Finite Group Databasebeta

← #18074382

Subgroups — #18074382

Order 4864.

692 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14577040C211yesmaximal, characteristic
2#14562293C212yesmaximal, complemented
3#14562037C212yesmaximal, complemented
4#14561949C211yesmaximal, characteristic
5C19×#1798C211yesmaximal, characteristic
6#11927175—21no—
7#11927175C412yes—
8#11927172—22no—
9#11927172—22no—
10#11927170—21no—
11#11927170C412yes—
12#11927101—21no—
13#11927101C2212yes—
14#11927097—24no—
15C2×#10597372—21no—
16#11926597C2212yes—
17#11926292—22no—
18#11926289—22no—
19#11926274—24no—
20#11926270—21no—
21#11926268—21no—
22C2×C19×#117C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C2×C19×C22⋊C8—21no—
26C19×#336—21no—
27C23×C4×C19D411yescharacteristic
28C22×C8×C19—21no—
29C22×C8×C19—21no—
30C19×#117—22no—
31C19×#117—22no—
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C22⋊C4×C19C2×C411yescharacteristic
35C2×C22⋊C4×C19D411yescharacteristic
36C2×C42×C19D411yescharacteristic
37C2×C42×C19C2311yescharacteristic
38C2×C22⋊Dic19—22no—
39#10597372—22no—
40#10597372—22no—
41#10597372—22no—
42#10597372—22no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45#10597370—22no—
46#10597370—22no—
47#10597370—22no—
48#10597370C2×C414yes—
49C2×C4×Dic19—22no—
50#10597336—24no—
51#10597336—24no—
52#10597334—24no—
53#10597334—24no—
54#10597324—24no—
55#10597324—24no—
56#10597324—24no—
57#10597324—24no—
58#10597316—22no—
59#10597316—22no—
60#10597315—21no—
61#10597315—21no—
62#10597315D412yes—
63#10597315D412yes—
64C4×Dic38—22no—
65C4×Dic38—22no—
66C4×Dic38—22no—
67C4×Dic38D414yes—
68C19×C4⋊C8—22no—
69C19×C4⋊C8—22no—
70C19×C22⋊C8—42no—
71C22⋊(C19⋊C8)—22no—
72C4⋊(C19⋊C8)—22no—
73C4×C19⋊C8—22no—
74C24×C19C22⋊C411yescharacteristic
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22⋊C411yescharacteristic
82C22×C4×C19SD1612yes—
83C22×C4×C19Q1612yes—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×Dic19—22no—
88C22×Dic19—22no—
89C2×Dic38—22no—
90C2×Dic38—22no—
91C2×Dic38—22no—
92C2×Dic38C22⋊C414yes—
93C2×C8×C19—41no—
94C2×C8×C19—41no—
95C2×C8×C19—41no—
96C2×C8×C19—41no—
97C2×C8×C19—41no—
98C2×C8×C19—41no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—22no—
101C22⋊C4×C19—22no—
102C22⋊C4×C19—22no—
103C42×C19—21no—
104C42×C19—21no—
105C42×C19C2×D412yes—
106C42×C19C2×D412yes—
107C22⋊Dic19—24no—
108C22⋊Dic19—24no—
109C4⋊Dic19—22no—
110C4⋊Dic19—22no—
111C4⋊Dic19—22no—
112C4⋊Dic19—22no—
113C4⋊Dic19—22no—
114C4⋊Dic19—22no—
115C4⋊Dic19—22no—
116C4⋊Dic19C22⋊C414yes—
117Dic19⋊C4—24no—
118Dic19⋊C4—24no—
119Dic19⋊C4—24no—
120Dic19⋊C4—24no—
121C4×Dic19—24no—
122C4×Dic19—24no—
123C2×C19⋊C8—42no—
124#8410—191nomaximal, Sylow
125C23×C19—21no—
126C23×C19—21no—
127C23×C19—41no—
128C23×C19—41no—
129C23×C19#10312yes—
130C23×C19C2×C22⋊C411yescharacteristic
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—22no—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19#10312yes—
144C2×C4×C19C2×C22⋊C412yes—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12012yes—
148C2×C4×C19C2×SD1611yescharacteristic
149C2×C4×C19C2×Q1611yescharacteristic
150C2×C4×C19#13711yescharacteristic
151C2×C4×C19#13711yescharacteristic
152C2×Dic19—24no—
153C2×Dic19—24no—
154C2×Dic19—82no—
155C2×Dic19—82no—
156Dic38—44no—
157Dic38—82no—
158Dic38—82no—
159Dic38—82no—
160C8×C19—81no—
161C8×C19—81no—
162C19⋊C8—82no—
163#3458—191no—
164#1798D1911yescharacteristic
165#1542—192no—
166#1481—192no—
167#1458—191no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—22no—
171C22×C19—42no—
172C22×C19—41no—
173C22×C19—41no—
174C22×C19—81no—
175C22×C19#37911yescharacteristic
176C22×C19C2×#10311yescharacteristic
177C22×C19#41911yescharacteristic
178C4×C19—22no—
179C4×C19—22no—
180C4×C19—22no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19#44811yescharacteristic
184C4×C19#44811yescharacteristic
185C4×C19#45111yescharacteristic
186C4×C19#45111yescharacteristic
187Dic19—44no—
188Dic19—44no—
189#544—192no—
