Finite Group Databasebeta

← #29582617

Subgroups — #29582617

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840113C211yesmaximal, characteristic, complemented
2C2×#16840053C211yesmaximal, characteristic
3C2×#16840043C211yesmaximal, characteristic
4#21446613C211yesmaximal, characteristic
5C2×#16839510C211yesmaximal, characteristic, complemented
6C2×#16839507C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16840113—22no—
12#16840113—22no—
13#16840053—22no—
14#16840053—22no—
15#16840043—22no—
16#16840043—22no—
17C2×#14519711—21no—
18C2×#14519709—21no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519702—22no—
21C2×#14519699—21no—
22C2×#14519699—21no—
23C2×#14519689—22no—
24#16839510—22no—
25#16839507—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×C4×C8×C61C2211yescharacteristic
29C22×Dic122—21no—
30C22×Dic122—21no—
31C22×D244D411yescharacteristic
32C22×C4×D61—21no—
33C22×#92418—21no—
34#14519777—21no—
35#14519777—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777D412yes—
41#14519777D412yes—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61D411yescharacteristic
51C2×#11758198—21no—
52#14519711—24no—
53#14519709—24no—
54C4⋊#92418—21no—
55C4⋊#92418—21no—
56#14519702—28no—
57#14519699—24no—
58#14519699—24no—
59#14519689—44no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62C22×C8×C61D412yes—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61D412yes—
67C4⋊C8×C61D412yes—
68C4×C8×C61—21no—
69C4×C8×C61—21no—
70C23×D61—21no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4111yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244Q1612yes—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×Dic122—22no—
88C2×Dic122—22no—
89C2×Dic122—42no—
90C2×Dic122—42no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—82no—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—22no—
97C2×C8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107#11758198—41no—
108#11758198—41no—
109C4⋊Dic61—22no—
110C4⋊Dic61—22no—
111C4⋊Dic61—22no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—22no—
115C4⋊Dic61—41no—
116C4⋊Dic61—41no—
117C4⋊Dic61—41no—
118C4⋊Dic61—41no—
119C2×#92418—41no—
120C2×#92418—42no—
121C23×C61#12111yescharacteristic
122C22×D61—22no—
123C22×D61—41no—
124C22×D61—42no—
125C22×D61—41no—
126C22×D61—42no—
127C2×C4×C61—22no—
128C2×C4×C61#12011yescharacteristic
129C2×C4×C61#12011yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12711yescharacteristic
134C2×C4×C61C2×Q1611yescharacteristic
135C2×C4×C61#13512yes—
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)12yes—
138C2×C4×C61#13711yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—82no—
145C2×Dic61—82no—
146D244—22no—
147D244—22no—
148D244—41no—
149D244—41no—
150C4×D61—82no—
151C4×D61—81no—
152C4×D61—81no—
153Dic122—44no—
154Dic122—82no—
155Dic122—81no—
156Dic122—81no—
157Dic122—82no—
158C8×C61—42no—
159C8×C61—42no—
160C8×C61—42no—
161#92418—81no—
162#10275—611nomaximal, Sylow
163C22×C61#39211yescharacteristic
164C22×C61#46312yes—
165C22×C61#46711yescharacteristic
166C22×C61#47011yescharacteristic
167C22×C61#47112yes—
168C2×D61—44no—
169C2×D61—42no—
170C2×D61—82no—
171C2×D61—81no—
172C2×D61—81no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61#44912yes—
176C4×C61#45111yescharacteristic
177C4×C61#45111yescharacteristic
178C4×C61#45211yescharacteristic
179C4×C61#45211yescharacteristic
180C4×C61#49511yescharacteristic
181C4×C61#49611yescharacteristic
182Dic61—82no—
183Dic61—81no—
184Dic61—82no—
185C2×#487—611no—
186C2×#476—611no—
187C2×#474—611no—
188#1954—611no—
189C2×#333—611no—
190C2×#332—611no—
191#1277D6111yescharacteristic, complemented
192C2×C61#168312yes—
193C2×C61#170312yes—
194C2×C61#200111yescharacteristic
195C2×C61#201211yescharacteristic
196C2×C61#201911yescharacteristic
197D61—82no—
198C2×C4⋊Q8—611no—
199C2×C4⋊Q8—611no—
200C2×C4×D4—611no—
201#487—1222no—
202#487—1222no—
203#476—1222no—
