Finite Group Databasebeta

← #29574330

Subgroups — #29574330

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#21454384C211yesmaximal, characteristic
2#21445840C211yesmaximal, characteristic
3#21444589C211yesmaximal, characteristic, complemented
4#21444575C211yesmaximal, characteristic, complemented
5#21444202C211yesmaximal, characteristic
6#21443722C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#14519783—21no—
9C4×#11758222C2211yescharacteristic
10#16839815C2211yescharacteristic
11#16839788—21no—
12#16839787—22no—
13#16839786C2211yescharacteristic
14#16839786C2211yescharacteristic
15#16839784—21no—
16C4⋊C8×D61—21no—
17C2×#14519705—21no—
18#16839522—21no—
19#16839513—22no—
20#16839512—21no—
21#16839512—21no—
22#16839494C411yescharacteristic, complemented
23#16839494C411yescharacteristic, complemented
24#16839491C411yescharacteristic, complemented
25#16839491C411yescharacteristic, complemented
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C2×#11758222D411yescharacteristic
30#14519783—42no—
31#14519783—42no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34C2×#11758189—22no—
35C2×C8×D61—22no—
36C4×Dic122C2×C411yescharacteristic
37C4×Dic122Q811yescharacteristic
38C4×D244C2×C411yescharacteristic
39C4×D244Q811yescharacteristic
40C4×C22⋊D61—21no—
41C4×C22⋊D61—21no—
42#14519736D411yescharacteristic
43#14519734—21no—
44C42×D61—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418C2×C411yescharacteristic
49C4⋊#92418C2×C411yescharacteristic
50C4⋊#92418D412yes—
51#14519706—22no—
52#14519706—22no—
53#14519705—42no—
54C22⋊#92418—21no—
55C4×#92418—21no—
56C22×C8×C61—21no—
57C22×C8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61D411yescharacteristic
63C4⋊C8×C61D411yescharacteristic
64C4×C8×C61—21no—
65C4×C8×C61C2×C411yescharacteristic
66C4×C8×C61C2×C411yescharacteristic
67#95×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C22×C4×C61#4111yescharacteristic
72C2×C22⋊D61—21no—
73#11758222—21no—
74#11758222—21no—
75#11758222SD1612yes—
76#11758222SD1612yes—
77C2×D244C4⋊C411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×Dic122C4⋊C411yescharacteristic
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—21no—
85C2×C8×C61—21no—
86C2×C8×C61—42no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—41no—
91C42×C61—41no—
92C42×C61—41no—
93C42×C61C22×C411yescharacteristic
94C42×C61C2×D411yescharacteristic
95C42×C61C2×D411yescharacteristic
96C42×C61C2×Q811yescharacteristic
97C22⋊Dic61—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61C4⋊C411yescharacteristic
101C4⋊Dic61C4⋊C411yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107#11758194—41no—
108#11758194—41no—
109#11758194—41no—
110#11758194—41no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—22no—
114C2×#92418—41no—
115#11758189—44no—
116C8×D61—44no—
117C23×C61#12311yescharacteristic
118C22×D61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—42no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61C2×C4⋊C411yescharacteristic
126C2×C4×C61C4×D411yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×C4×C61#12011yescharacteristic
129C2×C4×C61C22⋊Q811yescharacteristic
130C2×C4×C61C22⋊Q811yescharacteristic
131C2×C4×C61C2×SD1611yescharacteristic
132C2×C4×C61C2×SD1611yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C22⋊D61—22no—
136C22⋊D61—22no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140D244—21no—
141D244#10612yes—
142C4×D61—22no—
143C4×D61—22no—
144C4×D61—41no—
145C4×D61—41no—
146C4×D61—81no—
147Dic122—21no—
148Dic122#10612yes—
149C8×C61—22no—
150C8×C61—41no—
151C8×C61—41no—
152C8×C61—41no—
153#92418—41no—
154#92418—41no—
155#92418—42no—
156#92418—81no—
157#8904—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61#38511yescharacteristic
161C22×C61#48111yescharacteristic
162C22×C61#48311yescharacteristic
163C2×D61—22no—
164C2×D61—41no—
165C2×D61—41no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—82no—
170C4×C61C2×#10611yescharacteristic
171C4×C61#42811yescharacteristic
172C4×C61#44311yescharacteristic
173C4×C61#44411yescharacteristic
174C4×C61#44811yescharacteristic
175C4×C61#45011yescharacteristic
176Dic61—22no—
177Dic61—41no—
178Dic61—41no—
179#2906—611no—
