Finite Group Databasebeta

← #29835201

Subgroups — #29835201

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456458C211yesmaximal, characteristic, complemented
2#21454696C211yesmaximal, characteristic, complemented
3#21448022C211yesmaximal, characteristic, complemented
4#21448000C211yesmaximal, characteristic, complemented
5#21447972C211yesmaximal, characteristic, complemented
6#21447957C211yesmaximal, characteristic, complemented
7#21447882C211yesmaximal, characteristic, complemented
8#21447875C211yesmaximal, characteristic, complemented
9#21447761C211yesmaximal, characteristic, complemented
10#21447744C211yesmaximal, characteristic
11#21447685C211yesmaximal, characteristic, complemented
12#21447685C211yesmaximal, characteristic, complemented
13C4×Dic488C211yesmaximal, characteristic, complemented
14C4×D976C211yesmaximal, characteristic, complemented
15C61×#2164C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17#16840383—21no—
18#16840242—21no—
19C2×Dic488C2211yescharacteristic
20C2×#14519722C2211yescharacteristic
21C2×#14519722C2211yescharacteristic
22C2×D976C2211yescharacteristic
23#16840167C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840122—21no—
26#16840008—21no—
27#16840003C2211yescharacteristic
28#16839998C2211yescharacteristic
29#16839864—21no—
30#16839864—21no—
31#16839864—21no—
32C4×Dic244C2211yescharacteristic
33C4×Dic244C2211yescharacteristic
34C4×Dic244C2211yescharacteristic
35C4×D488C2211yescharacteristic
36C4×D488C2211yescharacteristic
37C4×D488C2211yescharacteristic
38C2×#14519711C2211yescharacteristic
39#16839764—21no—
40#16839588C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839588C2211yescharacteristic
43#16839588C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839567C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839564C2211yescharacteristic
51#16839564C2211yescharacteristic
52C61×#405C2211yescharacteristic
53C61×C4⋊C16C2211yescharacteristic
54C61×C4⋊C16C2211yescharacteristic
55C61×C22⋊C16C2211yescharacteristic
56C61×C22⋊C16C2211yescharacteristic
57C61×#346C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×#11758222—21no—
60#14519799—22no—
61#14519799—22no—
62C2×Dic244C2311yescharacteristic
63C2×Dic244C2311yescharacteristic
64C2×#11758190—21no—
65C2×#11758190—21no—
66C2×D488C2311yescharacteristic
67C2×D488C2311yescharacteristic
68#14519777—21no—
69#14519772—41no—
70#14519765—21no—
71#14519763—41no—
72#14519759—41no—
73#14519756—21no—
74#14519755—41no—
75#14519751—21no—
76C4×Dic122—21no—
77C4×Dic122—21no—
78C4×Dic122—21no—
79C4×D244—21no—
80C4×D244—21no—
81C4×D244—21no—
82#14519737—41no—
83#14519737—41no—
84#14519735—41no—
85C2×C4⋊Dic61—21no—
86C4⋊C4×D61—41no—
87Dic488—22no—
88#14519722—22no—
89#14519722—22no—
90D976—22no—
91#14519711—21no—
92#14519711—21no—
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519711C2311yescharacteristic
96#14519711C2311yescharacteristic
97#14519702—21no—
98#14519702—21no—
99#14519702—21no—
100#14519702—21no—
101#14519699—21no—
102#14519699—21no—
103#14519699—21no—
104#14519699—21no—
105C2×M16×C61D411yescharacteristic
106C22×C8×C61C2311yescharacteristic
107#117×C61D411yescharacteristic
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C22×Dic61—41no—
120#11758222—24no—
121#11758222—42no—
122C2×D244—21no—
123C2×D244—21no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×Dic122—21no—
129C2×Dic122—21no—
130C2×Dic122—41no—
131M16×C61—41no—
132C2×C8×C61—21no—
133C2×C8×C61—21no—
134C2×C8×C61C2×D411yescharacteristic
135C2×C8×C61C2×D411yescharacteristic
136C2×C8×C61C2×D411yescharacteristic
137C2×C8×C61C2411yescharacteristic
138C4⋊C4×C61D811yescharacteristic
