Finite Group Databasebeta

← #29579100

Subgroups — #29579100

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454177C211yesmaximal, characteristic
2#21445970C211yesmaximal, characteristic, complemented
3#21445674C211yesmaximal, characteristic, complemented
4C2×#16839508C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6C2×#16839505C211yesmaximal, characteristic
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×#14519766—21no—
10C2×#14519766—21no—
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519706—22no—
14C2×#14519687—21no—
15#16839663—22no—
16#16839663C414yes—
17C42×Dic61C2211yescharacteristic
18#16839516—21no—
19#16839508—22no—
20#16839505—22no—
21#16839505—22no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C61×#332—22no—
26C22×D244—21no—
27C22×D244—21no—
28C22×D244C2×C412yes—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519774—21no—
32#14519774—21no—
33#14519774—21no—
34#14519774—21no—
35#14519766—42no—
36#14519766—42no—
37#14519766—42no—
38#14519766—42no—
39C2×#11758198—24no—
40C2×#11758198—24no—
41C2×C4×Dic61C2×C412yes—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D412yes—
44C2×C4×Dic61D411yescharacteristic
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418D412yes—
49#14519706—44no—
50#14519687—42no—
51C22×Q8×C61—21no—
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C412yes—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61D412yes—
65C23×D61—22no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C22×C4×C61—22no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61C22⋊C412yes—
77C22×Dic61C22⋊C412yes—
78C2×D244—22no—
79C2×D244—22no—
80C2×D244—44no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—42no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—42no—
91C2×C8×C61—22no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—42no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103C42×C61#4111yescharacteristic
104#11758198—48no—
105#11758198—48no—
106C4×Dic61—22no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—22no—
110C4×Dic61—42no—
111C4×Dic61D812yes—
112C4×Dic61SD1612yes—
113C2×#92418—22no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—42no—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—42no—
120C22×D61—44no—
121C22×D61—42no—
122C22×D61—44no—
123C22×D61—42no—
124Q8×C61—81no—
125Q8×C61—81no—
126Q8×C61—81no—
127Q8×C61—81no—
128C2×C4×C61—22no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12411yescharacteristic
137C2×C4×C61#12711yescharacteristic
138C2×C4×C61C2×D811yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)12yes—
143C2×C4×C61#13712yes—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61#10214yes—
150D244—82no—
151D244—82no—
152D244—81no—
153D244—81no—
154D244—81no—
155D244—81no—
156D244—82no—
157D244—81no—
158D244—81no—
159C8×C61—42no—
160C8×C61—81no—
161#92418—42no—
162#92418—81no—
163#9704—611nomaximal, Sylow
164C22×C61#39011yescharacteristic
165C22×C61#41312yes—
166C22×C61C2×#10211yescharacteristic
167C22×C61#41712yes—
168C22×C61#41811yescharacteristic
169C2×D61—84no—
170C2×D61—84no—
171C2×D61—82no—
172C2×D61—82no—
173C2×D61—82no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—82no—
177C4×C61#45911yescharacteristic
178C4×C61#45911yescharacteristic
179C4×C61#46011yescharacteristic
180C4×C61#46011yescharacteristic
181C4×C61#48912yes—
182C4×C61#49611yescharacteristic
183C4×C61#49711yescharacteristic
184Dic61—24no—
185Dic61—42no—
186#2858—611no—
187#1842—611no—
188#1767—611no—
189C2×#332—611no—
190C2×#332D6111yescharacteristic, complemented
191C2×#331—611no—
192C2×#331—611no—
193C2×C61#154712yes—
194C2×C61#155712yes—
195C2×C61#195911yescharacteristic
196C2×C61#196711yescharacteristic
197C2×C61#198211yescharacteristic
198D61—162no—
199C2×C4⋊Q8C2×D6111yescharacteristic
200C2×#127—611no—
201C2×#124—1221no—
202C2×#124—1221no—
203C2×C4⋊C8—611no—
204C2×C4⋊C8—611no—
205C2×C4⋊C8—1222no—
