Finite Group Databasebeta

← #29574315

Subgroups — #29574315

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#21445839C211yesmaximal, characteristic
3#21444594C211yesmaximal, characteristic, complemented
4#21444578C211yesmaximal, characteristic, complemented
5#21443721C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1476C211yesmaximal, characteristic
8C2×#14519784—21no—
9#16839789—22no—
10#16839789—21no—
11#16839786—21no—
12#16839786C2211yescharacteristic
13#16839786C2211yescharacteristic
14C2×C4⋊#92418—21no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×#14519704—21no—
17C4×C4⋊Dic61C2211yescharacteristic
18#16839521—21no—
19#16839515—22no—
20#16839515—21no—
21#16839515—21no—
22C4×#41×C61C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C2×C4×C8×C61C2211yescharacteristic
25C61×Q8⋊C8C411yescharacteristic, complemented
26C61×Q8⋊C8C411yescharacteristic, complemented
27C61×D4⋊C8C411yescharacteristic, complemented
28C61×D4⋊C8C411yescharacteristic, complemented
29#14519784—42no—
30#14519784—42no—
31C2×#11758194—22no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34C22×#92418—22no—
35C22×#92418—21no—
36C2×C4⋊Dic61—21no—
37C2×C4×Dic61—21no—
38C4⋊#92418—22no—
39C4⋊#92418—22no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418D411yescharacteristic
45C4⋊#92418D411yescharacteristic
46C4⋊#92418D412yes—
47#14519704—42no—
48#14519684—21no—
49C2×#41×C61D411yescharacteristic
50C22×C8×C61—21no—
51C4×Q8×C61C2×C411yescharacteristic
52C4×Q8×C61Q811yescharacteristic
53C4×D4×C61—21no—
54C4×D4×C61—21no—
55C4×D4×C61C2×C411yescharacteristic
56C4×D4×C61Q811yescharacteristic
57#117×C61—21no—
58#117×C61D411yescharacteristic
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61C2×C411yescharacteristic
62C4⋊C8×C61C2×C411yescharacteristic
63C22⋊C8×C61—21no—
64C4×C8×C61—21no—
65C4×C8×C61—21no—
66C4×C8×C61C2×C411yescharacteristic
67C4×C8×C61C2×C411yescharacteristic
68#41×C61—21no—
69#41×C61—21no—
70#41×C61D812yes—
71#41×C61Q1612yes—
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×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C22×Dic61—41no—
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—21no—
85C2×C8×C61—21no—
86C2×C8×C61—42no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
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×C61C22×C411yescharacteristic
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×Q811yescharacteristic
101C4⋊Dic61—22no—
102C4⋊Dic61—41no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105#11758194—44no—
106#11758194—41no—
107#11758194—41no—
108#11758194—41no—
109#11758194—41no—
110C2×#92418—21no—
111C2×#92418—22no—
112C2×#92418—21no—
113C2×#92418—44no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C23×C61—21no—
118C23×C61#12311yescharacteristic
119Q8×C61—21no—
120Q8×C61#10712yes—
121D4×C61—22no—
122D4×C61—22no—
123D4×C61—21no—
124D4×C61#10712yes—
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—81no—
136C2×C4×C61C2×C4⋊C411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61C22⋊Q811yescharacteristic
141C2×C4×C61C22⋊Q811yescharacteristic
142C2×C4×C61C2×D811yescharacteristic
143C2×C4×C61C2×Q1611yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C61#13711yescharacteristic
146C2×Dic61—42no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C8×C61—22no—
150C8×C61—41no—
151C8×C61—41no—
152C8×C61—41no—
153#92418—41no—
154#92418—42no—
155#92418—41no—
156#92418—81no—
157#8902—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—22no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61#38511yescharacteristic
164C22×C61#48011yescharacteristic
165C22×C61#48411yescharacteristic
166C4×C61—22no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C2×#10711yescharacteristic
173C4×C61#42811yescharacteristic
174C4×C61#44311yescharacteristic
175C4×C61#44411yescharacteristic
176C4×C61#44711yescharacteristic
177C4×C61#45111yescharacteristic
178Dic61—82no—
179#2906—611no—
180#1806—611no—
181#1571—611no—
182#1567—611no—
183#1476D6111yescharacteristic
184#1303—611no—
185#1279—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—42no—
189C2×C61#185211yescharacteristic
190C2×C61#186111yescharacteristic
191C2×C61#186611yescharacteristic
192C2×#131—1221no—
193C4×#41C2×D6111yescharacteristic
