Finite Group Databasebeta

← #29576545

Subgroups — #29576545

Order 15616.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456942C211yesmaximal, characteristic
2#21454562C211yesmaximal, characteristic
3#21446662C211yesmaximal, characteristic, complemented
4#21444497C211yesmaximal, characteristic
5C2×#16839509C211yesmaximal, characteristic, complemented
6#21443668C211yesmaximal, characteristic, complemented
7C61×#1301C211yesmaximal, characteristic, complemented
8C2×#14519783—21no—
9#16840312C2211yescharacteristic
10C2×#14519777C2211yescharacteristic
11#16840167—21no—
12#16840109—21no—
13#16840076C414yes—
14#16840043—22no—
15#16839839—21no—
16#16839832—22no—
17#16839827—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519695—21no—
20C2×#14519695—21no—
21#16839728—21no—
22C4×#11758194C2211yescharacteristic
23#16839509—21no—
24#16839509—21no—
25#16839509—21no—
26#16839505—21no—
27C61×#431C2211yescharacteristic
28C61×#423C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#11758222—21no—
31C22×Dic122—21no—
32#14519783—42no—
33#14519783—42no—
34C2×#11758194D411yescharacteristic
35C2×#11758194D411yescharacteristic
36C2×#11758189—22no—
37C22×#92418—21no—
38C2×C8×D61—22no—
39#14519777—21no—
40#14519777—21no—
41#14519777—21no—
42#14519777—21no—
43#14519777D411yescharacteristic
44#14519774D411yescharacteristic
45#14519765—21no—
46#14519751—21no—
47#14519751C2×C412yes—
48C4×D244—21no—
49C4×D244D412yes—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61C2×C412yes—
52#14519711—24no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55#14519699—24no—
56#14519695—42no—
57#14519695—42no—
58#14519689—22no—
59#14519689—22no—
60#14519688—21no—
61C4×#92418—21no—
62C2×M16×C61—21no—
63C22×C8×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61D411yescharacteristic
70C4⋊C8×C61D411yescharacteristic
71C22⋊C8×C61C2×C412yes—
72C4×C8×C61—21no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C2×C22⋊D61—22no—
77C22×Dic61—22no—
78#11758222—41no—
79#11758222—41no—
80#11758222—41no—
81#11758222—41no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244C22⋊C412yes—
85C2×C4×D61—22no—
86C2×Dic122—21no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93M16×C61—41no—
94M16×C61—41no—
95C2×C8×C61—22no—
96C2×C8×C61—21no—
97C2×C8×C61—21no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105#11758198—22no—
106#11758198—22no—
107C4⋊Dic61—21no—
108C4⋊Dic61—22no—
109C4⋊Dic61—22no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61C22⋊C412yes—
113#11758194—21no—
114#11758194—21no—
115#11758194—21no—
116#11758194D812yes—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—41no—
120C2×#92418—81no—
121#11758189—44no—
122C8×D61—44no—
123C23×C61C4×D411yescharacteristic
124C22×D61—22no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61C2×C22⋊C411yescharacteristic
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12311yescharacteristic
134C2×C4×C61C2×D811yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—42no—
140C2×Dic61—22no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144D244—42no—
145D244—41no—
146D244—41no—
147D244—41no—
148D244—41no—
149C4×D61—42no—
150C4×D61—42no—
151Dic122—41no—
152Dic122—41no—
153Dic122—81no—
154Dic122—81no—
155Dic122—81no—
156Dic122—81no—
157C8×C61—42no—
158C8×C61—41no—
159C8×C61—41no—
160C8×C61—81no—
161#92418—22no—
162#92418—41no—
163#92418—81no—
164#9271—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#38611yescharacteristic
168C22×C61C4×D811yescharacteristic
169C22×C61#44211yescharacteristic
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—42no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61#44711yescharacteristic
177C4×C61#44911yescharacteristic
178C4×C61#45911yescharacteristic
179C4×C61#46311yescharacteristic
180C4×C61#47111yescharacteristic
181C4×C61#47311yescharacteristic
182Dic61—42no—
183Dic61—82no—
184#3226—611no—
185#2935—611no—
186#1966—611no—
187#1547—611no—
188C2×#332—611no—
189#1301D6111yescharacteristic, complemented
190#1283—611no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#187911yescharacteristic
194C2×C61#190811yescharacteristic
