Finite Group Databasebeta

← #29580858

Subgroups — #29580858

Order 15616.

598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455846C211yesmaximal, characteristic, complemented
2#21449103C211yesmaximal, characteristic, complemented
3#21446652C211yesmaximal, characteristic, complemented
4#21444249C211yesmaximal, characteristic, complemented
5#21444244C211yesmaximal, characteristic, complemented
6#21443647C211yesmaximal, characteristic, complemented
7C61×#3100C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16840078—21no—
10#16840044—21no—
11#16839959—21no—
12#16839900—21no—
13C4×#11758200—22no—
14#16839815C2211yescharacteristic
15#16839786C2211yescharacteristic
16C2×#14519704—22no—
17#16839700—21no—
18#16839687—21no—
19#16839676—21no—
20#16839674—21no—
21C4×C22⋊Dic61—22no—
22#16839608C2211yescharacteristic
23#16839494—22no—
24D4⋊#92418—22no—
25C61×#532C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#480—21no—
28C61×#474—21no—
29C61×#459—21no—
30C61×#447—21no—
31C4×D8×C61—22no—
32C61×#431C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34C2×#11758200—22no—
35C2×#11758194—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×C22⋊Dic61—22no—
43C2×C22⋊Dic61—22no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61D412yes—
46#14519708—22no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519704—44no—
51#14519700—22no—
52#14519698—22no—
53C22⋊#92418—21no—
54C4×#92418D412yes—
55#14519684—22no—
56#14519684—22no—
57#14519684—21no—
58#14519684—21no—
59C2×#41×C61—21no—
60C22×D4×C61D411yescharacteristic
61C23×C4×C61—21no—
62C2×D8×C61—22no—
63C4⋊Q8×C61D411yescharacteristic
64#127×C61D411yescharacteristic
65#124×C61—21no—
66#121×C61—21no—
67#121×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C22⋊C4×C61—21no—
76C2×C42×C61C2311yescharacteristic
77#107×C61—22no—
78C4⋊C8×C61—21no—
79#102×C61—22no—
80#102×C61—22no—
81C22⋊C8×C61—21no—
82C4×C8×C61D412yes—
83C24×C61—21no—
84#41×C61—42no—
85#41×C61—42no—
86C2×Q8×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—42no—
93C2×D4×C61—41no—
94C22×C4×C61—21no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
98C22×C4×C61—42no—
99C22×C4×C61—42no—
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×Dic61—21no—
104C22×Dic61—22no—
105C22×Dic61—21no—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122—42no—
109D8×C61—44no—
110C2×C8×C61—22no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123C22⋊Dic61—44no—
124C22⋊Dic61—44no—
125#11758200—44no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128#11758196—41no—
129#11758196—41no—
130C4×Dic61—22no—
131C4×Dic61—22no—
132C4×Dic61—41no—
133C4×Dic61—41no—
134#11758194—42no—
135C2×#92418—22no—
136C2×#92418—41no—
137C23×C61—22no—
138C23×C61—42no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—42no—
142C23×C61—41no—
143C23×C61#12011yescharacteristic
144Q8×C61—42no—
145D4×C61—22no—
146D4×C61—22no—
147D4×C61—41no—
148D4×C61—41no—
149D4×C61—42no—
150D4×C61—42no—
151D4×C61—42no—
152D4×C61—82no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—42no—
158C2×C4×C61—82no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61#12011yescharacteristic
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12711yescharacteristic
169C2×C4×C61#13512yes—
170C2×C4×C61AGL(1,ℤ/8)12yes—
171C2×Dic61—22no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—42no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—41no—
178C2×Dic61—42no—
179Dic122—22no—
180Dic122—22no—
181Dic122—41no—
182Dic122—41no—
183C8×C61—42no—
184#92418—42no—
185#92418—81no—
186#10013—611nomaximal, Sylow
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—44no—
190C22×C61—42no—
191C22×C61—82no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61#39211yescharacteristic
198C22×C61#44912yes—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—81no—
204C4×C61—81no—
205C4×C61#46312yes—
206C4×C61#49511yescharacteristic
207C4×C61#49611yescharacteristic
208Dic61—42no—
209Dic61—82no—
210Dic61—81no—
211#3103—611no—
212#3100D6111yescharacteristic
213#2398—611no—
214#1963—611no—
215#1487—611no—
216#1486—611no—
217#1274—611no—
218C2×C61—22no—
