Finite Group Databasebeta

← #29572912

Subgroups — #29572912

Order 15616.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839833C211yesmaximal, characteristic
2#21445848C211yesmaximal, characteristic, complemented
3#21445804C212yesmaximal
4#21443686C212yesmaximal, complemented
5C61×#1807C211yesmaximal, characteristic, complemented
6C22×#11758189C411yescharacteristic, complemented
7C2×C4×C22⋊D61C2211yescharacteristic
8#16839833—21no—
9#16839833—21no—
10#16839833—21no—
11#16839833—21no—
12C2×#14519711—21no—
13C2×#14519706C411yescharacteristic, complemented
14C2×#14519691—22no—
15C2×C22⋊#92418C2211yescharacteristic
16C2×#14519689C411yescharacteristic, complemented
17C2×#14519687C411yescharacteristic, complemented
18#16839622C2212yes—
19#16839528—22no—
20#16839525—21no—
21C23×C8×C61C2211yescharacteristic
22C2×#106×C61—21no—
23C61×#380C2212yes—
24C61×#340—21no—
25C22×C22⋊D61D411yescharacteristic
26C22×C4×D61C2×C411yescharacteristic
27C2×#11758189—21no—
28C2×#11758189—21no—
29C2×#11758189—42no—
30C22×#92418C2×C411yescharacteristic
31C22×#92418C2×C411yescharacteristic
32C4×C22⋊D61—21no—
33C4×C22⋊D61—21no—
34C4×C22⋊D61—21no—
35C4×C22⋊D61—21no—
36C2×C4⋊Dic61—22no—
37C2×#11758196Q811yescharacteristic
38C2×C22⋊Dic61—22no—
39C2×C22⋊Dic61D411yescharacteristic
40C2×#11758198Q811yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42#14519711—42no—
43#14519706—21no—
44#14519706—21no—
45#14519691—44no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519689—21no—
49#14519689—21no—
50#14519687—21no—
51#14519687—21no—
52#14519684—22no—
53C23×C4×C61C2311yescharacteristic
54C22×C8×C61—42no—
55C22×C8×C61C2×C411yescharacteristic
56C22×C8×C61C2×C411yescharacteristic
57C22×C8×C61D411yescharacteristic
58C22×C8×C61D411yescharacteristic
59C22×C8×C61D411yescharacteristic
60C22×C8×C61D411yescharacteristic
61C2×C4⋊C4×C61—22no—
62C2×C22⋊C4×C61—22no—
63#106×C61—42no—
64#95×C61—22no—
65C24×C61C2×D411yescharacteristic
66C23×D61C4⋊C411yescharacteristic
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61—42no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×Q811yescharacteristic
74C22×C4×C61#4111yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C22×Dic61—42no—
81C22×Dic61C4⋊C411yescharacteristic
82C22×Dic61C4⋊C411yescharacteristic
83C22×Dic61C4⋊C411yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C8×C61—22no—
89C2×C8×C61—22no—
90C2×C8×C61—22no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61C22⋊C411yescharacteristic
95C2×C8×C61C22⋊C411yescharacteristic
96C2×C8×C61C22⋊C411yescharacteristic
97C2×C8×C61C22⋊C411yescharacteristic
98C4⋊C4×C61—42no—
99C4⋊C4×C61—42no—
100C22⋊C4×C61—42no—
101C22⋊C4×C61—42no—
102C22⋊Dic61—21no—
103C22⋊Dic61—21no—
104C22⋊Dic61—42no—
105C22⋊Dic61—42no—
106#11758198—21no—
107#11758198—21no—
108C4⋊Dic61—42no—
109C4⋊Dic61—42no—
110#11758196—21no—
111#11758196—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—41no—
117C2×#92418—41no—
118#11758189—42no—
119#11758189—42no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×C4⋊C411yescharacteristic
123C23×C61#12111yescharacteristic
124C23×C61#12111yescharacteristic
125C23×C61AGL(1,ℤ/8)12yes—
126C23×C61#13712yes—
127C22×D61—21no—
128C22×D61—22no—
129C22×D61—41no—
130C22×D61—41no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—82no—
141C2×C4×C61—82no—
142C2×C4×C61—82no—
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×C4×C61#11711yescharacteristic
145C2×C4×C61C22⋊Q811yescharacteristic
146C2×C4×C61C22⋊Q811yescharacteristic
147C22⋊D61—42no—
148C22⋊D61—41no—
149C22⋊D61—41no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—22no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—82no—
157C2×Dic61—82no—
158C2×Dic61—82no—
159C4×D61—42no—
160C4×D61—41no—
161C4×D61—41no—
162C8×C61—21no—
163C8×C61—21no—
164C8×C61—21no—
165C8×C61#9912yescomplemented
166#92418—41no—
167#92418—41no—
168#8610—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61#38011yescharacteristic
178C22×C61#42812yes—
179C22×C61#46812yes—
180C22×C61#46911yescharacteristic
181C22×C61#47011yescharacteristic
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—82no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—162no—
190C4×C61C2×#9911yescharacteristic
191C4×C61#41011yescharacteristic
192Dic61—41no—
193Dic61—41no—
194Dic61—41no—
195Dic61—162no—
196C2×#435—611no—
197#1808—611no—
198#1807D6111yescharacteristic, complemented
