Finite Group Databasebeta

← #29836433

Subgroups — #29836433

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#21456471C211yesmaximal, characteristic, complemented
2#21456462C211yesmaximal, characteristic
3#21447985C211yesmaximal, characteristic, complemented
4#21447982C211yesmaximal, characteristic, complemented
5#21447979C211yesmaximal, characteristic, complemented
6#21447974C211yesmaximal, characteristic, complemented
7#21447932C211yesmaximal, characteristic, complemented
8#21447917C211yesmaximal, characteristic, complemented
9#21447913C211yesmaximal, characteristic, complemented
10#21447863C211yesmaximal, characteristic, complemented
11#21447862C211yesmaximal, characteristic, complemented
12#21447858C211yesmaximal, characteristic, complemented
13#21447857C211yesmaximal, characteristic, complemented
14#21447579C211yesmaximal, characteristic, complemented
15C61×#2220C211yesmaximal, characteristic, complemented
16#16840372—21no—
17#16840365—21no—
18C2×#14519722C2211yescharacteristic
19C2×#14519721C2211yescharacteristic
20C2×#14519720C2211yescharacteristic
21C22×#11758185C2211yescharacteristic
22#16840163C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840140C2211yescharacteristic
25#16840137C2211yescharacteristic
26#16840129—21no—
27#16840125—21no—
28#16840018—21no—
29#16840013—21no—
30#16840003C2211yescharacteristic
31#16839998C2211yescharacteristic
32#16839871—21no—
33#16839866—21no—
34Q16×Dic61C2211yescharacteristic
35#16839856C2211yescharacteristic
36D8×Dic61C2211yescharacteristic
37#16839844C2211yescharacteristic
38#16839717C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839580C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839566C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839563C2211yescharacteristic
51#16839562C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C2×M32×C61C2211yescharacteristic
54C61×#467C2211yescharacteristic
55C61×#466C2211yescharacteristic
56C61×#366C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758202—21no—
61C2×D488C2311yescharacteristic
62C2×#11758199—21no—
63C2×#11758194D411yescharacteristic
64#14519775—21no—
65#14519773—21no—
66#14519770—41no—
67#14519770—41no—
68#14519768—21no—
69#14519768—21no—
70#14519768—41no—
71#14519767—41no—
72#14519761—41no—
73#14519759—41no—
74#14519756—21no—
75#14519751—21no—
76#14519749—41no—
77#14519748—41no—
78Q8×Dic61—21no—
79#14519742—21no—
80D4×Dic61—21no—
81#14519739—21no—
82#14519736D411yescharacteristic
83#14519722—41no—
84#14519721—41no—
85#14519720—41no—
86C2×#11758185—41no—
87C2×#11758185C2311yescharacteristic
88C2×#11758185C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519708—21no—
92#14519708—21no—
93#14519702—21no—
94#14519701—21no—
95#14519700—21no—
96#14519699—21no—
97#14519698—21no—
98#14519697—21no—
99#14519687D411yescharacteristic
100#14519687D411yescharacteristic
101C8×Dic61C2311yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×Q16×C61C2311yescharacteristic
104C2×D8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22⋊Q8×C61—21no—
107#121×C61—21no—
108SD32×C61—41no—
109M32×C61—41no—
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#103×C61—21no—
115#102×C61—21no—
116C2×Q8×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—41no—
119C22×C4×C61C2×D411yescharacteristic
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C22×Dic61—41no—
124C2×D244—21no—
125C2×C4×D61—41no—
126C2×Dic122—21no—
127Q16×C61—21no—
128Q16×C61—21no—
129D8×C61—21no—
130D8×C61—21no—
131C2×C8×C61—21no—
132C2×C8×C61—21no—
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2411yescharacteristic
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊Dic61—41no—
141C22⋊Dic61—41no—
142C22⋊Dic61D811yescharacteristic
143C22⋊Dic61D811yescharacteristic
144#11758202—42no—
145#11758199—42no—
146#11758198—41no—
147#11758198—41no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—41no—
151C4⋊Dic61—41no—
152C4⋊Dic61—41no—
153C4⋊Dic61D811yescharacteristic
154C4⋊Dic61D811yescharacteristic
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61—41no—
162C4×Dic61—41no—
163C4×Dic61C2×D411yescharacteristic
164C4×Dic61C2×D411yescharacteristic
165#11758194—41no—
166C2×#92418C2×D411yescharacteristic
167C2×#92418C2×D411yescharacteristic
168Dic244—21no—
169Dic244—21no—
170D488—21no—
171D488—21no—
172C16×C61—21no—
173C16×C61—21no—
174#11758185—21no—
175#11758185—21no—
176C23×C61—41no—
177C23×C61C2×D811yescharacteristic
178C22×D61—41no—
179Q8×C61—41no—
180Q8×C61—41no—
181D4×C61—41no—
182D4×C61—41no—
183D4×C61—161no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C22⋊D61—161no—
192C22⋊D61—161no—
193C22⋊D61—161no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—161no—
198C2×Dic61C2×D811yescharacteristic
199C2×Dic61C2×D811yescharacteristic
200C2×Dic61C2×D811yescharacteristic
201C2×Dic61C2×D811yescharacteristic
202D244—41no—
203D244—41no—
204C4×D61—161no—
205Dic122—41no—
206Dic122—41no—
207C8×C61—21no—
208C8×C61H(5,𝔽2)11yescharacteristic
209C8×C612−1+411yescharacteristic
210#92418—21no—
211#92418—21no—
212#33826—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61C22×D811yescharacteristic
