Finite Group Databasebeta

← #18083854

Subgroups — #18083854

Order 4864.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926950C211yesmaximal, characteristic
2#14571702C211yesmaximal, characteristic
3#14564609C211yesmaximal, characteristic
4C2×#11926286C211yesmaximal, characteristic
5C2×#11926285C211yesmaximal, characteristic
6#14561517C211yesmaximal, characteristic
7C2×C19×#491C211yesmaximal, characteristic
8C2×#10597316C2211yescharacteristic
9#11926950—22no—
10#11926950—22no—
11C2×#10597264—21no—
12C2×#10597265—21no—
13C2×#10597260C2211yescharacteristic
14C2×#10597260C2211yescharacteristic
15#11926483—21no—
16#11926482—21no—
17#11926477—22no—
18#11926475—21no—
19#11926474—21no—
20#11926410C2211yescharacteristic
21#11926306—22no—
22#11926286—22no—
23#11926285—22no—
24C2×C19×C4⋊Q8C2211yescharacteristic
25C2×C19×#125C2211yescharacteristic
26C19×#491—22no—
27C19×#491—22no—
28C2×C19×#103—21no—
29C2×C19×#103—21no—
30C2×C19×#97C2211yescharacteristic
31C22×Q8×C19—21no—
32C22×C8×C19—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8D412yes—
37C19×#125—21no—
38C19×#125—21no—
39C19×#125—21no—
40C19×#125—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19D411yescharacteristic
46C2×C4⋊C4×C19D411yescharacteristic
47C2×C42×C19C2311yescharacteristic
48C2×C4⋊Dic19D411yescharacteristic
49C2×C4⋊Dic19D411yescharacteristic
50C2×C4⋊Dic19D412yes—
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—21no—
53C2×Dic19⋊C4—22no—
54C22×C19⋊C8—21no—
55C22×C19⋊C8—21no—
56#10597316—21no—
57#10597316—21no—
58#10597316—21no—
59#10597316—21no—
60C19×#103—24no—
61C19×#103—24no—
62C19×#97—21no—
63C19×#97D412yes—
64C19⋊#95—22no—
65C19⋊#95—22no—
66C19⋊#95—22no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69#10597265—24no—
70#10597264—24no—
71#10597260—21no—
72#10597260—21no—
73#10597260—21no—
74#10597260D412yes—
75C2×Q8×C19—22no—
76C2×Q8×C19—44no—
77C2×Q8×C19—41no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—41no—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×Dic19—22no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C2×C8×C19—22no—
88C2×C8×C19—42no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—22no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C4⋊C4×C19—41no—
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19C2×D411yescharacteristic
104C42×C19#4111yescharacteristic
105C4⋊Dic19—21no—
106C4⋊Dic19—21no—
107C4⋊Dic19—21no—
108C4⋊Dic19—21no—
109C4⋊Dic19—42no—
110Dic19⋊C4—41no—
111Dic19⋊C4—41no—
112Dic19⋊C4—41no—
113Dic19⋊C4—41no—
114Dic19⋊C4—82no—
115C2×C19⋊C8—24no—
116C2×C19⋊C8—22no—
117C2×C19⋊C8—22no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120#10084—191nomaximal, Sylow
121C23×C19#12011yescharacteristic
122Q8×C19—44no—
123Q8×C19—82no—
124C2×C4×C19—22no—
125C2×C4×C19—21no—
126C2×C4×C19—22no—
127C2×C4×C19—21no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—41no—
132C2×C4×C19—42no—
133C2×C4×C19—41no—
134C2×C4×C19—82no—
135C2×C4×C19#12011yescharacteristic
136C2×C4×C19#12011yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19#12111yescharacteristic
139C2×C4×C19#12111yescharacteristic
140C2×C4×C19#12711yescharacteristic
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—42no—
144C2×Dic19—42no—
145C2×Dic19—41no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—41no—
149C8×C19—42no—
150C19⋊C8—24no—
151C19⋊C8—42no—
152C2×#501—191no—
153C2×#491D1911yescharacteristic
154#2822—191no—
155#1993—191no—
156C2×#330—191no—
157C2×#330—191no—
158#1295—191no—
159C22×C19#39211yescharacteristic
