Finite Group Databasebeta

← #29572681

Subgroups — #29572681

Order 15616.

682 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839613C211yesmaximal, characteristic
2#21445797C212yesmaximal
3C2×#16839487C212yesmaximal
4#21443662C211yesmaximal, characteristic
5C61×#1280C211yesmaximal, characteristic
6C22×#11758196C411yescharacteristic
7C22×#11758196C2211yescharacteristic
8C22×C4×Dic61C411yescharacteristic
9C22×C4×Dic61C411yescharacteristic
10C22×C4×Dic61C2211yescharacteristic
11C2×#14519706—22no—
12C2×C22⋊#92418C2212yes—
13#16839613—22no—
14#16839613—22no—
15C2×#14519684C411yescharacteristic
16#16839516—22no—
17#16839487—24no—
18C2×C22⋊C8×C61C2212yes—
19C2×#95×C61C2211yescharacteristic
20C23×Dic61C2×C411yescharacteristic
21C23×Dic61C2×C411yescharacteristic
22C23×Dic61C2×C411yescharacteristic
23C23×Dic61C2×C411yescharacteristic
24C22×#92418—22no—
25C2×#11758196—22no—
26C2×#11758196—22no—
27C2×#11758196—22no—
28C2×#11758196—22no—
29C2×#11758196C814yescomplemented
30C2×#11758196D412yes—
31C2×#11758196Q812yes—
32C2×C4×Dic61—22no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61—22no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61—42no—
39C2×C4×Dic61—42no—
40C2×C4×Dic61D412yes—
41C2×C4×Dic61D412yes—
42#14519706—44no—
43C22⋊#92418—22no—
44C22⋊#92418—22no—
45#14519684—22no—
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61C2311yescharacteristic
49C22×C8×C61—22no—
50C22⋊C8×C61—22no—
51C22⋊C8×C61—22no—
52#95×C61—22no—
53C24×C61C22×C411yescharacteristic
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61C2×C812yes—
65C22×C4×C61M1612yes—
66C22×C4×C61C2×D412yes—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×Q811yescharacteristic
69C22×C4×C61#4112yes—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—22no—
77C22×Dic61—22no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61C22⋊C412yes—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C4⋊C412yes—
88C22×Dic61C4⋊C412yes—
89C22×Dic61C2×C812yes—
90C22×Dic61C2×C812yes—
91C22×Dic61M1612yes—
92C22×Dic61M1612yes—
93C2×C8×C61—42no—
94C2×C8×C61—42no—
95C2×C8×C61—42no—
96#11758196—24no—
97#11758196—24no—
98#11758196—28no—
99C4×Dic61—24no—
100C4×Dic61—24no—
101C4×Dic61—24no—
102C4×Dic61—42no—
103C4×Dic61—42no—
104C4×Dic61—42no—
105C2×#92418—42no—
106C2×#92418—42no—
107C2×#92418—42no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61C2×C22⋊C411yescharacteristic
113C23×C61C2×C4⋊C411yescharacteristic
114C23×C61#11711yescharacteristic
115C23×C61C22×C811yescharacteristic
116C23×C61C2×M1611yescharacteristic
117C23×C61C2×M1611yescharacteristic
118C23×C61C2×M1611yescharacteristic
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61#12112yes—
135C2×C4×C61C22⋊Q812yes—
136C2×Dic61—24no—
137C2×Dic61—24no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—22no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61C22⋊C814yes—
158C2×Dic61#9912yes—
159C2×Dic61#10112yes—
160C2×Dic61C4⋊C814yescomplemented
161C8×C61—82no—
162#92418—82no—
163#8560—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61#38011yescharacteristic
177C22×C61C2×C22⋊C811yescharacteristic
178C22×C61#40711yescharacteristic
179C22×C61C2×#9911yescharacteristic
180C22×C61#41011yescharacteristic
181C22×C61C2×#10111yescharacteristic
182C22×C61#41311yescharacteristic
183C22×C61C2×C4⋊C811yescharacteristic
184C22×C61#42311yescharacteristic
185C22×C61#43111yescharacteristic
186C22×C61#43211yescharacteristic
187C4×C61—22no—
188C4×C61—22no—
189C4×C61—42no—
190C4×C61—42no—
191Dic61—24no—
192Dic61—24no—
193Dic61—22no—
194Dic61—22no—
195Dic61—42no—
196C2×C4×C4⋊C4—611no—
197#1797—612no—
198C2×#324—612no—
199#1280—611no—
200#1280D6111yescharacteristic
