Finite Group Databasebeta

← #29663877

Subgroups — #29663877

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456379C211yesmaximal, characteristic
2#21455945C211yesmaximal, characteristic, complemented
3#21455942C211yesmaximal, characteristic
4C2×#16839886C211yesmaximal, characteristic, complemented
5#21445276C212yesmaximal, complemented
6#21445266C212yesmaximal, complemented
7#21445200C212yesmaximal, complemented
8#21445170C212yesmaximal, complemented
9#21444580C211yesmaximal, characteristic, complemented
10#21444512C211yesmaximal, characteristic
11C61×#1552C211yesmaximal, characteristic, complemented
12#16840312C2211yescharacteristic
13C2×C4×Dic122C2211yescharacteristic
14#16840158C2211yescharacteristic
15#16840136C2211yescharacteristic
16#16840112C2211yescharacteristic
17#16840110C2211yescharacteristic
18#16840090—21no—
19#16840076—21no—
20#16840058C2212yes—
21#16840044C2212yes—
22#16839993—21no—
23#16839993—21no—
24#16839969C2212yes—
25#16839963C2212yes—
26#16839917—21no—
27#16839903—21no—
28#16839886—21no—
29#16839886—21no—
30#16839886C2212yes—
31#16839886C2212yes—
32#16839867—22no—
33#16839864—22no—
34C4×#11758201—21no—
35C4×#11758201—21no—
36#16839819C2211yescharacteristic
37C2×#14519706—21no—
38C2×C4×#92418C2211yescharacteristic
39C2×C8×Dic61—21no—
40#16839514C2212yes—
41#16839512C2212yes—
42#16839510C2212yes—
43#16839505C2212yes—
44C61×#533C2211yescharacteristic
45C61×#432C2211yescharacteristic
46C2×C4⋊C8×C61C2211yescharacteristic
47C61×#332C2212yes—
48C61×#332C2212yes—
49C2×#11758222—21no—
50C22×Dic122D411yescharacteristic
51C2×#11758202—22no—
52C2×#11758190—22no—
53C2×#11758201—21no—
54C2×#11758201—21no—
55C22×#92418D411yescharacteristic
56C22×#92418D411yescharacteristic
57#14519777C2311yescharacteristic
58#14519774C2311yescharacteristic
59#14519765—21no—
60#14519751—21no—
61#14519751—21no—
62C4×Dic122—21no—
63C4×Dic122—21no—
64C4×Dic122D412yes—
65C4×Dic122C2312yes—
66C4×D244—21no—
67C4×D244—21no—
68C2×C4⋊Dic61D411yescharacteristic
69C2×#11758196—21no—
70C2×C4×Dic61—21no—
71#14519711—22no—
72#14519708—22no—
73#14519708—21no—
74#14519708—21no—
75C4⋊#92418C2312yes—
76#14519706—22no—
77#14519706—22no—
78#14519702—22no—
79#14519701—22no—
80#14519701—21no—
81#14519701—21no—
82#14519700—22no—
83#14519699—22no—
84#14519697—21no—
85#14519697—21no—
86C22⋊#92418—21no—
87#14519688—21no—
88C4×#92418D411yescharacteristic
89C4×#92418D411yescharacteristic
90C4×#92418C2311yescharacteristic
91C4×#92418C2311yescharacteristic
92C8×Dic61—22no—
93C8×Dic61—22no—
94C22×C8×C61—21no—
95C4⋊Q8×C61C2311yescharacteristic
96C4⋊Q8×C61C2311yescharacteristic
97#125×C61—21no—
98C22⋊Q8×C61—21no—
99C22⋊Q8×C61—21no—
100C4×Q8×C61—21no—
101C4×Q8×C61—21no—
102#117×C61—21no—
103C2×C42×C61C2311yescharacteristic
104C4⋊C8×C61—21no—
105C4⋊C8×C61C2312yes—
106C4⋊C8×C61C2312yes—
107C22⋊C8×C61—21no—
108#97×C61—21no—
109C2×Q8×C61—21no—
110C2×Q8×C61—21no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C2×C22⋊D61—41no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117#11758222—82no—
118C2×D244—21no—
119C2×D244—21no—
120C2×D244—21no—
121C2×C4×D61—41no—
122C2×Dic122—21no—
123C2×Dic122—24no—
124C2×Dic122—21no—
125C2×Dic122C2×D412yes—
126C2×C8×C61—22no—
127C2×C8×C61—22no—
