Finite Group Databasebeta

← #29573963

Subgroups — #29573963

Order 15616.

516 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839839C211yesmaximal, characteristic
2#21446535C211yesmaximal, characteristic, complemented
3C4×#14519699C211yesmaximal, characteristic
4C2×#16839489C211yesmaximal, characteristic
5#21443658C211yesmaximal, characteristic, complemented
6#21443646C211yesmaximal, characteristic, complemented
7C2×C61×#334C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×C4×D244C2211yescharacteristic
10#16839839—22no—
11#16839839—22no—
12C2×#14519706—21no—
13C2×#14519699C411yescharacteristic
14C2×#14519699C411yescharacteristic
15C2×#14519689—21no—
16C2×C4×#92418C2211yescharacteristic
17C2×C4×#92418C2211yescharacteristic
18C4×C4⋊Dic61C2211yescharacteristic
19#16839525C411yescharacteristic
20#16839525C411yescharacteristic
21#16839516—21no—
22#16839489—22no—
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C61×#334—22no—
27C22×D244C2×C411yescharacteristic
28C22×C4×D61—21no—
29C2×#11758189—24no—
30C2×#11758189—42no—
31C2×#11758189—42no—
32C22×#92418—21no—
33C22×#92418D411yescharacteristic
34C22×#92418D411yescharacteristic
35C4×D244—21no—
36C4×D244—21no—
37C4×D244D412yes—
38C4×D244Q812yes—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758198—21no—
43C2×C4×Dic61—21no—
44#14519706—42no—
45#14519699—22no—
46#14519699—22no—
47#14519689—24no—
48C4×#92418—21no—
49C4×#92418—21no—
50C4×#92418—21no—
51C4×#92418—21no—
52#14519684—21no—
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C22×C8×C61C2×C411yescharacteristic
56C22×C8×C61C2×C411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61D412yes—
62C4×C8×C61—21no—
63C4×C8×C61—21no—
64C23×D61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61#4111yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244C4⋊C412yes—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C8×C61—21no—
84C2×C8×C61—21no—
85C2×C8×C61—21no—
86C2×C8×C61—22no—
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61M1612yescomplemented
95C42×C61C2×D411yescharacteristic
96C42×C61C2×D411yescharacteristic
97C42×C61C2×Q811yescharacteristic
98C42×C61#4111yescharacteristic
99#11758198—22no—
100#11758198—22no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61C4⋊C412yes—
106C4⋊Dic61M1612yescomplemented
107C4×Dic61—41no—
108C4×Dic61—41no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—22no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418SD1612yes—
118#11758189—48no—
119C23×C61C4×D411yescharacteristic
120C22×D61—22no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61C2×C4⋊C411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61C22⋊Q811yescharacteristic
133C2×C4×C61C22⋊Q811yescharacteristic
134C2×C4×C61#12311yescharacteristic
135C2×C4×C61C2×M1611yescharacteristic
136C2×C4×C61C2×M1611yescharacteristic
137C2×C4×C61#13111yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152D244—22no—
153D244—22no—
154D244—41no—
155D244—41no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61—42no—
160C8×C61—22no—
161C8×C61—41no—
162C8×C61—42no—
163C8×C61—81no—
164#92418—22no—
165#92418—42no—
166#92418—41no—
167#8849—611nomaximal, Sylow
168C22×C61#38511yescharacteristic
169C22×C61#43511yescharacteristic
170C22×C61#43611yescharacteristic
171C22×C61C4×SD1611yescharacteristic
172C22×C61#44211yescharacteristic
173C22×C61#44311yescharacteristic
174C22×C61#44411yescharacteristic
175C2×D61—42no—
176C2×D61—42no—
177C2×D61—42no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61#42311yescharacteristic
185C4×C61#42411yescharacteristic
186C4×C61#43511yescharacteristic
187C4×C61#43611yescharacteristic
188C4×C61#44911yescharacteristic
189C4×C61#45011yescharacteristic
190C4×C61#47611yescharacteristic
191C4×C61#47811yescharacteristic
192Dic61—42no—
193Dic61—42no—
194Dic61—81no—
195C2×#436—611no—
196#1939—611no—
197C4×#102—611no—
198C2×#334D6111yescharacteristic, complemented
199C2×D4⋊C8—611no—
200#1279—611no—
201#1273—611no—
202C2×C61#158311yescharacteristic
203C2×C61#158611yescharacteristic
204C2×C61#159011yescharacteristic
205C2×C61#159411yescharacteristic
206C2×C61#185111yescharacteristic
207C2×C61#186411yescharacteristic
208C2×C61#186611yescharacteristic
209D61—82no—
210C22×M16—1221no—
211C2×C4×D4—611no—
212#436—1222no—
213#436—1222no—
214C2×C4⋊C8—1221no—