160C22×C19#45412yes—
161C22×C19#45511yescharacteristic
162C22×C19#45611yescharacteristic
163C22×C19#45612yes—
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—82no—
171C4×C19—81no—
172C4×C19—81no—
173Dic19—82no—
174Dic19—81no—
175Dic19—81no—
176C2×C4⋊Q8C2×D1911yescharacteristic
177C2×#125—191no—
178C2×#125C2×D1911yescharacteristic
179#501—382no—
180#501—382no—
181#491—22no—
182#491—22no—
183C2×#107—381no—
184C2×#106—381no—
185C2×#103—21no—
186C2×#103—21no—
187C2×#97—191no—
188C2×#97—191no—
189C2×#97C2×D1911yescharacteristic
190#400—381no—
191#400—381no—
192#398—381no—
193#398—382no—
194#398—381no—
195#382—191no—
196#340—382no—
197#330—382no—
198#330—382no—
199C2×C19#166312yes—
200C2×C19#166412yes—
201C2×C19#200311yescharacteristic
202C2×C19#200511yescharacteristic
203C2×C19#200711yescharacteristic
204C22×Q8—21no—
205C22×C8—21no—
206C22×C8—381no—
207C22×C8—381no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8C22⋊D1912yes—
212#125—21no—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—381no—
217#125—381no—
218#125—381no—
219#125—381no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—191no—
226C2×C4⋊C4—192no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—382no—
230C2×C4⋊C4C22⋊D1911yescharacteristic
231C2×C4⋊C4C22⋊D1911yescharacteristic
232C2×C42C22×D1911yescharacteristic
233#107—384no—
234#106—384no—
235#103—24no—
236#103—24no—
237#97—21no—
238#97—192no—
239#97—381no—
240#97—381no—
241#97—381no—
242#97C22⋊D1912yes—
243#95—382no—
244#95—382no—
245#95—382no—
246#95—381no—
247#95—381no—
248C19#1008411yescharacteristic, complemented, Sylow
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—382no—
256C22×C4—381no—
257C22×C4—381no—
258C22×C4D4×D1911yescharacteristic
259C22×C4D4×D1911yescharacteristic
260C22×C4C2×C22⋊D1911yescharacteristic
261C2×C8—22no—
262C2×C8—42no—
263C2×C8—384no—
264C2×C8—382no—
265C2×C8—382no—
266C2×C8—761no—
267C2×C8—761no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—381no—
281C4⋊C4—381no—
282C4⋊C4—381no—
283C4⋊C4—381no—
284C4⋊C4—762no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—1522no—
290C42D4×D1911yescharacteristic
291C42#6454311yescharacteristic
292C42C2×C22⋊D1911yescharacteristic
293C42C2×C22⋊D1911yescharacteristic
294C23#1059738311yescharacteristic
295Q8—44no—
296Q8—82no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—82no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—762no—
311C2×C4—762no—
312C2×C4—762no—
313C2×C4—761no—
314C2×C4—761no—
315C2×C4—762no—
316C2×C4#1059738311yescharacteristic
317C2×C4#1059738411yescharacteristic
318C2×C4#1059738511yescharacteristic
319C2×C4#1059738511yescharacteristic
320C2×C4#1059738611yescharacteristic
321C2×C4#1059739911yescharacteristic
322C8—42no—
323C8—384no—
324C8—762no—
325C22#1192645211yescharacteristic
326C22#1192671612yes—
327C22#1192672011yescharacteristic
328C22#1192672512yes—
329C22#1192672511yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—81no—
338C4—81no—
339C4—1521no—
340C4—1521no—
341C4—1522no—
342C2#1456296112yes—
343C2#1456296612yes—
344C2#1456465711yescharacteristic
345C2#1456466811yescharacteristic
346C2#1456468011yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#491C2
socle, prime radicalC23×C19#120
hypercenterC2×#491D19
hypocenterC19#10084
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
248. C19#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#119269502
#145717022
#145646092
C2×#119262862
C2×#119262852
#145615172
C2×C19×#4912
#1008419