Finite Group Databasebeta

← #29836434

Subgroups — #29836434

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#21456475C211yesmaximal, characteristic, complemented
2#21456465C211yesmaximal, characteristic
3#21447985C211yesmaximal, characteristic, complemented
4#21447981C211yesmaximal, characteristic, complemented
5#21447977C211yesmaximal, characteristic, complemented
6#21447976C211yesmaximal, characteristic, complemented
7#21447935C211yesmaximal, characteristic, complemented
8#21447929C211yesmaximal, characteristic, complemented
9#21447918C211yesmaximal, characteristic, complemented
10#21447912C211yesmaximal, characteristic, complemented
11#21447861C211yesmaximal, characteristic, complemented
12#21447857C211yesmaximal, characteristic, complemented
13#21447857C211yesmaximal, characteristic, complemented
14#21447576C211yesmaximal, characteristic, complemented
15C61×#2208C211yesmaximal, characteristic, complemented
16#16840373—21no—
17#16840363—21no—
18C2×#14519720C2211yescharacteristic
19C2×#14519720C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22#16840164C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840137C2211yescharacteristic
25#16840130—21no—
26#16840125—21no—
27#16840017—21no—
28#16840014—21no—
29#16840000C2211yescharacteristic
30#16840000C2211yescharacteristic
31#16839999C2211yescharacteristic
32#16839995C2211yescharacteristic
33#16839872—21no—
34#16839869—21no—
35Q16×Dic61C2211yescharacteristic
36Q16×Dic61C2211yescharacteristic
37C4×D488C2211yescharacteristic
38#16839716C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43C4⋊#11758185C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839566C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839563C2211yescharacteristic
51#16839563C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C2×SD32×C61C2211yescharacteristic
54C61×#494C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×D488C2311yescharacteristic
60C2×#11758199—21no—
61C2×#11758189D411yescharacteristic
62C2×C8×D61C2311yescharacteristic
63#14519773—21no—
64#14519772—41no—
65#14519772—41no—
66#14519769—21no—
67#14519768—21no—
68#14519767—41no—
69#14519767—41no—
70#14519760—41no—
71#14519759—41no—
72#14519753—21no—
73#14519753—21no—
74#14519752—21no—
75#14519751—41no—
76#14519750—41no—
77#14519748—21no—
78Q8×Dic61—21no—
79Q8×Dic61—21no—
80C4×D244—21no—
81#14519734D411yescharacteristic
82#14519720—41no—
83#14519720—41no—
84#14519716—41no—
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87C16×D61—41no—
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519709—21no—
92#14519708—21no—
93#14519701—21no—
94#14519701—21no—
95#14519701—21no—
96#14519701—21no—
97#14519699—21no—
98#14519698—21no—
99#14519697—21no—
100#14519688D411yescharacteristic
101#14519687D411yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×Q16×C61—21no—
104C2×Q16×C61C2311yescharacteristic
105C2×Q16×C61C2311yescharacteristic
106C2×D8×C61C2311yescharacteristic
107C4⋊Q8×C61—21no—
108C4×D4×C61—21no—
109SD32×C61—41no—
110SD32×C61—41no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×D4×C61—21no—
119C22×C4×C61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×D244—21no—
124C2×D244—41no—
125C2×C4×D61—41no—
126C2×C4×D61C2×D411yescharacteristic
127Q16×C61—21no—
128Q16×C61—21no—
129Q16×C61—21no—
130Q16×C61—21no—
131Q16×C61—42no—
132D8×C61—21no—
133D8×C61—21no—
134C2×C8×C61C2×D411yescharacteristic
135C2×C8×C61C2411yescharacteristic
