Finite Group Databasebeta

← #18085161

Subgroups — #18085161

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926947C211yesmaximal, characteristic
2C2×#11926839C211yesmaximal, characteristic
3#14564572C211yesmaximal, characteristic
4C2×#11926293C211yesmaximal, characteristic
5C2×#11926292C211yesmaximal, characteristic
6#14561469C211yesmaximal, characteristic
7C2×C19×#477C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9#11926947—22no—
10#11926947—22no—
11#11926839—22no—
12#11926839—22no—
13C2×#10597264—22no—
14C2×#10597264—21no—
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×C4⋊(C19⋊C8)C2211yescharacteristic
17C2×#10597292—21no—
18C2×C4×C19⋊C8C2211yescharacteristic
19#11926299—22no—
20#11926293—22no—
21#11926292—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C4×Q8×C19C2211yescharacteristic
24C19×#477—22no—
25C19×#477—22no—
26C2×C19×#107—21no—
27C2×C19×C4⋊C8C2211yescharacteristic
28C2×C19×#103—21no—
29C22×Q8×C19—21no—
30C22×Q8×C19D411yescharacteristic
31C22×Dic38—21no—
32C22×C8×C19—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8D412yes—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51C22×C19⋊C8D412yes—
52#10597315—21no—
53#10597315—21no—
54#10597315—21no—
55#10597315D412yes—
56C19×#107—24no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8D412yes—
59C19×#103—24no—
60#10597292—24no—
61#10597264—24no—
62#10597264—28no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)D412yes—
67C4×C19⋊C8—21no—
68C4×C19⋊C8—21no—
69C2×Q8×C19—21no—
70C2×Q8×C19—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—22no—
73C2×Q8×C19—21no—
74C2×Q8×C19—21no—
75C2×Q8×C19—41no—
76C2×Q8×C19—82no—
77C2×Q8×C19Q1612yes—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—41no—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×Dic19—41no—
85C2×Dic38—22no—
86C2×Dic38—41no—
87C2×Dic38—82no—
88C2×C8×C19—22no—
89C2×C8×C19—41no—
90C2×C8×C19—41no—
91C4⋊C4×C19—22no—
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—
99C42×C19—41no—
100C42×C19—41no—
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19C2×D411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C4⋊Dic19—22no—
106C4⋊Dic19—22no—
107C4⋊Dic19—41no—
108C4⋊Dic19—41no—
109C2×C19⋊C8—22no—
110C2×C19⋊C8—22no—
111C2×C19⋊C8—22no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—41no—
115C2×C19⋊C8—42no—
116C2×C19⋊C8Q1614yes—
117#10279—191nomaximal, Sylow
118C23×C19#12111yescharacteristic
119Q8×C19—22no—
120Q8×C19—22no—
121Q8×C19—41no—
122Q8×C19—41no—
123Q8×C19—82no—
124Q8×C19—82no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19—82no—
133C2×C4×C19#12011yescharacteristic
134C2×C4×C19#12011yescharacteristic
135C2×C4×C19#12011yescharacteristic
136C2×C4×C19#12111yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19#12711yescharacteristic
139C2×C4×C19C2×Q1611yescharacteristic
140C2×C4×C19C2×Q1612yes—
141C2×C4×C19#13511yescharacteristic
142C2×C4×C19#13711yescharacteristic
143C2×C4×C19#13711yescharacteristic
144C2×C4×C19#13712yes—
145C2×Dic19—42no—
146C2×Dic19—82no—
147Dic38—82no—
148Dic38—82no—
149C8×C19—42no—
150C19⋊C8—24no—
151C19⋊C8—42no—
152C19⋊C8—81no—
153C2×#500—191no—
154C2×#477—191no—
155C2×#477D1911yescharacteristic
156#1984—191no—
157C2×#333—191no—
158C2×#333—191no—
159#1277—191no—
160C22×C19#39211yescharacteristic
161C22×C19#46212yes—
162C22×C19#46711yescharacteristic
163C22×C19#47011yescharacteristic
164C22×C19#47212yes—
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—42no—
168C4×C19—81no—
169C4×C19—82no—
170C4×C19#45112yes—
171C4×C19#45111yescharacteristic
172C4×C19#45111yescharacteristic
173C4×C19#45211yescharacteristic
174C4×C19#45211yescharacteristic
175C4×C19#49411yescharacteristic
176C4×C19#49711yescharacteristic
