Finite Group Databasebeta

← #29575865

Subgroups — #29575865

Order 15616.

478 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455635C211yesmaximal, characteristic
2#21454388C211yesmaximal, characteristic
3#21444501C211yesmaximal, characteristic, complemented
4C2×#16839509C211yesmaximal, characteristic, complemented
5#21444204C211yesmaximal, characteristic
6#21443714C211yesmaximal, characteristic, complemented
7C61×#1292C211yesmaximal, characteristic, complemented
8C2×#14519785—21no—
9C2×#14519777C2211yescharacteristic
10C4×#11758222C2211yescharacteristic
11#16840058C412yes—
12#16840053C412yes—
13#16840048—21no—
14#16840043—21no—
15#16839815C2211yescharacteristic
16#16839804—21no—
17#16839790—21no—
18#16839787—22no—
19#16839784—21no—
20C2×C4⋊#92418C2211yescharacteristic
21C4⋊C8×D61—21no—
22#16839764—21no—
23#16839510—22no—
24#16839509—21no—
25#16839509—21no—
26#16839492—21no—
27#16839489—21no—
28C61×#423C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C22×Dic122—21no—
33#14519785—42no—
34#14519785—42no—
35C2×#11758189—22no—
36C22×#92418—21no—
37C2×C8×D61—22no—
38#14519777—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777C2×C412yes—
42C4×Dic122C2×C411yescharacteristic
43C4×Dic122D411yescharacteristic
44C4×D244C2×C411yescharacteristic
45C4×D244D411yescharacteristic
46C4×C22⋊D61—21no—
47C4×C22⋊D61—21no—
48#14519736D411yescharacteristic
49#14519734—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C42×D61—21no—
53#14519711—22no—
54#14519709—22no—
55C4⋊#92418—21no—
56C4⋊#92418—21no—
57C4⋊#92418D411yescharacteristic
58C4⋊#92418D411yescharacteristic
59#14519706—22no—
60#14519706—22no—
61#14519702—22no—
62#14519699—22no—
63C22⋊#92418—21no—
64C4×#92418—21no—
65C2×M16×C61—21no—
66C2×M16×C61—21no—
67C22×C8×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61C2×C412yes—
74C4⋊C8×C61D412yes—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C2×C22⋊D61—21no—
79C22×Dic61—41no—
80#11758222—21no—
81#11758222—21no—
82#11758222SD1612yes—
83#11758222Q1612yes—
84C2×D244C22⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×Dic122—22no—
89C2×Dic122—41no—
90C2×Dic122—81no—
91C2×Dic122—81no—
92C2×Dic122C22⋊C411yescharacteristic
93M16×C61—41no—
94M16×C61—41no—
95M16×C61—41no—
96M16×C61—41no—
97C2×C8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61—41no—
100C2×C8×C61—81no—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C22⋊Dic61—21no—
106#11758198—21no—
107#11758198—21no—
108C4⋊Dic61—22no—
109C4⋊Dic61—22no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61C22⋊C411yescharacteristic
113C4⋊Dic61C22⋊C411yescharacteristic
114#11758196—21no—
115#11758196—21no—
116C4×Dic61—21no—
117C4×Dic61—21no—
118C4×Dic61—21no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124#11758189—44no—
125C8×D61—44no—
126C23×C61#12311yescharacteristic
127C22×D61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61C2×C22⋊C411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61#12011yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61C2×SD1611yescharacteristic
138C2×C4×C61C2×Q1611yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61#13711yescharacteristic
141C22⋊D61—22no—
142C22⋊D61—22no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—42no—
147C2×Dic61—82no—
148D244—21no—
149D244#10312yes—
150C4×D61—22no—
151C4×D61—22no—
152C4×D61—41no—
153C4×D61—41no—
154C4×D61—81no—
155Dic122—21no—
156Dic122—81no—
157Dic122—81no—
158Dic122—82no—
159Dic122#10312yes—
160C8×C61—42no—
161C8×C61—42no—
162C8×C61—81no—
163#92418—41no—
164#92418—41no—
165#92418—81no—
166#9167—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#38611yescharacteristic
170C22×C61#48311yescharacteristic
171C22×C61#48411yescharacteristic
172C2×D61—22no—
173C2×D61—41no—
174C2×D61—41no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61C2×#10311yescharacteristic
179C4×C61#41711yescharacteristic
180C4×C61#45011yescharacteristic
181C4×C61#45111yescharacteristic
182C4×C61#47111yescharacteristic
183C4×C61#47211yescharacteristic
184Dic61—22no—
185Dic61—41no—
186Dic61—41no—
187Dic61—82no—
188#3079—611no—
189#2906—611no—
190#1548—611no—
191C2×#332—611no—
192#1477—611no—
193#1301—611no—
194#1292D6111yescharacteristic, complemented
195C2×C61—21no—
