Finite Group Databasebeta

← #18076813

Subgroups — #18076813

Order 4864.

390 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572760C211yesmaximal, characteristic
2#14563807C211yesmaximal, characteristic, complemented
3#14562424C211yesmaximal, characteristic, complemented
4#14562074C211yesmaximal, characteristic
5#14561526C211yesmaximal, characteristic, complemented
6#14561472C211yesmaximal, characteristic, complemented
7C19×#1476C211yesmaximal, characteristic
8#11926675—21no—
9#11926616—22no—
10D4×C19⋊C8—21no—
11#11926601—21no—
12#11926597C2211yescharacteristic
13C2×#10597276—22no—
14#11926568C2211yescharacteristic
15#11926568C2211yescharacteristic
16C2×C4⋊(C19⋊C8)—21no—
17C4×#64520C2211yescharacteristic
18#11926297—21no—
19#11926295—21no—
20Q8⋊(C19⋊C8)—21no—
21D4⋊(C19⋊C8)—21no—
22C4×#41×C19C2211yescharacteristic
23C19×#431C2211yescharacteristic
24C2×C4×C8×C19C2211yescharacteristic
25C19×Q8⋊C8C411yescharacteristic
26C19×Q8⋊C8C411yescharacteristic
27C19×D4⋊C8C411yescharacteristic
28C19×D4⋊C8C411yescharacteristic
29C2×#41×C19Q811yescharacteristic
30C22×C8×C19—21no—
31C4×Q8×C19C2×C411yescharacteristic
32C4×Q8×C19D411yescharacteristic
33C4×D4×C19—21no—
34C4×D4×C19—21no—
35C4×D4×C19C2×C411yescharacteristic
36C4×D4×C19D411yescharacteristic
37C19×#117—21no—
38C19×#117Q811yescharacteristic
39C2×C42×C19—21no—
40C2×C42×C19C2311yescharacteristic
41C2×#64520—21no—
42C2×#64520—21no—
43C2×#64520D412yes—
44C22×C19⋊C8—22no—
45C19×C4⋊C8C2×C411yescharacteristic
46C19×C4⋊C8C2×C411yescharacteristic
47C19×C22⋊C8—21no—
48C4×C8×C19—21no—
49C4×C8×C19—21no—
50C4×C8×C19C2×C411yescharacteristic
51C4×C8×C19C2×C411yescharacteristic
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—21no—
54#10597276—44no—
55C4⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)D411yescharacteristic
61C4⋊(C19⋊C8)D411yescharacteristic
62#10597260—22no—
63#10597260—21no—
64C4×C19⋊C8—21no—
65C4×C19⋊C8—21no—
66#41×C19—22no—
67#41×C19—41no—
68C2×Q8×C19C4⋊C411yescharacteristic
69C2×D4×C19—21no—
70C2×D4×C19C4⋊C411yescharacteristic
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×Q811yescharacteristic
76C22×C4×C19#4111yescharacteristic
77C2×C8×C19—22no—
78C2×C8×C19—22no—
79C2×C8×C19—21no—
80C2×C8×C19—21no—
81C2×C8×C19—21no—
82C2×C8×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19—21no—
85C4⋊C4×C19C4⋊C411yescharacteristic
86C4⋊C4×C19C4⋊C411yescharacteristic
87C22⋊C4×C19—21no—
88C22⋊C4×C19—21no—
89C22⋊C4×C19—21no—
90C42×C19—21no—
91C42×C19—21no—
92C42×C19—21no—
93C42×C19C22×C411yescharacteristic
94C42×C19C2×D411yescharacteristic
95C42×C19C2×D411yescharacteristic
96C42×C19#4111yescharacteristic
97#64520—22no—
98#64520—41no—
99#64520—42no—
100#64520—42no—
101C2×C19⋊C8—21no—
102C2×C19⋊C8—21no—
103C2×C19⋊C8—22no—
104C2×C19⋊C8—41no—
105C2×C19⋊C8—41no—
106C2×C19⋊C8—82no—
107#8898—191nomaximal, Sylow
108C23×C19—21no—
109C23×C19C22⋊Q811yescharacteristic
110Q8×C19—21no—
111Q8×C19—21no—
112D4×C19—21no—
113D4×C19—42no—
114D4×C19#10812yescomplemented
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
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—42no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19C2×C4⋊C411yescharacteristic
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19#12011yescharacteristic
133C2×C4×C19C22⋊Q811yescharacteristic
134C2×C4×C19#12311yescharacteristic
135C8×C19—22no—
136C8×C19—22no—
137C8×C19—41no—
138C8×C19—41no—
139C19⋊C8—42no—
140C19⋊C8—41no—
141C19⋊C8—42no—
142C19⋊C8—41no—
143C19⋊C8—81no—
144#2990—191no—
145#1848—191no—
146#1574—191no—
147#1489—191no—
148#1476D1911yescharacteristic
149#1299—191no—
150#1278—191no—
151C22×C19—21no—
152C22×C19—22no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—41no—
156C22×C19—41no—
157C22×C19#38511yescharacteristic
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—41no—
162C4×C19—41no—
163C4×C19—41no—
164C4×C19C2×#10811yescharacteristic
