Finite Group Databasebeta

← #29596075

Subgroups — #29596075

Order 15616.

422 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519799C211yesmaximal, characteristic
2C2×#16839570C212yesmaximal
3#21445991C211yesmaximal, characteristic, complemented
4#21443915C212yesmaximal, complemented
5C2×C61×C4⋊C16C211yesmaximal, characteristic, complemented
6C2×#14519799C2211yescharacteristic
7C4×#11758222—21no—
8C4×Dic244C411yescharacteristic
9C4×Dic244C411yescharacteristic
10C4×#11758190—21no—
11C4×#11758190—21no—
12C4×D488C411yescharacteristic
13C4×D488C411yescharacteristic
14C2×#14519713—21no—
15C2×#14519713C2212yes—
16#16839800C2211yescharacteristic
17#16839786—21no—
18#16839759—21no—
19#16839570—24no—
20C22×C16×C61C2212yes—
21C2×C4×C8×C61C2211yescharacteristic
22C61×C4⋊C16—21no—
23C61×C4⋊C16—21no—
24C2×#11758222—21no—
25#14519799—21no—
26#14519799—21no—
27#14519799D412yes—
28#14519799Q812yes—
29C2×Dic244C2×C411yescharacteristic
30C2×#11758190—21no—
31C2×D488C2×C411yescharacteristic
32C2×#11758194—22no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×D244—21no—
36C4×D244—21no—
37C4×C22⋊D61—41no—
38C4×C22⋊D61—41no—
39#14519736—21no—
40#14519734—41no—
41C42×D61—41no—
42#14519713—22no—
43#14519713—22no—
44#14519713—42no—
45#14519711C2×C411yescharacteristic
46#14519711C2×C411yescharacteristic
47#14519709—21no—
48C4⋊#92418—41no—
49C4⋊#92418—41no—
50#14519702—21no—
51#14519702—21no—
52#14519699—21no—
53#14519699—21no—
54C22×C8×C61D411yescharacteristic
55C22×C8×C61C2311yescharacteristic
56C2×C42×C61D411yescharacteristic
57C2×C16×C61—22no—
58C2×C16×C61—22no—
59C2×C16×C61—22no—
60C4×C8×C61C2×C411yescharacteristic
61C4×C8×C61C2×C411yescharacteristic
62C4×C8×C61D411yescharacteristic
63C4×C8×C61D411yescharacteristic
64C22×C4×C61SD1611yescharacteristic
65C22×C4×C61SD1611yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C2×C22⋊D61—41no—
68#11758222—22no—
69#11758222—22no—
70#11758222—41no—
71#11758222—41no—
72C2×D244—21no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×Dic122—21no—
77C2×C8×C61—21no—
78C2×C8×C61—21no—
79C2×C8×C61C22⋊C411yescharacteristic
80C2×C8×C61C22⋊C411yescharacteristic
81C2×C8×C61C22×C411yescharacteristic
82C2×C8×C61C2×D411yescharacteristic
83C2×C8×C61C2×D411yescharacteristic
84C2×C8×C61C2×Q811yescharacteristic
85C2×C8×C61#4111yescharacteristic
86C2×C8×C61#4111yescharacteristic
87C42×C61C22⋊C411yescharacteristic
88C42×C61C22⋊C411yescharacteristic
89C42×C61D811yescharacteristic
90C42×C61D811yescharacteristic
91C22⋊Dic61—41no—
92#11758198—41no—
93#11758198—41no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101#11758194—42no—
102#11758194—42no—
103C2×#92418—42no—
104Dic244—21no—
105Dic244C4⋊C412yes—
106D488—21no—
107D488C4⋊C412yes—
108#11758190—22no—
109#11758190—22no—
110C16×C61—42no—
111C23×C61C2×SD1611yescharacteristic
112C22×D61—41no—
113C2×C4×C61—22no—
114C2×C4×C61—41no—
115C2×C4×C61#10211yescharacteristic
116C2×C4×C61#10211yescharacteristic
117C2×C4×C61#10211yescharacteristic
118C2×C4×C61#10211yescharacteristic
119C2×C4×C61C2×C22⋊C411yescharacteristic
120C2×C4×C61#12111yescharacteristic
121C2×C4×C61C22⋊Q811yescharacteristic
122C2×C4×C61C2×D811yescharacteristic
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C22⋊D61—42no—
126C22⋊D61—42no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130D244—22no—
131D244—41no—
132C4×D61—42no—
133C4×D61—42no—
134C4×D61—82no—
135C4×D61—82no—
136Dic122—22no—
137Dic122—41no—
138C8×C61—21no—
139C8×C61—21no—
140C8×C61C2×C4⋊C411yescharacteristic
141C8×C61#11711yescharacteristic
142C8×C61#12111yescharacteristic
143C8×C61C22⋊Q811yescharacteristic
144#92418—82no—
145#12815—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61C2×#10211yescharacteristic
149C22×C61#46111yescharacteristic
150C22×C61#47611yescharacteristic
151C2×D61—42no—
152C2×D61—81no—
153C2×D61—81no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61#35912yescomplemented
158C4×C61#38011yescharacteristic
159C4×C61#41711yescharacteristic
160C4×C61#45911yescharacteristic
161C4×C61#47411yescharacteristic
162Dic61—42no—
163Dic61—81no—
164Dic61—81no—
165C4×#135—611no—
166C2×C4⋊C16D6111yescharacteristic, complemented
167C2×#359—612no—
168#1848—611no—
169#1382—612no—
170C2×C61—21no—
171C2×C61—21no—
172C2×C61#180211yescharacteristic
