Finite Group Databasebeta

← #29583239

Subgroups — #29583239

Order 15616.

396 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 73 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#21452016C211yesmaximal, characteristic
2#21446803C211yesmaximal, characteristic
3#21444353C211yesmaximal, characteristic
4#21444340C211yesmaximal, characteristic
5#21443704C211yesmaximal, characteristic
6#21443673C211yesmaximal, characteristic
7C61×#1305C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16839698—21no—
10#16839695—21no—
11#16839695—21no—
12#16839685—21no—
13#16839659—21no—
14#16839645—21no—
15#16839625C2211yescharacteristic
16C4×C22⋊Dic61C2211yescharacteristic
17C4×C22⋊Dic61C2211yescharacteristic
18#16839528—21no—
19#16839528—21no—
20#16839500—21no—
21#16839500—21no—
22#16839500—21no—
23#16839500—21no—
24C61×#407C2211yescharacteristic
25C61×#407C2211yescharacteristic
26C61×#380C2211yescharacteristic
27C22×Dic122Q811yescharacteristic
28#14519756—21no—
29#14519756—21no—
30#14519756—21no—
31#14519756—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61Q811yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684D411yescharacteristic
51#14519684D411yescharacteristic
52#14519684D411yescharacteristic
53#14519684D411yescharacteristic
54C23×C4×C61C2311yescharacteristic
55C2×M16×C61—21no—
56C2×M16×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C22⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61D411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61—21no—
65C24×C61C2×D411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—81no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×Q811yescharacteristic
72C22×C4×C61#4111yescharacteristic
73C22×C4×C61#4111yescharacteristic
74C22×C4×C61#4111yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C2×Dic122—21no—
83C2×Dic122—21no—
84C2×Dic122—81no—
85M16×C61—81no—
86M16×C61—81no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—81no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊Dic61—22no—
93C22⋊Dic61—42no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97C22⋊Dic61—81no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—42no—
101C4⋊Dic61—81no—
102#11758196—42no—
103#11758196—41no—
104#11758196—41no—
105#11758196—81no—
106#11758196—81no—
107#11758196—81no—
108C4×Dic61—81no—
109C4×Dic61—81no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61#12011yescharacteristic
115C23×C61C22⋊Q811yescharacteristic
116C23×C61#12411yescharacteristic
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61C22⋊Q811yescharacteristic
130C2×C4×C61C22⋊Q811yescharacteristic
131C2×C4×C61#12411yescharacteristic
132C2×C4×C61#12411yescharacteristic
133C2×Dic61—22no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152Dic122—81no—
153Dic122—81no—
154C8×C61—81no—
155C8×C61—81no—
156#10385—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61#39311yescharacteristic
168C22×C61#45511yescharacteristic
169C22×C61#45611yescharacteristic
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—81no—
175C4×C61—81no—
176Dic61—42no—
177Dic61—81no—
178Dic61—81no—
179Dic61—81no—
180Dic61—82no—
181Dic61—81no—
182Dic61—81no—
183#2667—611no—
184#1996—611no—
185#1511—611no—
186#1508—611no—
187#1305D6111yescharacteristic
188#1297—611no—
189#1284—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—41no—
193C2×C61—41no—
194C2×C61#202811yescharacteristic
195C2×C61#203111yescharacteristic
196C2×C61#203211yescharacteristic
197C2×C22⋊Q8—611no—
198#407C2×D6111yescharacteristic
199#407C2×D6111yescharacteristic
200#399—1221no—
201#398—1221no—
202#398—1221no—
203#396—1221no—
204#389—1221no—
205#387—1221no—
206#381—611no—
207#380C2×D6111yescharacteristic
208C4×C22⋊C4—611no—
209C4×C22⋊C4—611no—
210#342—1221no—
211#342—1221no—
212#328—1221no—
213#328—1221no—
214#328—1221no—
215#328—1221no—
216C61#1038511yescharacteristic, complemented, Sylow
217C22×Q8—611no—
218C23×C4C22×D6111yescharacteristic
219C2×M16—21no—
220C2×M16—21no—
221C22⋊Q8—1221no—
222C22⋊Q8—1221no—
223C22⋊Q8—1221no—
224C22⋊Q8—1221no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4D24411yescharacteristic
239C2×C22⋊C4D24411yescharacteristic
240C2×C42—1221no—
241C2×C42—1221no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246#95—21no—
247#95—611no—
248#95—611no—
249#95—611no—
250#95—611no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255C24C2×D24411yescharacteristic
256C2×Q8—1221no—
257C2×Q8—1221no—
258C2×Q8—4881no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—81no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—2441no—
269C22×C4#1175822211yescharacteristic
270C22×C4#1175822211yescharacteristic
271C22×C4D4×D6111yescharacteristic
272C22×C4D4×D6111yescharacteristic
273C22×C4#1175822411yescharacteristic
274C22×C4Q8×D6111yescharacteristic
275M16—81no—
276M16—81no—
277C2×C8—41no—
278C2×C8—41no—
279C4⋊C4—81no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—4881no—
283C4⋊C4—4881no—
284C4⋊C4—4881no—
285C4⋊C4—4881no—
286C4⋊C4—2442no—
287C4⋊C4—2442no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—1222no—
293C22⋊C4—4881no—
294C22⋊C4—2442no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C42—4881no—
299C42—4881no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23#1451974711yescharacteristic
305C23#1451975711yescharacteristic
306C23#1451976511yescharacteristic
307Q8—4881no—
308Q8—4881no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—1222no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—2441no—
327C2×C4—2442no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4#1451975511yescharacteristic
341C2×C4#1451975511yescharacteristic
342C2×C4#1451976311yescharacteristic
343C2×C4#1451976311yescharacteristic
344C8—81no—
345C8—81no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22#1683967511yescharacteristic
357C22#1683994211yescharacteristic
358C22#1683994711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—81no—
364C4—81no—
365C4—4881no—
366C4—4881no—
367C4—4881no—
368C4—4882no—
369C4—4881no—
370C4—4881no—
371C4—2442no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2#2144698111yescharacteristic
377C2#2144699411yescharacteristic
378C2#2144699711yescharacteristic
subgroupG/H
centerC22#16839675
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1305C2
socleC22×C61#393
prime radicalC24×C61C2×D4
hypercenter#1305D61
hypocenterC61#10385
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
216. C61#10385semidirect

Maximal subgroups

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

subgroupindex
#214520162
#214468032
#214443532
#214443402
#214437042
#214436732
C61×#13052
#1038561