Finite Group Databasebeta

← #29576043

Subgroups — #29576043

Order 15616.

624 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454381C211yesmaximal, characteristic, complemented
2#21451570C211yesmaximal, characteristic
3#21444487C211yesmaximal, characteristic, complemented
4#21444131C211yesmaximal, characteristic, complemented
5#21443679C211yesmaximal, characteristic, complemented
6#21443678C211yesmaximal, characteristic, complemented
7C61×#1545C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519748—21no—
10C2×#14519734C2211yescharacteristic
11#16839815C2211yescharacteristic
12#16839787—22no—
13#16839787—22no—
14#16839786C2211yescharacteristic
15#16839785—21no—
16#16839676—21no—
17#16839676C412yes—
18#16839670—21no—
19#16839670C412yes—
20#16839665—21no—
21#16839628C2211yescharacteristic
22#16839506—22no—
23#16839487—21no—
24#16839485—21no—
25C2×#127×C61C2211yescharacteristic
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C61×#331—22no—
29C22×C22⋊D61—22no—
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×#11758189—22no—
33M16×D61—42no—
34M16×D61—42no—
35C2×C8×D61—22no—
36#14519748—42no—
37#14519748—42no—
38#14519734—21no—
39#14519734—21no—
40#14519734—21no—
41#14519734—21no—
42C2×C4⋊Dic61—21no—
43C2×#11758196C2×C411yescharacteristic
44C2×#11758196D411yescharacteristic
45C2×C22⋊Dic61—22no—
46C2×C22⋊Dic61—22no—
47C2×C22⋊Dic61—22no—
48C2×#11758198C2×C411yescharacteristic
49C2×#11758198D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418D412yescomplemented
54#14519706—24no—
55C22⋊#92418—21no—
56C4×#92418—21no—
57#14519684—21no—
58#14519684C2×C412yes—
59C22×D4×C61—21no—
60C22×D4×C61—21no—
61C22×D4×C61C2×C412yes—
62C2×M16×C61—21no—
63#127×C61—21no—
64#127×C61—21no—
65#127×C61—21no—
66#127×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61D412yescomplemented
71C22⋊C8×C61—21no—
72C4×C8×C61—21no—
73C24×C61—22no—
74C23×D61C22⋊C411yescharacteristic
75C2×D4×C61—22no—
76C2×D4×C61—22no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—82no—
86C2×D4×C61—82no—
87C22×C4×C61C22×C411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C2×C22⋊D61—44no—
91C2×C22⋊D61—82no—
92C2×C22⋊D61—82no—
93C22×Dic61—22no—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61D812yes—
102C2×C4×D61SD1612yes—
103M16×C61—41no—
104M16×C61—41no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61#4111yescharacteristic
110C42×C61#4111yescharacteristic
111C22⋊Dic61—44no—
112C22⋊Dic61—82no—
113C22⋊Dic61—82no—
114#11758198—21no—
115#11758198—21no—
116#11758198—21no—
117#11758198—21no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120#11758196—21no—
121#11758196—21no—
122#11758196—21no—
123#11758196—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126#11758194—41no—
127#11758194—41no—
128C2×#92418—22no—
129C2×#92418—41no—
130#11758189—44no—
131C8×D61—44no—
132C23×C61—42no—
133C23×C61—42no—
134C23×C61—42no—
135C23×C61—42no—
136C23×C61—42no—
137C23×C61—42no—
138C23×C61—42no—
139C23×C61C2×C22⋊C411yescharacteristic
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61#10212yes—
145D4×C61—82no—
146D4×C61—82no—
147D4×C61—82no—
148D4×C61—82no—
149D4×C61—81no—
150D4×C61—81no—
151D4×C61—81no—
152D4×C61—81no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×C4×C61C2×D811yescharacteristic
162C2×C4×C61C2×SD1611yescharacteristic
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C61#13711yescharacteristic
165C22⋊D61—88no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61#10212yes—
176C4×D61—22no—
177C4×D61—22no—
178C4×D61—22no—
179C4×D61—22no—
180C8×C61—42no—
181C8×C61—81no—
182#92418—42no—
183#92418—81no—
184#9197—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—82no—
188C22×C61—82no—
189C22×C61—82no—
190C22×C61—82no—
191C22×C61—82no—
192C22×C61—82no—
193C22×C61—82no—
194C22×C61#38611yescharacteristic
195C22×C61C2×#10211yescharacteristic
196C22×C61#41711yescharacteristic
197C2×D61—22no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—42no—
201C2×D61—81no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61#44711yescharacteristic
207C4×C61#44811yescharacteristic
208C4×C61#48011yescharacteristic
209C4×C61#48111yescharacteristic
210Dic61—22no—
211Dic61—41no—
212Dic61—41no—
213Dic61—82no—
214#2905—611no—
215#2619—611no—
216#1545—611no—
217#1545D6111yescharacteristic, complemented
218#1458—611no—
219#1286—611no—
220#1286—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—162no—
224C2×C61#187411yescharacteristic
225C2×C61#191011yescharacteristic