199#1799—612no—
200#1289—612no—
201C2×C61—21no—
202C2×C61—22no—
203C2×C61—22no—
204C2×C61—21no—
205C2×C61#179911yescharacteristic
206C2×C61#180911yescharacteristic
207C2×C61#181211yescharacteristic
208D61—81no—
209C22×M16—611no—
210C23×C8C2×D6111yescharacteristic
211C2×C4×D4—611no—
212#435—1221no—
213#435—1221no—
214#435—1221no—
215#435—1221no—
216C2×#107—1221no—
217C2×#106—21no—
218C2×C4⋊C8—611no—
219C2×#99—1222no—
220C2×C22⋊C8—611no—
221C2×C22⋊C8—611no—
222C2×#97—611no—
223#380—612no—
224#380C2×D6112yes—
225#342—1222no—
226#340—21no—
227#340—1221no—
228C61#861011yescharacteristic, complemented, Sylow
229C22×D4—611no—
230C23×C4—611no—
231C23×C4C22×D6111yescharacteristic
232C2×M16—1221no—
233C2×M16—1221no—
234C2×M16—2442no—
235C22×C8—42no—
236C22×C8—611no—
237C22×C8—611no—
238C22×C8C4×D6111yescharacteristic
239C22×C8C4×D6111yescharacteristic
240C22×C8D24411yescharacteristic
241C22×C8D24411yescharacteristic
242C22×C8C22⋊D6111yescharacteristic
243C22×C8C22⋊D6111yescharacteristic
244C4×D4—1221no—
245C4×D4—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1222no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—611no—
254C2×C22⋊C4—1222no—
255C2×C42—611no—
256#107—2442no—
257#106—42no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260#99—2444no—
261C22⋊C8—1221no—
262C22⋊C8—1221no—
263C22⋊C8—1221no—
264C22⋊C8—1221no—
265#97—1221no—
266#97—1221no—
267#95—22no—
268#95—1222no—
269C24—611no—
270C24D4×D6111yescharacteristic
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1222no—
274C2×D4—1222no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4—2442no—
286C22×C4C2×C4×D6111yescharacteristic
287C22×C4C2×D24411yescharacteristic
288C22×C4#1175822411yescharacteristic
289C22×C4Q8×D6111yescharacteristic
290C22×C4#1175822611yescharacteristic
291C22×C4C2×C22⋊D6111yescharacteristic
292M16—2442no—
293M16—2442no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—1221no—
301C2×C8—1221no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8#1175819811yescharacteristic
305C2×C8#1175819811yescharacteristic
306C2×C8#1175819811yescharacteristic
307C2×C8#1175819811yescharacteristic
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—2442no—
313C4⋊C4—2442no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—2442no—
321C22⋊C4—2442no—
322C42—1221no—
323C42—1221no—
324C23—41no—
325C23—41no—
326C23—1222no—
327C23—1221no—
328C23—2441no—
329C23—2441no—
330C23C4⋊C4×D6111yescharacteristic
331C23#1451974811yescharacteristic
332C23#1451975211yescharacteristic
333C23#1451980412yes—
334C23#1451980612yes—
335D4—2442no—
336D4—2441no—
337D4—2441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—1222no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—4882no—
355C2×C4—4882no—
356C2×C4—4882no—
357C2×C4—2442no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4C2×#1175819811yescharacteristic
363C2×C4#1451973511yescharacteristic
364C2×C4#1451975311yescharacteristic
365C2×C4#1451975711yescharacteristic
366C8—21no—
367C8—21no—
368C8—21no—
369C8—2441no—
370C8—2441no—
371C8#1451969112yescomplemented
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—42no—
380C22—4882no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22#1683961911yescharacteristic
385C22#1683980112yes—
386C22#1684000512yes—
387C22#1684001611yescharacteristic
388C22#1684002111yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—162no—
393C4—9762no—
394C4—2441no—
395C4—2441no—
396C4—2441no—
397C4C2×#1451969111yescharacteristic
398C4#1683973511yescharacteristic
399C2—22no—
400C2—21no—
401C2—22no—
402C2—21no—
403C2—4881no—
404C2#2144580411yescharacteristic
405C2#2144584911yescharacteristic
406C2#2144586211yescharacteristic
subgroupG/H
centerC22#16839619
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1807C2
socleC22×C61#380
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1807D61
hypocenterC61#8610
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
2. #21445848C2semidirect
4. #21443686C2semidirect
5. C61×#1807C2semidirect
6. C22×#11758189C4semidirect
13. C2×#14519706C4semidirect
16. C2×#14519689C4semidirect
17. C2×#14519687C4semidirect
165. C8×C61#99semidirect
198. #1807D61semidirect
228. C61#8610semidirect
371. C8#14519691semidirect

Maximal subgroups

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

subgroupindex
C2×#168398332
#214458482
#214458042
#214436862
C61×#18072
#861061