Finite Group Databasebeta

← #29590533

Subgroups — #29590533

Order 15616.

488 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 73 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#21451295C211yesmaximal, characteristic
2#343×D61C211yesmaximal, characteristic, complemented
3#21444147C211yesmaximal, characteristic, complemented
4#21443846C211yesmaximal, characteristic, complemented
5#21443823C211yesmaximal, characteristic, complemented
6#21443821C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519752C411yescharacteristic
10C2×C4⋊C4×D61C2211yescharacteristic
11#16839724—21no—
12#16839700C411yescharacteristic
13#16839680C411yescharacteristic
14#16839679C2211yescharacteristic
15#16839654—21no—
16#16839651—21no—
17#16839640—21no—
18#16839640—21no—
19#16839609C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#400C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758189—41no—
34C2×#11758189—41no—
35M16×D61—24no—
36M16×D61—42no—
37C2×C8×D61—41no—
38#14519752—41no—
39#14519752—41no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196C2×C411yescharacteristic
42C2×#11758196D411yescharacteristic
43C4⋊C4×D61—41no—
44C4⋊C4×D61—41no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×C4×Dic61—21no—
52C22⋊#92418—21no—
53#14519689—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61—21no—
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×D244—41no—
76C2×D244—42no—
77C2×D244—42no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—81no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—22no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—81no—
91C2×C4×D61—81no—
92M16×C61—22no—
93M16×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98#11758198—42no—
99#11758198—42no—
100#11758198—41no—
101#11758198—41no—
102#11758198—42no—
103#11758198—81no—
104#11758198—81no—
105C4⋊Dic61—41no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—81no—
109#11758194—22no—
110#11758194—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113#11758189—44no—
114#11758189—82no—
115C8×D61—44no—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—22no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61#9911yescharacteristic
129C22×D61#9911yescharacteristic
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61#10412yes—
154D244—82no—
155D244—82no—
156D244—82no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—22no—
161C4×D61—42no—
162C4×D61—81no—
163C4×D61—81no—
164C4×D61—81no—
165C8×C61—42no—
166C8×C61—81no—
167#92418—42no—
168#92418—81no—
169#11766—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61C2×#9911yescharacteristic
173C22×C61#41711yescharacteristic
174C22×C61C2×#10411yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—42no—
181C2×D61—42no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61#35512yes—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61—81no—
195C4×C61—81no—
196Dic61—22no—
197Dic61—41no—
198Dic61—41no—
199Dic61—81no—
200#2591—611no—
201C2×#343—611no—
202#1463—611no—
203#1353—611no—
204#1353D6111yescharacteristic, complemented
205#1345—611no—
206#1345—611no—
207C2×C61—21no—
208C2×C61—21no—
209C2×C61#150411yescharacteristic
210C2×C61#212111yescharacteristic
211C2×C61C2×#35511yescharacteristic
212D61—22no—
213D61—41no—
214D61—161no—
215C22×M16—1221no—
216C2×#121—611no—
217C22×C4⋊C4—611no—
218#407—1221no—
219#400—611no—
220#400C2×D6111yescharacteristic
221#394—611no—
222#394—611no—
223#388—1221no—
224#388—1221no—
225#386—1221no—
226#386—1221no—
227C4×C22⋊C4—611no—
228#343—611no—
229#343—1221no—
230#343C2×D6111yescharacteristic
231#324—611no—
232#324—1221no—
233#324C2×D6111yescharacteristic
234C61#1176611yescharacteristic, complemented, Sylow
235C22×D4—611no—
236C22×D4—1221no—
237C23×C4—611no—
238C23×C4—611no—
239C23×C4—611no—
240C2×M16—21no—
241C2×M16—1224no—
242C2×M16—1221no—
243C2×M16—2441no—
244C2×M16—2441no—
245C2×M16—2442no—
246C22×C8—2441no—
247#121—2441no—
248#121—2441no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—2441no—
253C2×C4⋊C4—2441no—
254C2×C4⋊C4C4×D6111yescharacteristic
255C2×C4⋊C4C22×D6111yescharacteristic
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C42—1221no—
263C22⋊C8—21no—
264C22⋊C8—1221no—
265C22⋊C8—2441no—
266#95—21no—
267#95—21no—
268#95—611no—
269#95—1221no—
270#95—1221no—
271#95C4×D6111yescharacteristic
272C24—611no—
273C24—1221no—
274C2×D4—4881no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2442no—
279C2×D4—2442no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1222no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—4881no—
296C22×C4—4881no—
297C22×C4C2×C4×D6111yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4D4×D6111yescharacteristic
300M16—22no—
301M16—41no—
302M16—1222no—
303M16—4882no—
304M16—2444no—
305M16—2441no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—2444no—
309C2×C8—2441no—
310C2×C8—2441no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C22⋊C4—4881no—
317C22⋊C4—4881no—
318C22⋊C4—2442no—
319C22⋊C4—2442no—
320C22⋊C4—2442no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C42—4881no—
324C23—611no—
325C23—611no—
326C23—1222no—
327C23—1221no—
328C23—1221no—
329C23—2441no—
330C23—2441no—
331C23—2441no—
332C23—2441no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23C22⋊C4×D6111yescharacteristic
338D4—4882no—
339D4—4882no—
340D4—4882no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—612no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—4881no—
363C2×C4—4881no—
364C2×C4—4881no—
365C2×C4—2442no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4#1451980411yescharacteristic
372C2×C4#1451980911yescharacteristic
373C8—42no—
374C8—81no—
375C8—4881no—
376C8—2442no—
377C22—21no—
378C22—21no—
379C22—612no—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—1221no—
385C22—4881no—
386C22—4881no—
387C22—4881no—
388C22—4881no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22—2442no—
393C22—2442no—
394C22#99×D6111yescharacteristic
395C22#1683976211yescharacteristic
396C22#104×D6111yescharacteristic
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—81no—
402C4—81no—
403C4—1222no—
404C4—4881no—
405C4—2441no—
406C4—2441no—
407C2—21no—
408C2—21no—
409C2—1222no—
410C2—9761no—
411C2—2441no—
412C2#2144432211yescharacteristic
413C2#2144746411yescharacteristic
414C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1353C2
socleC22×C61C2×#99
prime radicalC2×#14519752C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1353D61
hypocenterC61#11766
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
2. #343×D61C2semidirect
3. #21444147C2semidirect
4. #21443846C2semidirect
5. #21443823C2semidirect
6. #21443821C2semidirect
7. C61×#1353C2semidirect
204. #1353D61semidirect
234. C61#11766semidirect

Maximal subgroups

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

subgroupindex
#214512952
#343×D612
#214441472
#214438462
#214438232
#214438212
C61×#13532
#1176661