Finite Group Databasebeta

← #29574325

Subgroups — #29574325

Order 15616.

438 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454387C211yesmaximal, characteristic
2#21444591C211yesmaximal, characteristic, complemented
3#21444574C211yesmaximal, characteristic, complemented
4#21444201C211yesmaximal, characteristic
5#21443722C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1806C211yesmaximal, characteristic
8C2×#14519784—21no—
9#16839815C2211yescharacteristic
10#16839789—22no—
11#16839789—21no—
12#16839786—21no—
13#16839786C2211yescharacteristic
14C2×C4⋊#92418—21no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×C4×#92418C2211yescharacteristic
17#16839512—22no—
18#16839512—21no—
19#16839512—21no—
20Q8⋊#92418C411yescharacteristic, complemented
21Q8⋊#92418C411yescharacteristic, complemented
22D4⋊#92418C411yescharacteristic, complemented
23D4⋊#92418C411yescharacteristic, complemented
24C4×#41×C61C2211yescharacteristic
25C61×#423C2211yescharacteristic
26C2×#104×C61—21no—
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#339—21no—
29#14519784—42no—
30#14519784—42no—
31C2×#11758194—22no—
32C2×#11758194—21no—
33C22×#92418—22no—
34C22×#92418—21no—
35C22×#92418—21no—
36C4⋊#92418—22no—
37C4⋊#92418—22no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418C2×C411yescharacteristic
41C4⋊#92418C2×C411yescharacteristic
42C4⋊#92418D411yescharacteristic
43C4⋊#92418D411yescharacteristic
44C4⋊#92418D412yes—
45C22⋊#92418—21no—
46C4×#92418—21no—
47C4×#92418—21no—
48C4×#92418C2×C411yescharacteristic
49C4×#92418C2×C411yescharacteristic
50C2×#41×C61D411yescharacteristic
51C2×M16×C61—21no—
52C4×Q8×C61C2×C411yescharacteristic
53C4×Q8×C61Q811yescharacteristic
54C4×D4×C61—21no—
55C4×D4×C61—21no—
56C4×D4×C61C2×C411yescharacteristic
57C4×D4×C61Q811yescharacteristic
58#117×C61—21no—
59#117×C61D411yescharacteristic
60C2×C4⋊C4×C61—21no—
61C2×C42×C61—21no—
62C2×C42×C61—21no—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66#104×C61—42no—
67#95×C61—21no—
68#41×C61—21no—
69#41×C61—21no—
70#41×C61SD1612yes—
71#41×C61SD1612yes—
72C2×Q8×C61C4⋊C411yescharacteristic
73C2×D4×C61—21no—
74C2×D4×C61C4⋊C411yescharacteristic
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C22×C4×C61#4111yescharacteristic
82M16×C61—41no—
83M16×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61C4⋊C411yescharacteristic
90C4⋊C4×C61C4⋊C411yescharacteristic
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C42×C61—21no—
95C42×C61—21no—
96C42×C61—21no—
97C42×C61—41no—
98C42×C61—41no—
99C42×C61C22×C411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×Q811yescharacteristic
103#11758194—44no—
104#11758194—41no—
105#11758194—41no—
106C2×#92418—21no—
107C2×#92418—21no—
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—22no—
112C2×#92418—21no—
113C2×#92418—42no—
114C2×#92418—44no—
115C2×#92418—41no—
116C2×#92418—41no—
117C23×C61—21no—
118C23×C61#12311yescharacteristic
119Q8×C61—21no—
120Q8×C61#10612yes—
121D4×C61—22no—
122D4×C61—22no—
123D4×C61—21no—
124D4×C61#10612yes—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61C2×C4⋊C411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61C22⋊Q811yescharacteristic
144C2×C4×C61C22⋊Q811yescharacteristic
145C2×C4×C61C2×SD1611yescharacteristic
146C2×C4×C61C2×SD1611yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61#13711yescharacteristic
149C8×C61—81no—
150#92418—22no—
151#92418—41no—
152#92418—41no—
153#92418—41no—
154#92418—41no—
155#92418—42no—
156#92418—41no—
157#8904—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—22no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61#38511yescharacteristic
164C22×C61#48111yescharacteristic
165C22×C61#48311yescharacteristic
166C4×C61—22no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—82no—
173C4×C61C2×#10611yescharacteristic
174C4×C61#42811yescharacteristic
175C4×C61#44311yescharacteristic
176C4×C61#44411yescharacteristic
177C4×C61#44811yescharacteristic
178C4×C61#45011yescharacteristic
179#2906—611no—
180#1806D6111yescharacteristic
181#1570—611no—
182#1566—611no—
183#1476—611no—
184#1303—611no—
