#467C2×D6111yescharacteristic
267#467C2×D6111yescharacteristic
268#441—21no—
269#440—1221no—
270#440—1221no—
271C4×Q16—611no—
272C4×Q16—611no—
273C4×Q16C2×D6111yescharacteristic
274C4×Q16C2×D6111yescharacteristic
275C4×D8—611no—
276C4×D8—611no—
277C2×#107—611no—
278#417—1221no—
279#405C2×D6111yescharacteristic
280#367—611no—
281#367—611no—
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#358—611no—
291#358—611no—
292#357—611no—
293#357—611no—
294C22⋊C16—611no—
295C22⋊C16—611no—
296#346—611no—
297C4×C16—611no—
298C61#3368011yescharacteristic, complemented, Sylow
299C2×#41—1221no—
300#135—1222no—
301#135—1222no—
302C2×Q16—21no—
303C2×Q16—611no—
304C2×Q16C22×D6111yescharacteristic
305C2×Q16C22×D6111yescharacteristic
306C2×SD16—1221no—
307C2×D8—611no—
308C2×M16C22⋊D6111yescharacteristic
309C22×C8C22×D6111yescharacteristic
310C4⋊Q8—21no—
311#126—41no—
312#126—41no—
313#125—21no—
314#125—41no—
315#125—41no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—1221no—
321C4×Q8—1221no—
322C4×D4—1221no—
323C4×D4—1221no—
324C4×D4—2441no—
325C4×D4—2441no—
326#117—2441no—
327#117C22⋊D6111yescharacteristic
328C2×C4⋊C4—1221no—
329C2×C4⋊C4—2441no—
330Q32—1222no—
331Q32—1222no—
332SD32—1222no—
333SD32—1222no—
334C2×C16—611no—
335C2×C16—611no—
336C2×C16—611no—
337C2×C16—611no—
338#107—611no—
339#107—611no—
340#107—1221no—
341#107C22×D6111yescharacteristic
342#107C22×D6111yescharacteristic
343#106—21no—
344#103—21no—
345#103—21no—
346#103—21no—
347#103—21no—
348#103—1221no—
349#103—1221no—
350#102—1221no—
351#102—1221no—
352#97C22⋊D6111yescharacteristic
353#97C22⋊D6111yescharacteristic
354C4×C8C22×D6111yescharacteristic
355C4×C8C22×D6111yescharacteristic
356#41—1224no—
357#41—2442no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—1221no—
361C2×D4—1221no—
362C2×D4—2441no—
363C22×C4—2441no—
364C22×C4—2441no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4C2×C22⋊D6111yescharacteristic
368Q16—21no—
369Q16—21no—
370Q16—21no—
371Q16—21no—
372Q16—42no—
373Q16—612no—
374Q16—1221no—
375SD16—1224no—
376D8—612no—
377D8—1221no—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D6111yescharacteristic
382C2×C8C2×C22⋊D6111yescharacteristic
383C2×C8C2×C22⋊D6111yescharacteristic
384C2×C8C23×D6111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—1221no—
396C4⋊C4—1221no—
397C4⋊C4—2441no—
398C4⋊C4—2441no—
399C4⋊C4—2441no—
400C4⋊C4#1175819911yescharacteristic
401C4⋊C4#1175819911yescharacteristic
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—2441no—
405C22⋊C4—2441no—
406C22⋊C4#1175819911yescharacteristic
407C22⋊C4#1175819911yescharacteristic
408C42—41no—
409C42—41no—
410C42—2441no—
411C42—2441no—
412C42C2×C22⋊D6111yescharacteristic
413C42C2×C22⋊D6111yescharacteristic
414C16—1221no—
415C16—1221no—
416C16—1221no—
417C16—1221no—
418C23—2441no—
419C23C2×#1175819911yescharacteristic
420Q8—41no—
421Q8—41no—
422Q8—41no—
423Q8—41no—
424Q8—1222no—
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—9761no—
436C2×C4—9761no—
437C2×C4—9761no—
438C2×C4—2444no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4C2×#1175819911yescharacteristic
443C2×C4C2×#1175819911yescharacteristic
444C2×C4C2×#1175819911yescharacteristic
445C2×C4C2×#1175819911yescharacteristic
446C2×C4C2×#1175819911yescharacteristic
447C2×C4C22×C22⋊D6111yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8#41×D6111yescharacteristic
452C8#41×D6111yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—4881no—
457C22—4881no—
458C22—2442no—
459C22C22×#1175819911yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—4881no—
470C4—4881no—
471C4—2442no—
472C4#1684026911yescharacteristic
473C4#1684056011yescharacteristic
474C2—41no—
475C2—4882no—
476C2#2145581511yescharacteristic
477C2#2145896311yescharacteristic
478C2#2145897011yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3177C2
socleC22×C61C22×D8
prime radicalC2×#14519799C22
hypercenter#3177D61
hypocenterC61#33680
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3177

Complements

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

NH ≅ G/Ntype
2. #21448019C2semidirect
3. #21448014C2semidirect
4. #21447980C2semidirect
5. #21447973C2semidirect
6. #21447866C2semidirect
7. #21447861C2semidirect
10. #21447688C2semidirect
11. #21447681C2semidirect
12. C4×#14519723C2semidirect
13. C4×#14519720C2semidirect
14. #21447626C2semidirect
15. C61×#3177C2semidirect
235. #3177D61semidirect
298. C61#33680semidirect

Maximal subgroups

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

subgroupindex
#214546962
#214480192
#214480142
#214479802
#214479732
#214478662
#214478612
#214477572
#214476882
#214476812
C4×#145197232
C4×#145197202
#214476262
C61×#31772
#3368061