190#544—382no—
191#544—382no—
192#544—381no—
193#543—192no—
194#543—381no—
195#533—192no—
196#533—384no—
197#533—381no—
198C2×#117—381no—
199C2×#117C2×D1911yescharacteristic
200#431—192no—
201C2×C4⋊C8C2×D1911yescharacteristic
202C2×C4⋊C8C2×D1911yescharacteristic
203C2×C22⋊C8—21no—
204#336—21no—
205#333—382no—
206#332—382no—
207Q8⋊C8—384no—
208#324—381no—
209#323—381no—
210C2×C19—21no—
211C2×C19—21no—
212C2×C19—42no—
213C2×C19#178711yescharacteristic
214C2×C19#179111yescharacteristic
215C2×C19#179411yescharacteristic
216C23×C4C22⋊D1911yescharacteristic
217C22×C8—21no—
218C22×C8—21no—
219C4⋊Q8—192no—
220C4⋊Q8—192no—
221C4⋊Q8—381no—
222C4⋊Q8—381no—
223C4⋊Q8—384no—
224C4⋊Q8—384no—
225#125—382no—
226#125—384no—
227#125—384no—
228#125—382no—
229C22⋊Q8—194no—
230C22⋊Q8—384no—
231C22⋊Q8—384no—
232C22⋊Q8—384no—
233C22⋊Q8—384no—
234C22⋊Q8—382no—
235C22⋊Q8—382no—
236C22⋊Q8—382no—
237C4×Q8—194no—
238C4×Q8—382no—
239C4×Q8—382no—
240C4×Q8—382no—
241#117—22no—
242#117—22no—
243#117—382no—
244#117—382no—
245#117—382no—
246#117—382no—
247C2×C4⋊C4—381no—
248C2×C4⋊C4—381no—
249C2×C4⋊C4C4×D1911yescharacteristic
250C2×C4⋊C4D7611yescharacteristic
251C2×C22⋊C4—382no—
252C2×C22⋊C4C4×D1911yescharacteristic
253C2×C22⋊C4D7611yescharacteristic
254C2×C42—382no—
255C2×C42C22⋊D1911yescharacteristic
256C2×C42C22×D1911yescharacteristic
257C4⋊C8—22no—
258C4⋊C8—22no—
259C4⋊C8—382no—
260C22⋊C8—42no—
261C22⋊C8—382no—
262C4×C8—382no—
263C19#841011yescharacteristic, complemented, Sylow
264C24(C2×D19)⋊C411yescharacteristic
265C2×Q8—194no—
266C2×Q8—382no—
267C2×Q8—382no—
268C2×Q8—382no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—382no—
274C22×C4—382no—
275C22×C4(C2×D19)⋊C411yescharacteristic
276C22×C4(C2×D19)⋊C411yescharacteristic
277C22×C4(C2×D19)⋊C411yescharacteristic
278C22×C4#6452612yes—
279C22×C4#6452812yes—
280C22×C4C2×C4×D1911yescharacteristic
281C22×C4C2×D7611yescharacteristic
282C22×C4C2×C22⋊D1911yescharacteristic
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—762no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—194no—
293C4⋊C4—384no—
294C4⋊C4—384no—
295C4⋊C4—382no—
296C4⋊C4—382no—
297C4⋊C4—382no—
298C4⋊C4—382no—
299C4⋊C4—382no—
300C4⋊C4—382no—
301C4⋊C4—384no—
302C4⋊C4—384no—
303C4⋊C4—382no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—384no—
307C22⋊C4—384no—
308C42—21no—
309C42—21no—
310C42—384no—
311C42—384no—
312C42D4×D1912yes—
313C42D4×D1912yes—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23#1059726712yes—
319C23C2×(C2×D19)⋊C411yescharacteristic
320Q8—764no—
321Q8—1522no—
322Q8—1522no—
323Q8—1522no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—384no—
337C2×C4—384no—
338C2×C4—1522no—
339C2×C4—1522no—
340C2×C4#1059726712yes—
341C2×C4C22⋊C4×D1912yes—
342C2×C4#1059732812yes—
343C2×C4C2×#6452611yescharacteristic
344C2×C4#1059738311yescharacteristic
345C2×C4#1059738311yescharacteristic
346C2×C4C2×#6452811yescharacteristic
347C2×C4#1059739711yescharacteristic
348C2×C4#1059739711yescharacteristic
349C8—81no—
350C8—81no—
351C8—1522no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22#1192639911yescharacteristic
360C22C2×#1059726711yescharacteristic
361C22#1192655211yescharacteristic
362C4—22no—
363C4—22no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—764no—
368C4—764no—
369C4#1192668211yescharacteristic
370C4#1192668211yescharacteristic
371C4#1192669911yescharacteristic
372C4#1192669911yescharacteristic
373C2—21no—
374C2—21no—
375C2—42no—
376C2#1456356911yescharacteristic
377C2#1456358511yescharacteristic
378C2#1456359811yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1798C2
socleC22×C19#379
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1798D19
hypocenterC19#8410
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #14562293C2semidirect
3. #14562037C2semidirect
263. C19#8410semidirect

Maximal subgroups

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

subgroupindex
#145770402
#145622932
#145620372
#145619492
C19×#17982
#841019