Finite Group Databasebeta

← #29837616

Subgroups — #29837616

Order 15616.

514 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458239C211yesmaximal, characteristic, complemented
2#21458163C211yesmaximal, characteristic, complemented
3#21448100C211yesmaximal, characteristic, complemented
4#21448009C211yesmaximal, characteristic, complemented
5#21448006C211yesmaximal, characteristic, complemented
6#21448005C211yesmaximal, characteristic, complemented
7#21447964C211yesmaximal, characteristic, complemented
8#21447955C211yesmaximal, characteristic, complemented
9#21447921C211yesmaximal, characteristic, complemented
10#21447920C211yesmaximal, characteristic, complemented
11#21447663C211yesmaximal, characteristic, complemented
12#21447648C211yesmaximal, characteristic, complemented
13#21447608C211yesmaximal, characteristic, complemented
14#21447604C211yesmaximal, characteristic, complemented
15C61×#2234C211yesmaximal, characteristic, complemented
16#16840475—21no—
17#16840412—21no—
18C2×#14519718C2211yescharacteristic
19C2×#14519717C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21#16840166C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840088—21no—
24#16840086—21no—
25#16840074—21no—
26#16840073—21no—
27#16840051—21no—
28#16840040—21no—
29#16839999C2211yescharacteristic
30#16839998C2211yescharacteristic
31#16839995C2211yescharacteristic
32D8×Dic61C2211yescharacteristic
33#16839844C2211yescharacteristic
34C8×C22⋊D61C2211yescharacteristic
35#16839799C2211yescharacteristic
36C2×#14519711C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839589C2211yescharacteristic
42#16839589C2211yescharacteristic
43#16839587C2211yescharacteristic
44#16839587C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839563C2211yescharacteristic
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#466C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758224—41no—
60C2×D488C2311yescharacteristic
61C2×C8×D61C2311yescharacteristic
62#14519776—21no—
63#14519776—21no—
64#14519765—41no—
65#14519763—41no—
66#14519759—41no—
67#14519758—41no—
68#14519754—41no—
69#14519752—21no—
70#14519751—21no—
71#14519750—41no—
72#14519748—21no—
73D4×Dic61—21no—
74#14519739—21no—
75C4×C22⋊D61D411yescharacteristic
76#14519735—21no—
77#14519734—41no—
78C2×C4⋊Dic61—21no—
79C4⋊C4×D61—21no—
80#14519718—22no—
81#14519717—22no—
82#14519716—22no—
83C2×#11758185C2311yescharacteristic
84C2×#11758185C2311yescharacteristic
85#14519711—21no—
86#14519711C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519710—21no—
90#14519710—21no—
91#14519710—21no—
92#14519708—21no—
93#14519706D411yescharacteristic
94#14519699—21no—
95#14519698—21no—
96#14519698—21no—
97#14519697—21no—
98#14519697—21no—
99C22⋊#92418D411yescharacteristic
100#14519689D411yescharacteristic
101C8×Dic61C2311yescharacteristic
102C2×D8×C61C2311yescharacteristic
103C22×C8×C61C2311yescharacteristic
104#121×C61—21no—
105#117×C61—21no—
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#106×C61—21no—
112#102×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—41no—
115C22×C4×C61C2×D411yescharacteristic
116C2×C22⋊D61—41no—
117C2×C22⋊D61—41no—
118C2×C22⋊D61D811yescharacteristic
119C22×Dic61—41no—
120C22×Dic61—41no—
121#11758224—84no—
122C2×D244—21no—
123C2×D244—41no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61C2×D411yescharacteristic
127C2×Dic122—41no—
128C2×Dic122—41no—
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—21no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C42×C61—41no—
