Finite Group Databasebeta

← #29836390

Subgroups — #29836390

Order 15616.

496 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#21456392C211yesmaximal, characteristic, complemented
2#21456386C211yesmaximal, characteristic, complemented
3#21447985C211yesmaximal, characteristic, complemented
4#21447983C211yesmaximal, characteristic, complemented
5#21447978C211yesmaximal, characteristic, complemented
6#21447977C211yesmaximal, characteristic, complemented
7#21447935C211yesmaximal, characteristic, complemented
8#21447929C211yesmaximal, characteristic, complemented
9#21447924C211yesmaximal, characteristic, complemented
10#21447921C211yesmaximal, characteristic
11#21447883C211yesmaximal, characteristic, complemented
12#21447876C211yesmaximal, characteristic, complemented
13#21447871C211yesmaximal, characteristic, complemented
14#21447573C211yesmaximal, characteristic, complemented
15C61×#2211C211yesmaximal, characteristic, complemented
16#16840299—21no—
17#16840291—21no—
18C2×#14519720C2211yescharacteristic
19C2×#14519718C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21C2×#14519716C2211yescharacteristic
22#16840164C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840147C2211yescharacteristic
25#16840118—21no—
26#16840116—21no—
27#16840000C2211yescharacteristic
28#16840000C2211yescharacteristic
29#16839999C2211yescharacteristic
30#16839995C2211yescharacteristic
31#16839994—21no—
32#16839988—21no—
33Q16×Dic61C2211yescharacteristic
34SD16×Dic61—21no—
35C4×#11758201—21no—
36C4×D488C2211yescharacteristic
37D8×Dic61C2211yescharacteristic
38C4×C8×D61C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43C4⋊#11758185C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839566C2211yescharacteristic
48#16839566C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839564C2211yescharacteristic
51#16839563C2211yescharacteristic
52C2×Q32×C61C2211yescharacteristic
53C2×SD32×C61C2211yescharacteristic
54C61×#495C2211yescharacteristic
55C4×Q16×C61C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758201—21no—
60C2×D488C2311yescharacteristic
61C2×C8×D61D411yescharacteristic
62C2×C8×D61C2311yescharacteristic
63#14519772—41no—
64#14519770—41no—
65#14519769—21no—
66#14519768—21no—
67#14519766—21no—
68#14519762—41no—
69#14519759—41no—
70#14519753—21no—
71#14519753—21no—
72#14519752—21no—
73#14519748—21no—
74Q8×Dic61—21no—
75C4×D244—21no—
76C4×D244—41no—
77D4×Dic61—21no—
78#14519737—41no—
79#14519734—41no—
80#14519733—41no—
81C42×D61D411yescharacteristic
82#14519720—41no—
83#14519718—41no—
84#14519716—41no—
85#14519716—41no—
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519709—21no—
92#14519708—21no—
93#14519701—21no—
94#14519701—21no—
95#14519701—21no—
96#14519699—21no—
97#14519698—21no—
98#14519698—21no—
99#14519697—21no—
100C4×#92418D411yescharacteristic
101C8×Dic61D411yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×Q16×C61C2311yescharacteristic
104C2×Q16×C61C2311yescharacteristic
105C2×SD16×C61—21no—
106C2×D8×C61C2311yescharacteristic
107#124×C61—21no—
108C4×Q8×C61—21no—
109Q32×C61—41no—
110SD32×C61—41no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#103×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×D4×C61—21no—
119C2×C22⋊D61—41no—
120C22×Dic61—41no—
121C2×D244—21no—
122C2×D244—41no—
123C2×C4×D61—41no—
124C2×C4×D61D811yescharacteristic
125C2×C4×D61D811yescharacteristic
126C2×C4×D61C2×D411yescharacteristic
127Q16×C61—21no—
128Q16×C61—21no—
129Q16×C61—21no—
130Q16×C61—21no—
131SD16×C61—42no—
132D8×C61—21no—
133D8×C61—21no—
134C2×C8×C61C2×D411yescharacteristic
135C2×C8×C61C2411yescharacteristic
136C4⋊C4×C61—21no—
137C4⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C42×C61—41no—
141C42×C61C2×D411yescharacteristic
142C22⋊Dic61—41no—
143C22⋊Dic61—41no—
144#11758201—42no—
145#11758198—41no—
146#11758198—41no—
147#11758198—41no—
148#11758198—41no—
149#11758198—41no—
150#11758198—41no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—41no—
155C4⋊Dic61—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61—41no—
162C4×Dic61D811yescharacteristic
163C4×Dic61D811yescharacteristic
164C4×Dic61C2×D411yescharacteristic
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167D488—21no—
168D488—21no—
169C8×D61—21no—
170C8×D61—21no—
171C8×D61—41no—
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×C61C2×D811yescharacteristic
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C22⋊D61—82no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—82no—
