Finite Group Databasebeta

← #18076874

Subgroups — #18076874

Order 4864.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564410C211yesmaximal, characteristic
2#14562393C211yesmaximal, characteristic
3#14562064C211yesmaximal, characteristic
4C2×Q8⋊(C19⋊C8)C211yesmaximal, characteristic
5#14561530C211yesmaximal, characteristic
6#14561473C211yesmaximal, characteristic
7Q8×M16×C19C211yesmaximal, characteristic
8#11926597C2211yescharacteristic
9C2×#10597279—21no—
10#11926568C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×C4×C19⋊C8C2211yescharacteristic
13#11926308—21no—
14#11926296—22no—
15Q8⋊(C19⋊C8)—21no—
16Q8⋊(C19⋊C8)—21no—
17Q8⋊(C19⋊C8)C411yescharacteristic
18Q8⋊(C19⋊C8)C411yescharacteristic
19Q8⋊(C19⋊C8)C411yescharacteristic
20Q8⋊(C19⋊C8)C411yescharacteristic
21C2×C4×Q8×C19C2211yescharacteristic
22C19×#446—22no—
23C19×#446—21no—
24C8×Q8×C19—21no—
25C19×#423—21no—
26C19×#423C2211yescharacteristic
27C4×M16×C19—21no—
28C4×M16×C19C2211yescharacteristic
29C22×Q8×C19Q811yescharacteristic
30C2×M16×C19—21no—
31C2×M16×C19D411yescharacteristic
32C2×M16×C19D411yescharacteristic
33C4×Q8×C19—21no—
34C4×Q8×C19—21no—
35C4×Q8×C19C2×C411yescharacteristic
36C4×Q8×C19C2×C411yescharacteristic
37C4×Q8×C19D411yescharacteristic
38C4×Q8×C19D411yescharacteristic
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19Q811yescharacteristic
41C2×C42×C19—21no—
42C2×C42×C19C2311yescharacteristic
43C2×#64520—21no—
44C22×C19⋊C8—21no—
45C22×C19⋊C8—21no—
46C19×C4⋊C8—22no—
47C19×C4⋊C8—22no—
48C19×C4⋊C8—21no—
49C19×C4⋊C8D412yes—
50C19×#97—22no—
51C19×#97—21no—
52C4×C8×C19—22no—
53C4×C8×C19—21no—
54C22⋊(C19⋊C8)—21no—
55#10597279—42no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)C2×C411yescharacteristic
61C4⋊(C19⋊C8)C2×C411yescharacteristic
62C4×C19⋊C8—21no—
63C4×C19⋊C8—21no—
64C4×C19⋊C8C2×C411yescharacteristic
65C4×C19⋊C8C2×C411yescharacteristic
66C2×Q8×C19—21no—
67C2×Q8×C19—22no—
68C2×Q8×C19—41no—
69C2×Q8×C19C4⋊C411yescharacteristic
70C2×Q8×C19C4⋊C411yescharacteristic
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×Q811yescharacteristic
75C22×C4×C19#4111yescharacteristic
76M16×C19—21no—
77M16×C19—21no—
78M16×C19—21no—
79M16×C19—41no—
80M16×C19—41no—
81M16×C19Q1612yes—
82C2×C8×C19—21no—
83C2×C8×C19—22no—
84C2×C8×C19—21no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19C4⋊C411yescharacteristic
91C4⋊C4×C19C4⋊C411yescharacteristic
92C42×C19—21no—
93C42×C19—21no—
94C42×C19—21no—
95C42×C19—21no—
96C42×C19C22×C411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C42×C19#4111yescharacteristic
100#64520—41no—
101#64520—41no—
102C2×C19⋊C8—21no—
103C2×C19⋊C8—21no—
104C2×C19⋊C8—21no—
105C2×C19⋊C8—21no—
106C2×C19⋊C8—42no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—41no—
111#8907—191nomaximal, Sylow
112C23×C19C22⋊Q811yescharacteristic
113Q8×C19—21no—
114Q8×C19—21no—
115Q8×C19—21no—
116Q8×C19—42no—
117Q8×C19#10812yescomplemented
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19—81no—
127C2×C4×C19C2×C4⋊C411yescharacteristic
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19#12011yescharacteristic
131C2×C4×C19C22⋊Q811yescharacteristic
132C2×C4×C19#12311yescharacteristic
133C2×C4×C19C2×Q1611yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C19#13711yescharacteristic
137C8×C19—22no—
138C8×C19—41no—
139C8×C19—42no—
140C19⋊C8—22no—
141C19⋊C8—41no—
142C19⋊C8—41no—
143C19⋊C8—41no—
144C19⋊C8—81no—
145C19⋊C8—81no—
146Q8×M16D1911yescharacteristic
147#1950—191no—
148#1567—191no—
149#1487—191no—
150C2×Q8⋊C8—191no—
151#1301—191no—
152#1278—191no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19#38511yescharacteristic
156C22×C19#47711yescharacteristic
157C22×C19#47911yescharacteristic
158C4×C19—21no—
159C4×C19—22no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—41no—
163C4×C19—41no—
164C4×C19—41no—
165C4×C19C2×#10811yescharacteristic
166C4×C19#43011yescharacteristic
167C4×C19C4×Q1611yescharacteristic
