Finite Group Databasebeta

← #29592438

Subgroups — #29592438

Order 15616.

416 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447043C211yesmaximal, characteristic, complemented
2#21444821C211yesmaximal, characteristic, complemented
3#21444753C211yesmaximal, characteristic
4#21443825C211yesmaximal, characteristic, complemented
5#21443822C211yesmaximal, characteristic, complemented
6#21443765C211yesmaximal, characteristic, complemented
7C61×#2823C211yesmaximal, characteristic, complemented
8#16840343C2211yescharacteristic
9#16840075—21no—
10#16839896—21no—
11C2×#14519705—21no—
12#16839761—21no—
13#16839531C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C2×#126×C61—21no—
19C61×#398—21no—
20C61×#398C2211yescharacteristic
21C61×#396—21no—
22C61×#396—21no—
23C61×#396—21no—
24C61×#394—21no—
25C61×#394C2211yescharacteristic
26C61×#384C2211yescharacteristic
27C2×#11758222—21no—
28C2×#11758199—41no—
29C2×#11758194—21no—
30#14519757—41no—
31#14519752—41no—
32#14519751—21no—
33#14519751—21no—
34#14519710—41no—
35#14519705—42no—
36#14519700—41no—
37#14519698—41no—
38#14519697—41no—
39#14519697—41no—
40C22⋊#92418—21no—
41C22⋊#92418—21no—
42C22×D4×C61D411yescharacteristic
43#126×C61—42no—
44#126×C61—42no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61C2311yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C42×C61D411yescharacteristic
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C24×C61—21no—
66C2×D4×C61—41no—
67C2×D4×C61—81no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—41no—
77#11758222—41no—
78#11758222—41no—
79#11758222—41no—
80#11758222—41no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×C4×D61—41no—
85C2×Dic122—21no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61—42no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—81no—
94C4⋊C4×C61—81no—
95C4⋊C4×C61—81no—
96C22⋊C4×C61—42no—
97C22⋊C4×C61—42no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—81no—
101C22⋊C4×C61—81no—
102C22⋊C4×C61—81no—
103C42×C61—21no—
104C42×C61D812yescomplemented
105#11758199—82no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110#11758194—41no—
111#11758194—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61#12011yescharacteristic
123C22×D61—41no—
124D4×C61—42no—
125D4×C61—81no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—22no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C22⋊D61—81no—
150C22⋊D61—81no—
151C2×Dic61—41no—
152D244—41no—
153D244—41no—
154D244—81no—
155D244—81no—
156C4×D61—81no—
157C4×D61—81no—
158Dic122—41no—
159Dic122—41no—
160#92418—81no—
161#92418—81no—
162#92418—81no—
163#12155—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61#44711yescharacteristic
174C22×C61#45411yescharacteristic
175C22×C61B(4,𝔽2)11yescharacteristic
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—42no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—81no—
185C4×C61—81no—
186C4×C61—81no—
187C4×C61—81no—
188Dic61—81no—
189#2823D6111yescharacteristic, complemented
190#2039—611no—
191#1610—611no—
192#1598—611no—
193#1346—611no—
194#1345—611no—
195#1325—611no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—161no—
199C2×C61#159811yescharacteristic
200C2×C61#220011yescharacteristic
201C2×C61#220311yescharacteristic
202D61—161no—
203#537—611no—
204C2×#126—21no—
205#480—1221no—
206#447—1221no—
207C2×#104—1221no—
208#417—1221no—
209#398—21no—
210#398C2×D6111yescharacteristic
211#396—21no—
212#396—21no—
213#396—21no—
214#394—21no—
215#394C2×D6111yescharacteristic
216#384C2×D6111yescharacteristic
217#343—611no—
218#327—1221no—
219#327—1221no—
220#324—611no—
221#324—611no—
222C61#1215511yescharacteristic, complemented, Sylow
223C2×#41—1221no—
224C22×D4C22⋊D6111yescharacteristic
225C2×D8—2441no—
226C2×M16—1221no—
227#126—42no—
228#126—42no—
229C22⋊Q8—2441no—
230#121—1221no—
231#121—1221no—
232#121—2441no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4C22⋊D6111yescharacteristic
240C2×C4⋊C4C22⋊D6111yescharacteristic
241C2×C4⋊C4C22×D6111yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C42C22⋊D6111yescharacteristic
249#107—2441no—
250#104—2442no—
251#103—2441no—
252#102—2441no—
253#102—2441no—
254#102—2441no—
255C22⋊C8—1221no—
256C22⋊C8—1221no—
257#95—21no—
258#95—21no—
259#95C22⋊D6111yescharacteristic
260#95C22⋊D6111yescharacteristic
261C24—21no—
262#41—2441no—
263#41—2441no—
264#41—2441no—
265#41—2441no—
266C2×Q8—1221no—
267C2×D4—41no—
268C2×D4—81no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—2441no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—2441no—
279C22×C4C2×C22⋊D6111yescharacteristic
280C22×C4C2×C22⋊D6111yescharacteristic
281C22×C4C2×C22⋊D6111yescharacteristic
282D8—4882no—
283M16—2441no—
284M16—2441no—
285C2×C8—2441no—
286C2×C8—2441no—
287C2×C8—2441no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—81no—
296C4⋊C4—81no—
297C4⋊C4—81no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42—21no—
310C42#1175819912yescomplemented
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—2441no—
319C23#1451974611yescharacteristic
320Q8—2441no—
321Q8—2441no—
322D4—42no—
323D4—81no—
324D4—4881no—
325D4—4881no—
326D4—4881no—
327D4—4881no—
328D4—2441no—
329D4—2441no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—4881no—
352C2×C4—4881no—
353C2×C4—2441no—
354C2×C4C2×#1175819911yescharacteristic
355C2×C4#1451980311yescharacteristic
356C8—4881no—
357C8—4881no—
358C8—4881no—
359C22—21no—
360C22—21no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22#1683989611yescharacteristic
372C22#1683993511yescharacteristic
373C22#1683994911yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—4881no—
384C2—21no—
385C2—21no—
386C2—161no—
387C2—9761no—
388C2#2144475411yescharacteristic
389C2#2144782611yescharacteristic
390C2#2144784011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2823C2
socleC22×C61B(4,𝔽2)
prime radical#21444753C2
hypercenter#2823D61
hypocenterC61#12155
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2823

Complements

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

NH ≅ G/Ntype
1. #21447043C2semidirect
2. #21444821C2semidirect
4. #21443825C2semidirect
5. #21443822C2semidirect
6. #21443765C2semidirect
7. C61×#2823C2semidirect
104. C42×C61D8semidirect
189. #2823D61semidirect
222. C61#12155semidirect
310. C42#11758199semidirect

Maximal subgroups

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

subgroupindex
#214470432
#214448212
#214447532
#214438252
#214438222
#214437652
C61×#28232
#1215561