Finite Group Databasebeta

← #18085155

Subgroups — #18085155

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926895C211yesmaximal, characteristic
2C2×#11926840C211yesmaximal, characteristic
3C2×#11926830C211yesmaximal, characteristic
4#14564571C211yesmaximal, characteristic
5C2×#11926292C211yesmaximal, characteristic
6C2×#11926289C211yesmaximal, characteristic
7C19×#1277C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597315C2211yescharacteristic
10C2×C4×Dic38C2211yescharacteristic
11#11926895—22no—
12#11926895—22no—
13#11926840—22no—
14#11926840—22no—
15#11926830—22no—
16#11926830—22no—
17C2×#10597275—21no—
18C2×#10597274—21no—
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20C2×#10597273—21no—
21C2×#10597273—21no—
22C2×#10597273—22no—
23#11926298—22no—
24#11926292—22no—
25#11926289—22no—
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C19×C4⋊C8C2211yescharacteristic
28C2×C4×C8×C19C2211yescharacteristic
29C22×Dic38—21no—
30C22×Dic38—21no—
31C22×Dic38D411yescharacteristic
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C22×C8×C19D412yes—
35C2×C42×C19C2311yescharacteristic
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19D411yescharacteristic
41C2×Dic19⋊C4—21no—
42C2×C4×Dic19—21no—
43C22×C19⋊C8—21no—
44#10597315—21no—
45#10597315—21no—
46#10597315—21no—
47#10597315—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315D412yes—
51#10597315D412yes—
52C4×Dic38—21no—
53C4×Dic38—21no—
54C4×Dic38—21no—
55C4×Dic38—21no—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8D412yes—
59C19×C4⋊C8D412yes—
60C4×C8×C19—21no—
61C4×C8×C19—21no—
62#10597275—24no—
63#10597274—24no—
64#10597273—24no—
65#10597273—24no—
66#10597273—28no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—21no—
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19#4111yescharacteristic
72C22×Dic19—21no—
73C22×Dic19—21no—
74C22×Dic19—41no—
75C22×Dic19—41no—
76C2×Dic38—21no—
77C2×Dic38—21no—
78C2×Dic38—21no—
79C2×Dic38—21no—
80C2×Dic38—21no—
81C2×Dic38—22no—
82C2×Dic38—22no—
83C2×Dic38—42no—
84C2×Dic38—42no—
85C2×Dic38—41no—
86C2×Dic38—41no—
87C2×Dic38—82no—
88C2×Dic38Q1612yes—
89C2×C8×C19—22no—
90C2×C8×C19—22no—
91C2×C8×C19—22no—
92C2×C8×C19—22no—
93C2×C8×C19—22no—
94C2×C8×C19—41no—
95C2×C8×C19—41no—
96C2×C8×C19—41no—
97C2×C8×C19—41no—
98C42×C19C2×D411yescharacteristic
99C42×C19C2×D411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C4⋊Dic19—22no—
103C4⋊Dic19—22no—
104C4⋊Dic19—22no—
105C4⋊Dic19—21no—
106C4⋊Dic19—21no—
107C4⋊Dic19—22no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19—41no—
112Dic19⋊C4—41no—
113Dic19⋊C4—41no—
114C4×Dic19—41no—
115C4×Dic19—41no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—42no—
118#10277—191nomaximal, Sylow
119C23×C19#12111yescharacteristic
120C2×C4×C19—22no—
121C2×C4×C19#12011yescharacteristic
122C2×C4×C19#12011yescharacteristic
123C2×C4×C19#12011yescharacteristic
124C2×C4×C19#12111yescharacteristic
125C2×C4×C19#12111yescharacteristic
126C2×C4×C19#12711yescharacteristic
127C2×C4×C19C2×Q1611yescharacteristic
128C2×C4×C19#13512yes—
129C2×C4×C19#13511yescharacteristic
130C2×C4×C19#13712yes—
131C2×C4×C19#13711yescharacteristic
132C2×C4×C19#13711yescharacteristic
133C2×Dic19—22no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—42no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140C2×Dic19—82no—
141C2×Dic19—82no—
142Dic38—22no—
143Dic38—22no—
144Dic38—41no—
145Dic38—41no—
146Dic38—44no—
147Dic38—82no—
148Dic38—81no—
149Dic38—81no—
150Dic38—82no—
151C8×C19—42no—
152C8×C19—42no—
153C8×C19—42no—
154C19⋊C8—81no—
155C2×#487—191no—
156C2×#477—191no—
157C2×#475—191no—
158#1984—191no—
159C2×#333—191no—
160C2×#332—191no—
161#1277D1911yescharacteristic
162C22×C19#39211yescharacteristic
163C22×C19#46412yes—
164C22×C19#46711yescharacteristic
165C22×C19#47011yescharacteristic
166C22×C19#47112yes—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19#45111yescharacteristic
170C4×C19#45111yescharacteristic
171C4×C19#45211yescharacteristic
172C4×C19#45211yescharacteristic
173C4×C19#45212yes—