204#476—1222no—
205#474—1222no—
206#474—1222no—
207C2×#107—1221no—
208C2×#106—1221no—
209C2×C4⋊C8—611no—
210C2×C4⋊C8C2×D6111yescharacteristic
211C2×C4⋊C8C2×D6111yescharacteristic
212C2×#103—1222no—
213C2×#102—1221no—
214C2×#102—1221no—
215C2×C22⋊C8—1222no—
216C2×C4×C8C2×D6111yescharacteristic
217#333—1222no—
218#332—1222no—
219C61#1027511yescharacteristic, complemented, Sylow
220C22×Q8—1221no—
221C22×Q8—1221no—
222C22×D4—611no—
223C23×C4—1221no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—1221no—
227C22×C8D24412yes—
228C4⋊Q8—612no—
229C4⋊Q8—612no—
230C4⋊Q8—1221no—
231C4⋊Q8—1221no—
232C4⋊Q8—1221no—
233C4⋊Q8—1221no—
234C4⋊Q8—1221no—
235C4⋊Q8—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238C4×D4—1221no—
239C4×D4—1221no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C42C22×D6111yescharacteristic
247#107—1224no—
248#106—1224no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253C4⋊C8D24412yes—
254C4⋊C8D24412yes—
255#103—1228no—
256#102—1224no—
257#102—1224no—
258C22⋊C8—2444no—
259C4×C8—21no—
260C4×C8—21no—
261C24—1221no—
262C2×Q8—1222no—
263C2×Q8—1222no—
264C2×Q8—4882no—
265C2×Q8—2442no—
266C2×Q8—2442no—
267C2×Q8—2441no—
268C2×Q8—2441no—
269C2×D4—612no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C22×C4—1221no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4—2442no—
281C22×C4—2442no—
282C22×C4C2×D24411yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4#1175822611yescharacteristic
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—2441no—
295C2×C8—2442no—
296C4⋊C4—1222no—
297C4⋊C4—1222no—
298C4⋊C4—1222no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1222no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42C2×D24411yescharacteristic
309C42C2×D24411yescharacteristic
310C42D4×D6111yescharacteristic
311C42D4×D6111yescharacteristic
312C23—1222no—
313C23—2442no—
314C23—2441no—
315C23—2442no—
316C23—2441no—
317C23#1451975211yescharacteristic
318Q8—4882no—
319Q8—4882no—
320Q8—4881no—
321Q8—4881no—
322Q8—2444no—
323D4—1222no—
324D4—1222no—
325D4—2441no—
326D4—2441no—
327C2×C4—22no—
328C2×C4—4882no—
329C2×C4—4882no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4—4882no—
333C2×C4—2442no—
334C2×C4—2441no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4#1451974711yescharacteristic
338C2×C4#1451974711yescharacteristic
339C2×C4#1451974711yescharacteristic
340C2×C4#1451975211yescharacteristic
341C2×C4#1451975211yescharacteristic
342C2×C4#1451977411yescharacteristic
343C2×C4Q16×D6111yescharacteristic
344C2×C4#1451979611yescharacteristic
345C2×C4#1451979912yes—
346C2×C4#1451980512yes—
347C2×C4#1451980611yescharacteristic
348C2×C4#1451980611yescharacteristic
349C8—42no—
350C8—42no—
351C8—42no—
352C8—4881no—
353C22—4882no—
354C22—4881no—
355C22—4881no—
356C22—2444no—
357C22—2442no—
358C22#1683967211yescharacteristic
359C22#1683997812yes—
360C22#1684000411yescharacteristic
361C22#1684002111yescharacteristic
362C22#1684002612yes—
363C4—21no—
364C4—21no—
365C4—4882no—
366C4—4881no—
367C4—4882no—
368C4#1683990912yes—
369C4#1683991911yescharacteristic
370C4#1683991911yescharacteristic
371C4#1683992511yescharacteristic
372C4#1683992511yescharacteristic
373C4#1684014611yescharacteristic
374C4#1684015111yescharacteristic
375C2—4882no—
376C2#2144527112yes—
377C2#2144539512yes—
378C2#2144683011yescharacteristic
379C2#2144689911yescharacteristic
380C2#2144693611yescharacteristic
subgroupG/H
centerC23#14519752
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1277D61
hypocenterC61#10275
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
1. C2×#16840113C2semidirect
5. C2×#16839510C2semidirect
6. C2×#16839507C2semidirect
7. C61×#1277C2semidirect
191. #1277D61semidirect
219. C61#10275semidirect

Maximal subgroups

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

subgroupindex
C2×#168401132
C2×#168400532
C2×#168400432
#214466132
C2×#168395102
C2×#168395072
C61×#12772
#1027561