Finite Group Databasebeta

← #29596965

Subgroups — #29596965

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×#16840004C211yesmaximal, characteristic
2C2×#16839799C211yesmaximal, characteristic
3C2×#16839567C211yesmaximal, characteristic, complemented
4C2×#16839565C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic
6#21443910C211yesmaximal, characteristic, complemented
7C61×#1380C211yesmaximal, characteristic, complemented
8C22×Dic244C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C2×#14519757—21no—
11C2×#14519735—21no—
12C22×#11758185C2211yescharacteristic
13#16840004—22no—
14#16840004C414yescomplemented
15#16839799—22no—
16#16839799—22no—
17C2×#14519711C2211yescharacteristic
18C2×#14519708—21no—
19C2×#14519700—21no—
20#16839567—22no—
21#16839565—22no—
22#16839541—22no—
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C2×#107×C61C2211yescharacteristic
26C22×Dic122—21no—
27C22×C4×D61D411yescharacteristic
28C2×Dic244—21no—
29C2×Dic244—21no—
30C2×Dic244—21no—
31C2×Dic244—21no—
32C2×Dic244—21no—
33C2×Dic244C2×C412yes—
34C22×#92418D411yescharacteristic
35C2×C8×D61—21no—
36C2×C8×D61—21no—
37C2×C8×D61—21no—
38C2×C8×D61—21no—
39C2×C8×D61C2×C412yes—
40C2×C8×D61D412yes—
41#14519757—24no—
42#14519757—42no—
43#14519735—24no—
44#14519735—42no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—41no—
47C2×#11758198—41no—
48C2×#11758198—41no—
49C2×C4×Dic61—41no—
50C2×#11758185—21no—
51C2×#11758185—21no—
52C2×#11758185—21no—
53#14519711—21no—
54#14519711D412yes—
55#14519708—24no—
56#14519700—24no—
57C22×C8×C61C2311yescharacteristic
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63#107×C61—21no—
64#107×C61—21no—
65#107×C61C2×C412yes—
66#107×C61D412yes—
67C23×D61D811yescharacteristic
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61D811yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C22⋊C412yes—
79C2×C4×D61SD1612yes—
80C2×Dic122—22no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×C8×C61C22×C411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C4⋊C4×C61—22no—
93C4⋊C4×C61—22no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96#11758198—44no—
97#11758198—44no—
98C4⋊Dic61—22no—
99C4⋊Dic61—41no—
100C4⋊Dic61—44no—
101C4×Dic61—44no—
102C2×#92418—21no—
103C2×#92418—21no—
104C2×#92418C22⋊C412yes—
105Dic244—22no—
106Dic244—22no—
107Dic244—41no—
108Dic244—41no—
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—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61C2×C22⋊C411yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12311yescharacteristic
132C2×C4×C61C2×SD1611yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143C2×Dic61#10212yes—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—22no—
148Dic122—42no—
149Dic122—42no—
150Dic122—81no—
151Dic122—81no—
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×#358—611no—
185C2×C22⋊C16—611no—
186#1380—611no—
187#1380D6111yescharacteristic, complemented
188C2×C61#187411yescharacteristic
189C2×C61#213811yescharacteristic
190C2×C61#214111yescharacteristic
191C2×C61#218911yescharacteristic
192C2×C61#218911yescharacteristic
193C2×C61#223711yescharacteristic
194C2×C61#223711yescharacteristic
195D61—42no—
196C22×Q16—611no—
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×#107C2×D6111yescharacteristic
208C2×#107C2×D6111yescharacteristic
209C2×#106—1221no—
210C2×#103—1221no—
211#358—1222no—
212#358—1222no—
213C22⋊C16—1222no—
214C61#1299411yescharacteristic, complemented, Sylow
215C22×Q8—1221no—
216C23×C4—611no—
217C2×Q16—612no—
218C2×Q16—1221no—
219C2×Q16—1221no—
220C2×Q16—1221no—
221C2×Q16—1221no—
222C2×Q16—1221no—
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—21no—
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—21no—
250#107—612no—
251#107—1221no—
252#107C4×D6112yes—
253#107D24412yes—
254#106—1224no—
255#103—1224no—
256C24—611no—
257C2×Q8—1222no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×Q8—2441no—
261C2×Q8—2441no—
262C2×Q8—2441no—
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—1222no—
276Q16—1222no—
277Q16—2441no—
278Q16—2441no—
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×C8C2×D24411yescharacteristic
288C2×C8#1175822211yescharacteristic
289C2×C8D4×D6111yescharacteristic
290C2×C8D4×D6111yescharacteristic
291C2×C8#1175822611yescharacteristic
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—1222no—
297C4⋊C4—2444no—
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—4881no—
313Q8—4881no—
314Q8—2442no—
315Q8—2442no—
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#1451974711yescharacteristic
337C2×C4#1451976211yescharacteristic
338C2×C4SD16×D6111yescharacteristic
339C2×C4#1451980411yescharacteristic
340C2×C4#1451980911yescharacteristic
341C8—1222no—
342C8#1451973911yescharacteristic
343C8C4×D24411yescharacteristic
344C8#1451975011yescharacteristic
345C8#1451975211yescharacteristic
346C22—1222no—
347C22—1222no—
348C22—1222no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22#102×D6111yescharacteristic
354C22#1683989711yescharacteristic
355C22#1684007711yescharacteristic
356C22#1684019111yescharacteristic
357C22#1684019311yescharacteristic
358C22#1684020111yescharacteristic
359C22#1684020411yescharacteristic
360C4—82no—
361C4—82no—
362C4—1222no—
363C4—4882no—
364C4—4882no—
365C4#1683964011yescharacteristic
366C4#1683976211yescharacteristic
367C4#1683990211yescharacteristic
368C4#1684008211yescharacteristic
369C2—2442no—
370C2#2144613511yescharacteristic
371C2#2144752311yescharacteristic
372C2#2144753711yescharacteristic
373C2#2144776011yescharacteristic
374C2#2144776211yescharacteristic
375C2#2144802911yescharacteristic
376C2#2144803011yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1380C2
socleC23×C61C2×D8
prime radicalC23×D61D8
cosocleC22×C8×C61C23
hypercenter#1380D61
hypocenterC61#12994
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#16839567C2semidirect
4. C2×#16839565C2semidirect
6. #21443910C2semidirect
7. C61×#1380C2semidirect
14. #16840004C4semidirect
187. #1380D61semidirect
214. C61#12994semidirect

Maximal subgroups

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

subgroupindex
C2×#168400042
C2×#168397992
C2×#168395672
C2×#168395652
C2×#168395412
#214439102
C61×#13802
#1299461