Finite Group Databasebeta

← #18083859

Subgroups — #18083859

Order 4864.

484 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11926954C211yesmaximal, characteristic
2C2×#11926913C211yesmaximal, characteristic
3#14571702C211yesmaximal, characteristic
4#14564608C211yesmaximal, characteristic
5C2×#11926285C211yesmaximal, characteristic
6#14561517C211yesmaximal, characteristic
7C2×C19×#330C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597316C2211yescharacteristic
10#11926954—22no—
11#11926954—22no—
12#11926913—22no—
13#11926913—22no—
14C2×#10597264—21no—
15C2×#10597265—21no—
16C2×#10597273—21no—
17C2×#10597273—21no—
18C2×#10597260C2211yescharacteristic
19#11926483—21no—
20#11926482—21no—
21#11926477—22no—
22#11926475—21no—
23#11926474—21no—
24#11926410C2211yescharacteristic
25#11926307—22no—
26#11926285—22no—
27C2×C19×#125C2211yescharacteristic
28C2×C19×#97C2211yescharacteristic
29C2×C19×#97C2211yescharacteristic
30C19×#330—22no—
31C22×Dic38—21no—
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C19×#125—21no—
35C19×#125—21no—
36C19×#125—21no—
37C19×#125—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19D411yescharacteristic
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C42×C19C2311yescharacteristic
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19D411yescharacteristic
46C2×C4⋊Dic19D411yescharacteristic
47C2×C4⋊Dic19D412yes—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—22no—
51C22×C19⋊C8—21no—
52#10597316—21no—
53#10597316—21no—
54#10597316—21no—
55#10597316—21no—
56#10597315—21no—
57#10597315—21no—
58#10597315—21no—
59#10597315D412yes—
60C19×#97—21no—
61C19×#97—21no—
62C19×#97—21no—
63C19×#97D412yes—
64C19⋊#95—22no—
65C19⋊#95—22no—
66C19⋊#95—22no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69#10597273—24no—
70#10597273—24no—
71#10597265—24no—
72#10597264—24no—
73#10597260—21no—
74#10597260D412yes—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×Dic19—22no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—41no—
84C2×Dic38—22no—
85C2×Dic38—44no—
86C2×Dic38—41no—
87C2×C8×C19—22no—
88C2×C8×C19—22no—
89C2×C8×C19—42no—
90C2×C8×C19—41no—
91C2×C8×C19—41no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19#4111yescharacteristic
104C4⋊Dic19—22no—
105C4⋊Dic19—21no—
106C4⋊Dic19—21no—
107C4⋊Dic19—22no—
108C4⋊Dic19—21no—
109C4⋊Dic19—21no—
110C4⋊Dic19—41no—
111C4⋊Dic19—41no—
112C4⋊Dic19—42no—
113Dic19⋊C4—41no—
114Dic19⋊C4—41no—
115Dic19⋊C4—41no—
116Dic19⋊C4—41no—
117Dic19⋊C4—82no—
118C2×C19⋊C8—24no—
119C2×C19⋊C8—22no—
120#10084—191nomaximal, Sylow
121C23×C19#12011yescharacteristic
122C2×C4×C19—22no—
123C2×C4×C19—21no—
124C2×C4×C19—22no—
125C2×C4×C19—21no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19#12011yescharacteristic
132C2×C4×C19#12011yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12111yescharacteristic
135C2×C4×C19#12111yescharacteristic
136C2×C4×C19#12711yescharacteristic
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—41no—
142C2×Dic19—42no—
143C2×Dic19—41no—
144C2×Dic19—42no—
145C2×Dic19—42no—
146C2×Dic19—82no—
147Dic38—44no—
148Dic38—82no—
149C8×C19—42no—
150C8×C19—42no—
151C19⋊C8—24no—
152C2×#501—191no—
153C2×#491—191no—
154#2822—191no—
155#1993—191no—
156C2×#330—191no—
157C2×#330D1911yescharacteristic
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—81no—
171C4×C19—81no—
172Dic19—82no—
173Dic19—82no—
174Dic19—81no—
175Dic19—81no—
176C2×C4⋊Q8—191no—
177C2×#125—191no—
178C2×#125C2×D1911yescharacteristic
179#501—382no—
180#501—382no—
181#491—382no—
182#491—382no—
183C2×#107—381no—
184C2×#106—381no—
185C2×#103—381no—
186C2×#103—381no—
187C2×#97—191no—
188C2×#97C2×D1911yescharacteristic
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—22no—
198#330—382no—
199C2×C19#166312yes—
200C2×C19#166412yes—
201C2×C19#200311yescharacteristic
202C2×C19#200511yescharacteristic
203C2×C19#200711yescharacteristic
204C22×Q8—381no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—381no—
208C4⋊Q8—192no—
209C4⋊Q8—381no—
210C4⋊Q8—381no—
211C4⋊Q8—381no—
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—191no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—192no—
225C2×C4⋊C4—381no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—382no—
230C2×C4⋊C4D7611yescharacteristic
231C2×C4⋊C4D7611yescharacteristic
232C2×C42C22×D1911yescharacteristic
233#107—384no—
234#106—384no—
235#103—384no—
236#103—384no—
237#97—21no—
238#97—21no—
239#97—21no—
240#97—192no—
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—382no—
250C2×Q8—764no—
251C2×Q8—761no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—382no—
255C22×C4—381no—
256C22×C4—381no—
257C22×C4—761no—
258C22×C4C2×D7611yescharacteristic
259C22×C4D4×D1911yescharacteristic
260C22×C4D4×D1911yescharacteristic
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—42no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—384no—
267C2×C8—382no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—381no—
277C4⋊C4—381no—
278C4⋊C4—382no—
279C4⋊C4—381no—
280C4⋊C4—381no—
281C4⋊C4—382no—
282C4⋊C4—762no—
283C4⋊C4—761no—
284C4⋊C4—761no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—1522no—
290C42#6454111yescharacteristic
291C42D4×D1911yescharacteristic
292C42D4×D1911yescharacteristic
293C42C2×C22⋊D1911yescharacteristic
294C23#1059732811yescharacteristic
295Q8—764no—
296Q8—1522no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—761no—
307C2×C4—761no—
308C2×C4—762no—
309C2×C4—762no—
310C2×C4—762no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4—762no—
314C2×C4—762no—
315C2×C4—1522no—
316C2×C4#1059732811yescharacteristic
317C2×C4#1059733011yescharacteristic
318C2×C4#1059733011yescharacteristic
319C2×C4#1059737611yescharacteristic
320C2×C4#1059738311yescharacteristic
321C2×C4#1059738611yescharacteristic
322C8—42no—
323C8—42no—
324C8—384no—
325C22#1192645311yescharacteristic
326C22#1192671812yes—
327C22#1192672311yescharacteristic
328C22#1192672811yescharacteristic
329C22#1192672912yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—1522no—
339C4—1521no—
340C4—1521no—
341C4—1522no—
342C2#1456296512yes—
343C2#1456297112yes—
344C2#1456465611yescharacteristic
345C2#1456467311yescharacteristic
346C2#1456468311yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#330C2
socle, prime radicalC23×C19#120
hypercenterC2×#330D19
hypocenterC19#10084
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

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×#119269542
C2×#119269132
#145717022
#145646082
C2×#119262852
#145615172
C2×C19×#3302
#1008419