Finite Group Databasebeta

← #29886737

Subgroups — #29886737

Order 15616.

1304 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454094C211yesmaximal, characteristic
2#21454061C214yesmaximal
3#21454059C214yesmaximal
4#21454057C214yesmaximal
5#21453887C211yesmaximal, characteristic
6#21453886C212yesmaximal
7#21449127C214yesmaximal
8#21449126C214yesmaximal
9#21449126C214yesmaximal
10C4×#14519769C212yesmaximal
11C4×#125×C61C211yesmaximal, characteristic
12C2×#14519769C2212yes—
13#16839704C2214yes—
14#16839704C2214yes—
15#16839703C2214yes—
16#16839703C2214yes—
17#16839703C2214yes—
18#16839703C2214yes—
19#16839702C2214yes—
20#16839702C2214yes—
21#16839701C2214yes—
22#16839701C2214yes—
23#16839700C2214yes—
24#16839700C2214yes—
25#16839696C2214yes—
26#16839696C2214yes—
27#16839695C2214yes—
28#16839695C2214yes—
29#16839695C2214yes—
30#16839695C2214yes—
31#16839694C2214yes—
32#16839694C2214yes—
33#16839693C2214yes—
34#16839693C2214yes—
35#16839692C2214yes—
36#16839692C2214yes—
37#16839660C2212yes—
38#16839660C2212yes—
39#16839646C2214yes—
40#16839646C2214yes—
41#16839628C2212yes—
42C4×#11758196C2214yes—
43C4×#11758196C2214yes—
44C4×#11758196C2214yes—
45C4×#11758196C2214yes—
46C4×C4⋊Dic61C2212yes—
47C4×C4⋊Dic61C2214yes—
48C4×C4⋊Dic61C2212yes—
49#16839608C2214yes—
50C2×#125×C61C2211yescharacteristic
51C61×#389C2212yes—
52C61×#387C2214yes—
53C61×#382C2211yescharacteristic
54C4×C4⋊C4×C61C2212yes—
55C4×C4⋊C4×C61C2214yes—
56C43×C61C2211yescharacteristic
57#14519769—28no—
58C2×C4⋊Dic61C2312yes—
59C2×C4⋊Dic61C2312yes—
60C2×C4⋊Dic61C2314yes—
61C2×C4⋊Dic61C2312yes—
62C2×C4⋊Dic61C2314yes—
63C2×C4⋊Dic61C2312yes—
64C2×#11758196C2314yes—
65C2×#11758196C2314yes—
66C2×#11758196C2314yes—
67C2×#11758196C2314yes—
68C2×#11758196C2314yes—
69C2×#11758196C2314yes—
70C2×#11758196C2314yes—
71C2×#11758196C2314yes—
72C2×C4×Dic61C2314yes—
73C2×C4×Dic61C2314yes—
74#14519684C2314yes—
75#14519684C2314yes—
76#14519684C2314yes—
77#14519684C2314yes—
78#14519684C2314yes—
79#14519684C2314yes—
80#14519684C2314yes—
81#14519684C2314yes—
82#14519684C2314yes—
83#14519684C2314yes—
84#14519684C2314yes—
85#14519684C2314yes—
86#14519684C2314yes—
87#14519684C2314yes—
88#14519684C2314yes—
89#14519684C2314yes—
90#125×C61—24no—
91C2×C4⋊C4×C61C2314yes—
92C2×C4⋊C4×C61C2312yes—
93C2×C4⋊C4×C61C2312yes—
94C2×C4⋊C4×C61C2314yes—
95C2×C42×C61C2312yes—
96C2×C42×C61C2311yescharacteristic
97C2×C42×C61C2314yes—
98C2×C42×C61C2312yes—
99C2×C42×C61C2311yescharacteristic
100C2×C42×C61C2311yescharacteristic
101#95×C61C2314yes—
102#95×C61C2314yes—
103#95×C61C2314yes—
104C22×C4×C61C2411yescharacteristic
105C22×C4×C61C2414yes—
106C22×C4×C61C2412yes—
107C22×C4×C61C2414yes—
108C22×C4×C61C2412yes—
109C22×C4×C61C2411yescharacteristic
110C22×C4×C61C2411yescharacteristic
111C22×Dic61C2414yes—
112C22×Dic61C2414yes—
