Finite Group Databasebeta

← #29570548

Subgroups — #29570548

Order 15616.

400 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839824C211yesmaximal, characteristic
2#21444131C211yesmaximal, characteristic
3#21444131C211yesmaximal, characteristic
4#21444112C211yesmaximal, characteristic, complemented
5#21444103C211yesmaximal, characteristic, complemented
6#21443664C211yesmaximal, characteristic, complemented
7C61×#1281C211yesmaximal, characteristic, complemented
8C2×#14519734C2211yescharacteristic
9#16839824—21no—
10#16839824—21no—
11#16839824—21no—
12#16839824—21no—
13#16839815C2211yescharacteristic
14#16839815C2211yescharacteristic
15C2×#14519706C411yescharacteristic
16C2×#14519706C411yescharacteristic
17C2×#14519689C411yescharacteristic
18C2×#14519689C411yescharacteristic
19C2×C4×#92418C2211yescharacteristic
20#16839487C412yes—
21#16839487C412yes—
22#16839485C412yes—
23#16839485C412yes—
24#16839484—21no—
25#16839484—21no—
26#16839483—21no—
27C8×#92418—21no—
28C61×#431C2211yescharacteristic
29C61×#431C2211yescharacteristic
30C2×#97×C61C2211yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×#92418C2×C411yescharacteristic
33C22×#92418C2×C411yescharacteristic
34#14519734—21no—
35#14519734—21no—
36#14519734—21no—
37#14519734—21no—
38C2×#11758196C2×C411yescharacteristic
39C2×#11758196C2×C411yescharacteristic
40C2×#11758198C2×C411yescharacteristic
41C2×#11758198C2×C411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45#14519706—21no—
46#14519706—21no—
47#14519706—21no—
48#14519706—21no—
49C22⋊#92418C2×C412yes—
50C22⋊#92418C2×C412yes—
51#14519689—21no—
52#14519689—21no—
53#14519689—21no—
54#14519689—21no—
55C4×#92418—21no—
56C4×#92418—21no—
57C4×#92418D411yescharacteristic
58C4×#92418D411yescharacteristic
59C4×#92418D411yescharacteristic
60C4×#92418D411yescharacteristic
61C22×C8×C61C2×C411yescharacteristic
62C22×C8×C61C2×C411yescharacteristic
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C22⋊C8×C61C2×C412yes—
67C22⋊C8×C61C2×C412yes—
68#97×C61—21no—
69#97×C61—21no—
70C4×C8×C61—21no—
71C4×C8×C61—21no—
72C23×D61C4211yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×Dic61C4211yescharacteristic
77C22×Dic61C4211yescharacteristic
78C22×Dic61C4211yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C8×C61—21no—
86C2×C8×C61—21no—
87C2×C8×C61—22no—
88C2×C8×C61—22no—
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C42×C61C2×D411yescharacteristic
94C42×C61C2×D411yescharacteristic
95C42×C61#4111yescharacteristic
96C42×C61#4111yescharacteristic
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C2×#92418—21no—
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—22no—
112C2×#92418—22no—
113C2×#92418C22⋊C411yescharacteristic
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418C22⋊C411yescharacteristic
116C2×#92418C22⋊C411yescharacteristic
117C23×C61C2×C4211yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—41no—
122C22×D61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61C2×C22⋊C411yescharacteristic
126C2×C4×C61#11711yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61#13111yescharacteristic
132C2×C4×C61#13111yescharacteristic
133C2×C4×C61#13111yescharacteristic
134C2×C4×C61#13111yescharacteristic
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C4×D61—41no—
143C4×D61—41no—
144C4×D61—41no—
145C4×D61—41no—
146C8×C61—42no—
147C8×C61—42no—
148C8×C61—41no—
149C8×C61—41no—
150#92418—21no—
151#92418—21no—
152#92418—21no—
153#92418—21no—
154#92418—42no—
155#92418—42no—
156#8158—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61C4×C22⋊C411yescharacteristic
160C22×C61#40511yescharacteristic
161C22×C61#40511yescharacteristic
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—81no—
166C2×D61—81no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61#40811yescharacteristic
172C4×C61#40811yescharacteristic
173C4×C61#43311yescharacteristic
174C4×C61#43311yescharacteristic
