Finite Group Databasebeta

← #29590816

Subgroups — #29590816

Order 15616.

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

normal subgroups only

This group has 416 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#21449107C211yesmaximal, characteristic
2#21445814C211yesmaximal, characteristic, complemented
3#21444161C211yesmaximal, characteristic, complemented
4#21443847C211yesmaximal, characteristic, complemented
5#21443845C211yesmaximal, characteristic, complemented
6#21443822C211yesmaximal, characteristic
7C61×#1345C211yesmaximal, characteristic
8C2×#14519742C2211yescharacteristic
9C2×D4×Dic61C411yescharacteristic
10#16839816—21no—
11#16839785—21no—
12C2×#14519695—21no—
13#16839702C411yescharacteristic
14#16839701C2211yescharacteristic
15#16839690—21no—
16#16839676C411yescharacteristic
17#16839674—21no—
18C22⋊C4×Dic61—21no—
19C22⋊C4×Dic61—21no—
20#16839607C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C23×Dic61—21no—
29C2×#11758194—21no—
30#14519742—41no—
31#14519742—41no—
32D4×Dic61—41no—
33D4×Dic61—41no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196C2×C411yescharacteristic
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519706—41no—
45#14519706—41no—
46#14519706—41no—
47#14519695—42no—
48C22⋊#92418—21no—
49#14519687—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C22×D4×C61C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C22⋊C8×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61—42no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—42no—
73C22×Dic61—42no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84M16×C61—41no—
85M16×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—42no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊Dic61—42no—
93C22⋊Dic61—42no—
94C22⋊Dic61—42no—
95C4⋊Dic61—41no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—42no—
105#11758194—41no—
106#11758194—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C23×C61—22no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61C2×C22⋊C411yescharacteristic
117D4×C61—42no—
118D4×C61—42no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×Dic61—22no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—82no—
146C2×Dic61—82no—
147C2×Dic61#9911yescharacteristic
148C2×Dic61#9911yescharacteristic
149Dic122—42no—
150Dic122—42no—
151C8×C61—81no—
152C8×C61—81no—
153#92418—81no—
154#92418—81no—
155#11829—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—42no—
159C22×C61—42no—
160C22×C61—42no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61C2×#9911yescharacteristic
166C22×C61#41711yescharacteristic
167C22×C61#42111yescharacteristic
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—81no—
173Dic61—21no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—81no—
178Dic61—81no—
179Dic61#35512yes—
180#2398—611no—
181#1801—611no—
182#1467—611no—
183#1353—611no—
184#1353—611no—
185#1345—611no—
186#1345D6111yescharacteristic
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—82no—
190C2×C61#151311yescharacteristic
191C2×C61#212011yescharacteristic
192C2×C61C2×#35511yescharacteristic
193C2×C4×Q8—611no—
194C2×C4×D4—611no—
195#432—1221no—
196#423—1221no—
197C2×#101—1221no—
198#400—611no—
199#400—611no—
200#397—1221no—
201#394—611no—
202#394C2×D6111yescharacteristic
203#393—1221no—
204C4×C22⋊C4—1221no—
205C4×C22⋊C4—1221no—
206#376—611no—
207#343—611no—
208#343C2×D6111yescharacteristic
209#324—611no—
210#324—1221no—
211#324C2×D6111yescharacteristic
212C61#1182911yescharacteristic, complemented, Sylow
213C22×Q8—611no—
214C22×D4C4×D6111yescharacteristic
215C23×C4—1221no—
216C2×M16—21no—
217C2×M16—1221no—
218C4×Q8—2441no—
219C4×Q8—2441no—
220C4×D4—2441no—
221C4×D4—2441no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4C22×D6111yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—1221no—
235C4⋊C8—2441no—
236C4⋊C8—2441no—
237C4⋊C8—2441no—
238#101—2442no—
239C22⋊C8—21no—
240C22⋊C8—1221no—
241#97—2441no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248#95C4×D6111yescharacteristic
249C24—21no—
250C2×Q8—1221no—
251C2×Q8—1221no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×D4—41no—
255C2×D4—42no—
256C22×C4—21no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4C2×C4×D6111yescharacteristic
268C22×C4D4×D6111yescharacteristic
269C22×C4D4×D6111yescharacteristic
270M16—41no—
271M16—41no—
272M16—2441no—
273M16—2441no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—2441no—
277C2×C8—2441no—
278C4⋊C4—41no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C22⋊C4—42no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—2442no—
286C22⋊C4—2442no—
287C22⋊C4—2442no—
288C42—1221no—
289C42—1221no—
290C42—1221no—
291C42—1221no—
292C42—1221no—
293C42—1221no—
294C42—2442no—
295C23—22no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23C22⋊C4×D6111yescharacteristic
303Q8—2442no—
304Q8—2442no—
305D4—42no—
306D4—42no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—1222no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—4882no—
327C2×C4—4882no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4#1451980111yescharacteristic
336C2×C4#1451980611yescharacteristic
337C8—81no—
338C8—81no—
339C8—4881no—
340C8—4881no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—42no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22#99×D6111yescharacteristic
351C22#1683976011yescharacteristic
352C22#1683977711yescharacteristic
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—612no—
359C4—1221no—
360C4—4881no—
361C4—4881no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C2—21no—
366C2—21no—
367C2—82no—
368C2#2144435911yescharacteristic
369C2#2144745711yescharacteristic
370C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61#11829
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #21445814C2semidirect
3. #21444161C2semidirect
4. #21443847C2semidirect
5. #21443845C2semidirect
212. C61#11829semidirect

Maximal subgroups

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

subgroupindex
#214491072
#214458142
#214441612
#214438472
#214438452
#214438222
C61×#13452
#1182961