Finite Group Databasebeta

← #29574505

Subgroups — #29574505

Order 15616.

426 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454563C211yesmaximal, characteristic
2#21446595C211yesmaximal, characteristic, complemented
3#21444590C211yesmaximal, characteristic, complemented
4#21444270C211yesmaximal, characteristic
5#21443655C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1540C211yesmaximal, characteristic
8C2×#14519784—21no—
9#16839840—21no—
10#16839834—22no—
11D4×#92418—21no—
12C2×#14519713—21no—
13#16839786C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15#16839729—21no—
16C4×#11758194C2211yescharacteristic
17C2×C4×#92418C2211yescharacteristic
18#16839527—21no—
19#16839513—21no—
20#16839513—21no—
21D4⋊#92418—22no—
22C61×#532C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C61×#332C411yescharacteristic
26C61×#332C411yescharacteristic
27C61×#331C411yescharacteristic
28C61×#331C411yescharacteristic
29#14519784—42no—
30#14519784—42no—
31C2×#11758194—22no—
32C2×#11758194—21no—
33C2×#11758194D411yescharacteristic
34C2×#11758194D411yescharacteristic
35C22×#92418—22no—
36C22×#92418—21no—
37C22×#92418—21no—
38#14519713—42no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418D411yescharacteristic
43C4⋊#92418D411yescharacteristic
44C22⋊#92418—22no—
45C22⋊#92418—22no—
46#14519688—21no—
47C4×#92418—21no—
48C4×#92418—21no—
49C4×#92418—21no—
50C2×#41×C61—21no—
51C22×C8×C61—21no—
52C4⋊Q8×C61C2×C411yescharacteristic
53#127×C61C2×C411yescharacteristic
54#124×C61—21no—
55#121×C61—21no—
56#121×C61Q812yes—
57C4×D4×C61—21no—
58C4×D4×C61D412yes—
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61C2×C411yescharacteristic
62C4⋊C8×C61C2×C411yescharacteristic
63C4⋊C8×C61C2×C411yescharacteristic
64C4⋊C8×C61C2×C411yescharacteristic
65C22⋊C8×C61—21no—
66C4×C8×C61—21no—
67#41×C61—41no—
68#41×C61—41no—
69#41×C61—41no—
70#41×C61—41no—
71C2×Q8×C61—21no—
72C2×D4×C61—22no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61C4⋊C412yes—
76C22×C4×C61—22no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×Q811yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C8×C61—21no—
81C2×C8×C61—21no—
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61C4⋊C412yes—
88C22⋊C4×C61—22no—
89C22⋊C4×C61—22no—
90C42×C61C22×C411yescharacteristic
91C42×C61C2×D411yescharacteristic
92C42×C61C2×D411yescharacteristic
93C42×C61#4111yescharacteristic
94#11758194—21no—
95#11758194—21no—
96#11758194—21no—
97#11758194—44no—
98#11758194—41no—
99#11758194—41no—
100#11758194SD1612yes—
101C2×#92418—21no—
102C2×#92418—22no—
103C2×#92418—21no—
104C2×#92418—21no—
105C2×#92418—21no—
106C2×#92418—44no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C23×C61—22no—
113C23×C61C22⋊Q811yescharacteristic
114Q8×C61—41no—
115Q8×C61—41no—
116D4×C61—42no—
117D4×C61—42no—
118D4×C61—42no—
119D4×C61—41no—
120D4×C61—41no—
121D4×C61—41no—
122D4×C61—41no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—41no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61C2×C4⋊C411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61C22⋊Q811yescharacteristic
134C2×C4×C61#12311yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C8×C61—41no—
140C8×C61—41no—
141C8×C61—41no—
142C8×C61—41no—
143#92418—22no—
144#92418—42no—
145#92418—41no—
146#92418—41no—
147#92418—41no—
148#92418—81no—
149#8932—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—42no—
155C22×C61#38511yescharacteristic
156C22×C61#47611yescharacteristic
157C22×C61#47811yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—42no—
162C4×C61C4×SD1611yescharacteristic
163C4×C61#44211yescharacteristic
164C4×C61#44311yescharacteristic
165C4×C61#44411yescharacteristic
166C4×C61#44911yescharacteristic
167C4×C61#45011yescharacteristic
168#2935—611no—
169#1950—611no—
170#1570—611no—
171#1540D6111yescharacteristic
172#1492—611no—
173#1278—611no—
174#1277—611no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61—82no—