128C2×C8×C61—42no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C42×C61—41no—
137C42×C61C2×D411yescharacteristic
138C42×C61C2×D411yescharacteristic
139C42×C61#4111yescharacteristic
140C42×C61C2411yescharacteristic
141#11758202—44no—
142#11758201—42no—
143#11758201—42no—
144#11758198—41no—
145#11758198—41no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61C2×D412yes—
150#11758196—22no—
151#11758196—22no—
152C4×Dic61—22no—
153C4×Dic61—22no—
154C2×#92418—22no—
155C2×#92418—22no—
156C2×#92418—41no—
157C2×#92418C2×D411yescharacteristic
158C2×#92418C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161#11758190—44no—
162C23×C61#12111yescharacteristic
163C22×D61—41no—
164Q8×C61—42no—
165Q8×C61—41no—
166Q8×C61—41no—
167C2×C4×C61—22no—
168C2×C4×C61—22no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61C22×D411yescharacteristic
177C2×C4×C61C22×D411yescharacteristic
178C2×C4×C61C2×#4111yescharacteristic
179C22⋊D61—82no—
180C2×Dic61—24no—
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—42no—
184C2×Dic61—41no—
185D244—42no—
186D244—41no—
187D244—41no—
188D244—81no—
189C4×D61—82no—
190Dic122—24no—
191Dic122—22no—
192Dic122—81no—
193Dic122#13514yes—
194C8×C61—42no—
195C8×C61—42no—
196#92418—21no—
197#92418—21no—
198#92418—21no—
199#92418—42no—
200#92418#13712yes—
201#19263—611nomaximal, Sylow
202C22×C61—21no—
203C22×C61—21no—
204C22×C61#47112yes—
205C22×C61C2×#12111yescharacteristic
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61C2×#13512yes—
216C4×C61C2×#13711yescharacteristic
217C4×C61#57511yescharacteristic
218Dic61—24no—
219Dic61—42no—
220Dic61—81no—
221#3167—611no—
222#3113—611no—
223#3112—611no—
224C2×C8×Q8—611no—
225#1684—612no—
226#1682—612no—
227#1672—612no—
228#1666—612no—
229#1568—611no—
230#1552D6111yescharacteristic, complemented
231#1551—611no—
232C2×C61—22no—
233C2×C61#303711yescharacteristic
234C2×C61#305011yescharacteristic
235C2×C61C2×#47111yescharacteristic
236D61—161no—
237#533C2×D6111yescharacteristic
238#532—611no—
239C2×C4×Q8—611no—
240#498—611no—
241#492—611no—
242#487—611no—
243#486—611no—
244#483—1221no—
245#480—1221no—
246#477—612no—
247#475—612no—
248#465—1221no—
249#465—1221no—
250#462—612no—
251#460—612no—
252#451—1221no—
253#448—1221no—
254C8×Q8—612no—
255C8×Q8—612no—
256C8×Q8—1221no—
257C8×Q8—1221no—
258#441—1222no—
259#440—1222no—
260C4×SD16—1221no—
261C4×SD16—1221no—
262#432—611no—
263#432C2×D6111yescharacteristic
264C2×C4⋊C8—1221no—
265C2×C4⋊C8C2×D6111yescharacteristic
266C2×C4×C8—611no—
267C2×C4×C8—1221no—
268#335—612no—
269#334—612no—
270#333—612no—
271#332C2×D6112yes—
272#332C2×D6112yes—
273#331—612no—
274C61#1926311yescharacteristic, complemented, Sylow
275C2×#41—1221no—
276C22×Q8—611no—
277C2×Q16—1222no—
278C2×SD16—1222no—
279C2×SD16—1221no—
280C2×SD16—1221no—
281C22×C8—21no—
282C22×C8—611no—
283C22×C8—611no—
284C4⋊Q8—611no—
285C4⋊Q8C22×D6111yescharacteristic
286C4⋊Q8C22×D6111yescharacteristic
287#127—611no—
288#125—21no—
289#124—1221no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292#121—1221no—
293#121—1221no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—612no—
297C4×Q8—612no—
298C4×Q8—1221no—
299C4×Q8—1221no—
300C4×D4—1221no—
301C4×D4—1221no—
302#117—21no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—1221no—
305C2×C42—1221no—