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—21no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61#53711yescharacteristic
228C4×C61#57511yescharacteristic
229Dic61—21no—
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#2220D6111yescharacteristic, complemented
244#2217—611no—
245#2217—611no—
246#2208—611no—
247#2208—611no—
248#2207—611no—
249#2207—611no—
250#2151—611no—
251C2×C61—41no—
252C2×C61—161no—
253C2×C61#324511yescharacteristic
254C2×C61#341611yescharacteristic
255C2×C61#341611yescharacteristic
256D61—161no—
257#541—1221no—
258#540—1221no—
259C2×SD32—611no—
260C2×SD32—611no—
261C2×SD32—611no—
262C2×SD32C2×D6111yescharacteristic
263C2×M32C2×D6111yescharacteristic
264C22×C16—611no—
265#499—611no—
266#499—611no—
267#494—611no—
268#493—611no—
269#491—1221no—
270#490—1221no—
271#470—1221no—
272#469—1221no—
273#467—611no—
274#467C2×D6111yescharacteristic
275#466—611no—
276#466C2×D6111yescharacteristic
277#442—1221no—
278#441—1221no—
279C4×Q16—611no—
280C4×Q16—611no—
281C4×D8—611no—
282C4×D8—611no—
283#405—611no—
284#367—611no—
285#367—611no—
286#366—611no—
287#366C2×D6111yescharacteristic
288C4⋊C16—611no—
289C4⋊C16—611no—
290C4⋊C16—611no—
291C4⋊C16—611no—
292#358—611no—
293#358—611no—
294#358—611no—
295#358C2×D6111yescharacteristic
296#357—611no—
297#357—611no—
298#357—611no—
299#357C2×D6111yescharacteristic
300C61#3382611yescharacteristic, complemented, Sylow
301C2×Q16—611no—
302C2×Q16—1221no—
303C2×Q16C22×D6111yescharacteristic
304C2×D8—611no—
305C2×D8—1221no—
306C2×D8C22×D6111yescharacteristic
307C2×M16—611no—
308C22×C8C22×D6111yescharacteristic
309C4⋊Q8—1221no—
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—21no—
320C22⋊Q8—1221no—
321#121—21no—
322#121—1221no—
323#121—2441no—
324#121—2441no—
325C4×Q8—1221no—
326C4×Q8—1221no—
327C4×D4—1221no—
328C4×D4—1221no—
329#117—611no—
330SD32—41no—
331SD32—2441no—
332SD32—2441no—
333SD32—2441no—
334M32—41no—
335C2×C16—611no—
336C2×C16—611no—
337C2×C16—2441no—
338C2×C16C22×D6111yescharacteristic
339C2×C16C22×D6111yescharacteristic
340#107—611no—
341#107—611no—
342#107C22×D6111yescharacteristic
343#107C22×D6111yescharacteristic
344#106—1221no—
345#106—1221no—
346#103—21no—
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×C8—611no—
358C2×Q8—21no—
359C2×Q8—1221no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—1221no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C22×C4—2441no—
367C22×C4—2441no—
368C22×C4D4×D6111yescharacteristic
369Q16—21no—
370Q16—21no—
371Q16—1221no—
372Q16—1221no—
373Q16—2442no—
374D8—21no—
375D8—21no—
376D8—1221no—
377D8—1221no—
378D8—2442no—
379M16—2441no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—611no—
383C2×C8—611no—
384C2×C8D4×D6111yescharacteristic
385C2×C8C23×D6111yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—611no—
390C4⋊C4—611no—
391C4⋊C4—1221no—
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—41no—
404C22⋊C4—611no—
405C22⋊C4—611no—
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C42—611no—
411C42—611no—
412C42—2441no—
413C42—2441no—
414C16—21no—
415C16—21no—
416C16—1221no—
417C16—1221no—
418C23—41no—
419C23—2441no—
420C23D8×D6111yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—2441no—
424Q8—2441no—
425D4—41no—
426D4—41no—
427D4—161no—
428D4—9761no—
429D4—9761no—
430D4—9761no—
431D4—2441no—
432D4—2441no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—611no—
441C2×C4—611no—
442C2×C4—9761no—
443C2×C4—9761no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4D8×D6111yescharacteristic
448C2×C4C2×D4×D6111yescharacteristic
449C8—21no—
450C8—1221no—
451C8—1221no—
452C8#1451982211yescharacteristic
453C8#1451982411yescharacteristic
454C22—21no—
455C22—21no—
456C22—21no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—4881no—
461C22—4881no—
462C22—4881no—
463C22C2×D8×D6111yescharacteristic
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—1221no—
469C4—1221no—
470C4—1221no—
471C4—1221no—
472C4—4881no—
473C4—4881no—
474C4—4881no—
475C4#1684033911yescharacteristic
476C4#1684055911yescharacteristic
477C2—41no—
478C2—161no—
479C2—9761no—
480C2#2145712511yescharacteristic
481C2#2145896411yescharacteristic
482C2#2145896511yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2220C2
socleC22×C61C22×D8
prime radical#21456462C2
hypercenter#2220D61
hypocenterC61#33826
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
1. #21456471C2semidirect
3. #21447985C2semidirect
4. #21447982C2semidirect
5. #21447979C2semidirect
6. #21447974C2semidirect
7. #21447932C2semidirect
8. #21447917C2semidirect
9. #21447913C2semidirect
10. #21447863C2semidirect
11. #21447862C2semidirect
12. #21447858C2semidirect
13. #21447857C2semidirect
14. #21447579C2semidirect
15. C61×#2220C2semidirect
243. #2220D61semidirect
300. C61#33826semidirect

Maximal subgroups

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

subgroupindex
#214564712
#214564622
#214479852
#214479822
#214479792
#214479742
#214479322
#214479172
#214479132
#214478632
#214478622
#214478582
#214478572
#214475792
C61×#22202
#3382661