139C4⋊C4×C61D811yescharacteristic
140C22⋊C4×C61D811yescharacteristic
141C22⋊C4×C61D811yescharacteristic
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C22⋊Dic61—41no—
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—21no—
155C4⋊Dic61—41no—
156C4⋊Dic61—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61—41no—
162C4×Dic61—41no—
163C4×Dic61—41no—
164Dic244—21no—
165Dic244—21no—
166Dic244—21no—
167Dic244#4112yes—
168D488—21no—
169D488—21no—
170D488—21no—
171D488#4112yes—
172#11758190—24no—
173#11758190—42no—
174C16×C61—21no—
175C16×C61—21no—
176C16×C61—21no—
177C16×C61—21no—
178C23×C61C2×D811yescharacteristic
179C22×D61—41no—
180C22×D61—41no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61C2×D811yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C22⋊D61—44no—
190C22⋊D61—161no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—161no—
198D244—22no—
199D244—41no—
200D244—41no—
201D244—41no—
202C4×D61—44no—
203C4×D61—161no—
204C4×D61—161no—
205C4×D61—161no—
206Dic122—22no—
207Dic122—41no—
208Dic122—41no—
209Dic122—41no—
210Dic122—161no—
211C8×C61—21no—
212C8×C61—21no—
213C8×C61—21no—
214C8×C61C2×#4111yescharacteristic
215C8×C61C2×#4111yescharacteristic
216#33684—611nomaximal, Sylow
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61C22×D811yescharacteristic
221C2×D61—42no—
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61#52511yescharacteristic
233C4×C61#57511yescharacteristic
234Dic61—42no—
235Dic61—81no—
236Dic61—81no—
237Dic61—81no—
238Dic61—81no—
239Dic61—81no—
240#3175—611no—
241#2951—611no—
242#2236—611no—
243#2232—611no—
244#2227—611no—
245#2224—611no—
246#2211—611no—
247#2210—611no—
248#2189—611no—
249#2186—611no—
250#2175—611no—
251#2175—611no—
252C4×Q32—611no—
253C4×D16—611no—
254#2164D6111yescharacteristic, complemented
255C2×C61—41no—
256C2×C61#310011yescharacteristic
257C2×C61#341511yescharacteristic
258C2×C61#341711yescharacteristic
259D61—82no—
260D61—161no—
261C2×#135—611no—
262#542—1221no—
263#520—1221no—
264C2×Q32—611no—
265C2×SD32—611no—
266C2×SD32—611no—
267C2×D16—611no—
268#500—611no—
269#495—611no—
270#489—1221no—
271#468—1221no—
272#467—611no—
273#466—611no—
274#440—1221no—
275#440—1221no—
276#440—1221no—
277C4×Q16—611no—
278C4×Q16—611no—
279C4×Q16—611no—
280C4×D8—611no—
281C4×D8—611no—
282C4×D8—611no—
283C2×#107—611no—
284#417—1221no—
285#405C2×D6111yescharacteristic
286#366—611no—
287#366—611no—
288#366—611no—
289#366—611no—
290C4⋊C16C2×D6111yescharacteristic
291C4⋊C16C2×D6111yescharacteristic
292#358—611no—
293#358—611no—
294#358—611no—
295#358—611no—
296#357—611no—
297#357—611no—
298#357—611no—
299#357—611no—
300C22⋊C16C2×D6111yescharacteristic
301C22⋊C16C2×D6111yescharacteristic
302#346C2×D6111yescharacteristic
303C4×C16C2×D6111yescharacteristic
304C61#3368411yescharacteristic, complemented, Sylow
305C2×#41—1221no—
306#135—1222no—
307#135—1222no—
308C2×Q16—611no—
309C2×Q16—611no—
310C2×SD16—1221no—
311C2×SD16—1221no—
312C2×D8—611no—
313C2×D8—611no—
314C2×M16D24411yescharacteristic
315C22×C8C22×D6111yescharacteristic
316C4⋊Q8—1221no—
317#126—2441no—
318#124—1221no—
319#124—2441no—
320#123—2441no—
321C22⋊Q8—1221no—
322C22⋊Q8—2441no—
323#121—1221no—
324C4×Q8—1221no—
325C4×Q8—1221no—
326C4×Q8—1221no—
327C4×D4—1221no—
328C4×D4—1221no—
329C4×D4—1221no—
330C4×D4—2441no—
331C4×D4—2441no—
332#117—2441no—
333#117D24411yescharacteristic
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—2441no—
336Q32—1222no—
337SD32—1222no—
338SD32—1222no—
339D16—1222no—
340C2×C16C22×D6111yescharacteristic
341C2×C16C22×D6111yescharacteristic
342C2×C16C22×D6111yescharacteristic
343C2×C16C22×D6111yescharacteristic
344#107—611no—
345#107—611no—
346#107—611no—