194#431C2×D6111yescharacteristic
195#424—1222no—
196#424—1221no—
197#423—611no—
198#423—611no—
199#423—1221no—
200C2×C4⋊C8—611no—
201C2×C4⋊C8—1221no—
202C2×#104—1221no—
203C2×C4×C8C2×D6111yescharacteristic
204C4×C4⋊C4—611no—
205#339—1221no—
206#335—1222no—
207#335—1221no—
208#335—1221no—
209Q8⋊C8Dic6111yescharacteristic, complemented
210Q8⋊C8Dic6111yescharacteristic, complemented
211D4⋊C8Dic6111yescharacteristic, complemented
212D4⋊C8Dic6111yescharacteristic, complemented
213C61#890211yescharacteristic, complemented, Sylow
214C2×#41D24411yescharacteristic
215#131—2442no—
216#131—2442no—
217C2×M16—1222no—
218C2×M16—1221no—
219C2×M16—1221no—
220C22×C8—21no—
221C22×C8—1222no—
222C22×C8—1221no—
223C4×Q8Dic12211yescharacteristic
224C4×Q8C2×Dic6111yescharacteristic
225C4×D4—21no—
226C4×D4—21no—
227C4×D4Dic12211yescharacteristic
228C4×D4C2×Dic6111yescharacteristic
229#117—21no—
230#117D24411yescharacteristic
231C2×C4⋊C4—1221no—
232C2×C42—21no—
233C2×C42—1221no—
234C2×C42C22×D6111yescharacteristic
235C4⋊C8—611no—
236C4⋊C8—611no—
237C4⋊C8—612no—
238C4⋊C8—1222no—
239C4⋊C8—1222no—
240C4⋊C8—1221no—
241C4⋊C8—1221no—
242C4⋊C8—1221no—
243C4⋊C8—1221no—
244C4⋊C8C2×Dic6111yescharacteristic
245C4⋊C8C2×Dic6111yescharacteristic
246#104—2442no—
247C22⋊C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8C2×Dic6111yescharacteristic
251C4×C8C2×Dic6111yescharacteristic
252#95—1221no—
253#41—21no—
254#41—21no—
255#41D48812yes—
256#41Dic24412yes—
257C2×Q8C4⋊Dic6111yescharacteristic
258C2×D4—21no—
259C2×D4C4⋊Dic6111yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—2441no—
264C22×C4C2×D24411yescharacteristic
265C22×C4#1175822411yescharacteristic
266C22×C4#1175822411yescharacteristic
267M16—2441no—
268M16—2441no—
269M16—2444no—
270M16—2441no—
271M16—2441no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—42no—
277C2×C8—1221no—
278C2×C8—1221no—
279C2×C8—1222no—
280C2×C8—2441no—
281C2×C8—2444no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—1222no—
287C4⋊C4—2441no—
288C4⋊C4C4⋊Dic6111yescharacteristic
289C4⋊C4C4⋊Dic6111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—2441no—
297C42—2441no—
298C42C2×Dic12211yescharacteristic
299C42D4×D6111yescharacteristic
300C42D4×D6111yescharacteristic
301C42C22×Dic6111yescharacteristic
302C23—21no—
303C23#1451976111yescharacteristic
304Q8—21no—
305Q8#1451971112yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4#1451971112yes—
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—81no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—2442no—
324C2×C4C2×C4⋊Dic6111yescharacteristic
325C2×C4D4×Dic6111yescharacteristic
326C2×C4D4×Dic6111yescharacteristic
327C2×C4#1451974711yescharacteristic
328C2×C4#1451975411yescharacteristic
329C2×C4#1451975411yescharacteristic
330C2×C4C2×D48811yescharacteristic
331C2×C4C2×Dic24411yescharacteristic
332C2×C4#1451980511yescharacteristic
333C2×C4#1451981011yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—4881no—
339C8—2441no—
340C8—2442no—
341C8—2441no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22#1683963711yescharacteristic
348C22#1684007611yescharacteristic
349C22#1684009811yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—4882no—
357C4C2×#1451971111yescharacteristic
358C4#1683980411yescharacteristic
359C4#1683987911yescharacteristic
360C4#1683988411yescharacteristic
361C4#1683989811yescharacteristic
362C4#1683992011yescharacteristic
363C2—21no—
364C2—21no—
365C2—42no—
366C2#2144600911yescharacteristic
367C2#2144606111yescharacteristic
368C2#2144609611yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1476C2
socleC22×C61#385
prime radicalC2×#41×C61D4
cosocleC2×C42×C61C23
hypercenter#1476D61
hypocenterC61#8902
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
3. #21444594C2semidirect
4. #21444578C2semidirect
5. #21443721C2semidirect
6. #21443659C2semidirect
25. C61×Q8⋊C8C4semidirect
26. C61×Q8⋊C8C4semidirect
27. C61×D4⋊C8C4semidirect
28. C61×D4⋊C8C4semidirect
209. Q8⋊C8Dic61semidirect
210. Q8⋊C8Dic61semidirect
211. D4⋊C8Dic61semidirect
212. D4⋊C8Dic61semidirect
213. C61#8902semidirect

Maximal subgroups

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

subgroupindex
#214543872
#214458392
#214445942
#214445782
#214437212
#214436592
C61×#14762
#890261