113C22×Dic61C2414yes—
114C22×Dic61C2414yes—
115C4⋊C4×C61—24no—
116C4⋊C4×C61—28no—
117C4⋊C4×C61—42no—
118C4⋊C4×C61—44no—
119C42×C61—24no—
120C42×C61—22no—
121C42×C61—28no—
122C42×C61—42no—
123C42×C61—41no—
124C42×C61#4114yes—
125C4⋊Dic61—24no—
126C4⋊Dic61—24no—
127C4⋊Dic61—42no—
128C4⋊Dic61—44no—
129C4⋊Dic61—42no—
130C4⋊Dic61—44no—
131#11758196—28no—
132#11758196—28no—
133#11758196—44no—
134#11758196—44no—
135#11758196—44no—
136#11758196—44no—
137#11758196—44no—
138#11758196—44no—
139C4×Dic61—28no—
140C4×Dic61—28no—
141C23×C61C2511yescharacteristic
142C2×C4×C61—22no—
143C2×C4×C61—21no—
144C2×C4×C61—22no—
145C2×C4×C61—21no—
146C2×C4×C61—24no—
147C2×C4×C61—24no—
148C2×C4×C61—24no—
149C2×C4×C61—22no—
150C2×C4×C61—21no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—24no—
154C2×C4×C61—24no—
155C2×C4×C61—24no—
156C2×C4×C61—22no—
157C2×C4×C61C2×#4112yes—
158C2×C4×C61C2×#4114yes—
159C2×C4×C612−1+414yes—
160C2×C4×C612−1+412yes—
161C2×Dic61—24no—
162C2×Dic61—24no—
163C2×Dic61—24no—
164C2×Dic61—24no—
165C2×Dic61—24no—
166C2×Dic61—24no—
167C2×Dic61—24no—
168C2×Dic61—24no—
169C2×Dic61—24no—
170C2×Dic61—24no—
171C2×Dic61—24no—
172C2×Dic61—24no—
173#36701—611nomaximal, Sylow
174C22×C61C22×#4111yescharacteristic
175C22×C61C2×2−1+412yes—
176C22×C61C2×2−1+411yescharacteristic
177C22×C61#58512yes—
178C22×C61#58511yescharacteristic
179C4×C61—24no—
180C4×C61—22no—
181C4×C61—44no—
182C4×C61—42no—
183C4×C61—44no—
184C4×C61—41no—
185C4×C61#56414yes—
186Dic61—44no—
187Dic61—44no—
188Dic61—44no—
189Dic61—44no—
190#2845—611no—
191#2839—614no—
192#2839—614no—
193#2839—614no—
194#2822—611no—
195#2822—612no—
196#2402—614no—
197#2402—614no—
198#2402—614no—
199C4×#125—612no—
200C4×#125D6111yescharacteristic
201C2×C61#346112yes—
202C2×C61#346111yescharacteristic
203C2×C61C2×#56411yescharacteristic
204C2×C61#353112yes—
205C2×C61#353111yescharacteristic
206C2×#125—612no—
207C2×#125C2×D6111yescharacteristic
208#400—614no—
209#400—614no—
210#400—614no—
211#400—614no—
212#400—614no—
213#400—614no—
214#400—614no—
215#400—614no—
216#400—614no—
217#400—614no—
218#400—614no—
219#400—614no—
220#398—614no—
221#398—614no—
222#398—614no—
223#398—614no—
224#398—614no—
225#398—614no—
226#398—614no—
227#398—614no—
228#398—614no—
229#398—614no—
230#398—614no—
231#398—614no—
232#389—612no—
233#389—612no—
234#389C2×D6112yes—
235#387—614no—
236#387—614no—
237#387C2×D6114yes—
238#382—612no—
239#382C2×D6111yescharacteristic
240C4×C4⋊C4—612no—
241C4×C4⋊C4—612no—
242C4×C4⋊C4—614no—
243C4×C4⋊C4—614no—
244C4×C4⋊C4—614no—
245C4×C4⋊C4—614no—
246C4×C4⋊C4—614no—
247C4×C4⋊C4C2×D6114yes—
248C4×C4⋊C4C2×D6112yes—
249#376—614no—
250C43C2×D6111yescharacteristic
251C61#3670111yescharacteristic, complemented, Sylow
252#125—24no—
253#125—1228no—
254C2×C4⋊C4—614no—
255C2×C4⋊C4—614no—
256C2×C4⋊C4—612no—
