Finite Group Databasebeta

← #29596269

Subgroups — #29596269

Order 15616.

670 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 87 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#21448306C211yesmaximal, characteristic
2#21445735C212yesmaximal
3#21443944C211yesmaximal, characteristic, complemented
4#21443943C212yesmaximal, complemented
5C61×#1393C211yesmaximal, characteristic, complemented
6C22×#11758224C2211yescharacteristic
7C2×#14519735C411yescharacteristic, complemented
8C2×C42×D61C411yescharacteristic, complemented
9C2×#14519692C2212yes—
10C2×#14519691—22no—
11#16839668C411yescharacteristic, complemented
12#16839667C411yescharacteristic, complemented
13#16839665C2211yescharacteristic
14#16839638—22no—
15#16839623—22no—
16C22⋊C4×Dic61—22no—
17C2×#99×C61C2212yes—
18C61×#390C2211yescharacteristic
19C2×#11758224—22no—
20C2×#11758224—21no—
21C2×#11758224—21no—
22C2×#11758224—42no—
23C2×#11758224—42no—
24C22×Dic122C2×C411yescharacteristic
25C22×C22⋊D61D412yes—
26C23×Dic61D412yes—
27C22×C4×D61—21no—
28C22×C4×D61C2×C411yescharacteristic
29#14519735—42no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C22⋊Dic61—22no—
32C2×C22⋊Dic61—22no—
33C2×#11758198—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61C2×C411yescharacteristic
37C42×D61—42no—
38#14519692—22no—
39#14519692—22no—
40#14519691—44no—
41#14519684—22no—
42#14519684—22no—
43#14519684—44no—
44C22×D4×C61C2311yescharacteristic
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C22⋊C4×C61—22no—
47C2×C22⋊C4×C61—22no—
48C2×C42×C61C2×C411yescharacteristic
49#99×C61—22no—
50#99×C61—22no—
51C24×C61C2×D412yes—
52C23×D61C22⋊C411yescharacteristic
53C2×D4×C61—41no—
54C2×D4×C61—41no—
55C2×D4×C61#4112yes—
56C2×D4×C61#4111yescharacteristic
57C2×D4×C61#4111yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—42no—
61C22×C4×C61C22×C411yescharacteristic
62C2×C22⋊D61—22no—
63C2×C22⋊D61—22no—
64C2×C22⋊D61—24no—
65C2×C22⋊D61—42no—
66C22×Dic61—21no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—24no—
70C22×Dic61—21no—
71C22×Dic61—42no—
72C22×Dic61—42no—
73C22×Dic61C22⋊C412yes—
74C22×Dic61C22⋊C411yescharacteristic
75#11758224—44no—
76#11758224—48no—
77#11758224—44no—
78C2×C4×D61—22no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—22no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×Dic122—21no—
86C2×Dic122—21no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—44no—
91C22⋊C4×C61—42no—
92C22⋊C4×C61—42no—
93C42×C61—41no—
94C22⋊Dic61—44no—
95C22⋊Dic61—42no—
96C22⋊Dic61—42no—
97#11758198—42no—
98C4⋊Dic61—41no—
99C4×Dic61—42no—
100C4×Dic61—42no—
101C4×Dic61—41no—
102C23×C61—22no—
103C23×C61—22no—
104C23×C61—42no—
105C23×C61—42no—
106C23×C61C2×C22⋊C411yescharacteristic
107C23×C61#12312yes—
108C23×C61#12312yes—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61#9912yes—
114D4×C61—42no—
115D4×C61—41no—
116D4×C61—41no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—82no—
125C2×C4×C61—82no—
126C2×C4×C61—82no—
127C2×C4×C61#11711yescharacteristic
128C2×C4×C61#11711yescharacteristic
129C22⋊D61—44no—
130C22⋊D61—44no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—44no—
138C2×Dic61—44no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—82no—
144C2×Dic61—82no—
145C2×Dic61—82no—
146C2×Dic61#9912yes—
147C4×D61—24no—
148C4×D61—24no—
149C4×D61—48no—
150Dic122—42no—
151Dic122—42no—
152#12857—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—42no—
158C22×C61—42no—
159C22×C61—42no—
160C22×C61—42no—
161C22×C61—82no—
162C22×C61#38111yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C22×C61C2×#9911yescharacteristic
165C2×D61—22no—
166C2×D61—42no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—42no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—42no—
173C4×C61—81no—
174C4×C61—162no—
175Dic61—22no—
176Dic61—42no—
177Dic61—42no—
178Dic61—81no—
179Dic61—162no—
180#2297—611no—
181#1782—612no—
182#1393—612no—
183#1393—611no—
