Finite Group Databasebeta

← #18077782

Subgroups — #18077782

Order 4864.

432 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574221C211yesmaximal, characteristic
2#14572582C211yesmaximal, characteristic
3#14564579C211yesmaximal, characteristic
4#14562135C211yesmaximal, characteristic
5#14562039C211yesmaximal, characteristic
6#14561475C211yesmaximal, characteristic
7C19×#1278C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11927101C2211yescharacteristic
10#11926949C411yescharacteristic, complemented
11#11926924C411yescharacteristic, complemented
12#11926895C411yescharacteristic, complemented
13#11926895C411yescharacteristic, complemented
14#11926785—22no—
15#11926674—21no—
16#11926672—22no—
17C8×Dic38—21no—
18C4×Dic76—22no—
19#11926572—21no—
20C2×C4⋊(C19⋊C8)C2211yescharacteristic
21#11926502—21no—
22C4×C4⋊Dic19C2211yescharacteristic
23#11926305—21no—
24#11926305—21no—
25#11926282—22no—
26#11926276—21no—
27#11926276—21no—
28C19×#431C2211yescharacteristic
29C4×M16×C19C2211yescharacteristic
30C2×C4×C8×C19C2211yescharacteristic
31C2×M16×C19D411yescharacteristic
32C2×M16×C19D411yescharacteristic
33C22×C8×C19—21no—
34C2×C42×C19C2311yescharacteristic
35#10597372—21no—
36#10597372—21no—
37C2×C4⋊Dic19—21no—
38#10597370—21no—
39#10597370—21no—
40#10597370—21no—
41#10597370D412yes—
42C2×C4×Dic19—21no—
43C22×C19⋊C8—21no—
44C2×Dic76—22no—
45#10597316—21no—
46#10597316—21no—
47#10597315C2×C411yescharacteristic
48#10597315C2×C411yescharacteristic
49#10597315C2×C411yescharacteristic
50#10597315C2×C411yescharacteristic
51C4×Dic38—21no—
52C4×Dic38—21no—
53C4×Dic38—21no—
54C4×Dic38D412yes—
55C19×C4⋊C8—21no—
56C19×C22⋊C8—21no—
57C19×#97—21no—
58C4×C8×C19—21no—
59C4×C8×C19—21no—
60C4×C8×C19—21no—
61C4×C8×C19C2×C411yescharacteristic
62C4×C8×C19C2×C411yescharacteristic
63C19⋊#95—21no—
64#10597275—22no—
65#10597273—22no—
66#10597273—22no—
67#10597272—22no—
68Dic19⋊C8—22no—
69Dic19⋊C8—22no—
70C8×Dic19—22no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)D411yescharacteristic
73C4⋊(C19⋊C8)D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19#4111yescharacteristic
77C22×Dic19—41no—
78C2×Dic38—21no—
79C2×Dic38—21no—
80C2×Dic38—21no—
81C2×Dic38C22⋊C412yes—
82M16×C19—21no—
83M16×C19—21no—
84M16×C19—21no—
85M16×C19Q1612yescomplemented
86C2×C8×C19—21no—
87C2×C8×C19—21no—
88C2×C8×C19—21no—
89C2×C8×C19—21no—
90C2×C8×C19—42no—
91C2×C8×C19—41no—
92C42×C19C22×C411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19C2×D411yescharacteristic
95C42×C19#4111yescharacteristic
96C22⋊Dic19—22no—
97C22⋊Dic19—41no—
98C4⋊Dic19—21no—
99C4⋊Dic19—21no—
100C4⋊Dic19—21no—
101C4⋊Dic19—22no—
102C4⋊Dic19—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19—21no—
106C4⋊Dic19—41no—
107C4⋊Dic19C22⋊C412yes—
108Dic19⋊C4—22no—
109Dic19⋊C4—22no—
110Dic19⋊C4—41no—
111Dic19⋊C4—41no—
112C4×Dic19—22no—
113C4×Dic19—41no—
114C4×Dic19—41no—
115C4×Dic19—41no—
116C2×C19⋊C8—21no—
117C2×C19⋊C8—21no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120Dic76—44no—
121#9056—191nomaximal, Sylow
122C23×C19#12111yescharacteristic
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—41no—
126C2×C4×C19C2×C22⋊C411yescharacteristic
127C2×C4×C19C4×D411yescharacteristic
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19#12011yescharacteristic
130C2×C4×C19#12111yescharacteristic
131C2×C4×C19#12311yescharacteristic
132C2×C4×C19C2×Q1611yescharacteristic
133C2×C4×C19#13511yescharacteristic
134C2×C4×C19#13711yescharacteristic
135C2×C4×C19#13711yescharacteristic
136C2×Dic19—22no—
137C2×Dic19—22no—
138C2×Dic19—42no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—81no—
142C2×Dic19—81no—
143Dic38—41no—
144Dic38—41no—
145Dic38—42no—
146Dic38—42no—
147Dic38—41no—
148Dic38—41no—
149C8×C19—22no—
150C8×C19—22no—
151C8×C19—41no—
152C8×C19—41no—
153C8×C19—81no—
154C19⋊C8—41no—
155C19⋊C8—41no—
156#3170—191no—
157#2962—191no—
158#1986—191no—
159#1503—191no—
160#1481—191no—
161#1279—191no—
162#1278D1911yescharacteristic
163C22×C19—21no—
164C22×C19—21no—
165C22×C19#38611yescharacteristic
166C22×C19#46211yescharacteristic
167C22×C19#46411yescharacteristic
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19C4×Q1611yescharacteristic
172C4×C19#44111yescharacteristic
173C4×C19#44311yescharacteristic
