Finite Group Databasebeta

← #14577442

Subgroups — #14577442

Order 2432.

964 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic38C211yesmaximal, characteristic, complemented
2#11927274C213yesmaximal, complemented
3#11927272C213yesmaximal, complemented
4#11927271C213yesmaximal, complemented
5#11927271C213yesmaximal, complemented
6#11927270C211yesmaximal, characteristic, complemented
7#11927270C211yesmaximal, characteristic, complemented
8#11927174C213yesmaximal
9#11927171C213yesmaximal
10#11927100C213yesmaximal
11#11927098C213yesmaximal
12#11927020C211yesmaximal, characteristic
13#11927020C211yesmaximal, characteristic
14C4×Q8×D19C211yesmaximal, characteristic
15C19×#557C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C19×C4⋊Q8C2213yes—
18C19×#125C2213yes—
19C19×#125C2213yes—
20C4×Q8×C19C2213yes—
21C4×Q8×C19C2211yescharacteristic
22C4×Q8×C19C2211yescharacteristic
23C4×Q8×C19C2211yescharacteristic
24#10597392C2213yes—
25Q8×Dic19C2211yescharacteristic
26Q8×Dic19C2211yescharacteristic
27Q8×Dic19C2211yescharacteristic
28#10597390C2213yes—
29#10597390C2216yes—
30#10597343C2213yes—
31#10597342C2211yescharacteristic
32#10597342C2213yes—
33#10597342C2216yes—
34#10597338C2213yes—
35#10597338C2213yes—
36C4⋊C4×D19C2213yes—
37#10597336C2213yes—
38#10597336C2213yes—
39#10597335C2213yes—
40#10597335C2213yes—
41#10597335C2216yes—
42#10597335C2216yes—
43#10597334C2213yes—
44#10597334C2213yes—
45#10597334C2213yes—
46#10597334C2213yes—
47#10597334C2213yes—
48#10597334C2216yes—
49#10597333C2216yes—
50#10597333C2216yes—
51#10597333C2213yes—
52#10597333C2213yes—
53#10597333C2213yes—
54#10597318C2213yes—
55#10597318C2213yes—
56C42×D19C2213yes—
57#10597316C2213yes—
58#10597316C2213yes—
59#10597315C2213yes—
60C4×Dic38C2213yes—
61C4×Dic38C2213yes—
62C4×Dic38C2213yes—
63C4×Dic38C2213yes—
64C4×Dic38C2213yes—
65C4×Dic38C2213yes—
66C2×Q8×C19C2313yes—
67C2×Q8×C19C2311yescharacteristic
68Q8×D19Q818yescomplemented
69C2×C4×D19C2311yescharacteristic
70C2×C4×D19C2313yes—
71C2×C4×D19C2313yes—
72C2×Dic38C2311yescharacteristic
73C2×Dic38C2313yes—
74C2×Dic38C2313yes—
75C2×Dic38C2316yes—
76C2×Dic38C2313yes—
77C4⋊C4×C19C2311yescharacteristic
78C4⋊C4×C19C2313yes—
79C4⋊C4×C19C2313yes—
80C4⋊C4×C19C2313yes—
81C4⋊C4×C19C2313yes—
82C4⋊C4×C19C2313yes—
83C4⋊C4×C19C2316yes—
84C42×C19C2313yes—
85C42×C19C2313yes—
86C42×C19C2313yes—
87(C2×D19)⋊C4C2311yescharacteristic
88(C2×D19)⋊C4C2313yes—
89(C2×D19)⋊C4C2311yescharacteristic
90(C2×D19)⋊C4C2313yes—
91C4⋊Dic19C2313yes—
92C4⋊Dic19C2313yes—
93C4⋊Dic19C2313yes—
94C4⋊Dic19C2313yes—
