Finite Group Databasebeta

← #29596275

Subgroups — #29596275

Order 15616.

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

normal subgroups only

This group has 642 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#21448409C211yesmaximal, characteristic
2#21445735C212yesmaximal
3#21443944C211yesmaximal, characteristic, complemented
4#21443943C212yesmaximal, complemented
5C61×#1393C211yesmaximal, characteristic, complemented
6C22×#11758224C2211yescharacteristic
7C2×#14519734C411yescharacteristic, complemented
8C2×C4⋊C4×D61C411yescharacteristic, complemented
9C2×#14519692C2212yes—
10C2×#14519691—22no—
11#16839668C411yescharacteristic, complemented
12#16839667C411yescharacteristic, complemented
13#16839665C2211yescharacteristic
14#16839638—22no—
15#16839623—22no—
16#16839620—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#14519734—42no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C4⋊C4×D61—42no—
34C2×C22⋊Dic61—22no—
35C2×C22⋊Dic61—22no—
36C2×#11758198—21no—
37C2×C4×Dic61C2×C411yescharacteristic
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—22no—
67C22×Dic61—22no—
68C22×Dic61—24no—
69C22×Dic61—21no—
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—82no—
84C2×Dic122—21no—
85C2×Dic122—21no—
86C2×Dic122—41no—
87C2×Dic122—41no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—42no—
90C22⋊C4×C61—42no—
91C22⋊C4×C61—82no—
92C42×C61—41no—
93C22⋊Dic61—42no—
94C22⋊Dic61—42no—
95C22⋊Dic61—82no—
96#11758198—42no—
97C4⋊Dic61—41no—
98#11758196—42no—
99#11758196—42no—
100C4×Dic61—41no—
101C23×C61—22no—
102C23×C61—22no—
103C23×C61—42no—
104C23×C61—42no—
105C23×C61C2×C22⋊C411yescharacteristic
106C23×C61#12312yes—
107C23×C61#12312yes—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61#9912yes—
113D4×C61—42no—
114D4×C61—41no—
115D4×C61—41no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—82no—
124C2×C4×C61—82no—
125C2×C4×C61—82no—
126C2×C4×C61#11711yescharacteristic
127C2×C4×C61#11711yescharacteristic
128C22⋊D61—44no—
129C22⋊D61—44no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—44no—
136C2×Dic61—44no—
137C2×Dic61—41no—
138C2×Dic61—42no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—82no—
143C2×Dic61—82no—
144C2×Dic61—82no—
145C2×Dic61#9912yes—
146C4×D61—24no—
147C4×D61—24no—
148C4×D61—84no—
149Dic122—42no—
150Dic122—42no—
151#12859—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—42no—
157C22×C61—42no—
158C22×C61—42no—
159C22×C61—42no—
160C22×C61—82no—
161C22×C61#38111yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C2×D61—22no—
165C2×D61—42no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—42no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—81no—
172C4×C61—81no—
173C4×C61—162no—
174Dic61—22no—
175Dic61—42no—
176Dic61—81no—
177Dic61—81no—
178Dic61—162no—
179#2311—611no—
180#1782—612no—
181#1393—612no—
182#1393—611no—
183#1393D6111yescharacteristic, complemented
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—42no—
187C2×C61—42no—
188C2×C61#181911yescharacteristic
189C2×C61#212811yescharacteristic
190C2×C61#212911yescharacteristic
191D61—42no—
192C22×#41—611no—
193C2×#117—611no—
194C22×C4⋊C4—611no—
195C2×#99—612no—
196C2×#99—1222no—
197C2×#99C2×D6112yes—
198#391—611no—
199#391—611no—
200#390—611no—
201#390C2×D6111yescharacteristic
202#386—1222no—
203#381—1222no—
204#380—1222no—
205C61#1285911yescharacteristic, complemented, Sylow
206C2×#41—1222no—
207C2×#41—1221no—
208C2×#41—1221no—
209C2×#41—2442no—
210C2×#41—2442no—
211C22×Q8—611no—
212C22×D4—612no—
213C22×D4C22×D6111yescharacteristic
214C23×C4—612no—
215C23×C4—611no—
216C23×C4—1221no—
217#117—2442no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—2442no—
222C2×C4⋊C4C4×D6111yescharacteristic
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—1222no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1222no—
228C2×C42—611no—
229C2×C42C4×D6111yescharacteristic
230#99—22no—
231#99—22no—
232#99—1222no—
233#99—1222no—
234#99—2444no—
235#95—1222no—
236#95—1222no—
237#95—2444no—
238C24—611no—
239C24D4×D6112yes—
240#41—2448no—
241#41—2444no—
242#41—2444no—
243C2×Q8—1221no—
244C2×Q8—1221no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—1224no—
250C2×D4—1222no—
251C2×D4—1222no—
252C2×D4—2442no—
253C2×D4#1175822212yes—
254C2×D4#1175822411yescharacteristic
255C2×D4#1175822611yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—611no—
260C22×C4—612no—
261C22×C4—1222no—
262C22×C4—1222no—
263C22×C4—1224no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1222no—
267C22×C4—1222no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—4882no—
271C22×C4—2442no—
272C22×C4—2442no—
273C22×C4—2442no—
274C22×C4C2×C4×D6111yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—2441no—
277C4⋊C4—2442no—
278C4⋊C4—2442no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—82no—
282C22⋊C4—4882no—
283C22⋊C4—2442no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C42—41no—
287C42—2441no—
288C23—22no—
289C23—22no—
290C23—42no—
291C23—42no—
292C23—612no—
293C23—1221no—
294C23—1221no—
295C23—2441no—
296C23—2441no—
297C23C22⋊C4×D6111yescharacteristic
298C23#1451975912yes—
299C23#1451976212yes—
300Q8—2442no—
301Q8—2442no—
302D4—42no—
303D4—41no—
304D4—41no—
305D4—2444no—
306D4—2444no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—612no—
318C2×C4—1224no—
319C2×C4—1224no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—4884no—
326C2×C4—4882no—
327C2×C4—4882no—
328C2×C4—4882no—
329C2×C4—2444no—
330C2×C4—2444no—
331C2×C4—2441no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4#1451973411yescharacteristic
337C2×C4#1451973511yescharacteristic
338C22—21no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22—42no—
346C22—82no—
347C22—1222no—
348C22—2442no—
349C22—2442no—
350C22—2441no—
351C22—2441no—
352C22#1683962411yescharacteristic
353C22#99×D6111yescharacteristic
354C22#99×D6111yescharacteristic
355C4—21no—
356C4—21no—
357C4—81no—
358C4—81no—
359C4—162no—
360C4—1222no—
361C4—9762no—
362C4—4881no—
363C4—4881no—
364C4—2442no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2—42no—
369C2—2442no—
370C2#2144589211yescharacteristic
371C2#2144748911yescharacteristic
372C2#2144749211yescharacteristic
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#12859
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×#14519734C4semidirect
8. C2×C4⋊C4×D61C4semidirect
11. #16839668C4semidirect
12. #16839667C4semidirect
183. #1393D61semidirect
205. C61#12859semidirect

Maximal subgroups

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

subgroupindex
#214484092
#214457352
#214439442
#214439432
C61×#13932
#1285961