Finite Group Databasebeta

← #18078934

Subgroups — #18078934

Order 4864.

450 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926826C211yesmaximal, characteristic
2#14572586C211yesmaximal, characteristic
3#14564480C211yesmaximal, characteristic
4#14562065C211yesmaximal, characteristic
5#14561509C211yesmaximal, characteristic
6#14561484C211yesmaximal, characteristic
7C19×#1546C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9#11926826—21no—
10#11926826—21no—
11#11926826—21no—
12#11926826—21no—
13#11926673—22no—
14#11926671—21no—
15#11926668—21no—
16C2×#10597265C412yes—
17#11926568C2211yescharacteristic
18#11926567—21no—
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20C2×#10597267C412yes—
21C2×#10597293—21no—
22C2×#10597293—21no—
23C4×#64520C2211yescharacteristic
24M16×Dic19—21no—
25#11926276—21no—
26#11926276—21no—
27C2×C19×C4⋊Q8C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C19×#332—22no—
31C22×Q8×C19—21no—
32C22×Dic38C2×C411yescharacteristic
33C2×M16×C19—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19C2×C412yes—
40C2×C42×C19C2311yescharacteristic
41C2×C4⋊Dic19C2×C411yescharacteristic
42C2×Dic19⋊C4—21no—
43C2×C4×Dic19—21no—
44C2×#64520—21no—
45C2×#64520D411yescharacteristic
46C2×#64520D411yescharacteristic
47C22×C19⋊C8C2×C412yes—
48C4×Dic38—21no—
49C4×Dic38—21no—
50C4×Dic38D411yescharacteristic
51C4×Dic38D411yescharacteristic
52C4×Dic38D411yescharacteristic
53C4×Dic38D411yescharacteristic
54C19×C4⋊C8—21no—
55C19×C4⋊C8—21no—
56C19×C4⋊C8D412yes—
57C19×C22⋊C8—21no—
58C4×C8×C19—21no—
59#10597293—42no—
60#10597293—42no—
61#10597272—22no—
62Dic19⋊C8—22no—
63Dic19⋊C8—22no—
64C8×Dic19—22no—
65#10597267—22no—
66#10597267—22no—
67#10597265—22no—
68#10597265—22no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)—21no—
73#10597260—21no—
74C4×C19⋊C8—21no—
75C2×Q8×C19—41no—
76C2×Q8×C19—41no—
77C2×Q8×C19—41no—
78C2×Q8×C19—41no—
79C2×Q8×C19—41no—
80C2×Q8×C19—41no—
81C22×C4×C19—22no—
82C22×C4×C19C22×C411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19#4111yescharacteristic
85C22×Dic19—21no—
86C22×Dic19—21no—
87C2×Dic38—22no—
88C2×Dic38—21no—
89C2×Dic38—41no—
90C2×Dic38C22⋊C411yescharacteristic
91C2×Dic38C22⋊C411yescharacteristic
92M16×C19—41no—
93M16×C19—41no—
94C2×C8×C19—22no—
95C2×C8×C19—41no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19#4111yescharacteristic
104C4⋊Dic19—21no—
105C4⋊Dic19C22⋊C411yescharacteristic
106C4⋊Dic19C22⋊C411yescharacteristic
107Dic19⋊C4—21no—
108Dic19⋊C4—21no—
109Dic19⋊C4—21no—
110Dic19⋊C4—21no—
111C4×Dic19—21no—
112C4×Dic19—21no—
113C4×Dic19—21no—
114C4×Dic19—21no—
115#64520—21no—
116#64520—21no—
117#64520—21no—
118#64520—41no—
119#64520—41no—
120#64520SD1612yes—
121C2×C19⋊C8—21no—
122C2×C19⋊C8—22no—
123C2×C19⋊C8—21no—
124C2×C19⋊C8—42no—
125C2×C19⋊C8—41no—
126#9252—191nomaximal, Sylow
127C23×C19C4×D411yescharacteristic
128Q8×C19—81no—
129Q8×C19—81no—
130Q8×C19—81no—
131Q8×C19—81no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19C2×C22⋊C411yescharacteristic
139C2×C4×C19C4×D411yescharacteristic
140C2×C4×C19#12011yescharacteristic
141C2×C4×C19#12111yescharacteristic
142C2×C4×C19#12111yescharacteristic
143C2×C4×C19#12311yescharacteristic
144C2×C4×C19C2×SD1611yescharacteristic
145C2×C4×C19#13511yescharacteristic
146C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C19#13711yescharacteristic
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—42no—
153C2×Dic19—81no—
154Dic38—21no—
155Dic38—21no—
156Dic38—21no—
157Dic38—42no—
158Dic38#10112yescomplemented
159C8×C19—42no—
160C8×C19—81no—
161C19⋊C8—22no—
162C19⋊C8—42no—
163C19⋊C8—41no—
164C19⋊C8—81no—
165C2×#475—191no—
166Q8×M16—191no—
167#1966—191no—
168#1546D1911yescharacteristic
169#1487—191no—
170#1292—191no—
171#1283—191no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19#38611yescharacteristic
175C22×C19C4×SD1611yescharacteristic
176C22×C19#44011yescharacteristic
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—82no—
181C4×C19C2×#10111yescharacteristic
182C4×C19#41311yescharacteristic
183C4×C19#44811yescharacteristic
184C4×C19#44911yescharacteristic