215C2×C4⋊C8C2×D6111yescharacteristic
216C2×C4⋊C8C2×D6111yescharacteristic
217C2×#102—611no—
218C2×#102—611no—
219C2×C22⋊C8—1221no—
220C2×C4×C8—611no—
221C2×C4×C8—611no—
222C2×C4×C8C2×D6111yescharacteristic
223C4×C4⋊C4—611no—
224#340—611no—
225#340—611no—
226#336—1221no—
227#334—22no—
228D4⋊C8—1222no—
229C61#884911yescharacteristic, complemented, Sylow
230C22×D4—611no—
231C23×C4—1221no—
232C2×M16—1224no—
233C2×M16—2442no—
234C2×M16—2442no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—611no—
238C22×C8—611no—
239C22×C8—1221no—
240C22×C8C4×D6111yescharacteristic
241C22×C8C4×D6111yescharacteristic
242C4×D4—612no—
243C4×D4—612no—
244C4×D4—1221no—
245C4×D4—1221no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—611no—
249C2×C22⋊C4—1221no—
250C2×C42—1221no—
251C2×C42C22×D6111yescharacteristic
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—2442no—
256C4⋊C8C22⋊D6112yes—
257#102—1222no—
258#102—1222no—
259C22⋊C8—1224no—
260C4×C8—21no—
261C4×C8—21no—
262C4×C8—1221no—
263C4×C8—1221no—
264C4×C8—1221no—
265C4×C8—1221no—
266#95—1221no—
267C24—1221no—
268C2×D4—612no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1222no—
277C22×C4—1222no—
278C22×C4—1221no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4—2441no—
283C22×C4C2×C4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C22×C4#1175822611yescharacteristic
286M16—2448no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—22no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—612no—
299C2×C8—1221no—
300C2×C8—1221no—
301C2×C8—1222no—
302C2×C8—1221no—
303C2×C8—1221no—
304C2×C8—1221no—
305C2×C8—2441no—
306C2×C8—2441no—
307C2×C8#1175818912yescomplemented
308C4⋊C4—612no—
309C4⋊C4—612no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C22⋊C4—1222no—
315C22⋊C4—1222no—
316C42—2441no—
317C42—2441no—
318C42#1175822211yescharacteristic
319C42D4×D6111yescharacteristic
320C42Q8×D6111yescharacteristic
321C42C2×C22⋊D6111yescharacteristic
322C23—1222no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23#1451973911yescharacteristic
330D4—1222no—
331D4—1222no—
332D4—2441no—
333D4—2441no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4C4⋊C4×D6111yescharacteristic
350C2×C4C4×C22⋊D6111yescharacteristic
351C2×C4#1451974511yescharacteristic
352C2×C4#1451975311yescharacteristic
353C2×C4#1451975511yescharacteristic
354C2×C4#1451976211yescharacteristic
355C2×C4M16×D6111yescharacteristic
356C2×C4C2×#1175818911yescharacteristic
357C2×C4#1451978311yescharacteristic
358C2×C4#1451978511yescharacteristic
359C2×C4SD16×D6111yescharacteristic
360C2×C4#1451979811yescharacteristic
361C2×C4#1451980411yescharacteristic
362C2×C4#1451980411yescharacteristic
363C8—22no—
364C8—41no—
365C8—42no—
366C8—81no—
367C8—1222no—
368C8—2442no—
369C8—2441no—
370C22—4881no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—2442no—
375C22—2442no—
376C22—2442no—
377C22#1683963311yescharacteristic
378C22#1683983211yescharacteristic
379C22#1683983911yescharacteristic
380C22#1683984911yescharacteristic
381C22#1683987311yescharacteristic
382C22#1683987811yescharacteristic
383C22#1683988311yescharacteristic
384C4—21no—
385C4—21no—
386C4—4881no—
387C4—2442no—
388C4—2442no—
389C4#1683978411yescharacteristic
390C4#1683978711yescharacteristic
391C4#1683983311yescharacteristic
392C4#1683983811yescharacteristic
393C4#1683990611yescharacteristic
394C4#1683991111yescharacteristic
395C4#1684005111yescharacteristic
396C4#1684006111yescharacteristic
397C2—4882no—
398C2#2144466111yescharacteristic
399C2#2144468211yescharacteristic
400C2#2144470811yescharacteristic
401C2#2144473211yescharacteristic
402C2#2144600011yescharacteristic
403C2#2144607711yescharacteristic
404C2#2144609111yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#334C2
socleC23×C61C4×D4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenterC2×#334D61
hypocenterC61#8849
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #21446535C2semidirect
5. #21443658C2semidirect
6. #21443646C2semidirect
7. C2×C61×#334C2semidirect
94. C2×C8×C61M16semidirect
106. C4⋊Dic61M16semidirect
198. C2×#334D61semidirect
229. C61#8849semidirect
307. C2×C8#11758189semidirect

Maximal subgroups

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

subgroupindex
C2×#168398392
#214465352
C4×#145196992
C2×#168394892
#214436582
#214436462
C2×C61×#3342
#884961