177Dic19—82no—
178C2×C4⋊Q8—191no—
179C2×C4⋊Q8C2×D1911yescharacteristic
180C2×C4×Q8C2×D1911yescharacteristic
181#500—382no—
182#500—382no—
183#477—22no—
184#477—22no—
185#477—382no—
186#477—382no—
187C2×#107—21no—
188C2×#107—382no—
189C2×#107—381no—
190C2×C4⋊C8—191no—
191C2×C4⋊C8—191no—
192C2×C4⋊C8C2×D1911yescharacteristic
193C2×#103—21no—
194C2×#103—381no—
195C2×C4×C8—191no—
196#336—382no—
197#333—382no—
198#333—382no—
199C2×C19#167612yes—
200C2×C19#169612yes—
201C2×C19#200111yescharacteristic
202C2×C19#201611yescharacteristic
203C2×C19#201811yescharacteristic
204C22×Q8—21no—
205C22×Q8—381no—
206C22×Q8C22⋊D1911yescharacteristic
207C22×C8—21no—
208C22×C8—192no—
209C22×C8—381no—
210C22×C8—381no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—192no—
215C4⋊Q8—381no—
216C4⋊Q8—381no—
217C4⋊Q8—381no—
218C4⋊Q8C22⋊D1912yes—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4C22⋊D1911yescharacteristic
229C2×C42—21no—
230C2×C42C22×D1911yescharacteristic
231#107—24no—
232#107—384no—
233#107—388no—
234C4⋊C8—21no—
235C4⋊C8—192no—
236C4⋊C8—381no—
237C4⋊C8—381no—
238C4⋊C8—381no—
239C4⋊C8C22⋊D1912yes—
240#103—24no—
241#103—384no—
242C4×C8—381no—
243C4×C8—381no—
244C19#1027911yescharacteristic, complemented, Sylow
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—41no—
252C2×Q8—82no—
253C2×Q8—382no—
254C2×Q8—761no—
255C2×Q8—1522no—
256C2×Q8#6452812yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—761no—
261C22×C4D4×D1911yescharacteristic
262C22×C4#6454311yescharacteristic
263C22×C4C2×C22⋊D1911yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—194no—
268C2×C8—382no—
269C2×C8—382no—
270C2×C8—382no—
271C2×C8—761no—
272C2×C8—761no—
273C2×C8—761no—
274C2×C8—762no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—382no—
284C4⋊C4—382no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C42—41no—
288C42—41no—
289C42D4×D1911yescharacteristic
290C42D4×D1911yescharacteristic
291C42C2×C22⋊D1911yescharacteristic
292C42C2×C22⋊D1911yescharacteristic
293C23#1059738511yescharacteristic
294Q8—22no—
295Q8—22no—
296Q8—41no—
297Q8—41no—
298Q8—82no—
299Q8—82no—
300Q8—1522no—
301Q8—1522no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—762no—
311C2×C4—1522no—
312C2×C4Q16×D1912yes—
313C2×C4#1059736412yes—
314C2×C4#1059738311yescharacteristic
315C2×C4#1059738311yescharacteristic
316C2×C4#1059738411yescharacteristic
317C2×C4#1059738511yescharacteristic
318C2×C4#1059738611yescharacteristic
319C2×C4#1059738811yescharacteristic
320C2×C4C2×#6452811yescharacteristic
321C2×C4#1059739611yescharacteristic
322C2×C4#1059739711yescharacteristic
323C2×C4#1059739911yescharacteristic
324C8—42no—
325C8—384no—
326C8—762no—
327C8—1521no—
328C22#1192645211yescharacteristic
329C22#1192675212yes—
330C22#1192678311yescharacteristic
331C22#1192680011yescharacteristic
332C22#1192681212yes—
333C4—21no—
334C4—21no—
335C4—42no—
336C4—81no—
337C4—82no—
338C4—1522no—
339C4#1192669812yes—
340C4#1192669911yescharacteristic
341C4#1192670011yescharacteristic
342C4#1192670411yescharacteristic
343C4#1192670611yescharacteristic
344C4#1192692211yescharacteristic
345C4#1192693711yescharacteristic
346C2#1456303712yes—
347C2#1456316112yes—
348C2#1456464311yescharacteristic
349C2#1456473311yescharacteristic
350C2#1456474111yescharacteristic
subgroupG/H
centerC23#10597385
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#477C2
socle, prime radicalC23×C19#121
hypercenterC2×#477D19
hypocenterC19#10279
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
244. C19#10279semidirect

Maximal subgroups

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

subgroupindex
C2×#119269472
C2×#119268392
#145645722
C2×#119262932
C2×#119262922
#145614692
C2×C19×#4772
#1027919