Finite Group Databasebeta

← #29590541

Subgroups — #29590541

Order 15616.

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

normal subgroups only

This group has 462 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#21451193C211yesmaximal, characteristic
2#343×D61C211yesmaximal, characteristic
3#21444147C211yesmaximal, characteristic
4#21443850C211yesmaximal, characteristic, complemented
5#21443848C211yesmaximal, characteristic, complemented
6#21443825C211yesmaximal, characteristic, complemented
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519757C411yescharacteristic
10C2×C4⋊C4×D61C2211yescharacteristic
11#16839724—21no—
12#16839693C411yescharacteristic
13#16839683C411yescharacteristic
14#16839682C2211yescharacteristic
15#16839661—21no—
16#16839659—21no—
17#16839636—21no—
18#16839633—21no—
19#16839609C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×#11758189—41no—
33C2×#11758189—41no—
34M16×D61—24no—
35M16×D61—42no—
36C2×C8×D61—41no—
37#14519757—41no—
38#14519757—41no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196C2×C411yescharacteristic
45C2×#11758196D411yescharacteristic
46C4⋊C4×D61—41no—
47C4⋊C4×D61—41no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—21no—
51C22⋊#92418—21no—
52#14519689—41no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—81no—
85C2×C4×D61—81no—
86C2×Dic122—41no—
87C2×Dic122—81no—
88M16×C61—22no—
89M16×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96#11758198—24no—
97#11758198—41no—
98#11758198—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—42no—
101C4⋊Dic61—81no—
102#11758196—41no—
103#11758196—41no—
104#11758196—42no—
105#11758196—81no—
106C4×Dic61—81no—
107#11758194—22no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111#11758189—44no—
112#11758189—82no—
113C8×D61—44no—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—22no—
118C22×D61—41no—
119C22×D61#9911yescharacteristic
120C22×D61#9911yescharacteristic
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—22no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—22no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#10412yes—
148C4×D61—22no—
149C4×D61—22no—
150C4×D61—22no—
151C4×D61—22no—
152C4×D61—42no—
153C4×D61—81no—
154C4×D61—81no—
155C4×D61—81no—
156Dic122—82no—
157C8×C61—42no—
158C8×C61—81no—
159#92418—42no—
160#92418—81no—
161#11768—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61C2×#9911yescharacteristic
165C22×C61#41711yescharacteristic
166C22×C61C2×#10411yescharacteristic
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61#35612yes—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—42no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—81no—
181Dic61—22no—
182Dic61—42no—
183Dic61—41no—
184Dic61—41no—
185Dic61—81no—
186#2583—611no—
187C2×#343—611no—
188#1463—611no—
189#1354—611no—
190#1354—611no—
191#1346—611no—
192#1346D6111yescharacteristic, complemented
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#150411yescharacteristic
196C2×C61#212111yescharacteristic
197C2×C61C2×#35611yescharacteristic
198D61—22no—
199D61—41no—
200C22×M16—1221no—
201C2×C22⋊Q8—611no—
202C22×C4⋊C4—611no—
203#407—1221no—
204#398—611no—
205#398C2×D6111yescharacteristic
206#395—611no—
207#395—611no—
208#389—1221no—
209#389—1221no—
210#385—1221no—
211#385—1221no—
212C4×C22⋊C4—611no—
213#343—611no—
214#343—1221no—
215#343C2×D6111yescharacteristic
216#324—611no—
217#324—1221no—
218#324C2×D6111yescharacteristic
219C61#1176811yescharacteristic, complemented, Sylow
220C22×Q8—611no—
221C23×C4—611no—
222C23×C4—611no—
223C23×C4—611no—
224C2×M16—21no—
225C2×M16—1224no—
226C2×M16—1221no—
227C2×M16—2441no—
228C2×M16—2441no—
229C2×M16—2442no—
230C22×C8—2441no—
231C22⋊Q8—2441no—
232C22⋊Q8—2441no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—2441no—
242C2×C4⋊C4—2441no—
243C2×C4⋊C4C4×D6111yescharacteristic
244C2×C4⋊C4C22×D6111yescharacteristic
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C42—1221no—
248C22⋊C8—21no—
249C22⋊C8—1221no—
250C22⋊C8—2441no—
251#95—21no—
252#95—611no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256#95C4×D6111yescharacteristic
257C24—611no—
258C2×Q8—4881no—
259C2×Q8—2441no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—1222no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—4881no—
277C22×C4—4881no—
278C22×C4C2×C4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281M16—22no—
282M16—41no—
283M16—1222no—
284M16—4882no—
285M16—2444no—
286M16—2441no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—2444no—
290C2×C8—2441no—
291C2×C8—2441no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—4881no—
297C4⋊C4—4881no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4—2442no—
302C4⋊C4—2442no—
303C22⋊C4—1224no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C42—4881no—
307C23—611no—
308C23—611no—
309C23—1222no—
310C23—1221no—
311C23—1221no—
312C23—2441no—
313C23C22⋊C4×D6111yescharacteristic
314Q8—4882no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—612no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1222no—
331C2×C4—1222no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1222no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—2442no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4#1451980111yescharacteristic
349C2×C4#1451980611yescharacteristic
350C8—42no—
351C8—81no—
352C8—4881no—
353C8—2442no—
354C22—21no—
355C22—21no—
356C22—612no—
357C22—1221no—
358C22—1221no—
359C22—1221no—
360C22—1221no—
361C22—1221no—
362C22—2442no—
363C22—2442no—
364C22#99×D6111yescharacteristic
365C22#1683976011yescharacteristic
366C22#104×D6111yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4—1222no—
374C4—4881no—
375C4—2442no—
376C4—2441no—
377C4—2441no—
378C2—21no—
379C2—21no—
380C2—1222no—
381C2—2441no—
382C2#2144432011yescharacteristic
383C2#2144746411yescharacteristic
384C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11768
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #21443850C2semidirect
5. #21443848C2semidirect
6. #21443825C2semidirect
7. C61×#1346C2semidirect
192. #1346D61semidirect
219. C61#11768semidirect

Maximal subgroups

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

subgroupindex
#214511932
#343×D612
#214441472
#214438502
#214438482
#214438252
C61×#13462
#1176861