206C2×C4⋊C8C2×D6111yescharacteristic
207C2×C4⋊C8C2×D6111yescharacteristic
208C2×#97—1221no—
209#390—614no—
210#390—1222no—
211C43—611no—
212#336—1221no—
213#332—22no—
214#332—1222no—
215#331—1222no—
216#331—1222no—
217C61#970411yescharacteristic, complemented, Sylow
218C22×Q8—21no—
219C22×D4—612no—
220C22×D4—1221no—
221C22×D4—1221no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—1221no—
225C22×C8—1221no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230#127—1221no—
231#127—1221no—
232#127—1221no—
233#127—1221no—
234#124—2442no—
235#124—2442no—
236#124—2442no—
237#124—2442no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4C4×D6112yes—
240C2×C22⋊C4—1224no—
241C2×C22⋊C4—1224no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—612no—
245C2×C42—612no—
246C2×C42C22×D6111yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—612no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253C4⋊C8—1221no—
254C4⋊C8—2444no—
255C4⋊C8C22⋊D6112yes—
256#97—2442no—
257C24—1222no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×D4—1222no—
265C2×D4—1222no—
266C2×D4—2444no—
267C2×D4—2442no—
268C2×D4—2441no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4—2441no—
273C2×D4—2441no—
274C2×D4—2441no—
275C2×D4—2441no—
276C2×D4—2442no—
277C22×C4—22no—
278C22×C4—612no—
279C22×C4—612no—
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4D4×D6111yescharacteristic
282C22×C4D4×D6111yescharacteristic
283C2×C8—22no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—42no—
288C2×C8—1222no—
289C2×C8—2441no—
290C2×C8—2442no—
291C2×C8—2441no—
292C2×C8—2441no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C22⋊C4—2448no—
298C22⋊C4—2448no—
299C42—612no—
300C42—612no—
301C42—1222no—
302C42—1221no—
303C42—1222no—
304C42—1221no—
305C42—2442no—
306C42#1175822211yescharacteristic
307C42D4×D6111yescharacteristic
308C42#1175822411yescharacteristic
309C42C2×C22⋊D6111yescharacteristic
310C23—2444no—
311C23—2442no—
312C23—2444no—
313C23—2442no—
314C23—2442no—
315C23C22⋊C4×D6111yescharacteristic
316Q8—81no—
317Q8—81no—
318Q8—81no—
319Q8—81no—
320D4—4882no—
321D4—4882no—
322D4—4881no—
323D4—4881no—
324D4—4881no—
325D4—4881no—
326D4—4882no—
327D4—4881no—
328D4—4881no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—614no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4#1451973711yescharacteristic
340C2×C4C4×C22⋊D6111yescharacteristic
341C2×C4#1451974911yescharacteristic
342C2×C4#1451975011yescharacteristic
343C2×C4#1451976311yescharacteristic
344C2×C4#1451977311yescharacteristic
345C2×C4D8×D6111yescharacteristic
346C2×C4SD16×D6111yescharacteristic
347C2×C4#1451980111yescharacteristic
348C2×C4#1451980411yescharacteristic
349C2×C4#1451980412yes—
350C2×C4#1451980912yes—
351C8—42no—
352C8—81no—
353C8—4881no—
354C8—2442no—
355C22—4882no—
356C22—4882no—
357C22—4884no—
358C22—4884no—
359C22—4882no—
360C22#1683966211yescharacteristic
361C22#1683974512yes—
362C22#102×D6111yescharacteristic
363C22#1683976212yes—
364C22#1683976511yescharacteristic
365C4—21no—
366C4—21no—
367C4—82no—
368C4—1224no—
369C4—2442no—
370C4#1683995511yescharacteristic
371C4#1683995611yescharacteristic
372C4#1683996011yescharacteristic
373C4#1683996111yescharacteristic
374C4#1684012312yes—
375C4#1684014811yescharacteristic
376C4#1684015511yescharacteristic
377C2—9762no—
378C2#2144449512yes—
379C2#2144454012yes—
380C2#2144663211yescharacteristic
381C2#2144666711yescharacteristic
382C2#2144674411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenterC2×#332D61
hypocenterC61#9704
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #21445970C2semidirect
3. #21445674C2semidirect
4. C2×#16839508C2semidirect
7. C2×C61×#332C2semidirect
190. C2×#332D61semidirect
217. C61#9704semidirect

Maximal subgroups

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

subgroupindex
#214541772
#214459702
#214456742
C2×#168395082
C2×#168395052
C2×C61×#3322
#970461