Finite Group Databasebeta

← #29589596

Subgroups — #29589596

Order 15616.

414 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 71 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#21450296C211yesmaximal, characteristic
2#21444147C211yesmaximal, characteristic
3#324×D61C211yesmaximal, characteristic
4#21443764C211yesmaximal, characteristic, complemented
5#21443764C211yesmaximal, characteristic, complemented
6#21443753C211yesmaximal, characteristic, complemented
7C61×#1319C211yesmaximal, characteristic, complemented
8C2×#14519753C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10#16839724—21no—
11C22⋊C8×D61—21no—
12#16839696—21no—
13#16839696—21no—
14#16839669C411yescharacteristic
15#16839636—21no—
16#16839636—21no—
17#16839632C411yescharacteristic
18#16839631C2211yescharacteristic
19C4×#11758198C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839487—21no—
23#16839487—21no—
24C61×#391C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C2×#11758189—41no—
31C2×C8×D61—41no—
32#14519753—41no—
33#14519753—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×#11758196D411yescharacteristic
43C4⋊C4×D61—41no—
44C4⋊C4×D61—41no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50#14519689—41no—
51#14519689—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C22×Q8×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2311yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62C23×D61C22⋊C411yescharacteristic
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—41no—
86C2×C4×D61—81no—
87C2×C4×D61—81no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—41no—
91C42×C61—41no—
92#11758198—24no—
93#11758198—41no—
94#11758198—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—81no—
98C4⋊Dic61—81no—
99#11758196—41no—
100#11758196—41no—
101#11758196—42no—
102#11758196—81no—
103#11758196—81no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C2×#92418—41no—
107C2×#92418—41no—
108#11758189—82no—
109C8×D61—82no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—22no—
114C22×D61—41no—
115C22×D61#9911yescharacteristic
116C22×D61#9911yescharacteristic
117Q8×C61—81no—
118Q8×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—22no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61#13111yescharacteristic
132C2×C4×C61#13111yescharacteristic
133C2×Dic61—22no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C4×D61—41no—
147C4×D61—41no—
148C4×D61—41no—
149C4×D61—41no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—81no—
153C4×D61—81no—
154C8×C61—81no—
155C8×C61—81no—
156#92418—81no—
157#92418—81no—
158#11555—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61#40811yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61#41311yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—42no—
170C2×D61—42no—
171C2×D61#35612yes—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—42no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—81no—
178Dic61—42no—
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182Dic61—81no—
183#2502—611no—
184#1463—611no—
185C2×#324—611no—
186#1325—611no—
187#1325—611no—
188#1319—611no—
189#1319D6111yescharacteristic, complemented
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#146811yescharacteristic
193C2×C61#212711yescharacteristic
194C2×C61C2×#35611yescharacteristic
195D61—22no—
196D61—41no—
197C2×C22⋊Q8—611no—
198C22×C4⋊C4—611no—
199#407—1221no—
200C2×C22⋊C8—1221no—
201#398—1221no—
202#398—1221no—
203#391—611no—
204#391C2×D6111yescharacteristic
205#385—1221no—
206#385—1221no—
207#384—611no—
208#384—611no—
209C4×C22⋊C4—611no—
210#324—611no—
211#324—611no—
212#324—1221no—
213#324—1221no—
214#324C2×D6111yescharacteristic
215#324C2×D6111yescharacteristic
216C61#1155511yescharacteristic, complemented, Sylow
217C22×Q8C4×D6111yescharacteristic
218C23×C4—611no—
219C23×C4—611no—
220C23×C4—611no—
221C2×M16—2441no—
222C22×C8—2441no—
223C22⋊Q8—2441no—
224C22⋊Q8—2441no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—2441no—
235C2×C4⋊C4—2441no—
236C2×C4⋊C4C22×D6111yescharacteristic
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C42—611no—
240C2×C42C4×D6111yescharacteristic
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—1221no—
244C22⋊C8—1221no—
245C22⋊C8—2441no—
246C22⋊C8—2441no—
247#95—21no—
248#95—21no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252C24—611no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—4881no—
273C22×C4—4881no—
274C22×C4—2441no—
275C22×C4C2×C4×D6111yescharacteristic
276C22×C4D4×D6111yescharacteristic
277C22×C4D4×D6111yescharacteristic
278M16—4882no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—4882no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—41no—
285C4⋊C4—4881no—
286C4⋊C4—4881no—
287C4⋊C4—4881no—
288C4⋊C4—4881no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2442no—
294C22⋊C4—1224no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C42—41no—
298C42—1221no—
299C42—1221no—
300C23—611no—
301C23—611no—
302C23—1222no—
303C23—1221no—
304C23—1221no—
305C23—2441no—
306C23C22⋊C4×D6111yescharacteristic
307Q8—81no—
308Q8—81no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
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—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4#1451978311yescharacteristic
343C2×C4#1451978511yescharacteristic
344C8—81no—
345C8—81no—
346C8—4881no—
347C8—4881no—
348C22—21no—
349C22—21no—
350C22—612no—
351C22—1221no—
352C22—1221no—
353C22—1221no—
354C22—1221no—
355C22—1221no—
356C22—2442no—
357C22—2442no—
358C22#1683972711yescharacteristic
359C22#99×D6111yescharacteristic
360C22#1683974311yescharacteristic
361C4—21no—
362C4—21no—
363C4—42no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—4881no—
368C4—2442no—
369C4—2441no—
370C4—2441no—
371C4—2441no—
372C2—21no—
373C2—21no—
374C2—1222no—
375C2—2441no—
376C2#2144416411yescharacteristic
377C2#2144748711yescharacteristic
378C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1319C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1319D61
hypocenterC61#11555
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
4. #21443764C2semidirect
5. #21443764C2semidirect
6. #21443753C2semidirect
7. C61×#1319C2semidirect
189. #1319D61semidirect
216. C61#11555semidirect

Maximal subgroups

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

subgroupindex
#214502962
#214441472
#324×D612
#214437642
#214437532
C61×#13192
#1155561