Finite Group Databasebeta

← #29577287

Subgroups — #29577287

Order 15616.

434 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 93 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#21457051C211yesmaximal, characteristic
2#21454960C211yesmaximal, characteristic
3#21446742C211yesmaximal, characteristic, complemented
4#21444537C211yesmaximal, characteristic, complemented
5#21444342C211yesmaximal, characteristic
6#21443688C211yesmaximal, characteristic, complemented
7C61×#1285C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9#16840296C2211yescharacteristic
10#16840171C412yescomplemented
11#16840122C412yescomplemented
12#16840098—21no—
13#16840081—21no—
14#16840048—21no—
15#16840043—21no—
16#16839890—21no—
17#16839835—21no—
18#16839830—21no—
19#16839825—21no—
20#16839822—21no—
21#16839819C2211yescharacteristic
22#16839787—21no—
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519700—21no—
25C2×#14519700—21no—
26#16839509—21no—
27#16839509—21no—
28#16839498—21no—
29#16839495—21no—
30C61×#432C2211yescharacteristic
31C61×#432C2211yescharacteristic
32C4×C4⋊C4×C61C2211yescharacteristic
33C22×Dic122—21no—
34C2×#11758189—21no—
35C22×#92418D411yescharacteristic
36C22×#92418D411yescharacteristic
37C2×C8×D61—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777C2×C412yes—
42#14519771—21no—
43#14519769C2×C411yescharacteristic
44#14519765C2×C411yescharacteristic
45#14519760—21no—
46#14519756D411yescharacteristic
47#14519751D411yescharacteristic
48C4×Dic122D411yescharacteristic
49C4×D244D411yescharacteristic
50C4×C22⋊D61—21no—
51#14519734—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—21no—
54#14519711—22no—
55#14519709—22no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59#14519706—21no—
60#14519706—21no—
61#14519702—22no—
62#14519700—42no—
63#14519700—42no—
64#14519699—22no—
65C22⋊#92418—21no—
66#14519689—21no—
67#14519689—21no—
68#14519688—21no—
69#14519687—21no—
70C8×Dic61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C42×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61D411yescharacteristic
76C4⋊C8×C61D411yescharacteristic
77C22⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79#97×C61—21no—
80#97×C61C2×C412yes—
81#95×C61—21no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C2×C22⋊D61—21no—
87C22×Dic61—41no—
88C2×D244C22⋊C411yescharacteristic
89C2×C4×D61—21no—
90C2×Dic122—22no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×Dic122C22⋊C411yescharacteristic
97C2×C8×C61—22no—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—41no—
102C42×C61—81no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107C22⋊Dic61—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112C4⋊Dic61—22no—
113C4⋊Dic61—22no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4⋊Dic61C22⋊C411yescharacteristic
117C4⋊Dic61C22⋊C411yescharacteristic
118#11758196—21no—
119#11758196—21no—
120#11758196—21no—
121#11758196—21no—
122C4×Dic61—21no—
123C2×#92418—21no—
124C2×#92418—21no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128#11758189—81no—
129C8×D61—81no—
130C23×C61#12111yescharacteristic
131C22×D61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C22⋊D61—41no—
147C22⋊D61—41no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61—81no—
153C2×Dic61—81no—
154D244—41no—
155C4×D61—41no—
156C4×D61—41no—
157Dic122—41no—
158Dic122—42no—
159Dic122—42no—
160Dic122—81no—
161Dic122—81no—
162C8×C61—42no—
163C8×C61—41no—
164C8×C61—41no—
165#92418—41no—
166#92418—41no—
167#92418—81no—
168#9377—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61#38611yescharacteristic
172C22×C61#47111yescharacteristic
173C22×C61#47311yescharacteristic
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—82no—
183C4×C61#45311yescharacteristic
184C4×C61#45411yescharacteristic
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61—82no—
189#3239—611no—
190#2992—611no—
191#1981—611no—
192#1556—611no—
193#1509—611no—
194#1290—611no—
195#1285D6111yescharacteristic, complemented
196C2×C61—21no—
197C2×C61—21no—