95C4⋊Dic19C2313yes—
96C4⋊Dic19C2313yes—
97Dic19⋊C4C2311yescharacteristic
98Dic19⋊C4C2313yes—
99Dic19⋊C4C2313yes—
100Dic19⋊C4C2313yes—
101Dic19⋊C4C2316yes—
102Dic19⋊C4C2316yes—
103Dic19⋊C4C2313yes—
104Dic19⋊C4C2313yes—
105Dic19⋊C4C2311yescharacteristic
106Dic19⋊C4C2313yes—
107Dic19⋊C4C2313yes—
108Dic19⋊C4C2316yes—
109Dic19⋊C4C2313yes—
110C4×Dic19C2316yes—
111C4×Dic19C2313yes—
112C4×Dic19C2313yes—
113C4×Dic19C2313yes—
114C4×Dic19C2313yes—
115C4×Dic19C2313yes—
116C4×Dic19C2316yes—
117C22×D19C2411yescharacteristic
118Q8×C19—43no—
119Q8×C19C2×Q814yes—
120C2×C4×C19C2411yescharacteristic
121C2×C4×C19C2413yes—
122C2×C4×C19C2413yes—
123C2×C4×C19C2413yes—
124C2×C4×C19C2411yescharacteristic
125C2×C4×C19C2411yescharacteristic
126C2×C4×C19C2413yes—
127C2×Dic19C2413yes—
128C2×Dic19C2411yescharacteristic
129C2×Dic19C2411yescharacteristic
130C2×Dic19C2413yes—
131C2×Dic19C2413yes—
132C2×Dic19C2413yes—
133C2×Dic19C2411yescharacteristic
134C4×D19—22no—
135C4×D19—43no—
136C4×D19C2×Q8112yes—
137Dic38—22no—
138Dic38—26no—
139Dic38—43no—
140Dic38—46no—
141Dic38C2×Q8112yes—
142#3502—191nomaximal, Sylow
143C22×C19C2511yescharacteristic
144C2×D19—21no—
145C2×D19—21no—
146C2×D19C22×Q812yes—
147C4×C19—23no—
148C4×C19—21no—
149C4×C19—21no—
150C4×C19—23no—
151C4×C19—23no—
152C4×C19—21no—
153C4×C19C22×Q816yes—
154Dic19—21no—
155Dic19—23no—
156Dic19—21no—
157Dic19—23no—
158Dic19—23no—
159Dic19C22×Q816yes—
160Dic192−1+412yes—
161Q82—193no—
162Q82—191no—
163#557—193no—
164#557—193no—
165#557—191no—
166#557—191no—
167#557—193no—
168#557D1911yescharacteristic, complemented
169#544—193no—
170#544—193no—
171#533—193no—
172#533—193no—
173#519—191no—
174#519—191no—
175C2×C4×Q8—191no—
176C2×C19C23×Q811yescharacteristic
177C2×C19C2×2−1+411yescharacteristic
178C2×C19#58511yescharacteristic
179D19—22no—
180C22×Q8—191no—
181C4⋊Q8—193no—
182C4⋊Q8—196no—
183C4⋊Q8—193no—
184C4⋊Q8—193no—
185C4⋊Q8—193no—
186C4⋊Q8—196no—
187C4⋊Q8—193no—
188C4⋊Q8—193no—
189C4⋊Q8—193no—
190C4⋊Q8C2×D1913yes—
191#125—193no—
192#125—193no—
193#125—196no—
194#125—196no—
195#125—193no—
196#125—193no—
197#125—193no—
198#125—193no—
199#125C2×D1913yes—
200#125C2×D1913yes—
201C22⋊Q8—193no—
202C22⋊Q8—193no—
203C22⋊Q8—191no—
204C22⋊Q8—196no—
205C22⋊Q8—193no—
206C4×Q8—191no—
207C4×Q8—191no—
208C4×Q8—191no—
209C4×Q8—193no—
210C4×Q8—193no—
211C4×Q8—193no—
212C4×Q8—196no—
213C4×Q8—196no—
214C4×Q8—193no—
215C4×Q8—193no—
216C4×Q8—193no—
217C4×Q8—193no—
218C4×Q8—193no—
219C4×Q8—193no—
220C4×Q8C2×D1911yescharacteristic
221C4×Q8C2×D1911yescharacteristic