180#1806—611no—
181#1570—611no—
182#1566—611no—
183#1476—611no—
184#1303—611no—
185#1279D6111yescharacteristic, complemented
186C2×C61—21no—
187C2×C61—21no—
188C2×C61#185311yescharacteristic
189C2×C61#186111yescharacteristic
190C2×C61#186611yescharacteristic
191D61—42no—
192C2×#131—1221no—
193C4×#41—611no—
194#431—611no—
195#424—1222no—
196#424—1221no—
197#423—611no—
198#423—611no—
199#423—1221no—
200C2×C4⋊C8—1221no—
201C2×C4⋊C8C2×D6111yescharacteristic
202C2×#104—1221no—
203C2×C4×C8C2×D6111yescharacteristic
204C4×C4⋊C4C2×D6111yescharacteristic
205#339—1221no—
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×#41—611no—
215#131—2442no—
216#131—2442no—
217C2×M16—1222no—
218C2×M16—1221no—
219C2×M16—1221no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—1222no—
223C4×Q8—611no—
224C4×Q8—611no—
225C4×D4—611no—
226C4×D4—611no—
227C4×D4—1221no—
228C4×D4—1221no—
229#117—611no—
230#117—1221no—
231C2×C4⋊C4—21no—
232C2×C42—21no—
233C2×C42—1221no—
234C2×C42C22×D6111yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—611no—
237C4⋊C8—611no—
238C4⋊C8—612no—
239C4⋊C8—1222no—
240C4⋊C8—1222no—
241C4⋊C8—1221no—
242C4⋊C8—1221no—
243C4⋊C8—1221no—
244C4⋊C8D24411yescharacteristic
245C4⋊C8D24411yescharacteristic
246#104—2442no—
247C22⋊C8—1221no—
248C4×C8—21no—
249C4×C8—1221no—
250C4×C8C4×D6111yescharacteristic
251C4×C8C4×D6111yescharacteristic
252#95—21no—
253#41—612no—
254#41—612no—
255#41—1221no—
256#41—1221no—
257C2×Q8—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C22×C4—41no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4#1175822211yescharacteristic
265C22×C4D4×D6111yescharacteristic
266C22×C4#1175822411yescharacteristic
267M16—2444no—
268M16—2441no—
269M16—2441no—
270M16—2441no—
271M16—2441no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—42no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—1221no—
280C2×C8—1221no—
281C2×C8—1222no—
282C2×C8—2444no—
283C2×C8—2441no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—611no—
287C4⋊C4—611no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—41no—
294C42—41no—
295C42—1221no—
296C42—1221no—
297C42—1221no—
298C42C2×C4×D6111yescharacteristic
299C42C2×D24411yescharacteristic
300C42D4×D6111yescharacteristic
301C42Q8×D6111yescharacteristic
302C23—1221no—
303C23#1451975911yescharacteristic
304Q8—612no—
305Q8—1221no—
306D4—612no—
307D4—1222no—
308D4—1222no—
309D4—1221no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—1221no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—4881no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4C4⋊C4×D6111yescharacteristic
325C2×C4#1451973711yescharacteristic
326C2×C4C4×D24411yescharacteristic
327C2×C4#1451974711yescharacteristic
328C2×C4#1451975511yescharacteristic
329C2×C4#1451975711yescharacteristic
330C2×C4SD16×D6111yescharacteristic
331C2×C4SD16×D6111yescharacteristic
332C2×C4#1451980111yescharacteristic
333C2×C4#1451980911yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—4881no—
339C8—2441no—
340C8—2441no—
341C8—2442no—
342C22—21no—
343C22—21no—
344C22—1222no—
345C22—2441no—
346C22—2441no—
347C22#1683963611yescharacteristic
348C22#1684007911yescharacteristic
349C22#1684009111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—1222no—
355C4—2441no—
356C4—2441no—
357C4#106×D6111yescharacteristic
358C4#1683980311yescharacteristic
359C4#1683988011yescharacteristic
360C4#1683988511yescharacteristic
361C4#1683990211yescharacteristic
362C4#1683991411yescharacteristic
363C2—21no—
364C2—21no—
365C2—2442no—
366C2#2144601311yescharacteristic
367C2#2144606011yescharacteristic
368C2#2144609711yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC22×C61#385
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#8904
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #21444589C2semidirect
4. #21444575C2semidirect
6. #21443722C2semidirect
7. C61×#1279C2semidirect
22. #16839494C4semidirect
23. #16839494C4semidirect
24. #16839491C4semidirect
25. #16839491C4semidirect
185. #1279D61semidirect
213. C61#8904semidirect

Maximal subgroups

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

subgroupindex
#214543842
#214458402
#214445892
#214445752
#214442022
#214437222
C61×#12792
#890461