Finite Group Databasebeta

← #29582612

Subgroups — #29582612

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×#16840049C211yesmaximal, characteristic
2C2×#16840039C211yesmaximal, characteristic
3#21446613C211yesmaximal, characteristic
4C2×#16839511C211yesmaximal, characteristic, complemented
5C2×#16839508C211yesmaximal, characteristic, complemented
6#21443654C211yesmaximal, characteristic, complemented
7C2×C61×#487C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16840049—22no—
10#16840049—22no—
11#16840039—22no—
12#16840039—22no—
13C2×#14519710—21no—
14C2×#14519708—21no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519697—21no—
19C2×#14519697—21no—
20C2×#14519689—22no—
21#16839511—22no—
22#16839508—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4⋊Q8×C61C2211yescharacteristic
25C61×#487—22no—
26C61×#487—22no—
27C2×#103×C61—22no—
28C2×C4×C8×C61C2211yescharacteristic
29C22×D244D411yescharacteristic
30C22×C4×D61—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33C22×#92418—21no—
34C4×D244—21no—
35C4×D244—21no—
36C4×D244—21no—
37C4×D244—21no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758198—21no—
40#14519710—24no—
41#14519708—24no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418D412yes—
47C4⋊#92418D412yes—
48#14519697—24no—
49#14519697—24no—
50#14519689—44no—
51C22×Q8×C61—21no—
52C22×Q8×C61—21no—
53C22×C8×C61D412yes—
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61D412yes—
61C4⋊Q8×C61D412yes—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C42×C61C2311yescharacteristic
67#103×C61—28no—
68C4×C8×C61—21no—
69C4×C8×C61—21no—
70C23×D61—21no—
71C2×Q8×C61—22no—
72C2×Q8×C61—22no—
73C2×Q8×C61—41no—
74C2×Q8×C61—41no—
75C2×Q8×C61—42no—
76C2×Q8×C61—42no—
77C2×Q8×C61—82no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×Dic61—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244Q1612yes—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109#11758198—41no—
110#11758198—41no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C2×#92418—22no—
114C2×#92418—22no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—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—
127Q8×C61—44no—
128Q8×C61—82no—
129Q8×C61—82no—
130Q8×C61—81no—
131Q8×C61—81no—
132C2×C4×C61—22no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—82no—
136C2×C4×C61—82no—
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12711yescharacteristic
143C2×C4×C61C2×Q1611yescharacteristic
144C2×C4×C61#13512yes—
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)12yes—
147C2×C4×C61#13711yescharacteristic
148C2×C4×C61#13711yescharacteristic
149C2×Dic61—41no—
150C2×Dic61—42no—
151D244—22no—
152D244—22no—
153D244—41no—
154D244—41no—
155C4×D61—82no—
156C4×D61—81no—
157C4×D61—81no—
158C8×C61—42no—
159#92418—42no—
160#92418—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—82no—
176C4×C61—82no—
177C4×C61#44912yes—
178C4×C61#45111yescharacteristic
179C4×C61#45111yescharacteristic
180C4×C61#45211yescharacteristic
181C4×C61#45211yescharacteristic
182C4×C61#49511yescharacteristic
183C4×C61#49611yescharacteristic
184Dic61—81no—
185C2×#487D6111yescharacteristic, complemented
186C2×#476—611no—
187C2×#474—611no—
188#1954—611no—
189C2×#333—611no—
190C2×#332—611no—
191#1277—611no—
192C2×C61#168312yes—
193C2×C61#170312yes—
194C2×C61#200111yescharacteristic
195C2×C61#201211yescharacteristic
196C2×C61#201911yescharacteristic
197D61—82no—
198C2×C4⋊Q8C2×D6111yescharacteristic
199C2×C4⋊Q8C2×D6111yescharacteristic
200C2×C4×D4—611no—
201#487—22no—
202#487—22no—
203#476—1222no—
204#476—1222no—
205#474—1222no—
206#474—1222no—
