Finite Group Databasebeta

← #29575211

Subgroups — #29575211

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455823C211yesmaximal, characteristic
2#21454760C211yesmaximal, characteristic, complemented
3#21446616C211yesmaximal, characteristic
4#21444245C211yesmaximal, characteristic
5#21443716C211yesmaximal, characteristic, complemented
6#21443663C211yesmaximal, characteristic, complemented
7C61×#1542C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16840090C412yes—
10#16840049—21no—
11#16839964—21no—
12#16839912C412yes—
13#16839893—22no—
14#16839893—22no—
15C4×#11758201—22no—
16#16839815C2211yescharacteristic
17#16839789—21no—
18#16839786C2211yescharacteristic
19C2×#14519689—21no—
20C2×#14519689—21no—
21#16839718—21no—
22C2×#14519688C2211yescharacteristic
23#16839491—22no—
24C61×#533C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#333—21no—
28C61×#332—21no—
29C22×D244C2×C411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758201—22no—
32C2×#11758194—21no—
33C22×#92418D411yescharacteristic
34C22×#92418D411yescharacteristic
35C4×D244—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758198—21no—
41#14519708—22no—
42C4⋊#92418—24no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418D412yes—
46#14519701—22no—
47#14519697—22no—
48C22⋊#92418C2×C412yes—
49#14519689—42no—
50#14519689—42no—
51#14519688—22no—
52#14519688—21no—
53#14519688—21no—
54C4×#92418—22no—
55C4×#92418—21no—
56C22×C8×C61—21no—
57C4⋊Q8×C61D411yescharacteristic
58C4⋊Q8×C61D411yescharacteristic
59#125×C61—21no—
60C22⋊Q8×C61—21no—
61C22⋊Q8×C61C2×C412yes—
62C4×Q8×C61—21no—
63C4×Q8×C61D412yes—
64#117×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70C4×C8×C61—21no—
71C23×D61—21no—
72C2×Q8×C61—21no—
73C2×Q8×C61C22⋊C412yes—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×Dic61—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—42no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C4⋊C4×C61—22no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61C22⋊C412yes—
97C22⋊C4×C61—22no—
98C42×C61—22no—
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103#11758201—44no—
104#11758198—41no—
105#11758198—41no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108#11758194—41no—
109#11758194—41no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—22no—
113C2×#92418—22no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418SD1612yescomplemented
118C23×C61C4×D411yescharacteristic
119C22×D61—22no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126Q8×C61—42no—
127Q8×C61—81no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61C2×C22⋊C411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61#12011yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12311yescharacteristic
138C2×C4×C61C2×SD1611yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61#13711yescharacteristic
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145D244—22no—
146D244—22no—
147D244—41no—
148D244—41no—
149C4×D61—81no—
150C4×D61—81no—
151C4×D61—81no—
152C4×D61—81no—
153C8×C61—81no—
154C8×C61—81no—
155#92418—22no—
156#92418—42no—
157#92418—41no—
158#92418—42no—
159#9050—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61#38611yescharacteristic
163C22×C61C4×SD1611yescharacteristic
164C22×C61#44011yescharacteristic
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—42no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—42no—
177C4×C61—42no—
178C4×C61#44811yescharacteristic
179C4×C61#44911yescharacteristic
180C4×C61#46011yescharacteristic
181C4×C61#46411yescharacteristic
182Dic61—81no—
183#3101—611no—
184#2961—611no—
185#1955—611no—
186#1542D6111yescharacteristic, complemented
187#1486—611no—
188#1301—611no—
189#1281—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#188011yescharacteristic
193C2×C61#188111yescharacteristic