347#107—611no—
348#107—1221no—
349#107—1221no—
350#103—1221no—
351#103—1221no—
352#103—1221no—
353#103—1221no—
354#102—1221no—
355#102—1221no—
356#102—1221no—
357#102—1221no—
358#97D24411yescharacteristic
359#97D24411yescharacteristic
360C4×C8C22×D6111yescharacteristic
361C4×C8C22×D6111yescharacteristic
362#41—1224no—
363#41—2442no—
364C2×Q8—1221no—
365C2×Q8—1221no—
366C2×Q8—2441no—
367C2×D4—1221no—
368C2×D4—1221no—
369C2×D4—2441no—
370C2×D4—2441no—
371C22×C4—2441no—
372C22×C4—2441no—
373C22×C4—2441no—
374C22×C4—2441no—
375C22×C4—2441no—
376C22×C4C2×D24411yescharacteristic
377Q16—612no—
378Q16—1221no—
379Q16—1221no—
380Q16—1221no—
381SD16—1224no—
382SD16—2442no—
383D8—612no—
384D8—1221no—
385D8—1221no—
386D8—1221no—
387M16—41no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8C2×D24411yescharacteristic
391C2×C8C2×D24411yescharacteristic
392C2×C8C2×D24411yescharacteristic
393C2×C8C23×D6111yescharacteristic
394C4⋊C4—1221no—
395C4⋊C4—1221no—
396C4⋊C4—1221no—
397C4⋊C4—1221no—
398C4⋊C4—2441no—
399C4⋊C4—2441no—
400C4⋊C4—2441no—
401C4⋊C4—2441no—
402C4⋊C4—2441no—
403C4⋊C4—2441no—
404C4⋊C4D48811yescharacteristic
405C4⋊C4D48811yescharacteristic
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C22⋊C4—2441no—
411C22⋊C4—2441no—
412C22⋊C4—2441no—
413C22⋊C4D48811yescharacteristic
414C22⋊C4D48811yescharacteristic
415C42—2441no—
416C42—2441no—
417C42—2441no—
418C42C2×D24411yescharacteristic
419C42C2×D24411yescharacteristic
420C16—21no—
421C16—21no—
422C16—21no—
423C16—21no—
424C23—2441no—
425C23—2441no—
426C23C2×D48811yescharacteristic
427Q8—1222no—
428Q8—9761no—
429Q8—2441no—
430Q8—2441no—
431Q8—2441no—
432D4—1222no—
433D4—9761no—
434D4—2444no—
435D4—2441no—
436D4—2441no—
437D4—2441no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—9761no—
441C2×C4—9761no—
442C2×C4—9761no—
443C2×C4—9761no—
444C2×C4—2444no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4C2×D48811yescharacteristic
452C2×C4C2×D48811yescharacteristic
453C2×C4C2×D48811yescharacteristic
454C2×C4C2×D48811yescharacteristic
455C2×C4C2×D48811yescharacteristic
456C2×C4C22×D24411yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8#41×D6111yescharacteristic
461C8#41×D6111yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—4881no—
466C22—4881no—
467C22—4881no—
468C22—4881no—
469C22—4881no—
470C22—2442no—
471C22C22×D48811yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—4881no—
478C4—4881no—
479C4—4881no—
480C4—4881no—
481C4—4881no—
482C4—2442no—
483C4#1684027411yescharacteristic
484C4#1684056211yescharacteristic
485C2—41no—
486C2—9761no—
487C2—4882no—
488C2#2145582011yescharacteristic
489C2#2145896011yescharacteristic
490C2#2145897211yescharacteristic
subgroupG/H
centerC22C22×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2164C2
socleC22×C61C22×D8
prime radical#21447744C2
hypercenter#2164D61
hypocenterC61#33684
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2164

Complements

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

NH ≅ G/Ntype
1. #21456458C2semidirect
2. #21454696C2semidirect
3. #21448022C2semidirect
4. #21448000C2semidirect
5. #21447972C2semidirect
6. #21447957C2semidirect
7. #21447882C2semidirect
8. #21447875C2semidirect
9. #21447761C2semidirect
11. #21447685C2semidirect
12. #21447685C2semidirect
13. C4×Dic488C2semidirect
14. C4×D976C2semidirect
15. C61×#2164C2semidirect
254. #2164D61semidirect
304. C61#33684semidirect

Maximal subgroups

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

subgroupindex
#214564582
#214546962
#214480222
#214480002
#214479722
#214479572
#214478822
#214478752
#214477612
#214477442
#214476852
C4×Dic4882
C4×D9762
C61×#21642
#3368461