195C2×C61#191511yescharacteristic
196D61—82no—
197C2×#131—1221no—
198#532—611no—
199C2×C4⋊Q8—611no—
200#500—1221no—
201#486—1221no—
202#480—614no—
203#474—1222no—
204#436—1221no—
205#435—1222no—
206C8×D4—1221no—
207#431C2×D6111yescharacteristic
208#423C2×D6111yescharacteristic
209C2×C4⋊C8—611no—
210C2×C4⋊C8C2×D6111yescharacteristic
211C2×#101—1221no—
212C2×#101—1221no—
213#408—1221no—
214C4×M16—611no—
215#332—1221no—
216#332—1221no—
217#332—1221no—
218#331—1221no—
219C61#927111yescharacteristic, complemented, Sylow
220C2×#41—1221no—
221C22×Q8—1221no—
222#131—2442no—
223#131—2442no—
224C2×M16—21no—
225C2×M16—611no—
226C2×M16—611no—
227C2×M16—1222no—
228C22×C8—21no—
229C22×C8—1222no—
230C22×C8—1221no—
231C4⋊Q8—611no—
232C4⋊Q8—1221no—
233C4⋊Q8—1221no—
234C4⋊Q8—1221no—
235C4⋊Q8—1221no—
236#127—611no—
237#124—1221no—
238#121—612no—
239#121—1221no—
240C4×D4—612no—
241C4×D4—1221no—
242C2×C4⋊C4—612no—
243C2×C4⋊C4—1221no—
244C2×C42C22×D6111yescharacteristic
245#107—1224no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252C4⋊C8D24411yescharacteristic
253C4⋊C8D24411yescharacteristic
254#102—1224no—
255#101—2442no—
256#101—2442no—
257C22⋊C8—1222no—
258C22⋊C8—1222no—
259C22⋊C8C4×D6112yes—
260#97—1221no—
261C4×C8—21no—
262C4×C8—1221no—
263#41—2441no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267C2×Q8—1221no—
268C2×Q8—2441no—
269C2×Q8—2441no—
270C2×Q8—2441no—
271C2×Q8—2441no—
272C2×Q8—2441no—
273C2×Q8—2441no—
274C2×D4—612no—
275C2×D4—1222no—
276C2×D4—1221no—
277C2×D4—1221no—
278C22×C4—1222no—
279C22×C4—1222no—
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4D4×D6111yescharacteristic
282C22×C4#1175822611yescharacteristic
283M16—41no—
284M16—41no—
285M16—612no—
286M16—1221no—
287M16—1221no—
288M16—1221no—
289M16—2444no—
290C2×C8—22no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—1221no—
297C2×C8—1221no—
298C2×C8—4881no—
299C2×C8—2444no—
300C2×C8—2441no—
301C4⋊C4—612no—
302C4⋊C4—1221no—
303C4⋊C4—1222no—
304C4⋊C4—1222no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C22⋊C4—1222no—
308C22⋊C4—1222no—
309C42C2×D24411yescharacteristic
310C42#1175822211yescharacteristic
311C42D4×D6111yescharacteristic
312C42D4×D6111yescharacteristic
313C23—1222no—
314C23#1451973911yescharacteristic
315Q8—4881no—
316Q8—4881no—
317Q8—4881no—
318Q8—4881no—
319Q8—2441no—
320Q8—2441no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324D4—2441no—
325D4—2441no—
326D4—2441no—
327D4—2441no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—1222no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4C22⋊C4×D6111yescharacteristic
338C2×C4C4×D24411yescharacteristic
339C2×C4#1451974711yescharacteristic
340C2×C4#1451975011yescharacteristic
341C2×C4#1451975211yescharacteristic
342C2×C4#1451976211yescharacteristic
343C2×C4D8×D6111yescharacteristic
344C2×C4#1451980011yescharacteristic
345C2×C4#1451980411yescharacteristic
346C2×C4#1451980411yescharacteristic
347C8—42no—
348C8—41no—
349C8—41no—
350C8—81no—
351C8—1222no—
352C8—4881no—
353C8—2441no—
354C22—21no—
355C22—21no—
356C22—2442no—
357C22—2442no—
358C22—2442no—
359C22#1683964011yescharacteristic
360C22#1683984411yescharacteristic
361C22#1683987311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—4882no—
366C4—2442no—
367C4#1683989711yescharacteristic
368C4#1683991011yescharacteristic
369C4#1683995611yescharacteristic
370C4#1683998011yescharacteristic
371C4#1684002611yescharacteristic
372C4#1684003811yescharacteristic
373C2—21no—
374C2—21no—
375C2—4882no—
376C2#2144616811yescharacteristic
377C2#2144633311yescharacteristic
378C2#2144637011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1301C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1301D61
hypocenterC61#9271
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
3. #21446662C2semidirect
5. C2×#16839509C2semidirect
6. #21443668C2semidirect
7. C61×#1301C2semidirect
189. #1301D61semidirect
219. C61#9271semidirect

Maximal subgroups

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

subgroupindex
#214569422
#214545622
#214466622
#214444972
C2×#168395092
#214436682
C61×#13012
#927161