194C2×C61#189111yescharacteristic
195D61—82no—
196#533C2×D6111yescharacteristic
197C2×C4×D4—611no—
198#483—612no—
199#476—1221no—
200#461—1221no—
201#450—612no—
202#446—1222no—
203#446—1222no—
204C4×SD16—1222no—
205#431—611no—
206#431C2×D6111yescharacteristic
207#424—1221no—
208#423—611no—
209C2×C4⋊C8C2×D6111yescharacteristic
210C2×C22⋊C8—1221no—
211C2×C22⋊C8—1221no—
212#405—1221no—
213C2×#97—611no—
214#333—21no—
215#332—21no—
216D4⋊C8—1222no—
217C61#905011yescharacteristic, complemented, Sylow
218C22×D4—611no—
219C23×C4—1221no—
220C2×SD16—1222no—
221C2×M16—1221no—
222C22×C8—21no—
223C22×C8—611no—
224C22×C8—611no—
225C4⋊Q8C22⋊D6111yescharacteristic
226C4⋊Q8C22⋊D6111yescharacteristic
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8C4×D6112yes—
230C4×Q8—21no—
231C4×Q8D24412yes—
232C4×D4—1221no—
233C4×D4—1221no—
234C4×D4—1221no—
235C4×D4—1221no—
236#117—21no—
237C2×C4⋊C4—611no—
238C2×C22⋊C4—1221no—
239C2×C42C22×D6111yescharacteristic
240#106—1222no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—612no—
245C4⋊C8—1224no—
246C4⋊C8—1221no—
247C4⋊C8—1221no—
248#103—1222no—
249#102—1222no—
250C22⋊C8—21no—
251C22⋊C8—612no—
252C22⋊C8—2442no—
253C22⋊C8—2442no—
254#97—1222no—
255#97—1221no—
256#97—1221no—
257C4×C8—21no—
258C4×C8—1222no—
259C4×C8—1221no—
260C24—1221no—
261C2×Q8—21no—
262C2×Q8#1175819812yes—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—2442no—
266C22×C4—1221no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4C2×C4×D6111yescharacteristic
274C22×C4D4×D6111yescharacteristic
275C22×C4#1175822411yescharacteristic
276SD16—2444no—
277M16—2441no—
278M16—2441no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—612no—
284C2×C8—1221no—
285C2×C8—1221no—
286C2×C8—1222no—
287C2×C8—1222no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4#1175819812yes—
299C22⋊C4—22no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C42—22no—
303C42C2×D24411yescharacteristic
304C42D4×D6111yescharacteristic
305C42#1175822411yescharacteristic
306C42C2×C22⋊D6111yescharacteristic
307C23—1222no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23#1451973711yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—1222no—
318D4—1222no—
319D4—2441no—
320D4—2441no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4C2×#1175819811yescharacteristic
333C2×C4#1451973711yescharacteristic
334C2×C4#1451974711yescharacteristic
335C2×C4#1451974911yescharacteristic
336C2×C4#1451974911yescharacteristic
337C2×C4#1451976111yescharacteristic
338C2×C4SD16×D6111yescharacteristic
339C2×C4#1451980011yescharacteristic
340C2×C4#1451980411yescharacteristic
341C2×C4#1451980911yescharacteristic
342C8—81no—
343C8—81no—
344C8—1222no—
345C8—2442no—
346C8—2441no—
347C8—2442no—
348C22—21no—
349C22—21no—
350C22—4881no—
351C22—4881no—
352C22—4881no—
353C22—4881no—
354C22—2442no—
355C22—2442no—
356C22—2442no—
357C22#1683963911yescharacteristic
358C22#1683984711yescharacteristic
359C22#1683986511yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—4881no—
367C4#1683990211yescharacteristic
368C4#1683991011yescharacteristic
369C4#1683996011yescharacteristic
370C4#1683998611yescharacteristic
371C2—21no—
372C2—21no—
373C2—4882no—
374C2#2144617211yescharacteristic
375C2#2144617911yescharacteristic
376C2#2144623511yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1542C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1542D61
hypocenterC61#9050
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
2. #21454760C2semidirect
5. #21443716C2semidirect
6. #21443663C2semidirect
7. C61×#1542C2semidirect
117. C2×#92418SD16semidirect
186. #1542D61semidirect
217. C61#9050semidirect

Maximal subgroups

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

subgroupindex
#214558232
#214547602
#214466162
#214442452
#214437162
#214436632
C61×#15422
#905061