178C2×C61#185811yescharacteristic
179C2×C61#186411yescharacteristic
180C2×C61#186611yescharacteristic
181C2×#131—1221no—
182#532C2×D6111yescharacteristic
183#436—1221no—
184#435—1222no—
185C8×D4—1221no—
186#431C2×D6111yescharacteristic
187C2×#108—1221no—
188#423—611no—
189C2×C4⋊C8—611no—
190C2×C4⋊C8C2×D6111yescharacteristic
191#408—1221no—
192C4×M16—611no—
193C2×C4×C8—611no—
194#341—1221no—
195#334—1221no—
196#334—1221no—
197#332Dic6111yescharacteristic
198#332Dic6111yescharacteristic
199#331Dic6111yescharacteristic
200#331Dic6111yescharacteristic
201D4⋊C8—1222no—
202C61#893211yescharacteristic, complemented, Sylow
203C2×#41—21no—
204#131—2442no—
205#131—2442no—
206C2×M16—611no—
207C2×M16—611no—
208C2×M16—1222no—
209C2×M16—1221no—
210C22×C8—21no—
211C22×C8—1222no—
212C22×C8—1221no—
213C22×C8—1221no—
214C4⋊Q8C2×Dic6111yescharacteristic
215#127C2×Dic6111yescharacteristic
216#124—21no—
217#121—21no—
218#121Dic12212yes—
219C4×D4—21no—
220C4×D4D24412yes—
221C2×C42C22×D6111yescharacteristic
222#108—2442no—
223C4⋊C8—21no—
224C4⋊C8—611no—
225C4⋊C8—611no—
226C4⋊C8—1221no—
227C4⋊C8—1221no—
228C4⋊C8—1221no—
229C4⋊C8C2×Dic6111yescharacteristic
230C4⋊C8C2×Dic6111yescharacteristic
231C4⋊C8C2×Dic6111yescharacteristic
232C4⋊C8C2×Dic6111yescharacteristic
233C22⋊C8—21no—
234C22⋊C8—1222no—
235C22⋊C8—1222no—
236#97—1221no—
237C4×C8—21no—
238C4×C8—1221no—
239C4×C8—1221no—
240C4×C8—1221no—
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C4⋊Dic6112yes—
250C22×C4—22no—
251C22×C4C2×Dic12211yescharacteristic
252C22×C4D4×D6111yescharacteristic
253C22×C4#1175822411yescharacteristic
254M16—612no—
255M16—1221no—
256M16—1221no—
257M16—1221no—
258M16—2444no—
259M16—2441no—
260M16—2441no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—1221no—
268C2×C8—1222no—
269C2×C8—1221no—
270C2×C8—1221no—
271C2×C8—1221no—
272C2×C8—2444no—
273C2×C8—2441no—
274C2×C8—2441no—
275C2×C8—2441no—
276C2×C8—2441no—
277C2×C8—2441no—
278C4⋊C4—21no—
279C4⋊C4C4⋊Dic6112yes—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C42C2×D24411yescharacteristic
283C42D4×D6111yescharacteristic
284C42#1175822411yescharacteristic
285C42C22×Dic6111yescharacteristic
286C23—22no—
287C23#1451975411yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—42no—
291D4—42no—
292D4—42no—
293D4—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×C4⋊Dic6111yescharacteristic
304C2×C4D4×Dic6111yescharacteristic
305C2×C4D4×Dic6111yescharacteristic
306C2×C4#1451974711yescharacteristic
307C2×C4#1451975411yescharacteristic
308C2×C4#1451976111yescharacteristic
309C2×C4SD16×D6111yescharacteristic
310C2×C4#1451979811yescharacteristic
311C2×C4#1451980111yescharacteristic
312C2×C4#1451980111yescharacteristic
313C8—41no—
314C8—41no—
315C8—41no—
316C8—41no—
317C8—1222no—
318C8—4881no—
319C8—2442no—
320C8—2441no—
321C8—2441no—
322C8—2441no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22#1683963711yescharacteristic
329C22#1684005011yescharacteristic
330C22#1684006411yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4SD16×Dic6111yescharacteristic
336C4#1683987411yescharacteristic
337C4#1683987911yescharacteristic
338C4#1683988411yescharacteristic
339C4#1683990811yescharacteristic
340C4#1683991411yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#2144604111yescharacteristic
345C2#2144608211yescharacteristic
346C2#2144609611yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1540C2
socleC22×C61#385
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#1540D61
hypocenterC61#8932
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #21446595C2semidirect
3. #21444590C2semidirect
5. #21443655C2semidirect
6. #21443653C2semidirect
202. C61#8932semidirect

Maximal subgroups

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

subgroupindex
#214545632
#214465952
#214445902
#214442702
#214436552
#214436532
C61×#15402
#893261