Finite Group Databasebeta

← #29575464

Subgroups — #29575464

Order 15616.

536 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454860C211yesmaximal, characteristic, complemented
2C2×#16839872C211yesmaximal, characteristic
3#21444209C211yesmaximal, characteristic, complemented
4#21444139C211yesmaximal, characteristic, complemented
5#21443663C211yesmaximal, characteristic, complemented
6#21443649C211yesmaximal, characteristic, complemented
7C61×#1478C211yesmaximal, characteristic, complemented
8C22×#11758199C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10#16839872—22no—
11#16839872—22no—
12#16839840—22no—
13#16839840—22no—
14#16839815C2211yescharacteristic
15#16839815C2211yescharacteristic
16C2×#14519708C411yescharacteristic
17C2×#14519698C411yescharacteristic
18C2×#14519697C411yescharacteristic
19#16839726—22no—
20C2×#14519688C2211yescharacteristic
21#16839489—22no—
22#16839485—22no—
23C2×C4×D4×C61C2211yescharacteristic
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C61×D4⋊C8—22no—
27C22×D244C2×C411yescharacteristic
28C22×C4×D61—21no—
29C2×#11758199—22no—
30C2×#11758199—22no—
31C2×#11758199—22no—
32C2×#11758194—24no—
33C22×#92418C2×C411yescharacteristic
34C22×#92418C2×C411yescharacteristic
35C4×D244—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758198—21no—
41#14519708—22no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44#14519698—22no—
45#14519697—22no—
46C22⋊#92418—24no—
47C22⋊#92418—21no—
48C22⋊#92418D412yes—
49#14519688—21no—
50#14519688—21no—
51C4×#92418—21no—
52C4×#92418D412yes—
53C22×D4×C61C2×C411yescharacteristic
54C23×C4×C61—21no—
55C4×D4×C61—21no—
56C4×D4×C61—21no—
57C4×D4×C61D412yes—
58C4×D4×C61D412yes—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61—21no—
68C24×C61—21no—
69C23×D61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61C22⋊C412yes—
76C22×C4×C61—21no—
77C22×C4×C61—22no—
78C22×C4×C61—22no—
79C22×C4×C61—82no—
80C22×C4×C61C22×C411yescharacteristic
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×D244M1612yescomplemented
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—82no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61C22⋊C412yes—
97C22⋊C4×C61—22no—
98C22⋊C4×C61—22no—
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103#11758199—28no—
104#11758198—41no—
105#11758198—41no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108#11758194—84no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—22no—
113C2×#92418—22no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418M1612yescomplemented
117C23×C61—22no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—81no—
121C23×C61—81no—
122C23×C61C4×D411yescharacteristic
123C22×D61—22no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—81no—
127C22×D61—81no—
128D4×C61—22no—
129D4×C61—22no—
130D4×C61—41no—
131D4×C61—41no—
132C2×C4×C61—22no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—44no—
136C2×C4×C61—82no—
137C2×C4×C61—81no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12311yescharacteristic
144C2×C4×C61C2×M1611yescharacteristic
145C2×C4×C61C2×M1611yescharacteristic
146C2×C4×C61#13111yescharacteristic
147C2×C4×C61#13111yescharacteristic
148C2×Dic61—41no—
149C2×Dic61—81no—
150D244—22no—
151D244—22no—
152D244—41no—
153D244—41no—
154C4×D61—82no—
155C4×D61—82no—
156C8×C61—81no—
157C8×C61—81no—
158#92418—22no—
159#92418—42no—
160#92418—42no—
161#92418—41no—
162#9093—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61—82no—
169C22×C61—82no—
170C22×C61#38611yescharacteristic
171C22×C61#43511yescharacteristic
172C22×C61#43611yescharacteristic
173C2×D61—42no—
174C2×D61—82no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—82no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—42no—
183C4×C61#40711yescharacteristic
184C4×C61#40811yescharacteristic
185C4×C61#43511yescharacteristic
186C4×C61#43611yescharacteristic
187Dic61—81no—
188#2975—611no—
189C2×#442—611no—
190#1478—611no—
191#1478D6111yescharacteristic, complemented
192#1460—611no—
193#1281—611no—
194#1275—611no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—82no—
198C2×C61#187011yescharacteristic
199C2×C61#190311yescharacteristic
200C2×C61#190411yescharacteristic
201D61—82no—
202C22×D8—611no—