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178C2×#433—611no—
179#1458—611no—
180#1458—611no—
181#1452—611no—
182#1450—611no—
183#1281—611no—
184#1281D6111yescharacteristic, complemented
185C2×C61—21no—
186C2×C61—21no—
187C2×C61#175011yescharacteristic
188C2×C61#175711yescharacteristic
189C2×C61#175711yescharacteristic
190D61—81no—
191C2×#117—611no—
192#433—1221no—
193#433—1221no—
194#433—1221no—
195#433—1221no—
196#431—611no—
197#431—611no—
198#431C2×D6111yescharacteristic
199#431C2×D6111yescharacteristic
200C2×C4⋊C8—611no—
201C2×C4⋊C8—611no—
202C2×C22⋊C8—611no—
203C2×C22⋊C8—611no—
204C2×#97C2×D6111yescharacteristic
205C2×C4×C8—611no—
206#324—612no—
207#324—612no—
208#323—612no—
209#323—612no—
210#322—1221no—
211#322—1221no—
212#322—1221no—
213C82—1221no—
214C61#815811yescharacteristic, complemented, Sylow
215C23×C4—611no—
216C22×C8—611no—
217C22×C8—611no—
218C22×C8C4×D6111yescharacteristic
219C22×C8C4×D6111yescharacteristic
220#117—1221no—
221#117—1221no—
222#117—1221no—
223#117—1221no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C22⋊C4—611no—
227C2×C22⋊C4—611no—
228C2×C42—611no—
229C2×C42C22×D6111yescharacteristic
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—1221no—
233C4⋊C8—1221no—
234C4⋊C8—1221no—
235C4⋊C8—1221no—
236C4⋊C8—1221no—
237C4⋊C8—1221no—
238C22⋊C8—612no—
239C22⋊C8—612no—
240C22⋊C8—1221no—
241C22⋊C8—1221no—
242C22⋊C8—1221no—
243C22⋊C8—1221no—
244C22⋊C8C4×D6112yes—
245C22⋊C8C4×D6112yes—
246#97—21no—
247#97—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—611no—
251C4×C8—611no—
252C4×C8—611no—
253C4×C8—611no—
254C4×C8—1221no—
255C4×C8—1221no—
256C24—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4C2×C4×D6111yescharacteristic
267C22×C4C2×C4×D6111yescharacteristic
268C22×C4C2×C4×D6111yescharacteristic
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8—611no—
281C2×C8—1221no—
282C2×C8—1221no—
283C2×C8—1221no—
284C2×C8—1221no—
285C2×C8—1222no—
286C2×C8—1222no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C42—1221no—
296C42—1221no—
297C42D4×D6111yescharacteristic
298C42D4×D6111yescharacteristic
299C42#1175822411yescharacteristic
300C42#1175822611yescharacteristic
301C23—1221no—
302C23—1221no—
303C23—1221no—
304C23—2441no—
305C23—2441no—
306C23C42×D6111yescharacteristic
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4C22⋊C4×D6111yescharacteristic
321C2×C4#1451973511yescharacteristic
322C2×C4#1451973711yescharacteristic
323C2×C4#1451973711yescharacteristic
324C2×C4#1451973911yescharacteristic
325C2×C4#1451973911yescharacteristic
326C2×C4#1451978311yescharacteristic
327C2×C4#1451978311yescharacteristic
328C2×C4#1451978511yescharacteristic
329C2×C4#1451978511yescharacteristic
330C8—42no—
331C8—42no—
332C8—41no—
333C8—41no—
334C8—1221no—
335C8—1221no—
336C8—1221no—
337C8—1221no—
338C8—2442no—
339C8—2442no—
340C22—21no—
341C22—21no—
342C22—4881no—
343C22—4881no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22#1683960911yescharacteristic
348C22#1683971611yescharacteristic
349C22#1683971911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—2441no—
355C4—2441no—
356C4—2441no—
357C4#1683972711yescharacteristic
358C4#1683972711yescharacteristic
359C4#1683982211yescharacteristic
360C4#1683982211yescharacteristic
361C2—21no—
362C2—21no—
363C2—4881no—
364C2#2144558411yescharacteristic
365C2#2144561811yescharacteristic
366C2#2144561811yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C2×C42
FrattiniC2×C42C22×D61
FittingC61×#1281C2
socleC22×C61C4×C22⋊C4
prime radicalC23×D61C42
cosocleC2×C42×C61C23
hypercenter#1281D61
hypocenterC61#8158
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
4. #21444112C2semidirect
5. #21444103C2semidirect
6. #21443664C2semidirect
7. C61×#1281C2semidirect
184. #1281D61semidirect
214. C61#8158semidirect

Maximal subgroups

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

subgroupindex
C2×#168398242
#214441312
#214441122
#214441032
#214436642
C61×#12812
#815861