196C2×C61—21no—
197C2×C61#187211yescharacteristic
198C2×C61#190211yescharacteristic
199C2×C61#190711yescharacteristic
200D61—42no—
201C2×#131—1221no—
202C2×C4⋊Q8—611no—
203C4×#41—611no—
204#477—612no—
205#476—612no—
206#475—1221no—
207#474—1221no—
208#431—611no—
209#428—1221no—
210#424—1221no—
211#424—1222no—
212#423—1221no—
213#423C2×D6111yescharacteristic
214#423C2×D6111yescharacteristic
215C2×C4⋊C8—611no—
216C2×C4⋊C8—1221no—
217C2×C4⋊C8C2×D6111yescharacteristic
218#417—1221no—
219#333—1222no—
220#332—1221no—
221#332—1221no—
222Q8⋊C8—1221no—
223D4⋊C8—1221no—
224C61#916711yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C22×Q8—1221no—
227#131—2442no—
228#131—2442no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—1222no—
232C22×C8—21no—
233C22×C8—1222no—
234C22×C8—1221no—
235C4⋊Q8—612no—
236C4⋊Q8—1221no—
237C4⋊Q8—1221no—
238C4⋊Q8—1221no—
239C4×Q8—611no—
240C4×Q8—611no—
241C4×D4—611no—
242C4×D4—611no—
243C4×D4—1221no—
244C4×D4—1221no—
245#117—611no—
246#117—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C42—1221no—
250C2×C42C22×D6111yescharacteristic
251#107—1222no—
252#106—1222no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—611no—
258C4⋊C8—611no—
259C4⋊C8—1222no—
260C4⋊C8—1222no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8C4×D6112yes—
264C4⋊C8D24412yes—
265#103—1222no—
266#102—1222no—
267C22⋊C8—1221no—
268C4×C8—1221no—
269#41—612no—
270#41—612no—
271#41—1221no—
272#41—1221no—
273C2×Q8—611no—
274C2×Q8—1222no—
275C2×Q8—4881no—
276C2×Q8—4881no—
277C2×Q8—2441no—
278C2×D4—611no—
279C2×D4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—2441no—
284C22×C4#1175822211yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4#1175822611yescharacteristic
287M16—41no—
288M16—41no—
289M16—41no—
290M16—41no—
291M16—2444no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—81no—
296C2×C8—1221no—
297C2×C8—1221no—
298C2×C8—2444no—
299C2×C8—2441no—
300C2×C8—2441no—
301C2×C8—2441no—
302C4⋊C4—611no—
303C4⋊C4—611no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1222no—
307C4⋊C4—1222no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C42—1221no—
314C42—1221no—
315C42—1221no—
316C42C2×C4×D6111yescharacteristic
317C42C2×D24411yescharacteristic
318C42D4×D6111yescharacteristic
319C42D4×D6111yescharacteristic
320C23—1221no—
321C23#1451976211yescharacteristic
322Q8—612no—
323Q8—1221no—
324Q8—4882no—
325Q8—4881no—
326Q8—4881no—
327D4—612no—
328D4—1222no—
329D4—1222no—
330D4—1221no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—1221no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—4881no—
340C2×C4—4882no—
341C2×C4—2442no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4C22⋊C4×D6111yescharacteristic
345C2×C4#1451973911yescharacteristic
346C2×C4C4×D24411yescharacteristic
347C2×C4#1451974711yescharacteristic
348C2×C4#1451975011yescharacteristic
349C2×C4#1451975211yescharacteristic
350C2×C4SD16×D6111yescharacteristic
351C2×C4Q16×D6111yescharacteristic
352C2×C4#1451980111yescharacteristic
353C2×C4#1451980611yescharacteristic
354C8—42no—
355C8—42no—
356C8—81no—
357C8—4881no—
358C8—2441no—
359C8—2441no—
360C22—21no—
361C22—21no—
362C22—1222no—
363C22—2441no—
364C22—2441no—
365C22#1683964011yescharacteristic
366C22#1684009411yescharacteristic
367C22#1684009911yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—1222no—
372C4—4882no—
373C4—2441no—
374C4—2441no—
375C4#103×D6111yescharacteristic
376C4#1683976011yescharacteristic
377C4#1683991411yescharacteristic
378C4#1683991911yescharacteristic
379C4#1684002811yescharacteristic
380C4#1684003111yescharacteristic
381C2—21no—
382C2—21no—
383C2—2442no—
384C2#2144612511yescharacteristic
385C2#2144629311yescharacteristic
386C2#2144632811yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1292C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1292D61
hypocenterC61#9167
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #21444501C2semidirect
4. C2×#16839509C2semidirect
6. #21443714C2semidirect
7. C61×#1292C2semidirect
194. #1292D61semidirect
224. C61#9167semidirect

Maximal subgroups

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

subgroupindex
#214556352
#214543882
#214445012
C2×#168395092
#214442042
#214437142
C61×#12922
#916761