219C2×C61—82no—
220C2×C61—161no—
221C2×C61#201011yescharacteristic
222C2×C61#201011yescharacteristic
223C2×C61#201211yescharacteristic
224#532C2×D6111yescharacteristic
225C2×C4×Q8—611no—
226C2×C4×D4C2×D6111yescharacteristic
227#481—1221no—
228#480—21no—
229#475—1221no—
230#474—21no—
231#460—1221no—
232#459—21no—
233#448—1221no—
234#447—21no—
235C4×SD16—1222no—
236C4×D8—22no—
237#431—611no—
238#431C2×D6111yescharacteristic
239#423—611no—
240C2×#104—1222no—
241#400—1221no—
242#397—1221no—
243#394—1221no—
244#393—1221no—
245C4×C22⋊C4—1222no—
246#376—611no—
247Q8⋊C8—1222no—
248D4⋊C8—1222no—
249C61#1001311yescharacteristic, complemented, Sylow
250C2×#41—21no—
251C22×Q8—611no—
252C22×D4C22⋊D6111yescharacteristic
253C23×C4—21no—
254C2×SD16—1222no—
255C2×D8—22no—
256C2×M16—1221no—
257C4⋊Q8C22⋊D6111yescharacteristic
258#127C22⋊D6111yescharacteristic
259#124—21no—
260#121—21no—
261#121—21no—
262C4×Q8—1221no—
263C4×Q8—1221no—
264C4×Q8—1221no—
265C4×Q8—1221no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4C22⋊D6111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—1222no—
277C2×C22⋊C4—1222no—
278C2×C42—612no—
279C2×C42—1221no—
280C2×C42C22×D6111yescharacteristic
281#107—22no—
282#106—1222no—
283C4⋊C8—21no—
284C4⋊C8—1221no—
285C4⋊C8—1221no—
286C4⋊C8—1221no—
287#104—2444no—
288#103—1222no—
289#102—22no—
290#102—22no—
291#102—1222no—
292C22⋊C8—21no—
293C22⋊C8—1221no—
294C4×C8—612no—
295C4×C8C22⋊D6112yes—
296#95—1222no—
297#95—1222no—
298#95—1221no—
299#95—1221no—
300C24—21no—
301#41—42no—
302#41—42no—
303C2×Q8—21no—
304C2×Q8—1221no—
305C2×Q8—1221no—
306C2×Q8—2442no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—42no—
313C2×D4—41no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—1221no—
321C22×C4—1222no—
322C22×C4—1221no—
323C22×C4D4×D6111yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4C2×C22⋊D6111yescharacteristic
326SD16—2444no—
327D8—44no—
328M16—2442no—
329C2×C8—22no—
330C2×C8—1222no—
331C2×C8—2441no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C4⋊C4—2441no—
339C4⋊C4—2441no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—2444no—
345C22⋊C4—2444no—
346C42—1222no—
347C42—1222no—
348C42—2441no—
349C42—2441no—
350C42D4×D6111yescharacteristic
351C42#1175822411yescharacteristic
352C42C2×C22⋊D6111yescharacteristic
353C42C2×C22⋊D6111yescharacteristic
354C23—22no—
355C23—42no—
356C23—41no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23#1451974511yescharacteristic
361Q8—42no—
362Q8—1222no—
363Q8—1222no—
364Q8—2441no—
365Q8—2441no—
366D4—22no—
367D4—22no—
368D4—41no—
369D4—41no—
370D4—42no—
371D4—42no—
372D4—42no—
373D4—82no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—82no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—1222no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4#1451974511yescharacteristic
393C2×C4#1451974611yescharacteristic
394C2×C4#1451974811yescharacteristic
395C2×C4#1451974911yescharacteristic
396C2×C4#1451974911yescharacteristic
397C2×C4#1451977311yescharacteristic
398C2×C4#1451979612yes—
399C2×C4#1451980112yes—
400C8—42no—
401C8—4881no—
402C8—2442no—
403C22—21no—
404C22—21no—
405C22—44no—
406C22—42no—
407C22—82no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22#1683967011yescharacteristic
414C22#1683990412yes—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—81no—
420C4—81no—
421C4—4882no—
422C4—4881no—
423C4—2442no—
424C4#1683997512yes—
425C4#1684014511yescharacteristic
426C4#1684015011yescharacteristic
427C2—22no—
428C2—82no—
429C2—161no—
430C2#2144688311yescharacteristic
431C2#2144688411yescharacteristic
432C2#2144689411yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3100C2
socleC22×C61#392
hypercenter#3100D61
hypocenterC61#10013
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #21455846C2semidirect
2. #21449103C2semidirect
3. #21446652C2semidirect
4. #21444249C2semidirect
5. #21444244C2semidirect
6. #21443647C2semidirect
249. C61#10013semidirect

Maximal subgroups

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

subgroupindex
#214558462
#214491032
#214466522
#214442492
#214442442
#214436472
C61×#31002
#1001361