207C2×#107—1221no—
208C2×#106—1221no—
209C2×C4⋊C8—611no—
210C2×C4⋊C8—611no—
211C2×C4⋊C8—611no—
212C2×#103—22no—
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—21no—
221C22×Q8—21no—
222C22×D4—611no—
223C23×C4—1221no—
224C22×C8—1221no—
225C22×C8—1221no—
226C22×C8—1221no—
227C22×C8C22⋊D6112yes—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8C22⋊D6112yes—
235C4⋊Q8C22⋊D6112yes—
236C4×D4—1221no—
237C4×D4—1221no—
238C4×D4—1221no—
239C4×D4—1221no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—611no—
245C2×C22⋊C4—1221no—
246C2×C42C22×D6111yescharacteristic
247#107—1224no—
248#106—1224no—
249C4⋊C8—612no—
250C4⋊C8—612no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253C4⋊C8—1221no—
254C4⋊C8—1221no—
255#103—28no—
256#102—1224no—
257#102—1224no—
258C22⋊C8—2444no—
259C4×C8—21no—
260C4×C8—21no—
261C24—1221no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—82no—
269C2×D4—612no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—1221no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4—2442no—
281C22×C4—2442no—
282C22×C4D4×D6111yescharacteristic
283C22×C4#1175822411yescharacteristic
284C22×C4C2×C22⋊D6111yescharacteristic
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—1222no—
289C2×C8—1222no—
290C2×C8—2441no—
291C2×C8—2442no—
292C2×C8—2441no—
293C2×C8—2441no—
294C2×C8—2441no—
295C2×C8—2441no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42D4×D6111yescharacteristic
309C42D4×D6111yescharacteristic
310C42C2×C22⋊D6111yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C23—1222no—
313C23—2442no—
314C23—2441no—
315C23—2442no—
316C23—2441no—
317C23#1451974811yescharacteristic
318Q8—44no—
319Q8—82no—
320Q8—82no—
321Q8—81no—
322Q8—81no—
323D4—1222no—
324D4—1222no—
325D4—2441no—
326D4—2441no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4882no—
335C2×C4—2442no—
336C2×C4—2441no—
337C2×C4#1451974511yescharacteristic
338C2×C4#1451974511yescharacteristic
339C2×C4#1451974611yescharacteristic
340C2×C4#1451974911yescharacteristic
341C2×C4#1451974911yescharacteristic
342C2×C4#1451977311yescharacteristic
343C2×C4Q16×D6111yescharacteristic
344C2×C4#1451979712yes—
345C2×C4#1451980011yescharacteristic
346C2×C4#1451980212yes—
347C2×C4#1451980911yescharacteristic
348C2×C4#1451980911yescharacteristic
349C8—42no—
350C8—4881no—
351C8—2442no—
352C8—2442no—
353C22—4882no—
354C22—4881no—
355C22—4881no—
356C22—2444no—
357C22—2442no—
358C22#1683967011yescharacteristic
359C22#1683997412yes—
360C22#1684000011yescharacteristic
361C22#1684001711yescharacteristic
362C22#1684002212yes—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—82no—
367C4—4881no—
368C4#1683990712yes—
369C4#1683991611yescharacteristic
370C4#1683991611yescharacteristic
371C4#1683992311yescharacteristic
372C4#1683992311yescharacteristic
373C4#1684014411yescharacteristic
374C4#1684015211yescharacteristic
375C2—4882no—
376C2#2144526712yes—
377C2#2144539112yes—
378C2#2144682611yescharacteristic
379C2#2144689611yescharacteristic
380C2#2144693111yescharacteristic
subgroupG/H
centerC23#14519748
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#487C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenterC2×#487D61
hypocenterC61#10275
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. C2×#16839511C2semidirect
5. C2×#16839508C2semidirect
6. #21443654C2semidirect
7. C2×C61×#487C2semidirect
185. C2×#487D61semidirect
219. C61#10275semidirect

Maximal subgroups

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

subgroupindex
C2×#168400492
C2×#168400392
#214466132
C2×#168395112
C2×#168395082
#214436542
C2×C61×#4872
#1027561