Finite Group Databasebeta

← #29596963

Subgroups — #29596963

Order 15616.

530 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840000C211yesmaximal, characteristic
2C2×#16839799C211yesmaximal, characteristic
3C2×#16839566C211yesmaximal, characteristic, complemented
4C2×#16839541C211yesmaximal, characteristic
5#21443911C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C2×C61×#358C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9C2×#14519753—21no—
10C2×#14519735—21no—
11C22×#11758185C2211yescharacteristic
12#16840000—22no—
13#16840000C414yescomplemented
14#16839799—22no—
15#16839799—22no—
16C2×#14519711C2211yescharacteristic
17C2×#14519711C2211yescharacteristic
18C2×#14519708—21no—
19C2×#14519701—21no—
20#16839566—22no—
21#16839541—22no—
22C22×Q16×C61C2211yescharacteristic
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C61×#358—22no—
26C22×C4×D61D411yescharacteristic
27C22×#92418D411yescharacteristic
28C2×C8×D61—21no—
29C2×C8×D61—21no—
30C2×C8×D61—21no—
31C2×C8×D61—21no—
32C2×C8×D61C2×C412yes—
33C2×C8×D61D412yes—
34#14519753—24no—
35#14519753—42no—
36#14519735—24no—
37#14519735—42no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×#11758196—41no—
41C2×#11758198—41no—
42C2×#11758198—41no—
43C2×C4×Dic61—41no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47#14519711—21no—
48#14519711—21no—
49#14519711C2×C412yes—
50#14519711D412yes—
51#14519708—24no—
52#14519701—24no—
53C22×Q8×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61—21no—
56C2×Q16×C61—21no—
57C2×Q16×C61—21no—
58C2×Q16×C61—21no—
59C2×Q16×C61C2×C412yes—
60C22×C8×C61C2311yescharacteristic
61C2×C4⋊C4×C61—21no—
62C2×C16×C61—21no—
63C2×C16×C61—21no—
64C2×C16×C61—21no—
65#107×C61—21no—
66#107×C61D412yes—
67C23×D61D811yescharacteristic
68C2×Q8×C61—22no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C2×Q8×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61D811yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61C22⋊C412yes—
85C2×C4×D61SD1612yes—
86Q16×C61—22no—
87Q16×C61—22no—
88Q16×C61—41no—
89Q16×C61—41no—
90C2×C8×C61C22×C411yescharacteristic
91C2×C8×C61C2×D411yescharacteristic
92C2×C8×C61C2×D411yescharacteristic
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61#4111yescharacteristic
95C2×C8×C61#4111yescharacteristic
96C4⋊C4×C61—22no—
97C4⋊C4×C61—41no—
98#11758198—44no—
99#11758198—44no—
100C4⋊Dic61—22no—
101C4⋊Dic61—22no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104#11758196—44no—
105C4×Dic61—44no—
106C2×#92418—21no—
107C2×#92418—21no—
108C2×#92418C22⋊C412yes—
109C8×D61—22no—
110C8×D61—22no—
111C8×D61—22no—
112C8×D61—22no—
113C16×C61—41no—
114#11758185—41no—
115C23×C61C2×D811yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61#10212yes—
123Q8×C61—42no—
124Q8×C61—42no—
125Q8×C61—81no—
126Q8×C61—81no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61#12011yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61#10212yes—
148C4×D61—22no—
149C4×D61—22no—
150C4×D61—22no—
151C4×D61—22no—
152C8×C61C4×D411yescharacteristic
153C8×C61C4×D411yescharacteristic
154C8×C61#12111yescharacteristic
155C8×C61#12111yescharacteristic
156#92418—22no—
157#12994—611nomaximal, Sylow
158C22×C61C2×#10211yescharacteristic
159C22×C61#44711yescharacteristic
160C22×C61#48011yescharacteristic
161C22×C61#50811yescharacteristic
162C22×C61#50811yescharacteristic
163C22×C61#51011yescharacteristic
164C22×C61#51011yescharacteristic
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—22no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C4×C61—82no—
173C4×C61—82no—
174C4×C61#38611yescharacteristic
175C4×C61#41711yescharacteristic
176C4×C61#44811yescharacteristic
177C4×C61#48111yescharacteristic
178Dic61—22no—
179Dic61—82no—
180Dic61—82no—
181C2×#467—611no—
182C2×#427—611no—
183C2×#358—611no—
184C2×#358D6111yescharacteristic, complemented
185C2×C22⋊C16—611no—
186#1380—611no—
187#1380—611no—
188C2×C61#187411yescharacteristic
189C2×C61#213811yescharacteristic
190C2×C61#214111yescharacteristic
191C2×C61#218911yescharacteristic