174C4×C19#49511yescharacteristic
175C4×C19#49711yescharacteristic
176Dic19—42no—
177Dic19—82no—
178Dic19—82no—
179Dic19—81no—
180C2×C4⋊Q8—191no—
181C2×C4⋊Q8—191no—
182C2×C4×Q8—191no—
183#487—382no—
184#487—382no—
185#477—382no—
186#477—382no—
187#475—382no—
188#475—382no—
189C2×#107—381no—
190C2×#106—381no—
191C2×C4⋊C8—191no—
192C2×C4⋊C8C2×D1911yescharacteristic
193C2×C4⋊C8C2×D1911yescharacteristic
194C2×#103—381no—
195C2×#103—381no—
196C2×#103—382no—
197C2×C4×C8C2×D1911yescharacteristic
198#336—382no—
199#333—382no—
200#332—382no—
201C2×C19#168412yes—
202C2×C19#170412yes—
203C2×C19#200111yescharacteristic
204C2×C19#201511yescharacteristic
205C2×C19#201911yescharacteristic
206C22×Q8—191no—
207C22×Q8—381no—
208C22×Q8—381no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—381no—
212C22×C8D7612yes—
213C4⋊Q8—192no—
214C4⋊Q8—192no—
215C4⋊Q8—381no—
216C4⋊Q8—381no—
217C4⋊Q8—381no—
218C4⋊Q8—381no—
219C4⋊Q8—381no—
220C4⋊Q8—381no—
221C4×Q8—381no—
222C4×Q8—381no—
223C4×Q8—381no—
224C4×Q8—381no—
225C2×C4⋊C4—191no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4—381no—
231C2×C42—381no—
232C2×C42C22×D1911yescharacteristic
233#107—384no—
234#106—384no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—381no—
238C4⋊C8—381no—
239C4⋊C8D7612yes—
240C4⋊C8D7612yes—
241#103—384no—
242#103—384no—
243#103—388no—
244C4×C8—21no—
245C4×C8—21no—
246C19#1027711yescharacteristic, complemented, Sylow
247C2×Q8—192no—
248C2×Q8—381no—
249C2×Q8—381no—
250C2×Q8—381no—
251C2×Q8—382no—
252C2×Q8—382no—
253C2×Q8—381no—
254C2×Q8—381no—
255C2×Q8—761no—
256C2×Q8—761no—
257C2×Q8—762no—
258C2×Q8—762no—
259C2×Q8—1522no—
260C22×C4—381no—
261C22×C4—381no—
262C22×C4—761no—
263C22×C4—761no—
264C22×C4C2×D7611yescharacteristic
265C22×C4D4×D1911yescharacteristic
266C22×C4#6454511yescharacteristic
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—761no—
277C2×C8—762no—
278C4⋊C4—382no—
279C4⋊C4—382no—
280C4⋊C4—382no—
281C4⋊C4—381no—
282C4⋊C4—381no—
283C4⋊C4—382no—
284C4⋊C4—761no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—761no—
290C42—761no—
291C42—761no—
292C42C2×D7611yescharacteristic
293C42C2×D7611yescharacteristic
294C42D4×D1911yescharacteristic
295C42D4×D1911yescharacteristic
296C23#1059734111yescharacteristic
297Q8—382no—
298Q8—382no—
299Q8—761no—
300Q8—761no—
301Q8—764no—
302Q8—1522no—
303Q8—1522no—
304Q8—1521no—
305Q8—1521no—
306C2×C4—22no—
307C2×C4—382no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—762no—
311C2×C4—761no—
312C2×C4—762no—
313C2×C4—762no—
314C2×C4—1522no—
315C2×C4—1522no—
316C2×C4#1059732011yescharacteristic
317C2×C4#1059732811yescharacteristic
318C2×C4#1059732811yescharacteristic
319C2×C4#1059732811yescharacteristic
320C2×C4#1059734111yescharacteristic
321C2×C4#1059734111yescharacteristic
322C2×C4#1059735012yes—
323C2×C4#1059735512yes—
324C2×C4#1059735811yescharacteristic
325C2×C4#1059736111yescharacteristic
326C2×C4#1059736111yescharacteristic
327C2×C4Q16×D1911yescharacteristic
328C8—42no—
329C8—42no—
330C8—42no—
331C8—1521no—
332C22#1192645411yescharacteristic
333C22#1192676712yes—
334C22#1192678611yescharacteristic
335C22#1192680311yescharacteristic
336C22#1192680812yes—
337C4—21no—
338C4—21no—
339C4—762no—
340C4—1522no—
341C4—1521no—
342C4—1522no—
343C4#1192670111yescharacteristic
344C4#1192670111yescharacteristic
345C4#1192670711yescharacteristic
346C4#1192670711yescharacteristic
347C4#1192670812yes—
348C4#1192692811yescharacteristic
349C4#1192693811yescharacteristic
350C2#1456309412yes—
351C2#1456321812yes—
352C2#1456464611yescharacteristic
353C2#1456473211yescharacteristic
354C2#1456475211yescharacteristic
subgroupG/H
centerC23#10597341
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1277C2
socle, prime radicalC23×C19#121
hypercenter#1277D19
hypocenterC19#10277
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
246. C19#10277semidirect

Maximal subgroups

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

subgroupindex
C2×#119268952
C2×#119268402
C2×#119268302
#145645712
C2×#119262922
C2×#119262892
C19×#12772
#1027719