203C2×C4×D4—611no—
204C2×C4×D4C2×D6111yescharacteristic
205#442—1222no—
206#442—1222no—
207#436—1222no—
208#436—1222no—
209#431—611no—
210#431—611no—
211#431C2×D6111yescharacteristic
212#431C2×D6111yescharacteristic
213C2×#106—611no—
214C2×#102—611no—
215C2×#102—611no—
216#407—1222no—
217C2×#97—611no—
218D4⋊C8—22no—
219D4⋊C8—1222no—
220#323—1222no—
221C61#909311yescharacteristic, complemented, Sylow
222C22×D4—611no—
223C22×D4C4×D6111yescharacteristic
224C23×C4—21no—
225C23×C4—1221no—
226C2×D8—1222no—
227C2×D8—1222no—
228C2×D8—1222no—
229C2×M16—1224no—
230C22×C8—611no—
231C22×C8—611no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—1221no—
235C4×D4—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238C4×D4D24412yes—
239C4×D4C22⋊D6112yes—
240C2×C4⋊C4—611no—
241C2×C4⋊C4C4×D6111yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—1221no—
244C2×C42C22×D6111yescharacteristic
245#106—1222no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—1221no—
249C4⋊C8—1221no—
250#102—1222no—
251#102—1222no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—612no—
255C22⋊C8—1224no—
256C22⋊C8—1221no—
257#97—1221no—
258#97—1221no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8—612no—
262C4×C8—1221no—
263C24—21no—
264C24—1221no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—612no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4#1175819812yes—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—82no—
281C22×C4—1221no—
282C22×C4—4882no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4C2×C4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287C22×C4#1175822411yescharacteristic
288D8—1228no—
289M16—4884no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—612no—
293C2×C8—1221no—
294C2×C8—1221no—
295C2×C8—1221no—
296C2×C8—1222no—
297C2×C8—1222no—
298C2×C8—1221no—
299C2×C8—1221no—
300C4⋊C4—21no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4#1175819812yes—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42C2×D24411yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822411yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C23—22no—
313C23—41no—
314C23—41no—
315C23—81no—
316C23—81no—
317C23—1222no—
318C23—4881no—
319C23—4881no—
320C23—2441no—
321C23—2441no—
322C23#1451973711yescharacteristic
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327D4—1222no—
328D4—1222no—
329D4—2441no—
330D4—2441no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—4882no—
338C2×C4—4882no—
339C2×C4—4881no—
340C2×C4—2441no—
341C2×C4C2×#1175819811yescharacteristic
342C2×C4#1451973711yescharacteristic
343C2×C4#1451974711yescharacteristic
344C2×C4#1451974911yescharacteristic
345C2×C4#1451974911yescharacteristic
346C2×C4#1451976111yescharacteristic
347C2×C4M16×D6111yescharacteristic
348C2×C4M16×D6111yescharacteristic
349C2×C4#1451978311yescharacteristic
350C2×C4#1451978311yescharacteristic
351C8—81no—
352C8—81no—
353C8—1222no—
354C8—2442no—
355C8—2442no—
356C8—2441no—
357C22—21no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—82no—
363C22—82no—
364C22—4882no—
365C22—4882no—
366C22—4881no—
367C22—4881no—
368C22—2442no—
369C22#1683963911yescharacteristic
370C22#1683983611yescharacteristic
371C22#1683983711yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—42no—
377C4—4881no—
378C4#1683972511yescharacteristic
379C4#1683972811yescharacteristic
380C4#1683983611yescharacteristic
381C4#1683983711yescharacteristic
382C2—21no—
383C2—21no—
384C2—82no—
385C2—4882no—
386C2#2144611411yescharacteristic
387C2#2144629711yescharacteristic
388C2#2144630411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1478C2
socleC22×C61#386
prime radicalC22×#11758199C4
cosocleC2×C42×C61C23
hypercenter#1478D61
hypocenterC61#9093
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
1. #21454860C2semidirect
3. #21444209C2semidirect
4. #21444139C2semidirect
5. #21443663C2semidirect
6. #21443649C2semidirect
7. C61×#1478C2semidirect
89. C2×D244M16semidirect
116. C2×#92418M16semidirect
191. #1478D61semidirect
221. C61#9093semidirect

Maximal subgroups

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

subgroupindex
#214548602
C2×#168398722
#214442092
#214441392
#214436632
#214436492
C61×#14782
#909361