Finite Group Databasebeta

← #29582591

Subgroups — #29582591

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840160C211yesmaximal, characteristic, complemented
2C2×#16840053C211yesmaximal, characteristic
3C2×#16839968C211yesmaximal, characteristic
4#21446613C211yesmaximal, characteristic
5C2×#16839510C211yesmaximal, characteristic, complemented
6C2×#16839509C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519777C2211yescharacteristic
11C2×C4×D244C2211yescharacteristic
12#16840160—22no—
13#16840160—22no—
14#16840053—22no—
15#16840053—22no—
16#16839968—22no—
17#16839968—22no—
18C2×#14519709—21no—
19C2×#14519709—22no—
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519702—21no—
22C2×#14519699—21no—
23C2×#14519689—22no—
24#16839510—22no—
25#16839509—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—
33C2×#11758190—24no—
34C2×#11758190—42no—
35C2×#11758190—42no—
36C22×#92418—21no—
37#14519777—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777—21no—
42#14519777—21no—
43#14519777D412yes—
44#14519777D412yes—
45C4×D244—21no—
46C4×D244—21no—
47C4×D244—21no—
48C4×D244—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61D411yescharacteristic
54C2×#11758198—21no—
55#14519709—24no—
56#14519709—28no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59#14519702—24no—
60#14519699—24no—
61#14519689—44no—
62C22×C8×C61—21no—
63C22×C8×C61—21no—
64C22×C8×C61D412yes—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61D412yes—
69C4⋊C8×C61D412yes—
70C4×C8×C61—21no—
71C4×C8×C61—21no—
72C23×D61—21no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244SD1612yes—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×Dic122—22no—
90C2×Dic122—22no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×Dic122—41no—
97C2×Dic122—82no—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—22no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61SD1614yescomplemented
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111#11758198—41no—
112#11758198—41no—
113C4⋊Dic61—22no—
114C4⋊Dic61—21no—
115C4⋊Dic61—22no—
116C4⋊Dic61—22no—
117C4⋊Dic61—21no—
118C4⋊Dic61—22no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C2×#92418—41no—
124C2×#92418—42no—
125#11758190—48no—
126C23×C61#12111yescharacteristic
127C22×D61—22no—
128C22×D61—41no—
129C22×D61—42no—
130C22×D61—41no—
131C22×D61—42no—
132C2×C4×C61—22no—
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12011yescharacteristic
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12711yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×C4×C61C2×SD1612yes—
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×C4×C61#13712yes—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61—42no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151C2×Dic61—82no—
152D244—22no—
153D244—22no—
154D244—41no—
155D244—41no—
156C4×D61—82no—
157C4×D61—81no—
158C4×D61—81no—
159Dic122—42no—
160Dic122—42no—
161Dic122—82no—
162Dic122—81no—
163Dic122—81no—
164Dic122—82no—
165C8×C61—24no—
166C8×C61—42no—
167C8×C61—42no—
168#92418—81no—
169#10271—611nomaximal, Sylow
170C22×C61#39211yescharacteristic
171C22×C61#46112yes—
172C22×C61#46511yescharacteristic
173C22×C61#46811yescharacteristic
174C22×C61#47112yes—
175C2×D61—44no—
176C2×D61—42no—
177C2×D61—82no—
178C2×D61—81no—
179C2×D61—81no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61#44811yescharacteristic
183C4×C61#44812yes—
184C4×C61#44911yescharacteristic
185C4×C61#45011yescharacteristic
186C4×C61#45211yescharacteristic
187C4×C61#49211yescharacteristic
188C4×C61#49711yescharacteristic
189Dic61—82no—
190Dic61—81no—
191Dic61—82no—
192C2×#498—611no—
193C2×#476—611no—
194C2×#461—611no—
195#1954—611no—
196C2×#333—611no—
197C2×#332—611no—
198#1277D6111yescharacteristic, complemented
199C2×C61#167112yes—
200C2×C61#169112yes—
201C2×C61#200011yescharacteristic
202C2×C61#201311yescharacteristic
203C2×C61#201911yescharacteristic
204D61—82no—
205C22×SD16—1221no—
206C2×C4⋊Q8—611no—
207C2×C4⋊Q8—611no—
208C2×C4×D4—611no—
209#498—1222no—
210#498—1222no—
211#476—1222no—
212#476—1222no—
213#461—1222no—