165C4×C19#43011yescharacteristic
166C4×C19#44311yescharacteristic
167C4×C19#44411yescharacteristic
168C4×C19#45311yescharacteristic
169C4×C19#45611yescharacteristic
170C4×#41C2×D1911yescharacteristic
171#446—381no—
172#435—382no—
173C8×D4—381no—
174#432—381no—
175#431—191no—
176#431C2×D1911yescharacteristic
177C2×#108—382no—
178#423—191no—
179#423—191no—
180C2×C4⋊C8—381no—
181C4×M16—191no—
182C2×C4×C8C2×D1911yescharacteristic
183#335—381no—
184#334—381no—
185Q8⋊C8—381no—
186Q8⋊C8Dic1911yescharacteristic
187Q8⋊C8Dic1911yescharacteristic
188D4⋊C8—381no—
189D4⋊C8Dic1911yescharacteristic
190D4⋊C8Dic1911yescharacteristic
191C2×C19—41no—
192C2×C19—42no—
193C2×C19#185511yescharacteristic
194C2×C19#185911yescharacteristic
195C2×C19#186611yescharacteristic
196C2×#41Dic3811yescharacteristic
197C2×M16—192no—
198C2×M16—381no—
199C2×M16—381no—
200C22×C8—21no—
201C22×C8—382no—
202C4×Q8D7611yescharacteristic
203C4×Q8C2×Dic1911yescharacteristic
204C4×D4—21no—
205C4×D4—21no—
206C4×D4D7611yescharacteristic
207C4×D4C2×Dic1911yescharacteristic
208#117—21no—
209#117Dic3811yescharacteristic
210C2×C42—21no—
211C2×C42C22×D1911yescharacteristic
212#108—764no—
213C4⋊C8—191no—
214C4⋊C8—191no—
215C4⋊C8—382no—
216C4⋊C8—381no—
217C4⋊C8—381no—
218C4⋊C8—381no—
219C4⋊C8—381no—
220C4⋊C8C2×Dic1911yescharacteristic
221C4⋊C8C2×Dic1911yescharacteristic
222C22⋊C8—21no—
223C22⋊C8—382no—
224C22⋊C8—381no—
225#97—382no—
226#97—381no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—381no—
230C4×C8—381no—
231C4×C8C2×Dic1911yescharacteristic
232C4×C8C2×Dic1911yescharacteristic
233C19#889811yescharacteristic, complemented, Sylow
234#41—22no—
235#41—41no—
236C2×Q8C4⋊Dic1911yescharacteristic
237C2×D4—21no—
238C2×D4C4⋊Dic1911yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic3811yescharacteristic
243C22×C4D4×D1911yescharacteristic
244C22×C4#6454311yescharacteristic
245M16—382no—
246M16—761no—
247M16—762no—
248M16—762no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—381no—
256C2×C8—381no—
257C2×C8—382no—
258C2×C8—761no—
259C2×C8—761no—
260C2×C8—1522no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4C4⋊Dic1911yescharacteristic
264C4⋊C4C4⋊Dic1911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42C2×D7611yescharacteristic
272C42D4×D1911yescharacteristic
273C42#6454311yescharacteristic
274C42C22×Dic1911yescharacteristic
275C23—21no—
276C23#1059732411yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—21no—
280D4—42no—
281D4#1059727612yescomplemented
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4#1059732411yescharacteristic
297C2×C4#1059732811yescharacteristic
298C2×C4#1059733211yescharacteristic
299C2×C4C2×C4⋊Dic1911yescharacteristic
300C2×C4D4×Dic1911yescharacteristic
301C2×C4D4×Dic1911yescharacteristic
302C8—22no—
303C8—22no—
304C8—41no—
305C8—41no—
306C8—762no—
307C8—761no—
308C8—762no—
309C8—761no—
310C8—1521no—
311C22—21no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22#1192641911yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4C2×#1059727611yescharacteristic
325C4#1192659311yescharacteristic
326C4#1192666111yescharacteristic
327C4#1192666611yescharacteristic
328C4#1192671311yescharacteristic
329C4#1192672811yescharacteristic
330C2—41no—
331C2—42no—
332C2#1456384211yescharacteristic
333C2#1456386311yescharacteristic
334C2#1456391211yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1476C2
socleC22×C19#385
prime radicalC2×#41×C19Q8
cosocleC2×C42×C19C23
hypercenter#1476D19
hypocenterC19#8898
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #14563807C2semidirect
3. #14562424C2semidirect
5. #14561526C2semidirect
6. #14561472C2semidirect
114. D4×C19#108semidirect
233. C19#8898semidirect
281. D4#10597276semidirect

Maximal subgroups

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

subgroupindex
#145727602
#145638072
#145624242
#145620742
#145615262
#145614722
C19×#14762
#889819