192C2×C61#218911yescharacteristic
193C2×C61#223711yescharacteristic
194C2×C61#223711yescharacteristic
195D61—42no—
196C22×Q16C2×D6111yescharacteristic
197C23×C8—611no—
198C2×C22⋊Q8—1221no—
199C2×#117—1221no—
200C22×C16—611no—
201C22×C16C2×D6111yescharacteristic
202#467—614no—
203#467—1222no—
204#427—1222no—
205#427—1222no—
206C2×#107—611no—
207C2×#107—611no—
208C2×#107C2×D6111yescharacteristic
209C2×#106—1221no—
210C2×#103—1221no—
211#358—22no—
212#358—1222no—
213C22⋊C16—1222no—
214C61#1299411yescharacteristic, complemented, Sylow
215C22×Q8—21no—
216C23×C4—611no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16C4×D6112yes—
223C22×C8—611no—
224C22×C8—612no—
225C22×C8—612no—
226C22×C8—1221no—
227C22×C8—1221no—
228C22×C8—1221no—
229C22×C8—1221no—
230C22×C8C22×D6111yescharacteristic
231C22⋊Q8—1224no—
232C22⋊Q8—2442no—
233#117—1224no—
234#117—2442no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—2441no—
239C2×C22⋊C4—2441no—
240C2×C22⋊C4—2441no—
241C2×C42—2441no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—1221no—
246C2×C16—1221no—
247C2×C16—1221no—
248#107—21no—
249#107—612no—
250#107—612no—
251#107—1221no—
252#107—1221no—
253#107C22⋊D6112yes—
254#106—1224no—
255#103—1224no—
256C24—611no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—611no—
266C22×C4—612no—
267C22×C4—612no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4D4×D6111yescharacteristic
275Q16—22no—
276Q16—22no—
277Q16—41no—
278Q16—41no—
279C2×C8—612no—
280C2×C8—1221no—
281C2×C8—1221no—
282C2×C8—1222no—
283C2×C8—1222no—
284C2×C8—1222no—
285C2×C8—1222no—
286C2×C8C2×C4×D6111yescharacteristic
287C2×C8#1175822211yescharacteristic
288C2×C8D4×D6111yescharacteristic
289C2×C8D4×D6111yescharacteristic
290C2×C8#1175822411yescharacteristic
291C2×C8C2×C22⋊D6111yescharacteristic
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—1222no—
295C4⋊C4—1222no—
296C4⋊C4—2444no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C22⋊C4—2444no—
300C22⋊C4—2444no—
301C42—2444no—
302C16—41no—
303C16—2441no—
304C23—612no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23D8×D6111yescharacteristic
312Q8—42no—
313Q8—42no—
314Q8—81no—
315Q8—81no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—612no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4C22⋊C4×D6111yescharacteristic
336C2×C4#1451974511yescharacteristic
337C2×C4#1451975911yescharacteristic
338C2×C4SD16×D6111yescharacteristic
339C2×C4#1451980111yescharacteristic
340C2×C4#1451980611yescharacteristic
341C8—1222no—
342C8#1451973711yescharacteristic
343C8C4×C22⋊D6111yescharacteristic
344C8#1451974811yescharacteristic
345C8#1451975011yescharacteristic
346C22—1222no—
347C22—1222no—
348C22—1222no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22#102×D6111yescharacteristic
354C22#1683989411yescharacteristic
355C22#1684007411yescharacteristic
356C22#1684019311yescharacteristic
357C22#1684019511yescharacteristic
358C22#1684020111yescharacteristic
359C22#1684020411yescharacteristic
360C4—82no—
361C4—82no—
362C4—1222no—
363C4—4882no—
364C4—4882no—
365C4#1683963811yescharacteristic
366C4#1683976011yescharacteristic
367C4#1683989911yescharacteristic
368C4#1684007911yescharacteristic
369C2—2442no—
370C2#2144613311yescharacteristic
371C2#2144752511yescharacteristic
372C2#2144753711yescharacteristic
373C2#2144775611yescharacteristic
374C2#2144775811yescharacteristic
375C2#2144802511yescharacteristic
376C2#2144802611yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#358C2
socleC23×C61C2×D8
prime radicalC23×D61D8
cosocleC22×C8×C61C23
hypercenterC2×#358D61
hypocenterC61#12994
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
3. C2×#16839566C2semidirect
5. #21443911C2semidirect
6. #21443910C2semidirect
7. C2×C61×#358C2semidirect
13. #16840000C4semidirect
184. C2×#358D61semidirect
214. C61#12994semidirect

Maximal subgroups

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

subgroupindex
C2×#168400002
C2×#168397992
C2×#168395662
C2×#168395412
#214439112
#214439102
C2×C61×#3582
#1299461