136C4⋊C4×C61—21no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C42×C61C2×D411yescharacteristic
141C22⋊Dic61—41no—
142#11758199—42no—
143#11758198—41no—
144#11758198—41no—
145#11758198—41no—
146#11758198—41no—
147#11758198D811yescharacteristic
148#11758198D811yescharacteristic
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61—21no—
152C4⋊Dic61—41no—
153C4⋊Dic61—41no—
154C4⋊Dic61—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196D811yescharacteristic
161#11758196D811yescharacteristic
162C4×Dic61—41no—
163C4×Dic61—41no—
164C4×Dic61C2×D411yescharacteristic
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167D488—21no—
168D488—21no—
169#11758189—41no—
170C8×D61—21no—
171C8×D61—21no—
172C16×C61—21no—
173C16×C61—21no—
174#11758185—21no—
175#11758185—21no—
176C23×C61—41no—
177C22×D61—41no—
178C22×D61C2×D811yescharacteristic
179Q8×C61—41no—
180Q8×C61—41no—
181Q8×C61—41no—
182Q8×C61—41no—
183D4×C61—41no—
184D4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—161no—
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C2×D811yescharacteristic
191C2×C4×C61C22×D411yescharacteristic
192C22⋊D61—161no—
193C22⋊D61—161no—
194C22⋊D61—161no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61C2×D811yescharacteristic
199C2×Dic61C2×D811yescharacteristic
200C2×Dic61C2×D811yescharacteristic
201D244—41no—
202D244—41no—
203D244—161no—
204C4×D61—21no—
205C4×D61—21no—
206C4×D61—161no—
207C8×C61—21no—
208C8×C61H(5,𝔽2)11yescharacteristic
209C8×C612−1+411yescharacteristic
210#92418—21no—
211#92418—21no—
212#33826—611nomaximal, Sylow
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61C22×D811yescharacteristic
217C2×D61—21no—
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61—81no—
228C4×C61#53711yescharacteristic
229C4×C61#57511yescharacteristic
230Dic61—21no—
231Dic61—21no—
232Dic61—21no—
233Dic61—81no—
234Dic61—81no—
235Dic61—81no—
236#3177—611no—
237#3176—611no—
238#2229—611no—
239#2229—611no—
240#2228—611no—
241#2228—611no—
242#2220—611no—
243#2220—611no—
244#2217—611no—
245#2217—611no—
246#2208—611no—
247#2208D6111yescharacteristic, complemented
248#2207—611no—
249#2207—611no—
250#2151—611no—
251C2×C61—161no—
252C2×C61#324511yescharacteristic
253C2×C61#341611yescharacteristic
254C2×C61#341611yescharacteristic
255D61—41no—
256D61—161no—
257#541—1221no—
258#540—1221no—
259C2×SD32—611no—
260C2×SD32—611no—
261C2×SD32C2×D6111yescharacteristic
262C2×SD32C2×D6111yescharacteristic
263C2×M32—611no—
264C22×C16—611no—
265#499—611no—
266#499—611no—
267#494C2×D6111yescharacteristic
268#493—611no—
269#491—1221no—
270#490—1221no—
271#470—1221no—
272#469—1221no—
273#467—611no—
274#467—611no—
275#466—611no—
276#466—611no—
277#442—1221no—
278#441—1221no—
279C4×Q16—611no—
280C4×Q16—611no—
281C4×D8—611no—
282C4×D8C2×D6111yescharacteristic
283#405—611no—
284#367—611no—
285#367—611no—
286#366—611no—
287#366—611no—
288C4⋊C16—611no—
289C4⋊C16—611no—
290C4⋊C16—611no—
291C4⋊C16C2×D6111yescharacteristic
292#358—611no—
293#358—611no—
294#358C2×D6111yescharacteristic
295#358C2×D6111yescharacteristic
296#357—611no—
297#357—611no—
298#357—611no—
299#357—611no—
300C61#3382611yescharacteristic, complemented, Sylow
301C2×Q16—21no—
302C2×Q16C22×D6111yescharacteristic
303C2×Q16C22×D6111yescharacteristic
304C2×D8—611no—
305C2×D8—1221no—
306C2×D8C22×D6111yescharacteristic
307C2×M16—611no—
308C22×C8—611no—
309C4⋊Q8—21no—
310#127—1221no—
311#126—2441no—
312#126—2441no—
313#125—1221no—