174C4×C19#44411yescharacteristic
175C4×C19#45111yescharacteristic
176C4×C19#45211yescharacteristic
177Dic19—42no—
178Dic19—42no—
179Dic19—82no—
180Dic19—81no—
181Dic19—81no—
182#533—191no—
183#533—191no—
184#500—191no—
185#494—191no—
186#487—191no—
187#487—191no—
188#467—382no—
189#446—381no—
190#446—382no—
191C8×Q8—381no—
192C4×Q16—382no—
193#431C2×D1911yescharacteristic
194#424—381no—
195C2×C4⋊C8—191no—
196#405—381no—
197C4×M16C2×D1911yescharacteristic
198C2×C4×C8C2×D1911yescharacteristic
199C4×C4⋊C4—191no—
200#339—381no—
201#339—381no—
202#328—382no—
203Q8⋊C8—381no—
204Q8⋊C8—381no—
205C2×C19—21no—
206C2×C19—21no—
207C2×C19#187611yescharacteristic
208C2×C19#187811yescharacteristic
209C2×C19#188411yescharacteristic
210C2×Q16—382no—
211C2×M16D7611yescharacteristic
212C2×M16D7611yescharacteristic
213C22×C8—21no—
214C22×C8—381no—
215C4⋊Q8—191no—
216C4⋊Q8—191no—
217C4⋊Q8—191no—
218C4⋊Q8—191no—
219#125—381no—
220#125—381no—
221C22⋊Q8—192no—
222C22⋊Q8—381no—
223C22⋊Q8—381no—
224C22⋊Q8—381no—
225C4×Q8—192no—
226C4×Q8—381no—
227C4×Q8—381no—
228C4×Q8—381no—
229#117—381no—
230#117—381no—
231C2×C4⋊C4—381no—
232C2×C42—381no—
233C2×C42C22×D1911yescharacteristic
234#107—382no—
235C4⋊C8—21no—
236C4⋊C8—191no—
237C4⋊C8—191no—
238C4⋊C8—382no—
239C4⋊C8—382no—
240C4⋊C8—381no—
241#103—382no—
242#103—382no—
243C22⋊C8—21no—
244#97—21no—
245#97—382no—
246C4×C8—21no—
247C4×C8—21no—
248C4×C8—21no—
249C4×C8—382no—
250C4×C8C4×D1911yescharacteristic
251C4×C8C4×D1911yescharacteristic
252#95—381no—
253C19#905611yescharacteristic, complemented, Sylow
254C2×Q8—192no—
255C2×Q8—381no—
256C2×Q8—381no—
257C2×Q8—381no—
258C22×C4—761no—
259C22×C4C2×D7611yescharacteristic
260C22×C4D4×D1911yescharacteristic
261C22×C4#6454511yescharacteristic
262Q16—764no—
263M16—21no—
264M16—21no—
265M16—21no—
266M16Dic7612yescomplemented
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—42no—
272C2×C8—41no—
273C2×C8—381no—
274C2×C8—381no—
275C2×C8—761no—
276C2×C8—761no—
277C4⋊C4—192no—
278C4⋊C4—382no—
279C4⋊C4—381no—
280C4⋊C4—381no—
281C4⋊C4—382no—
282C4⋊C4—381no—
283C4⋊C4—382no—
284C4⋊C4—381no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4—381no—
288C4⋊C4—761no—
289C4⋊C4—761no—
290C4⋊C4—761no—
291C22⋊C4—382no—
292C22⋊C4—761no—
293C42—382no—
294C42—761no—
295C42—761no—
296C42—761no—
297C42C2×C4×D1911yescharacteristic
298C42#6454111yescharacteristic
299C42D4×D1911yescharacteristic
300C42D4×D1911yescharacteristic
301C23#1059734111yescharacteristic
302Q8—762no—
303Q8—762no—
304Q8—761no—
305Q8—761no—
306Q8—761no—
307Q8—761no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—382no—
312C2×C4—382no—
313C2×C4—762no—
314C2×C4—761no—
315C2×C4—761no—
316C2×C4—1521no—
317C2×C4—1521no—
318C2×C4C4×D7611yescharacteristic
319C2×C4C22⋊C4×D1911yescharacteristic
320C2×C4#1059732811yescharacteristic
321C2×C4#1059733011yescharacteristic
322C2×C4#1059733911yescharacteristic
323C2×C4#1059734011yescharacteristic
324C2×C4#1059735011yescharacteristic
325C2×C4C2×Dic7611yescharacteristic
326C2×C4#1059735511yescharacteristic
327C2×C4#1059735511yescharacteristic
328C8—22no—
329C8—22no—
330C8—41no—
331C8—41no—
332C8—81no—
333C8—761no—
334C8—761no—
335C22—21no—
336C22—21no—
337C22#1192642211yescharacteristic
338C22#1192675511yescharacteristic
339C22#1192676711yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—762no—
344C4—762no—
345C4—1522no—
346C4—1521no—
347C4—1521no—
348C4C4×Dic7611yescharacteristic
349C4#1192665211yescharacteristic
350C4#1192666011yescharacteristic
351C4#1192666511yescharacteristic
352C4#1192670211yescharacteristic
353C4#1192670811yescharacteristic
354C2—21no—
355C2—21no—
356C2#1456396311yescharacteristic
357C2#1456397511yescharacteristic
358C2#1456401711yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1278C2
socleC22×C19#386
prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenter#1278D19
hypocenterC19#9056
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
10. #11926949C4semidirect
11. #11926924C4semidirect
12. #11926895C4semidirect
13. #11926895C4semidirect
85. M16×C19Q16semidirect
253. C19#9056semidirect
266. M16Dic76semidirect

Maximal subgroups

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

subgroupindex
#145742212
#145725822
#145645792
#145621352
#145620392
#145614752
C19×#12782
#905619