173C2×C61C2×#35911yescharacteristic
174C2×C61#214311yescharacteristic
175D61—82no—
176C2×#135—611no—
177C4×#41—1221no—
178C22×C16C2×D6112yes—
179C4×Q16—611no—
180C4×Q16—611no—
181C4×SD16—1221no—
182C4×SD16—1221no—
183C4×D8—611no—
184C4×D8—611no—
185C2×#108—612no—
186C2×#108—1221no—
187#427—611no—
188#423—1221no—
189#416—1221no—
190C2×C4×C8C2×D6111yescharacteristic
191C4⋊C16—21no—
192C4⋊C16—21no—
193#359—1224no—
194C61#1281511yescharacteristic, complemented, Sylow
195C2×#41—1221no—
196#135—612no—
197#135—612no—
198#135—1221no—
199#135—1221no—
200C2×Q16—611no—
201C2×SD16—1221no—
202C2×D8—611no—
203C2×M16—1222no—
204C22×C8D24411yescharacteristic
205C22×C8C22×D6111yescharacteristic
206C4×Q8—1221no—
207C4×Q8—1221no—
208C4×D4—1221no—
209C4×D4—1221no—
210C4×D4—2441no—
211C4×D4—2441no—
212#117—1221no—
213#117—2441no—
214C2×C42—2441no—
215C2×C42D24411yescharacteristic
216C2×C16—22no—
217C2×C16—22no—
218C2×C16—22no—
219#108—1222no—
220#108—1222no—
221#108—2442no—
222#107—611no—
223#107—611no—
224#106—1221no—
225C4⋊C8—2441no—
226C4⋊C8—2441no—
227#103—1221no—
228#103—1221no—
229#102—1221no—
230#102—1221no—
231C4×C8C4×D6111yescharacteristic
232C4×C8C4×D6111yescharacteristic
233C4×C8C22⋊D6111yescharacteristic
234C4×C8C22⋊D6111yescharacteristic
235#41—1222no—
236#41—1222no—
237#41—2441no—
238#41—2441no—
239C2×Q8—1221no—
240C2×D4—1221no—
241C2×D4—2441no—
242C22×C4—2441no—
243C22×C4—2441no—
244C22×C4—2441no—
245C22×C4#1175819011yescharacteristic
246C22×C4#1175819011yescharacteristic
247C22×C4C2×D24411yescharacteristic
248Q16—612no—
249Q16—1221no—
250SD16—1222no—
251SD16—1222no—
252D8—612no—
253D8—1221no—
254M16—2442no—
255M16—2442no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—2442no—
259C2×C8#1175819811yescharacteristic
260C2×C8#1175819811yescharacteristic
261C2×C8C2×C4×D6111yescharacteristic
262C2×C8D4×D6111yescharacteristic
263C2×C8#1175822411yescharacteristic
264C2×C8Q8×D6111yescharacteristic
265C2×C8#1175822611yescharacteristic
266C2×C8C2×C22⋊D6111yescharacteristic
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C22⋊C4—2441no—
272C22⋊C4—2441no—
273C22⋊C4—2441no—
274C42—2441no—
275C42—2441no—
276C42—2441no—
277C42D48811yescharacteristic
278C42D48811yescharacteristic
279C42#1175819811yescharacteristic
280C42#1175819811yescharacteristic
281C16—42no—
282C23—2441no—
283C23C2×#1175819011yescharacteristic
284Q8—1222no—
285Q8—2441no—
286D4—1222no—
287D4—2442no—
288D4—2442no—
289D4—2441no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—4882no—
293C2×C4—4882no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4#1451969911yescharacteristic
300C2×C4#1451969911yescharacteristic
301C2×C4#1451969911yescharacteristic
302C2×C4#1451969911yescharacteristic
303C2×C4C2×#1175819811yescharacteristic
304C2×C4#1451975211yescharacteristic
305C2×C4#1451975711yescharacteristic
306C2×C4C2×D48811yescharacteristic
307C2×C4#1451980511yescharacteristic
308C2×C4#1451981011yescharacteristic
309C8—21no—
310C8—21no—
311C8—4882no—
312C8C4⋊C4×D6111yescharacteristic
313C8#1451973511yescharacteristic
314C8#1451974811yescharacteristic
315C8#1451975311yescharacteristic
316C22—21no—
317C22—21no—
318C22—4881no—
319C22—4881no—
320C22—2442no—
321C22C2×#1451969911yescharacteristic
322C22#1683996811yescharacteristic
323C22#1684005311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—4881no—
328C4—4881no—
329C4—2442no—
330C4#1683957012yescomplemented
331C4#1683961911yescharacteristic
332C4#1683976411yescharacteristic
333C4#1683995811yescharacteristic
334C4#1684004311yescharacteristic
335C2—21no—
336C2—21no—
337C2—4882no—
338C2#2144582011yescharacteristic
339C2C2×#1683957011yescharacteristic
340C2#2144754811yescharacteristic
subgroupG/H
centerC2×C4C2×D488
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×C4⋊C16C2
socleC22×C61C2×#102
prime radicalC2×#14519799C22
cosocleC22×C8×C61C23
hypercenterC2×C4⋊C16D61
hypocenterC61#12815
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
3. #21445991C2semidirect
4. #21443915C2semidirect
5. C2×C61×C4⋊C16C2semidirect
157. C4×C61#359semidirect
166. C2×C4⋊C16D61semidirect
194. C61#12815semidirect
330. C4#16839570semidirect

Maximal subgroups

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

subgroupindex
C4×#145197992
C2×#168395702
#214459912
#214439152
C2×C61×C4⋊C162
#1281561