141C22⋊Dic61—41no—
142C22⋊Dic61—41no—
143C22⋊Dic61D811yescharacteristic
144#11758198—41no—
145#11758198—41no—
146#11758198—41no—
147#11758198—41no—
148#11758198D811yescharacteristic
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61—21no—
152C4⋊Dic61—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156#11758196D811yescharacteristic
157C4×Dic61—41no—
158C4×Dic61C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161D488—21no—
162D488—21no—
163C8×D61—21no—
164C8×D61—21no—
165C16×C61—21no—
166C16×C61—21no—
167#11758185—21no—
168#11758185#4112yescomplemented
169C23×C61—41no—
170C23×C61C2×D811yescharacteristic
171C22×D61—41no—
172C22×D61C2×D811yescharacteristic
173D4×C61—41no—
174D4×C61—41no—
175D4×C61—82no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C22×D411yescharacteristic
183C22⋊D61—22no—
184C22⋊D61—82no—
185C22⋊D61—161no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—82no—
190C2×Dic61—82no—
191C2×Dic61C2×D811yescharacteristic
192C2×Dic61C2×D811yescharacteristic
193C2×Dic61C2×D811yescharacteristic
194D244—41no—
195D244—41no—
196D244—161no—
197C4×D61—21no—
198C4×D61—21no—
199C4×D61—82no—
200C4×D61—82no—
201Dic122—82no—
202Dic122—161no—
203C8×C61—21no—
204C8×C61C2×#4111yescharacteristic
205C8×C612−1+411yescharacteristic
206#92418—21no—
207#92418—21no—
208#33921—611nomaximal, Sylow
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61C22×D811yescharacteristic
216C2×D61—21no—
217C2×D61—21no—
218C2×D61—21no—
219C2×D61—81no—
220C2×D61—81no—
221C2×D61—81no—
222C4×C61—21no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61#54711yescharacteristic
227C4×C61#57811yescharacteristic
228Dic61—21no—
229Dic61—21no—
230Dic61—81no—
231Dic61—81no—
232Dic61—81no—
233Dic61#50912yes—
234#3341—611no—
235#3334—611no—
236#2254—611no—
237#2234—611no—
238#2234D6111yescharacteristic, complemented
239#2233—611no—
240#2233—611no—
241#2226—611no—
242#2224—611no—
243#2218—611no—
244#2218—611no—
245C4×D16—611no—
246#2169—611no—
247#2159—611no—
248#2159—611no—
249C2×C61—41no—
250C2×C61—161no—
251C2×C61#333411yescharacteristic
252C2×C61C2×#50911yescharacteristic
253C2×C61#341611yescharacteristic
254D61—41no—
255D61—161no—
256#555—1221no—
257#547—1221no—
258C2×D16—611no—
259C2×M32—611no—
260C2×M32—611no—
261#500—611no—
262#500—611no—
263#482—1221no—
264#482—1221no—
265#480—1221no—
266#480—1221no—
267#476—1221no—
268#474—1221no—
269#466—611no—
270#466—611no—
271#466—611no—
272#466C2×D6111yescharacteristic
273C4×D8—611no—
274C4×D8—611no—
275C8×D4—611no—
276#427—611no—
277#427C2×D6111yescharacteristic
278C2×#107—611no—
279C2×#107—611no—
280#367—611no—
281#367—611no—
282#367—611no—
283#367—611no—
284#367—611no—
285#367C2×D6111yescharacteristic
286#366—611no—
287#366—611no—
288#366C2×D6111yescharacteristic
289C4⋊C16—611no—
290#357—611no—
291#357—611no—
292#357—611no—
293#357—611no—
294#357C2×D6111yescharacteristic
295#357C2×D6111yescharacteristic
296C22⋊C16—611no—
297C22⋊C16C2×D6111yescharacteristic
298C4×C16—611no—
299C61#3392111yescharacteristic, complemented, Sylow
300C2×#41—2441no—
301C2×D8—611no—
302C2×D8C22×D6111yescharacteristic
303C22×C8—611no—
304C22×C8C22×D6111yescharacteristic
305C4⋊Q8—1221no—
306C4⋊Q8—1221no—
307#124—2441no—
308#124—2441no—
309#123—2441no—
310#123—2441no—
311C22⋊Q8—2441no—
312#121—21no—
313#121—1221no—
314#121—1221no—
315#121—1221no—
316#121—2441no—
317C4×D4—611no—
318C4×D4—1221no—
319C4×D4—1221no—
320#117—21no—
321#117—1221no—
322#117—2441no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4—1221no—