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61#145911yescharacteristic
206C2×C61#146111yescharacteristic
207C2×C61#146311yescharacteristic
208C2×C61#146411yescharacteristic
209C2×C61#179711yescharacteristic
210C2×C61#179911yescharacteristic
211C2×C61#180111yescharacteristic
212C22×C4⋊C4—611no—
213C22×C4⋊C4—611no—
214C22×C42—611no—
215C22×C42—611no—
216C22×C42—611no—
217C2×C4⋊C8—1222no—
218C2×C22⋊C8—612no—
219C2×C22⋊C8C2×D6112yes—
220C4×C4⋊C4—1222no—
221C4×C4⋊C4—1222no—
222C2×#95—611no—
223C2×#95C2×D6111yescharacteristic
224#336—1222no—
225#324—1224no—
226C61#856011yescharacteristic, complemented, Sylow
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C23×C4—611no—
231C23×C4C4×D6111yescharacteristic
232C23×C4C4×D6111yescharacteristic
233C23×C4C22×D6111yescharacteristic
234C22×C8—22no—
235C22×C8—1222no—
236C2×C4⋊C4—614no—
237C2×C4⋊C4—612no—
238C2×C4⋊C4—612no—
239C2×C4⋊C4—1222no—
240C2×C4⋊C4—1222no—
241C2×C4⋊C4—1222no—
242C2×C4⋊C4—1222no—
243C2×C42—612no—
244C2×C42—612no—
245C2×C42—1221no—
246C2×C42—1221no—
247C2×C42—1222no—
248C2×C42—1222no—
249C2×C42—1221no—
250C2×C42—1221no—
251C2×C42—2442no—
252C2×C42—2442no—
253C4⋊C8—2444no—
254C22⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—1222no—
257C22⋊C8—1222no—
258#95—22no—
259#95—1222no—
260C24C2×C4×D6111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—612no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—612no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4C8×D6112yes—
295C22×C4#1175818912yes—
296C22×C4#1175822212yes—
297C22×C4D4×D6112yes—
298C22×C4D4×D6111yescharacteristic
299C22×C4Q8×D6111yescharacteristic
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—2442no—
304C2×C8—2442no—
305C2×C8—2442no—
306C4⋊C4—1228no—
307C4⋊C4—1224no—
308C4⋊C4—1224no—
309C42—1224no—
310C42—1224no—
311C42—1224no—
312C42—2442no—
313C42—2442no—
314C42—2442no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23C22⋊C4×D6111yescharacteristic
320C23C4⋊C4×D6111yescharacteristic
321C23#1451973411yescharacteristic
322C23C2×C8×D6111yescharacteristic
323C23M16×D6111yescharacteristic
324C23M16×D6111yescharacteristic
325C23C2×#1175818911yescharacteristic
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—614no—
342C2×C4—612no—
343C2×C4—612no—
344C2×C4—614no—
345C2×C4—1224no—
346C2×C4—1224no—
347C2×C4—1222no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2442no—
366C2×C4#1451975012yes—
367C2×C4#1451975512yes—
368C8—82no—
369C8—4882no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22#1683962111yescharacteristic
383C22C22⋊C8×D6111yescharacteristic
384C22#1683972411yescharacteristic
385C22#99×D6111yescharacteristic
386C22#1683973411yescharacteristic
387C22#101×D6111yescharacteristic
388C22#1683974311yescharacteristic
389C22C4⋊C8×D6111yescharacteristic
390C22#1683978411yescharacteristic
391C22#1683981311yescharacteristic
392C22#1683981711yescharacteristic
393C4—22no—
394C4—22no—
395C4—42no—
396C4—42no—
397C4—1224no—
398C4—1222no—
399C4—1222no—
400C4—1224no—
401C4—2442no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#2144413411yescharacteristic
407C2#2144414111yescharacteristic
408C2#2144414711yescharacteristic
409C2#2144415011yescharacteristic
410C2#2144579811yescharacteristic
411C2#2144580611yescharacteristic
412C2#2144581411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×C4×C61C23
hypercenter#1280D61
hypocenterC61#8560
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
29. C2×#11758196C8semidirect
160. C2×Dic61C4⋊C8semidirect
226. C61#8560semidirect

Maximal subgroups

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

subgroupindex
C2×#168396132
#214457972
C2×#168394872
#214436622
C61×#12802
#856061