Finite Group Databasebeta

← #29582616

Subgroups — #29582616

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×#16840112C211yesmaximal, characteristic, complemented
2C2×#16840053C211yesmaximal, characteristic
3C2×#16840039C211yesmaximal, characteristic
4#21446612C211yesmaximal, characteristic
5C2×#16839510C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×C4×D244C2211yescharacteristic
10#16840112—22no—
11#16840112—22no—
12#16840053—22no—
13#16840053—22no—
14#16840039—22no—
15#16840039—22no—
16C2×#14519710—21no—
17C2×#14519709—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519701—22no—
20C2×#14519699—21no—
21C2×#14519697—21no—
22C2×#14519689—22no—
23C2×C4×#92418C2211yescharacteristic
24#16839510—22no—
25C2×C4⋊Q8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#332—22no—
29C22×Dic122—21no—
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32C22×#92418—21no—
33C22×#92418D412yes—
34#14519777—21no—
35#14519777—21no—
36#14519777—21no—
37#14519777D412yes—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758198—21no—
46#14519710—24no—
47#14519709—24no—
48C4⋊#92418—21no—
49C4⋊#92418D412yes—
50#14519701—28no—
51#14519699—24no—
52#14519697—24no—
53#14519689—44no—
54C4×#92418—21no—
55C4×#92418—21no—
56C22×Q8×C61—21no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61D412yes—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61D412yes—
70C23×D61—21no—
71C2×Q8×C61—22no—
72C2×Q8×C61—41no—
73C2×Q8×C61—42no—
74C2×Q8×C61—42no—
75C22×C4×C61—41no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—41no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244Q1612yes—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—42no—
90C2×C4×D61—42no—
91C2×Dic122—22no—
92C2×Dic122—41no—
93C2×Dic122—82no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—42no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—41no—
102C4⋊C4×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—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—41no—
114C4⋊Dic61—41no—
115C2×#92418—22no—
116C2×#92418—22no—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418—41no—
120C2×#92418—41no—
121C23×C61#12111yescharacteristic
122C22×D61—22no—
123C22×D61—41no—
124C22×D61—42no—
125C22×D61—41no—
126C22×D61—42no—
127Q8×C61—44no—
128Q8×C61—81no—
129Q8×C61—81no—
130C2×C4×C61—22no—
131C2×C4×C61—42no—
132C2×C4×C61—82no—
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×Q1611yescharacteristic
140C2×C4×C61#13512yes—
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)12yes—
143C2×C4×C61#13711yescharacteristic
144C2×C4×C61#13711yescharacteristic
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—82no—
149D244—22no—
150D244—22no—
151D244—41no—
152D244—41no—
153C4×D61—82no—
154C4×D61—81no—
155C4×D61—81no—
156Dic122—82no—
157Dic122—82no—
158C8×C61—42no—
159C8×C61—81no—
160#92418—42no—
161#92418—42no—
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—82no—
176C4×C61#44912yes—
177C4×C61#45111yescharacteristic
178C4×C61#45111yescharacteristic
179C4×C61#45211yescharacteristic
180C4×C61#45211yescharacteristic
181C4×C61#49511yescharacteristic
182C4×C61#49611yescharacteristic
183Dic61—81no—
184Dic61—82no—
185C2×#487—611no—
186C2×#476—611no—
187C2×#474—611no—
188#1954—611no—
189C2×#333—611no—
190C2×#332D6111yescharacteristic, complemented
191#1277—611no—
192C2×C61#168312yes—
193C2×C61#170312yes—
194C2×C61#200111yescharacteristic
195C2×C61#201211yescharacteristic
196C2×C61#201911yescharacteristic
197D61—82no—
198C2×C4⋊Q8—611no—
199C2×C4⋊Q8C2×D6111yescharacteristic
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×C8—611no—
217#333—1222no—
218#332—22no—
219C61#1027511yescharacteristic, complemented, Sylow
220C22×Q8—21no—
221C22×Q8—1221no—
222C22×D4—611no—
223C23×C4—1221no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—612no—
227C22×C8—1221no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—612no—
232C4⋊Q8—1221no—
233C4⋊Q8—1221no—
234C4⋊Q8—1221no—
235C4⋊Q8D24412yes—
236C4×D4—1221no—
237C4×D4—1221no—
238C4×D4—1221no—
239C4×D4—1221no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—611no—
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—21no—
252C4⋊C8—612no—
253C4⋊C8—1221no—
254C4⋊C8C22⋊D6112yes—
255#103—1228no—
256#102—1224no—
257#102—1224no—
258C22⋊C8—2444no—
259C4×C8—1221no—
260C4×C8—1221no—
261C24—1221no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—1222no—
267C2×Q8—4882no—
268C2×Q8—2441no—
269C2×D4—612no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C22×C4—41no—
276C22×C4—1221no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4—2442no—
281C22×C4—2442no—
282C22×C4#1175822211yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—42no—
290C2×C8—1222no—
291C2×C8—1222no—
292C2×C8—1222no—
293C2×C8—1222no—
294C2×C8—2441no—
295C2×C8—2441no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—1222no—
301C4⋊C4—1221no—
302C4⋊C4—1222no—
303C4⋊C4—1221no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42C2×D24411yescharacteristic
309C42D4×D6111yescharacteristic
310C42D4×D6111yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C23—1222no—
313C23—2442no—
314C23—2441no—
315C23—2442no—
316C23—2441no—
317C23#1451975011yescharacteristic
318Q8—44no—
319Q8—81no—
320Q8—81no—
321Q8—4882no—
322Q8—4882no—
323D4—1222no—
324D4—1222no—
325D4—2441no—
326D4—2441no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—82no—
330C2×C4—4882no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—4882no—
334C2×C4—2442no—
335C2×C4—2441no—
336C2×C4—2442no—
337C2×C4#1451974511yescharacteristic
338C2×C4#1451974711yescharacteristic
339C2×C4#1451974711yescharacteristic
340C2×C4#1451975011yescharacteristic
341C2×C4#1451975111yescharacteristic
342C2×C4#1451977311yescharacteristic
343C2×C4Q16×D6111yescharacteristic
344C2×C4#1451979812yes—
345C2×C4#1451979811yescharacteristic
346C2×C4#1451980112yes—
347C2×C4#1451980611yescharacteristic
348C2×C4#1451980911yescharacteristic
349C8—42no—
350C8—81no—
351C8—2442no—
352C8—2442no—
353C22—4882no—
354C22—4881no—
355C22—4881no—
356C22—2444no—
357C22—2442no—
358C22#1683967111yescharacteristic
359C22#1683997612yes—
360C22#1684000211yescharacteristic
361C22#1684001911yescharacteristic
362C22#1684002812yes—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—4882no—
367C4—4881no—
368C4#1683990812yes—
369C4#1683991611yescharacteristic
370C4#1683991911yescharacteristic
371C4#1683992111yescharacteristic
372C4#1683992711yescharacteristic
373C4#1684014311yescharacteristic
374C4#1684015011yescharacteristic
375C2—4882no—
376C2#2144526912yes—
377C2#2144539312yes—
378C2#2144682811yescharacteristic
379C2#2144689811yescharacteristic
380C2#2144693211yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenterC2×#332D61
hypocenterC61#10275
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#16840112C2semidirect
5. C2×#16839510C2semidirect
6. #21443653C2semidirect
7. C2×C61×#332C2semidirect
190. C2×#332D61semidirect
219. C61#10275semidirect

Maximal subgroups

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

subgroupindex
C2×#168401122
C2×#168400532
C2×#168400392
#214466122
C2×#168395102
#214436532
C2×C61×#3322
#1027561