196C2×Dic61C2×D811yescharacteristic
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199D244—41no—
200D244—41no—
201D244—82no—
202C4×D61—21no—
203C4×D61—21no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61—82no—
207C8×C61—21no—
208C8×C61H(5,𝔽2)11yescharacteristic
209C8×C612−1+411yescharacteristic
210#92418—21no—
211#92418—21no—
212#33822—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#3168—611no—
237#3168—611no—
238#2229—611no—
239#2229—611no—
240#2228—611no—
241#2228—611no—
242#2220—611no—
243#2220—611no—
244#2219—611no—
245#2218—611no—
246#2211—611no—
247#2211D6111yescharacteristic, complemented
248#2210—611no—
249#2210—611no—
250#2150—611no—
251C2×C61—161no—
252C2×C61#324511yescharacteristic
253C2×C61#341411yescharacteristic
254C2×C61#341411yescharacteristic
255D61—41no—
256D61—161no—
257#529—1221no—
258#529—1221no—
259C2×Q32C2×D6111yescharacteristic
260C2×SD32—611no—
261C2×SD32C2×D6111yescharacteristic
262C2×D16—611no—
263C2×M32—611no—
264C2×M32—611no—
265#499—611no—
266#499—611no—
267#495—611no—
268#495C2×D6111yescharacteristic
269#488—1221no—
270#488—1221no—
271#467—611no—
272#467—611no—
273#466—611no—
274#466—611no—
275#465—1221no—
276#465—1221no—
277C4×Q16—611no—
278C4×Q16C2×D6111yescharacteristic
279C4×SD16—1221no—
280C4×SD16—1221no—
281C4×D8—611no—
282C4×D8—611no—
283C2×C4×C8—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#358—611no—
295#358C2×D6111yescharacteristic
296#357—611no—
297#357—611no—
298#357—611no—
299#357C2×D6111yescharacteristic
300C61#3382211yescharacteristic, complemented, Sylow
301C2×Q16C22×D6111yescharacteristic
302C2×Q16C22×D6111yescharacteristic
303C2×SD16—21no—
304C2×SD16—1221no—
305C2×D8—611no—
306C2×D8C22×D6111yescharacteristic
307C22×C8—611no—
308C22×C8—611no—
309#126—2441no—
310#126—2441no—
311#125—1221no—
312#125—1221no—
313#124—21no—
314#124—1221no—
315#123—2441no—
316#123—2441no—
317C22⋊Q8—1221no—
318C22⋊Q8—1221no—
319#121—1221no—
320#121—1221no—
321C4×Q8—21no—
322C4×Q8—1221no—
323C4×D4—1221no—
324C4×D4—1221no—
325C4×D4—2441no—
326C4×D4—2441no—
327#117—2441no—
328#117—2441no—
329C2×C42—611no—
330Q32—41no—
331SD32—41no—
332SD32—2441no—
333D16—2441no—
334M32—2441no—
335M32—2441no—
336C2×C16—611no—
337C2×C16—611no—
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—21no—
347#103—1221no—
348#103—1221no—
349#103—1221no—
350#102—1221no—
351#102—1221no—
352#102—1221no—
353#102—1221no—
354C4×C8—611no—
355C4×C8—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—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—2441no—
368C22×C4—2441no—
369Q16—21no—
370Q16—21no—
371Q16—21no—
372Q16—21no—
373SD16—42no—
374SD16—2442no—
375D8—21no—
376D8—21no—
377D8—1221no—
378D8—1221no—
379C2×C8—611no—
380C2×C8—611no—
381C2×C8—1221no—
382C2×C8—1221no—
383C2×C8—2441no—
384C2×C8D4×D6111yescharacteristic
385C2×C8C23×D6111yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—1221no—
389C4⋊C4—1221no—
390C4⋊C4—1221no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C22⋊C4—2441no—
404C22⋊C4—2441no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C42—41no—
409C42—611no—
410C42—611no—
411C42—611no—
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—4882no—
428D4—4882no—
429D4—2441no—
430D4—2441no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—611no—
435C2×C4—611no—
436C2×C4—611no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—4882no—
440C2×C4—4882no—
441C2×C4—2441no—
442C2×C4—2441no—
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#2145895211yescharacteristic
482C2#2145895411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2211C2
socleC22×C61C22×D8
prime radical#21447921C2
hypercenter#2211D61
hypocenterC61#33822
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2211

Complements

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

NH ≅ G/Ntype
1. #21456392C2semidirect
2. #21456386C2semidirect
3. #21447985C2semidirect
4. #21447983C2semidirect
5. #21447978C2semidirect
6. #21447977C2semidirect
7. #21447935C2semidirect
8. #21447929C2semidirect
9. #21447924C2semidirect
11. #21447883C2semidirect
12. #21447876C2semidirect
13. #21447871C2semidirect
14. #21447573C2semidirect
15. C61×#2211C2semidirect
247. #2211D61semidirect
300. C61#33822semidirect

Maximal subgroups

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

subgroupindex
#214563922
#214563862
#214479852
#214479832
#214479782
#214479772
#214479352
#214479292
#214479242
#214479212
#214478832
#214478762
#214478712
#214475732
C61×#22112
#3382261