257C2×C4⋊C4—612no—
258C2×C4⋊C4—612no—
259C2×C4⋊C4—612no—
260C2×C4⋊C4—614no—
261C2×C4⋊C4—614no—
262C2×C4⋊C4—614no—
263C2×C4⋊C4—614no—
264C2×C4⋊C4—614no—
265C2×C4⋊C4—614no—
266C2×C4⋊C4—614no—
267C2×C4⋊C4—614no—
268C2×C4⋊C4C22×D6114yes—
269C2×C4⋊C4C22×D6112yes—
270C2×C4⋊C4C22×D6112yes—
271C2×C4⋊C4C22×D6114yes—
272C2×C42—614no—
273C2×C42—614no—
274C2×C42C22×D6112yes—
275C2×C42C22×D6111yescharacteristic
276C2×C42C22×D6114yes—
277C2×C42C22×D6111yescharacteristic
278C2×C42C22×D6112yes—
279C2×C42C22×D6111yescharacteristic
280#95—614no—
281#95—614no—
282#95—614no—
283#95—614no—
284#95—614no—
285#95—614no—
286#95—614no—
287#95—614no—
288#95—614no—
289#95—614no—
290#95—614no—
291#95—614no—
292#95—614no—
293#95—614no—
294#95—614no—
295#95—614no—
296#95C22×D6114yes—
297#95C22×D6114yes—
298#95C22×D6114yes—
299C22×C4—614no—
300C22×C4—614no—
301C22×C4—614no—
302C22×C4—614no—
303C22×C4C23×D6112yes—
304C22×C4C23×D6114yes—
305C22×C4C23×D6111yescharacteristic
306C22×C4C23×D6114yes—
307C22×C4C23×D6111yescharacteristic
308C22×C4C23×D6112yes—
309C22×C4C23×D6111yescharacteristic
310C4⋊C4—28no—
311C4⋊C4—24no—
312C4⋊C4—42no—
313C4⋊C4—44no—
314C4⋊C4—1228no—
315C4⋊C4—1228no—
316C4⋊C4—1224no—
317C4⋊C4—1224no—
318C4⋊C4—2444no—
319C4⋊C4—2444no—
320C4⋊C4—2444no—
321C4⋊C4—2444no—
322C4⋊C4—2444no—
323C4⋊C4—2444no—
324C4⋊C4—2442no—
325C4⋊C4—2442no—
326C4⋊C4—2444no—
327C4⋊C4—2444no—
328C42—24no—
329C42—28no—
330C42—22no—
331C42—41no—
332C42—42no—
333C42—1228no—
334C42—1228no—
335C42#1175822214yes—
336C23C24×D6111yescharacteristic
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—1224no—
353C2×C4—1224no—
354C2×C4—1224no—
355C2×C4—1224no—
356C2×C4—1224no—
357C2×C4—1224no—
358C2×C4—1224no—
359C2×C4—1224no—
360C2×C4—1224no—
361C2×C4—1224no—
362C2×C4—1224no—
363C2×C4—1224no—
364C2×C4C2×#1175822214yes—
365C2×C4C2×#1175822212yes—
366C2×C4#1451982414yes—
367C2×C4#1451982512yes—
368C22C22×#1175822211yescharacteristic
369C22C2×#1451982412yes—
370C22C2×#1451982511yescharacteristic
371C22#1684059812yes—
372C22#1684059811yescharacteristic
373C4—24no—
374C4—22no—
375C4—44no—
376C4—42no—
377C4—44no—
378C4—41no—
379C4—2444no—
380C4—2444no—
381C4—2444no—
382C4—2444no—
383C4C61⋊#56414yes—
384C2#2145924612yes—
385C2#2145925211yescharacteristic
386C2C2×C61⋊#56411yescharacteristic
387C2#2145996412yes—
388C2#2145996611yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutator, socle, prime radical, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC4×#125×C61C2
hypercenterC4×#125D61
hypocenterC61#36701
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
251. C61#36701semidirect

Maximal subgroups

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

subgroupindex
#214540942
#214540612
#214540592
#214540572
#214538872
#214538862
#214491272
#214491262
C4×#145197692
C4×#125×C612
#3670161