184#1393D6111yescharacteristic, complemented
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—42no—
188C2×C61—42no—
189C2×C61#181911yescharacteristic
190C2×C61#212611yescharacteristic
191C2×C61#212611yescharacteristic
192D61—42no—
193C22×#41—611no—
194C2×#117—611no—
195C22×C42—611no—
196C2×#99—612no—
197C2×#99—1222no—
198C2×#99C2×D6112yes—
199#391—611no—
200#391—611no—
201#390—611no—
202#390C2×D6111yescharacteristic
203#386—1222no—
204#381—1222no—
205C4×C22⋊C4—1222no—
206C61#1285711yescharacteristic, complemented, Sylow
207C2×#41—1222no—
208C2×#41—1221no—
209C2×#41—1221no—
210C2×#41—2442no—
211C2×#41—2442no—
212C22×Q8—611no—
213C22×D4—612no—
214C22×D4C22×D6111yescharacteristic
215C23×C4—612no—
216C23×C4—611no—
217C23×C4—1221no—
218#117—2442no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4C4×D6111yescharacteristic
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1222no—
225C2×C22⋊C4—1222no—
226C2×C42—611no—
227C2×C42—1221no—
228C2×C42—1221no—
229C2×C42—2442no—
230C2×C42C4×D6111yescharacteristic
231#99—22no—
232#99—22no—
233#99—1222no—
234#99—1222no—
235#99—2444no—
236#95—1222no—
237#95—1222no—
238#95—2444no—
239C24—611no—
240C24D4×D6112yes—
241#41—2448no—
242#41—2444no—
243#41—2444no—
244C2×Q8—1221no—
245C2×Q8—1221no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—1224no—
251C2×D4—1222no—
252C2×D4—1222no—
253C2×D4—2442no—
254C2×D4#1175822212yes—
255C2×D4#1175822411yescharacteristic
256C2×D4#1175822611yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—611no—
261C22×C4—612no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—1224no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1222no—
269C22×C4—1222no—
270C22×C4—1221no—
271C22×C4—2442no—
272C22×C4—2442no—
273C22×C4—2442no—
274C22×C4—2442no—
275C22×C4—2442no—
276C22×C4C2×C4×D6111yescharacteristic
277C4⋊C4—41no—
278C4⋊C4—2441no—
279C22⋊C4—44no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—2442no—
283C22⋊C4—2444no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C42—41no—
287C42—2441no—
288C42—2442no—
289C42—2442no—
290C23—22no—
291C23—22no—
292C23—42no—
293C23—42no—
294C23—612no—
295C23—1221no—
296C23—1221no—
297C23—2441no—
298C23—2441no—
299C23C22⋊C4×D6111yescharacteristic
300C23#1451975912yes—
301C23#1451976212yes—
302Q8—2442no—
303Q8—2442no—
304D4—42no—
305D4—41no—
306D4—41no—
307D4—2444no—
308D4—2444no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—612no—
320C2×C4—1224no—
321C2×C4—1224no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4—1222no—
328C2×C4—4882no—
329C2×C4—4882no—
330C2×C4—4882no—
331C2×C4—2448no—
332C2×C4—2444no—
333C2×C4—2444no—
334C2×C4—2442no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4#1451973411yescharacteristic
339C2×C4#1451973511yescharacteristic
340C22—21no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—82no—
349C22—1222no—
350C22—2442no—
351C22—2442no—
352C22—2441no—
353C22—2441no—
354C22#1683962411yescharacteristic
355C22#99×D6111yescharacteristic
356C22#99×D6111yescharacteristic
357C4—21no—
358C4—21no—
359C4—42no—
360C4—81no—
361C4—162no—
362C4—1222no—
363C4—9762no—
364C4—4881no—
365C4—2442no—
366C4—2442no—
367C2—21no—
368C2—21no—
369C2—42no—
370C2—42no—
371C2—2442no—
372C2#2144589211yescharacteristic
373C2#2144748111yescharacteristic
374C2#2144748311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×D4C22×D61
FittingC61×#1393C2
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×D4×C61C23
hypercenter#1393D61
hypocenterC61#12857
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #21443944C2semidirect
4. #21443943C2semidirect
5. C61×#1393C2semidirect
7. C2×#14519735C4semidirect
8. C2×C42×D61C4semidirect
11. #16839668C4semidirect
12. #16839667C4semidirect
184. #1393D61semidirect
206. C61#12857semidirect

Maximal subgroups

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

subgroupindex
#214483062
#214457352
#214439442
#214439432
C61×#13932
#1285761