325D16—1222no—
326M32—1222no—
327M32—1222no—
328C2×C16—611no—
329C2×C16—611no—
330C2×C16C22×D6111yescharacteristic
331C2×C16C22×D6111yescharacteristic
332#107—611no—
333#107—611no—
334#107—611no—
335#107—1221no—
336#107—1221no—
337#107—1221no—
338#107—1221no—
339#107C22×D6111yescharacteristic
340#107C22×D6111yescharacteristic
341#107C22×D6111yescharacteristic
342#106—21no—
343#106—1221no—
344C4⋊C8—611no—
345#102—21no—
346#102—1221no—
347#102—1221no—
348#102—1221no—
349#102—1221no—
350#102—1221no—
351C22⋊C8—611no—
352C22⋊C8—611no—
353C4×C8—611no—
354#41—4884no—
355C2×Q8—2441no—
356C2×Q8—2441no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—611no—
360C2×D4—1221no—
361C2×D4—2441no—
362C2×D4—2441no—
363C2×D4—2441no—
364C22×C4—611no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4—2441no—
368C22×C4—2441no—
369C22×C4D4×D6111yescharacteristic
370D8—21no—
371D8—21no—
372D8—1221no—
373D8—1221no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—611no—
377C2×C8—611no—
378C2×C8—1221no—
379C2×C8—1221no—
380C2×C8D4×D6111yescharacteristic
381C2×C8C23×D6111yescharacteristic
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—611no—
386C4⋊C4—1221no—
387C4⋊C4—1221no—
388C4⋊C4—1221no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—611no—
396C22⋊C4—611no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C42—41no—
404C42—611no—
405C42—2441no—
406C16—21no—
407C16—21no—
408C16—612no—
409C16—1221no—
410C23—41no—
411C23—611no—
412C23—2441no—
413C23D8×D6111yescharacteristic
414Q8—9761no—
415Q8—4882no—
416D4—41no—
417D4—41no—
418D4—82no—
419D4—1222no—
420D4—9761no—
421D4—9761no—
422D4—4882no—
423D4—2441no—
424D4—2441no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—611no—
431C2×C4—611no—
432C2×C4—611no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—4882no—
436C2×C4—4882no—
437C2×C4—4882no—
438C2×C4—4882no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4D8×D6111yescharacteristic
443C2×C4C2×D4×D6111yescharacteristic
444C8—21no—
445C8—1221no—
446C8—1221no—
447C8#41×D6111yescharacteristic
448C8#1451982411yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—1221no—
456C22—1221no—
457C22—1221no—
458C22—4881no—
459C22—4881no—
460C22—4881no—
461C22C2×D8×D6111yescharacteristic
462C4—21no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—612no—
467C4—1221no—
468C4—1221no—
469C4—4881no—
470C4—4881no—
471C4—4881no—
472C4#1684041011yescharacteristic
473C4#1684057811yescharacteristic
474C2—41no—
475C2—161no—
476C2—9761no—
477C2—2441no—
478C2#2145816111yescharacteristic
479C2#509×D6111yescharacteristic
480C2#2145896211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2234C2
socleC22×C61C22×D8
hypercenter#2234D61
hypocenterC61#33921
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
1. #21458239C2semidirect
2. #21458163C2semidirect
3. #21448100C2semidirect
4. #21448009C2semidirect
5. #21448006C2semidirect
6. #21448005C2semidirect
7. #21447964C2semidirect
8. #21447955C2semidirect
9. #21447921C2semidirect
10. #21447920C2semidirect
11. #21447663C2semidirect
12. #21447648C2semidirect
13. #21447608C2semidirect
14. #21447604C2semidirect
15. C61×#2234C2semidirect
168. #11758185#41semidirect
238. #2234D61semidirect
299. C61#33921semidirect

Maximal subgroups

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

subgroupindex
#214582392
#214581632
#214481002
#214480092
#214480062
#214480052
#214479642
#214479552
#214479212
#214479202
#214476632
#214476482
#214476082
#214476042
C61×#22342
#3392161