222C4×Q8C2×D1911yescharacteristic
223C4×Q8C2×D1913yes—
224#117—193no—
225#117—193no—
226#117—193no—
227#117—193no—
228C2×C4⋊C4—193no—
229C2×C42—193no—
230C19#350211yescharacteristic, complemented, Sylow
231C2×Q8—198no—
232C2×Q8—193no—
233C2×Q8—193no—
234C2×Q8—191no—
235C2×Q8—193no—
236C2×Q8—196no—
237C2×Q8C22×D1913yes—
238C2×Q8C22×D1911yescharacteristic
239C22×C4—193no—
240C22×C4—191no—
241C22×C4—193no—
242C4⋊C4—196no—
243C4⋊C4—193no—
244C4⋊C4—193no—
245C4⋊C4—193no—
246C4⋊C4—193no—
247C4⋊C4—191no—
248C4⋊C4—193no—
249C4⋊C4—193no—
250C4⋊C4—191no—
251C4⋊C4—196no—
252C4⋊C4—196no—
253C4⋊C4—193no—
254C4⋊C4—193no—
255C4⋊C4—193no—
256C4⋊C4—193no—
257C4⋊C4—193no—
258C4⋊C4—193no—
259C4⋊C4—193no—
260C4⋊C4—193no—
261C4⋊C4C22×D1913yes—
262C4⋊C4C22×D1913yes—
263C4⋊C4C22×D1913yes—
264C4⋊C4C22×D1913yes—
265C4⋊C4C22×D1916yes—
266C4⋊C4C22×D1911yescharacteristic
267C4⋊C4C22×D1913yes—
268C22⋊C4—193no—
269C22⋊C4—191no—
270C22⋊C4—193no—
271C22⋊C4—191no—
272C42—193no—
273C42—193no—
274C42—193no—
275C42—196no—
276C42—196no—
277C42—193no—
278C42—193no—
279C42C22×D1913yes—
280C42C22×D1913yes—
281C42C22×D1913yes—
282C23—191no—
283Q8—43no—
284Q8—1912no—
285Q8—386no—
286Q8—382no—
287Q8—763no—
288Q8—766no—
289Q8Q8×D1914yes—
290C2×C4—193no—
291C2×C4—191no—
292C2×C4—1912no—
293C2×C4—191no—
294C2×C4—193no—
295C2×C4—191no—
296C2×C4—193no—
297C2×C4—193no—
298C2×C4—382no—
299C2×C4—763no—
300C2×C4C23×D1911yescharacteristic
301C2×C4C23×D1913yes—
302C2×C4C23×D1913yes—
303C2×C4C23×D1913yes—
304C2×C4C23×D1911yescharacteristic
305C2×C4C23×D1911yescharacteristic
306C2×C4C23×D1913yes—
307C22—192no—
308C22—381no—
309C22—381no—
310C22C24×D1911yescharacteristic
311C4—21no—
312C4—23no—
313C4—21no—
314C4—23no—
315C4—21no—
316C4—23no—
317C4—196no—
318C4—192no—
319C4—381no—
320C4—383no—
321C4—383no—
322C4—381no—
323C4—383no—
324C4C2×Q8×D1916yes—
325C2—382no—
326C2C22×Q8×D1911yescharacteristic
327C22−1+4×D1911yescharacteristic
328C2#1192738011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#557C2
prime radicalC22×D19C24
hypercenter#557D19
hypocenterC19#3502
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. Q8×Dic38C2semidirect
2. #11927274C2semidirect
3. #11927272C2semidirect
4. #11927271C2semidirect
5. #11927271C2semidirect
6. #11927270C2semidirect
7. #11927270C2semidirect
15. C19×#557C2semidirect
68. Q8×D19Q8semidirect
168. #557D19semidirect
230. C19#3502semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic382
#119272742
#119272722
#119272712
#119272702
#119271742
#119271712
#119271002
#119270982
#119270202
C4×Q8×D192
C19×#5572
#350219