226C2×C61#191411yescharacteristic
227D61—42no—
228C22×M16—1221no—
229C2×#127C2×D6111yescharacteristic
230C2×#121—1221no—
231C2×#117—611no—
232#431—611no—
233#431C2×D6111yescharacteristic
234#424—1222no—
235#424—1222no—
236#423—611no—
237#423—1221no—
238#423C2×D6111yescharacteristic
239#394—612no—
240#394—1221no—
241#392—612no—
242#392—1221no—
243#390—1221no—
244#382—611no—
245#331—22no—
246#331—1222no—
247#324—1221no—
248#323—1221no—
249C61#919711yescharacteristic, complemented, Sylow
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—1222no—
253C22×D4C4×D6112yes—
254C23×C4—611no—
255C2×M16—21no—
256C2×M16—1222no—
257C2×M16—1221no—
258C2×M16—2442no—
259C2×M16—2442no—
260C22×C8—1222no—
261#127—21no—
262#127—21no—
263#127—21no—
264#127—21no—
265#121—2442no—
266#121—2442no—
267#117—1221no—
268#117—1221no—
269#117—1221no—
270#117—1221no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4—1221no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—611no—
276C2×C22⋊C4—1222no—
277C2×C22⋊C4—1222no—
278C2×C22⋊C4—1222no—
279C2×C42—611no—
280C2×C42C22×D6111yescharacteristic
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—612no—
284C4⋊C8—1224no—
285C4⋊C8—1221no—
286C4⋊C8—1221no—
287C4⋊C8C22⋊D6112yescomplemented
288C22⋊C8—21no—
289C22⋊C8—1221no—
290C4×C8—21no—
291C4×C8—1221no—
292#95—612no—
293#95—1221no—
294C24—22no—
295C24—611no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—82no—
307C2×D4—82no—
308C2×D4—4882no—
309C2×D4—4882no—
310C2×D4—2444no—
311C22×C4—611no—
312C22×C4—612no—
313C22×C4—612no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1222no—
321C22×C4C2×C4×D6111yescharacteristic
322C22×C4D4×D6111yescharacteristic
323C22×C4D4×D6111yescharacteristic
324M16—41no—
325M16—41no—
326M16—2444no—
327M16—2441no—
328M16—2441no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—1222no—
332C2×C8—2444no—
333C2×C8—2441no—
334C4⋊C4—1221no—
335C4⋊C4—1221no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C4⋊C4—2441no—
339C4⋊C4—2441no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—1221no—
344C22⋊C4—4882no—
345C22⋊C4—4882no—
346C22⋊C4—2444no—
347C42—1221no—
348C42—1221no—
349C42#1175822211yescharacteristic
350C42D4×D6111yescharacteristic
351C42#1175822411yescharacteristic
352C42C2×C22⋊D6111yescharacteristic
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—612no—
361C23—1221no—
362C23—1221no—
363C23—2441no—
364C23—2441no—
365C23C22⋊C4×D6111yescharacteristic
366D4—82no—
367D4—82no—
368D4—82no—
369D4—82no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—4888no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—612no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1222no—
381C2×C4—1222no—
382C2×C4—1222no—
383C2×C4—1222no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4#1451973711yescharacteristic
392C2×C4C4×C22⋊D6111yescharacteristic
393C2×C4#1451974511yescharacteristic
394C2×C4#1451974811yescharacteristic
395C2×C4#1451975011yescharacteristic
396C2×C4#1451975911yescharacteristic
397C2×C4D8×D6111yescharacteristic
398C2×C4SD16×D6111yescharacteristic
399C2×C4#1451980111yescharacteristic
400C2×C4#1451980611yescharacteristic
401C8—42no—
402C8—81no—
403C8—4881no—
404C8—2442no—
405C22—21no—
406C22—21no—
407C22—82no—
408C22—82no—
409C22—82no—
410C22—82no—
411C22—82no—
412C22—82no—
413C22—82no—
414C22—1222no—
415C22—4881no—
416C22—2442no—
417C22—2441no—
418C22—2441no—
419C22#1683963811yescharacteristic
420C22#102×D6111yescharacteristic
421C22#1683976011yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—1222no—
427C4—4882no—
428C4—2441no—
429C4—2441no—
430C4#1683989411yescharacteristic
431C4#1683989911yescharacteristic
432C4#1684007411yescharacteristic
433C4#1684007911yescharacteristic
434C2—21no—
435C2—21no—
436C2—162no—
437C2—2442no—
438C2#2144613311yescharacteristic
439C2#2144634311yescharacteristic
440C2#2144636311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1545C2
socleC22×C61#386
prime radical#21451570C2
cosocleC2×C42×C61C23
hypercenter#1545D61
hypocenterC61#9197
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
1. #21454381C2semidirect
3. #21444487C2semidirect
4. #21444131C2semidirect
5. #21443679C2semidirect
6. #21443678C2semidirect
7. C61×#1545C2semidirect
53. C4⋊#92418D4semidirect
70. C4⋊C8×C61D4semidirect
217. #1545D61semidirect
249. C61#9197semidirect
287. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214543812
#214515702
#214444872
#214441312
#214436792
#214436782
C61×#15452
#919761