214#461—1222no—
215C2×#106—1221no—
216C2×#106—1222no—
217C2×C4⋊C8—611no—
218C2×C4⋊C8C2×D6111yescharacteristic
219C2×C4⋊C8C2×D6111yescharacteristic
220C2×#103—1221no—
221C2×#102—1221no—
222C2×C22⋊C8—1222no—
223C2×C4×C8C2×D6111yescharacteristic
224#333—1222no—
225#332—1222no—
226C61#1027111yescharacteristic, complemented, Sylow
227C22×Q8—1221no—
228C22×Q8—1221no—
229C22×D4—611no—
230C23×C4—1221no—
231C2×SD16—1224no—
232C2×SD16—2442no—
233C2×SD16—2442no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—1221no—
237C22×C8D24412yes—
238C4⋊Q8—612no—
239C4⋊Q8—612no—
240C4⋊Q8—1221no—
241C4⋊Q8—1221no—
242C4⋊Q8—1221no—
243C4⋊Q8—1221no—
244C4⋊Q8—1221no—
245C4⋊Q8—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248C4×D4—1221no—
249C4×D4—1221no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C42C22×D6111yescharacteristic
257#106—1224no—
258#106—1228no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8D24412yes—
264C4⋊C8D24412yes—
265#103—1224no—
266#102—1224no—
267C22⋊C8—2444no—
268C4×C8—21no—
269C4×C8—21no—
270C24—1221no—
271C2×Q8—1222no—
272C2×Q8—1222no—
273C2×Q8—4882no—
274C2×Q8—2441no—
275C2×Q8—2441no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×D4—612no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C22×C4—1221no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4—2442no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2442no—
293C22×C4C2×D24411yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C22×C4#1175822611yescharacteristic
296SD16—2448no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—2441no—
306C2×C8—2442no—
307C2×C8#1175819014yescomplemented
308C4⋊C4—1222no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1222no—
312C4⋊C4—1222no—
313C4⋊C4—1222no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C42C2×D24411yescharacteristic
321C42C2×D24411yescharacteristic
322C42D4×D6111yescharacteristic
323C42D4×D6111yescharacteristic
324C23—1222no—
325C23—2442no—
326C23—2441no—
327C23—2442no—
328C23—2441no—
329C23#1451975211yescharacteristic
330Q8—4882no—
331Q8—4882no—
332Q8—4881no—
333Q8—4881no—
334Q8—2442no—
335Q8—2442no—
336D4—1222no—
337D4—1222no—
338D4—2441no—
339D4—2441no—
340C2×C4—22no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—4882no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—4882no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4#1451974711yescharacteristic
352C2×C4#1451974711yescharacteristic
353C2×C4#1451974711yescharacteristic
354C2×C4#1451975211yescharacteristic
355C2×C4#1451975211yescharacteristic
356C2×C4#1451977411yescharacteristic
357C2×C4SD16×D6111yescharacteristic
358C2×C4C2×#1175819012yes—
359C2×C4#1451979811yescharacteristic
360C2×C4#1451980111yescharacteristic
361C2×C4#1451980911yescharacteristic
362C2×C4#1451981012yes—
363C8—24no—
364C8—42no—
365C8—42no—
366C8—4881no—
367C22—4881no—
368C22—4882no—
369C22—4881no—
370C22—2444no—
371C22—2442no—
372C22#1683967211yescharacteristic
373C22#1683996812yes—
374C22#1683999211yescharacteristic
375C22#1684000911yescharacteristic
376C22#1684002612yes—
377C4—21no—
378C4—21no—
379C4—4882no—
380C4—4882no—
381C4—4881no—
382C4#1683990211yescharacteristic
383C4#1683990312yes—
384C4#1683990811yescharacteristic
385C4#1683991411yescharacteristic
386C4#1683992711yescharacteristic
387C4#1684013511yescharacteristic
388C4#1684015611yescharacteristic
389C2—4882no—
390C2#2144519512yes—
391C2#2144531912yes—
392C2#2144682511yescharacteristic
393C2#2144690411yescharacteristic
394C2#2144693611yescharacteristic
subgroupG/H
centerC23#14519752
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1277D61
hypocenterC61#10271
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×#16840160C2semidirect
5. C2×#16839510C2semidirect
6. C2×#16839509C2semidirect
7. C61×#1277C2semidirect
106. C2×C8×C61SD16semidirect
198. #1277D61semidirect
226. C61#10271semidirect
307. C2×C8#11758190semidirect

Maximal subgroups

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

subgroupindex
C2×#168401602
C2×#168400532
C2×#168399682
#214466132
C2×#168395102
C2×#168395092
C61×#12772
#1027161