Finite Group Databasebeta

← #29580764

Subgroups — #29580764

Order 15616.

554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 101 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#21455850C211yesmaximal, characteristic
2#21455291C211yesmaximal, characteristic
3#21444378C211yesmaximal, characteristic
4#21444248C211yesmaximal, characteristic, complemented
5#21444214C211yesmaximal, characteristic, complemented
6#21443677C211yesmaximal, characteristic, complemented
7C61×#2581C211yesmaximal, characteristic, complemented
8C2×#14519808—21no—
9#16840312C2211yescharacteristic
10#16840080—21no—
11#16840047—21no—
12#16839984—22no—
13#16839972—21no—
14#16839962—21no—
15#16839962—21no—
16#16839901—21no—
17C4×#11758201—22no—
18#16839815C2211yescharacteristic
19#16839815C2211yescharacteristic
20#16839786C2211yescharacteristic
21#16839761—21no—
22#16839495—22no—
23Q8⋊#92418—22no—
24Q8⋊#92418—22no—
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4×Q8×C61C2211yescharacteristic
27C61×#400—21no—
28C61×#395—21no—
29C61×#391—21no—
30C61×#389—21no—
31C61×#387—22no—
32C61×#382C2211yescharacteristic
33C2×#11758222—21no—
34#14519808—42no—
35#14519808—42no—
36C2×#11758202—22no—
37C2×#11758201—22no—
38C2×#11758201—22no—
39C2×#11758194—21no—
40#14519777D411yescharacteristic
41#14519774D411yescharacteristic
42#14519765—21no—
43#14519751—21no—
44#14519751—21no—
45C4×D244—21no—
46C4×D244—21no—
47#14519708—22no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418D412yes—
52#14519701—22no—
53#14519700—22no—
54#14519697—22no—
55#14519697—22no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58C4×#92418—21no—
59C4×#92418D412yes—
60C22×Q8×C61D411yescharacteristic
61C22×Q8×C61D411yescharacteristic
62C4×Q8×C61—21no—
63C4×Q8×C61—21no—
64C4×Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C2×C4⋊C4×C61—22no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C42×C61—21no—
77C2×C42×C61—21no—
78C2×C42×C61C2311yescharacteristic
79#95×C61—22no—
80#95×C61—22no—
81#95×C61—22no—
82#95×C61—21no—
83#95×C61D412yes—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61—21no—
89C2×Q8×C61—21no—
90C2×Q8×C61—21no—
91C2×Q8×C61—42no—
92C2×Q8×C61SD1612yescomplemented
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—22no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C2×C22⋊D61—41no—
102#11758222—41no—
103#11758222—41no—
104#11758222—41no—
105#11758222—41no—
106C2×D244—21no—
107C2×D244—21no—
108C2×D244—21no—
109C2×C4×D61—41no—
110C2×Dic122—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—44no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C42×C61—41no—
123C42×C61—41no—
124C42×C61—41no—
125C42×C61—41no—
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128C42×C61C2×D411yescharacteristic
129C42×C61#4111yescharacteristic
130#11758202—44no—
131#11758201—44no—
132#11758201—44no—
133#11758198—41no—
134#11758198—41no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137#11758194—41no—
138#11758194—41no—
139C2×#92418—22no—
140C2×#92418—22no—
141C2×#92418—41no—
142C23×C61#12011yescharacteristic
143C22×D61—41no—
144Q8×C61—22no—
145Q8×C61—22no—
146Q8×C61—22no—
147Q8×C61—22no—
148Q8×C61—41no—
149Q8×C61—41no—
150Q8×C61—41no—
151Q8×C61—41no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#12011yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12711yescharacteristic
173C2×C4×C61C2×SD1611yescharacteristic
174C2×C4×C61#13511yescharacteristic
175C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C61#13711yescharacteristic
177C22⋊D61—81no—
178C22⋊D61—81no—
179C2×Dic61—41no—
180D244—42no—
181D244—41no—
182D244—41no—
183D244—81no—
184C4×D61—81no—
185C4×D61—81no—
186Dic122—41no—
187Dic122—41no—
188#92418—42no—
189#92418—42no—
190#92418—81no—
191#9999—611nomaximal, Sylow
192C22×C61—21no—
193C22×C61—21no—
194C22×C61#39211yescharacteristic
195C22×C61#44811yescharacteristic
196C22×C61#44911yescharacteristic
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—42no—
205C4×C61—42no—
206C4×C61—82no—
207C4×C61—81no—
208C4×C61—81no—
209C4×C61#45011yescharacteristic
210C4×C61#45211yescharacteristic
211C4×C61#46511yescharacteristic
212C4×C61#46811yescharacteristic
213Dic61—81no—
214#3103—611no—
215#3037—611no—
216#2581D6111yescharacteristic, complemented
217#1517—611no—
218#1487—611no—