198C2×C61#188311yescharacteristic
199C2×C61#190811yescharacteristic
200C2×C61#190911yescharacteristic
201D61—81no—
202C2×C4⋊Q8—611no—
203#529—611no—
204#501—612no—
205#489—612no—
206#484—1221no—
207#481—1221no—
208#475—1221no—
209#474—1221no—
210#446—1221no—
211#435—1221no—
212#435—1221no—
213C8×D4—1221no—
214#433—1221no—
215#432—611no—
216#432C2×D6111yescharacteristic
217#432C2×D6111yescharacteristic
218#424—1221no—
219C2×C4⋊C8—611no—
220C2×#103—1221no—
221C2×#103—1221no—
222C4×C4⋊C4C2×D6111yescharacteristic
223#332—1221no—
224#332—1221no—
225#328—1221no—
226#327—1221no—
227C61#937711yescharacteristic, complemented, Sylow
228C22×Q8—1221no—
229C2×M16—1221no—
230C22×C8—611no—
231C22×C8—611no—
232C22×C8—1221no—
233C4⋊Q8—612no—
234C4⋊Q8—1221no—
235C4⋊Q8—1221no—
236C4⋊Q8—1221no—
237#126—1221no—
238#125—611no—
239#124—611no—
240#123—1221no—
241C22⋊Q8—611no—
242#121—611no—
243C4×Q8—611no—
244C4×D4—611no—
245C4×D4—1221no—
246#117—1221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C42—21no—
251C2×C42C22×D6111yescharacteristic
252#107—1222no—
253#106—1222no—
254C4⋊C8—21no—
255C4⋊C8—1221no—
256C4⋊C8—1221no—
257C4⋊C8—1221no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8D24411yescharacteristic
261C4⋊C8D24411yescharacteristic
262#103—1222no—
263#103—2442no—
264#103—2442no—
265#102—1222no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—1221no—
269C22⋊C8—1221no—
270C22⋊C8—1221no—
271#97—21no—
272#97—1221no—
273#97—1221no—
274#97C4×D6112yes—
275C4×C8—1221no—
276#95—21no—
277C2×Q8—611no—
278C2×Q8—1222no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×Q8—2441no—
282C2×Q8—2441no—
283C2×Q8—2441no—
284C2×D4—611no—
285C2×D4—1221no—
286C22×C4—41no—
287C22×C4—1221no—
288C22×C4—2441no—
289C22×C4#1175822211yescharacteristic
290C22×C4D4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292M16—4881no—
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—1221no—
297C2×C8—1221no—
298C2×C8—4881no—
299C2×C8—2441no—
300C2×C8—2441no—
301C2×C8—2441no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—611no—
305C4⋊C4—611no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1222no—
311C4⋊C4—1222no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C42—81no—
320C42—1221no—
321C42C2×C4×D6111yescharacteristic
322C42C2×D24411yescharacteristic
323C42D4×D6111yescharacteristic
324C42#1175822611yescharacteristic
325C23—1221no—
326C23#1451975011yescharacteristic
327Q8—4881no—
328Q8—4881no—
329Q8—2442no—
330Q8—2442no—
331Q8—2441no—
332D4—2441no—
333D4—2441no—
334D4—2441no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—4881no—
347C2×C4—4881no—
348C2×C4—2442no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4C22⋊C4×D6111yescharacteristic
352C2×C4#1451973911yescharacteristic
353C2×C4C4×D24411yescharacteristic
354C2×C4#1451974711yescharacteristic
355C2×C4#1451975211yescharacteristic
356C2×C4#1451976211yescharacteristic
357C8—42no—
358C8—41no—
359C8—41no—
360C8—4881no—
361C8—2441no—
362C8—2441no—
363C22—21no—
364C22—21no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22#1683964011yescharacteristic
369C22#1684002411yescharacteristic
370C22#1684003611yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—82no—
377C4—4882no—
378C4—2441no—
379C4—2441no—
380C4—2441no—
381C4#1683993111yescharacteristic
382C4#1683993611yescharacteristic
383C2—21no—
384C2—21no—
385C2—4881no—
386C2#2144619611yescharacteristic
387C2#2144633511yescharacteristic
388C2#2144634011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1285C2
socleC22×C61#386
prime radical#14519751D4
cosocleC2×C42×C61C23
hypercenter#1285D61
hypocenterC61#9377
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
3. #21446742C2semidirect
4. #21444537C2semidirect
6. #21443688C2semidirect
7. C61×#1285C2semidirect
10. #16840171C4semidirect
11. #16840122C4semidirect
195. #1285D61semidirect
227. C61#9377semidirect

Maximal subgroups

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

subgroupindex
#214570512
#214549602
#214467422
#214445372
#214443422
#214436882
C61×#12852
#937761