185C4×C19#46011yescharacteristic
186C4×C19#46411yescharacteristic
187Dic19—22no—
188Dic19—41no—
189Dic19—41no—
190Dic19—41no—
191C2×C4⋊Q8C2×D1911yescharacteristic
192C2×C4×Q8—191no—
193#475—381no—
194#475—381no—
195#475—381no—
196#475—381no—
197#446—381no—
198#446—382no—
199C8×Q8—381no—
200#431C2×D1911yescharacteristic
201C2×#106—192no—
202#423—191no—
203#423—381no—
204#423C2×D1911yescharacteristic
205C2×C4⋊C8—191no—
206C2×#103—192no—
207C2×#101—381no—
208C2×#101—381no—
209C4×M16—191no—
210C4×M16—381no—
211#332—22no—
212Q8⋊C8—381no—
213Q8⋊C8—381no—
214C2×C19—21no—
215C2×C19—21no—
216C2×C19#188011yescharacteristic
217C2×C19#190111yescharacteristic
218C2×C19#190211yescharacteristic
219C22×Q8—21no—
220C22×Q8—191no—
221C2×M16—21no—
222C2×M16—191no—
223C2×M16—191no—
224C2×M16—381no—
225C22×C8—192no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4×Q8—191no—
231C4×Q8—191no—
232C4×Q8—191no—
233C4×Q8—191no—
234C4×Q8—381no—
235C4×Q8—381no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—191no—
238C2×C4⋊C4—381no—
239C2×C4⋊C4C4×D1912yes—
240C2×C42—381no—
241C2×C42C22×D1911yescharacteristic
242#106—382no—
243#106—382no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—382no—
247C4⋊C8—382no—
248C4⋊C8—381no—
249C4⋊C8—381no—
250C4⋊C8—381no—
251C4⋊C8—381no—
252C4⋊C8C22⋊D1912yes—
253#103—382no—
254#103—382no—
255#101—762no—
256#101—762no—
257C22⋊C8—21no—
258#97—382no—
259#97—381no—
260C4×C8—21no—
261C4×C8—382no—
262C4×C8—381no—
263C19#925211yescharacteristic, complemented, Sylow
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—191no—
271C2×Q8—191no—
272C2×Q8—382no—
273C2×Q8—381no—
274C2×Q8—761no—
275C22×C4—22no—
276C22×C4—381no—
277C22×C4—381no—
278C22×C4C2×C4×D1911yescharacteristic
279C22×C4D4×D1911yescharacteristic
280C22×C4#6454311yescharacteristic
281M16—41no—
282M16—41no—
283M16—192no—
284M16—381no—
285M16—381no—
286M16—381no—
287M16—761no—
288M16—761no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—381no—
292C2×C8—381no—
293C2×C8—382no—
294C2×C8—762no—
295C2×C8—761no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—191no—
301C4⋊C4—191no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C4⋊C4—381no—
305C4⋊C4—381no—
306C4⋊C4—381no—
307C42—381no—
308C42—381no—
309C42—381no—
310C42—381no—
311C42#6454111yescharacteristic
312C42D4×D1911yescharacteristic
313C42D4×D1911yescharacteristic
314C42C2×C22⋊D1911yescharacteristic
315C23(C22⋊D19)⋊C411yescharacteristic
316Q8—81no—
317Q8—81no—
318Q8—81no—
319Q8—81no—
320Q8—192no—
321Q8—381no—
322Q8—381no—
323Q8—381no—
324Q8—762no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—762no—
336C2×C4—1521no—
337C2×C4C22⋊C4×D1911yescharacteristic
338C2×C4#1059732911yescharacteristic
339C2×C4#1059733011yescharacteristic
340C2×C4#1059735711yescharacteristic
341C2×C4#1059735811yescharacteristic
342C2×C4SD16×D1911yescharacteristic
343C2×C4#1059736111yescharacteristic
344C2×C4C4×C22⋊D1911yescharacteristic
345C2×C4#1059738311yescharacteristic
346C2×C4#1059738411yescharacteristic
347C8—42no—
348C8—81no—
349C8—382no—
350C8—761no—
351C8—762no—
352C8—1521no—
353C22—21no—
354C22—21no—
355C22#1192642011yescharacteristic
356C22#1192663511yescharacteristic
357C22#1192664111yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—82no—
362C4—382no—
363C4—761no—
364C4—761no—
365C4—761no—
366C4#101×D1911yescharacteristic
367C4#1192652711yescharacteristic
368C4#1192668111yescharacteristic
369C4#1192668611yescharacteristic
370C4#1192674311yescharacteristic
371C4#1192676511yescharacteristic
372C2—21no—
373C2—21no—
374C2#1456398711yescharacteristic
375C2#1456410011yescharacteristic
376C2#1456410511yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1546C2
socleC22×C19#386
prime radicalC23×C19C4×D4
cosocleC2×C42×C19C23
hypercenter#1546D19
hypocenterC19#9252
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
158. Dic38#101semidirect
263. C19#9252semidirect

Maximal subgroups

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

subgroupindex
C2×#119268262
#145725862
#145644802
#145620652
#145615092
#145614842
C19×#15462
#925219