185#1279—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—42no—
189C2×C61#185311yescharacteristic
190C2×C61#186111yescharacteristic
191C2×C61#186611yescharacteristic
192C2×#131—1221no—
193C4×#41C2×D6111yescharacteristic
194#431—611no—
195#424—1222no—
196#424—1221no—
197#423—611no—
198#423—1221no—
199#423C2×D6111yescharacteristic
200C2×C4⋊C8—611no—
201C2×C4⋊C8—1221no—
202C2×#104—21no—
203C2×C4×C8—611no—
204C4×C4⋊C4C2×D6111yescharacteristic
205#339—21no—
206#334—1222no—
207#334—1221no—
208#334—1221no—
209Q8⋊C8—611no—
210Q8⋊C8—611no—
211D4⋊C8—611no—
212D4⋊C8—611no—
213C61#890411yescharacteristic, complemented, Sylow
214C2×#41C22⋊D6111yescharacteristic
215#131—2442no—
216#131—2442no—
217C2×M16—21no—
218C2×M16—1222no—
219C2×M16—1221no—
220C22×C8—1222no—
221C22×C8—1221no—
222C22×C8—1221no—
223C4×Q8Dic12211yescharacteristic
224C4×Q8C4×D6111yescharacteristic
225C4×D4—21no—
226C4×D4—21no—
227C4×D4Dic12211yescharacteristic
228C4×D4C4×D6111yescharacteristic
229#117—21no—
230#117C22⋊D6111yescharacteristic
231C2×C4⋊C4—21no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42C22×D6111yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—611no—
238C4⋊C8—611no—
239C4⋊C8—611no—
240C4⋊C8—611no—
241C4⋊C8—612no—
242C4⋊C8—1222no—
243C4⋊C8—1222no—
244C4⋊C8—1221no—
245C4⋊C8—1221no—
246#104—42no—
247C22⋊C8—1221no—
248C4×C8—611no—
249C4×C8—611no—
250C4×C8—1221no—
251C4×C8—1221no—
252#95—21no—
253#41—21no—
254#41—21no—
255#41#1175820012yes—
256#41#1175820112yes—
257C2×Q8#1175819611yescharacteristic
258C2×D4—21no—
259C2×D4#1175819611yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4#1175822411yescharacteristic
265C22×C4#1175822411yescharacteristic
266C22×C4C2×C22⋊D6111yescharacteristic
267M16—41no—
268M16—41no—
269M16—2444no—
270M16—2441no—
271M16—2441no—
272C2×C8—41no—
273C2×C8—1221no—
274C2×C8—1221no—
275C2×C8—1221no—
276C2×C8—1221no—
277C2×C8—1221no—
278C2×C8—1221no—
279C2×C8—1222no—
280C2×C8—2442no—
281C2×C8—2444no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4#1175819611yescharacteristic
289C4⋊C4#1175819611yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—41no—
297C42—41no—
298C42C2×Dic12211yescharacteristic
299C42C2×C4×D6111yescharacteristic
300C42D4×D6111yescharacteristic
301C42D4×D6111yescharacteristic
302C23—21no—
303C23#1451975811yescharacteristic
304Q8—21no—
305Q8#1451970812yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4#1451970812yes—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C2×#1175819611yescharacteristic
325C2×C4#1451973711yescharacteristic
326C2×C4#1451973711yescharacteristic
327C2×C4#1451974511yescharacteristic
328C2×C4#1451975411yescharacteristic
329C2×C4#1451975411yescharacteristic
330C2×C4C2×#1175820111yescharacteristic
331C2×C4C2×#1175820011yescharacteristic
332C2×C4#1451980211yescharacteristic
333C2×C4#1451980711yescharacteristic
334C8—81no—
335C8—1222no—
336C8—2441no—
337C8—2441no—
338C8—2441no—
339C8—2441no—
340C8—2442no—
341C8—2441no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22#1683963411yescharacteristic
348C22#1684007811yescharacteristic
349C22#1684009011yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—82no—
357C4C2×#1451970811yescharacteristic
358C4#1683980511yescharacteristic
359C4#1683987611yescharacteristic
360C4#1683988111yescharacteristic
361C4#1683990011yescharacteristic
362C4#1683991211yescharacteristic
363C2—21no—
364C2—21no—
365C2—42no—
366C2#2144601111yescharacteristic
367C2#2144605711yescharacteristic
368C2#2144609211yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1806C2
socleC22×C61#385
prime radicalC2×#41×C61D4
cosocleC2×C42×C61C23
hypercenter#1806D61
hypocenterC61#8904
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #21444591C2semidirect
3. #21444574C2semidirect
5. #21443722C2semidirect
6. #21443660C2semidirect
20. Q8⋊#92418C4semidirect
21. Q8⋊#92418C4semidirect
22. D4⋊#92418C4semidirect
23. D4⋊#92418C4semidirect
213. C61#8904semidirect

Maximal subgroups

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

subgroupindex
#214543872
#214445912
#214445742
#214442012
#214437222
#214436602
C61×#18062
#890461