219#1479—611no—
220#1286—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61#200011yescharacteristic
224C2×C61#200911yescharacteristic
225C2×C61#201011yescharacteristic
226D61—161no—
227C2×#137—1221no—
228#532—611no—
229C2×C4×Q8C2×D6111yescharacteristic
230C2×C4×Q8C2×D6111yescharacteristic
231#481—1221no—
232#475—1221no—
233#464—1222no—
234#462—1221no—
235#460—1221no—
236#460—1221no—
237#448—1221no—
238C4×SD16—1222no—
239#431—611no—
240#431—611no—
241#423—611no—
242#417—1221no—
243#400—21no—
244#395—21no—
245#391—21no—
246#389—21no—
247#387—22no—
248#382C2×D6111yescharacteristic
249#327—1222no—
250Q8⋊C8—1222no—
251Q8⋊C8—1222no—
252C61#999911yescharacteristic, complemented, Sylow
253C2×#41—1221no—
254C22×Q8C22⋊D6111yescharacteristic
255C22×Q8C22⋊D6111yescharacteristic
256#137—2442no—
257#137—2442no—
258C2×Q16—1222no—
259C2×SD16—1222no—
260C2×SD16—1222no—
261C2×M16—1221no—
262C4⋊Q8—611no—
263#127—611no—
264#124—1221no—
265#121—1221no—
266#121—1221no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×D4—1221no—
276C4×D4—1221no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4C22⋊D6111yescharacteristic
282C2×C4⋊C4C22⋊D6111yescharacteristic
283C2×C42—21no—
284C2×C42—21no—
285C2×C42C22×D6111yescharacteristic
286#106—1222no—
287C4⋊C8—612no—
288C4⋊C8—1221no—
289C4⋊C8—1221no—
290C4⋊C8—1221no—
291#103—1222no—
292#103—1222no—
293#102—1222no—
294#102—1222no—
295C22⋊C8—1221no—
296C22⋊C8—1221no—
297C4×C8—612no—
298C4×C8—1221no—
299#95—22no—
300#95—22no—
301#95—22no—
302#95—21no—
303#95C22⋊D6112yes—
304#41—2441no—
305#41—2441no—
306#41—2441no—
307#41—2441no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—42no—
316C2×Q8—1221no—
317C2×Q8#1175820112yescomplemented
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—2441no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—2441no—
328C22×C4C2×C22⋊D6111yescharacteristic
329C22×C4C2×C22⋊D6111yescharacteristic
330C22×C4C2×C22⋊D6111yescharacteristic
331Q16—2444no—
332SD16—2444no—
333SD16—2444no—
334M16—2441no—
335M16—2441no—
336C2×C8—1222no—
337C2×C8—1222no—
338C2×C8—2441no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—44no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C22⋊C4—2441no—
353C22⋊C4—2441no—
354C42—41no—
355C42—41no—
356C42—41no—
357C42—41no—
358C42D4×D6111yescharacteristic
359C42D4×D6111yescharacteristic
360C42D4×D6111yescharacteristic
361C42#1175822411yescharacteristic
362C23—2441no—
363C23#1451974611yescharacteristic
364Q8—22no—
365Q8—22no—
366Q8—22no—
367Q8—22no—
368Q8—41no—
369Q8—41no—
370Q8—41no—
371Q8—41no—
372Q8—2441no—
373Q8—2441no—
374D4—4881no—
375D4—4881no—
376D4—4881no—
377D4—2442no—
378D4—2441no—
379D4—2441no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—4881no—
396C2×C4—4881no—
397C2×C4—2441no—
398C2×C4#1451974511yescharacteristic
399C2×C4#1451974511yescharacteristic
400C2×C4#1451974811yescharacteristic
401C2×C4#1451974911yescharacteristic
402C2×C4#1451974911yescharacteristic
403C2×C4#1451977311yescharacteristic
404C2×C4C2×#1175820111yescharacteristic
405C2×C4#1451979711yescharacteristic
406C2×C4#1451980211yescharacteristic
407C2×C4#1451980811yescharacteristic
408C8—4881no—
409C8—2442no—
410C8—2442no—
411C22—21no—
412C22—21no—
413C22—4881no—
414C22—4881no—
415C22—4881no—
416C22#1683967011yescharacteristic
417C22#1683990111yescharacteristic
418C22#1683990711yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—82no—
426C4—81no—
427C4—81no—
428C4—4881no—
429C4#1683991211yescharacteristic
430C4#1683992211yescharacteristic
431C4#1683999311yescharacteristic
432C4#1684001011yescharacteristic
433C2—21no—
434C2—21no—
435C2—9761no—
436C2#2144682011yescharacteristic
437C2#2144687911yescharacteristic
438C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2581C2
socleC22×C61#392
prime radical#16840312C22
hypercenter#2581D61
hypocenterC61#9999
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
4. #21444248C2semidirect
5. #21444214C2semidirect
6. #21443677C2semidirect
7. C61×#2581C2semidirect
92. C2×Q8×C61SD16semidirect
216. #2581D61semidirect
252. C61#9999semidirect
317. C2×Q8#11758201semidirect

Maximal subgroups

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

subgroupindex
#214558502
#214552912
#214443782
#214442482
#214442142
#214436772
C61×#25812
#999961