168C4×C19#44011yescharacteristic
169C4×C19#44911yescharacteristic
170C4×C19#45111yescharacteristic
171C2×C4×Q8C2×D1911yescharacteristic
172#446—21no—
173#446—22no—
174C8×Q8—21no—
175#431—191no—
176C2×#108—381no—
177#423—21no—
178#423—191no—
179#423C2×D1911yescharacteristic
180C2×C4⋊C8—191no—
181C4×M16—21no—
182C4×M16C2×D1911yescharacteristic
183C2×C4×C8—191no—
184#341—381no—
185#335—382no—
186Q8⋊C8—191no—
187Q8⋊C8—191no—
188Q8⋊C8—191no—
189Q8⋊C8—191no—
190Q8⋊C8—381no—
191Q8⋊C8—381no—
192C2×C19—21no—
193C2×C19—21no—
194C2×C19#185511yescharacteristic
195C2×C19#186111yescharacteristic
196C2×C19#186311yescharacteristic
197C22×Q8Dic3811yescharacteristic
198C2×M16—21no—
199C2×M16—381no—
200C2×M16C22⋊D1911yescharacteristic
201C2×M16C22⋊D1911yescharacteristic
202C22×C8—381no—
203C22×C8—381no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8C4×D1911yescharacteristic
207C4×Q8C4×D1911yescharacteristic
208C4×Q8C22⋊D1911yescharacteristic
209C4×Q8C22⋊D1911yescharacteristic
210C2×C4⋊C4—21no—
211C2×C4⋊C4Dic3811yescharacteristic
212C2×C42—21no—
213C2×C42C22×D1911yescharacteristic
214#108—762no—
215C4⋊C8—22no—
216C4⋊C8—22no—
217C4⋊C8—21no—
218C4⋊C8—191no—
219C4⋊C8—191no—
220C4⋊C8—381no—
221C4⋊C8—381no—
222C4⋊C8—381no—
223C4⋊C8—381no—
224C4⋊C8C22⋊D1912yes—
225C22⋊C8—381no—
226#97—22no—
227#97—21no—
228C4×C8—22no—
229C4×C8—21no—
230C4×C8—191no—
231C4×C8—191no—
232C4×C8—381no—
233C4×C8—381no—
234C19#890711yescharacteristic, complemented, Sylow
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8Dic19⋊C411yescharacteristic
239C2×Q8Dic19⋊C411yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic3811yescharacteristic
243C22×C4#6454111yescharacteristic
244C22×C4C2×C22⋊D1911yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—41no—
249M16—41no—
250M16—761no—
251M16—761no—
252M16#6452812yes—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—22no—
256C2×C8—381no—
257C2×C8—381no—
258C2×C8—381no—
259C2×C8—381no—
260C2×C8—762no—
261C2×C8—761no—
262C2×C8—761no—
263C2×C8—761no—
264C2×C8—761no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4Dic19⋊C411yescharacteristic
271C4⋊C4Dic19⋊C411yescharacteristic
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42C2×C4×D1911yescharacteristic
277C42#6454111yescharacteristic
278C42C2×C22⋊D1911yescharacteristic
279C42C2×C22⋊D1911yescharacteristic
280C23#1059737011yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8#1059727912yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4C2×Dic19⋊C411yescharacteristic
296C2×C4#1059737011yescharacteristic
297C2×C4C4×C22⋊D1911yescharacteristic
298C2×C4C4×C22⋊D1911yescharacteristic
299C2×C4#1059737511yescharacteristic
300C2×C4#1059738811yescharacteristic
301C2×C4C2×#6452811yescharacteristic
302C2×C4#1059739511yescharacteristic
303C2×C4#1059739611yescharacteristic
304C2×C4#1059739911yescharacteristic
305C8—22no—
306C8—41no—
307C8—42no—
308C8—382no—
309C8—761no—
310C8—761no—
311C8—761no—
312C8—1521no—
313C8—1521no—
314C22—21no—
315C22—21no—
316C22#1192641711yescharacteristic
317C22#1192683911yescharacteristic
318C22#1192685111yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4C2×#1059727911yescharacteristic
327C4#1192659211yescharacteristic
328C4C4×#6452811yescharacteristic
329C4#1192664211yescharacteristic
330C4#1192668911yescharacteristic
331C4#1192670011yescharacteristic
332C2—21no—
333C2—21no—
334C2#1456384011yescharacteristic
335C2#1456387511yescharacteristic
336C2#1456388911yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingQ8×M16×C19C2
socleC22×C19#385
prime radicalC23×C19C22⋊Q8
cosocleC2×C42×C19C23
hypercenterQ8×M16D19
hypocenterC19#8907
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
117. Q8×C19#108semidirect
234. C19#8907semidirect
285. Q8#10597279semidirect

Maximal subgroups

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

subgroupindex
#145644102
#145623932
#145620642
C2×Q8⋊(C19⋊C8)2
#145615302
#145614732
Q8×M16×C192
#890719