306C2×C42C22×D6111yescharacteristic
307#107—1222no—
308#106—1222no—
309#106—1221no—
310#106—1221no—
311C4⋊C8—21no—
312C4⋊C8—612no—
313C4⋊C8—1222no—
314C4⋊C8—1222no—
315C4⋊C8C22×D6112yes—
316C4⋊C8C22×D6112yes—
317#103—1222no—
318#103—1222no—
319#103—1222no—
320#103—1221no—
321#103—1221no—
322#102—1221no—
323#102—1221no—
324#102—1222no—
325C22⋊C8—21no—
326C22⋊C8—1221no—
327#97—21no—
328#97—1221no—
329C4×C8—611no—
330C4×C8—611no—
331C4×C8—611no—
332C4×C8—611no—
333C4×C8—1222no—
334C4×C8—1222no—
335#41—4882no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—612no—
339C2×Q8—1224no—
340C2×Q8—1221no—
341C2×Q8—1221no—
342C2×D4—1221no—
343C2×D4—1221no—
344C2×D4—1221no—
345C2×D4—2441no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—2441no—
349C22×C4#1175822211yescharacteristic
350C22×C4D4×D6111yescharacteristic
351C22×C4D4×D6111yescharacteristic
352Q16—2444no—
353SD16—2444no—
354SD16—2442no—
355SD16—2442no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—42no—
359C2×C8—611no—
360C2×C8—611no—
361C2×C8—611no—
362C2×C8—611no—
363C2×C8—1222no—
364C2×C8—1222no—
365C2×C8—2441no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—612no—
373C4⋊C4—1222no—
374C4⋊C4—1221no—
375C4⋊C4—1222no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C22⋊C4—41no—
379C22⋊C4—2441no—
380C22⋊C4—2441no—
381C42—41no—
382C42—1222no—
383C42—1222no—
384C42#1175822211yescharacteristic
385C42D4×D6111yescharacteristic
386C42D4×D6111yescharacteristic
387C42C23×D6111yescharacteristic
388C23—2441no—
389C23#1451975011yescharacteristic
390Q8—42no—
391Q8—41no—
392Q8—41no—
393Q8—614no—
394Q8—1224no—
395Q8—1222no—
396Q8—4881no—
397D4—4881no—
398D4—4882no—
399D4—2442no—
400D4—2441no—
401D4—2441no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—1224no—
409C2×C4—1222no—
410C2×C4—1222no—
411C2×C4—4882no—
412C2×C4—2441no—
413C2×C4—2442no—
414C2×C4#1451975011yescharacteristic
415C2×C4#1451975011yescharacteristic
416C2×C4#1451975011yescharacteristic
417C2×C4C2×D4×D6111yescharacteristic
418C2×C4C2×D4×D6111yescharacteristic
419C2×C4C2×#1175822211yescharacteristic
420C8—42no—
421C8—42no—
422C8—612no—
423C8—1221no—
424C8—1221no—
425C8—1221no—
426C8—2442no—
427C22—21no—
428C22—21no—
429C22—4881no—
430C22—4881no—
431C22—4881no—
432C22#1684002812yes—
433C22C2×#1451975011yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—81no—
440C4—1224no—
441C4—4881no—
442C4—2442no—
443C4#135×D6112yes—
444C4#137×D6111yescharacteristic
445C4#1684055811yescharacteristic
446C2—22no—
447C2—9761no—
448C2#2145529011yescharacteristic
449C2#2145539911yescharacteristic
450C2C2×#1684002811yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1552C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1552D61
hypocenterC61#19263
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
2. #21455945C2semidirect
4. C2×#16839886C2semidirect
5. #21445276C2semidirect
6. #21445266C2semidirect
7. #21445200C2semidirect
8. #21445170C2semidirect
9. #21444580C2semidirect
11. C61×#1552C2semidirect
230. #1552D61semidirect
274. C61#19263semidirect

Maximal subgroups

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

subgroupindex
#214563792
#214559452
#214559422
C2×#168398862
#214452762
#214452662
#214452002
#214451702
#214445802
#214445122
C61×#15522
#1926361