314#125—1221no—
315#125—2441no—
316#125—2441no—
317#123—2441no—
318#123—2441no—
319C22⋊Q8—1221no—
320C22⋊Q8—1221no—
321#121—1221no—
322#121—1221no—
323#121—2441no—
324#121—2441no—
325C4×Q8—1221no—
326C4×Q8—1221no—
327C4×D4—21no—
328C4×D4—1221no—
329#117—611no—
330SD32—41no—
331SD32—41no—
332SD32—2441no—
333SD32—2441no—
334M32—2441no—
335C2×C16—611no—
336C2×C16—611no—
337C2×C16—2441no—
338C2×C16C22×D6111yescharacteristic
339C2×C16C22×D6111yescharacteristic
340#107—611no—
341#107—611no—
342#107—611no—
343#107C22×D6111yescharacteristic
344#106—1221no—
345#106—1221no—
346#103—1221no—
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×C8C22×D6111yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×D4—21no—
361C2×D4—1221no—
362C2×D4—2441no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C22×C4—41no—
367C22×C4—611no—
368C22×C4—2441no—
369Q16—21no—
370Q16—21no—
371Q16—21no—
372Q16—21no—
373Q16—42no—
374D8—21no—
375D8—21no—
376D8—1221no—
377D8—1221no—
378D8—2442no—
379M16—2441no—
380C2×C8—611no—
381C2×C8—611no—
382C2×C8—1221no—
383C2×C8—1221no—
384C2×C8D4×D6111yescharacteristic
385C2×C8C23×D6111yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—611no—
390C4⋊C4—611no—
391C4⋊C4—1221no—
392C4⋊C4—1221no—
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—611no—
404C22⋊C4—611no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C42—611no—
411C42—2441no—
412C42—2441no—
413C42D4×D6111yescharacteristic
414C16—21no—
415C16—21no—
416C16—1221no—
417C16—1221no—
418C23—41no—
419C23—611no—
420C23—2441no—
421Q8—41no—
422Q8—41no—
423Q8—41no—
424Q8—41no—
425D4—41no—
426D4—41no—
427D4—9761no—
428D4—9761no—
429D4—9761no—
430D4—9761no—
431D4—2441no—
432D4—2441no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—161no—
437C2×C4—611no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—9761no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4D8×D6111yescharacteristic
447C2×C4D8×D6111yescharacteristic
448C2×C4C2×D4×D6111yescharacteristic
449C8—21no—
450C8—1221no—
451C8—1221no—
452C8#1451982211yescharacteristic
453C8#1451982411yescharacteristic
454C22—81no—
455C22—81no—
456C22—81no—
457C22—1221no—
458C22—1221no—
459C22—1221no—
460C22—4881no—
461C22—4881no—
462C22—4881no—
463C22C2×D8×D6111yescharacteristic
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—1221no—
470C4—1221no—
471C4—1221no—
472C4—4881no—
473C4—4881no—
474C4—4881no—
475C4#1684034111yescharacteristic
476C4#1684055811yescharacteristic
477C2—161no—
478C2—9761no—
479C2—2441no—
480C2#2145712711yescharacteristic
481C2#2145896111yescharacteristic
482C2#2145896411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2208C2
socleC22×C61C22×D8
prime radical#21456465C2
hypercenter#2208D61
hypocenterC61#33826
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
1. #21456475C2semidirect
3. #21447985C2semidirect
4. #21447981C2semidirect
5. #21447977C2semidirect
6. #21447976C2semidirect
7. #21447935C2semidirect
8. #21447929C2semidirect
9. #21447918C2semidirect
10. #21447912C2semidirect
11. #21447861C2semidirect
12. #21447857C2semidirect
13. #21447857C2semidirect
14. #21447576C2semidirect
15. C61×#2208C2semidirect
247. #2208D61semidirect
300. C61#33826semidirect

Maximal subgroups

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

subgroupindex
#214564752
#214564652
#214479852
#214479812
#214479772
#214479762
#214479352
#214479292
#214479182
#214479122
#214478612
#214478572
#214475762
C61×#22082
#3382661