Finite Group Databasebeta

← #18076885

Subgroups — #18076885

Order 4864.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572586C211yesmaximal, characteristic
2#14564408C211yesmaximal, characteristic
3#14562063C211yesmaximal, characteristic
4C2×#11926276C211yesmaximal, characteristic
5#14561530C211yesmaximal, characteristic
6#14561472C211yesmaximal, characteristic
7C19×#1566C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9#11926673—22no—
10#11926671—21no—
11#11926668—21no—
12#11926597C2211yescharacteristic
13C2×#10597279—21no—
14#11926567—21no—
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C4×#64520C2211yescharacteristic
17M16×Dic19—21no—
18#11926308—21no—
19#11926276C411yescharacteristic
20#11926276C411yescharacteristic
21#11926276C411yescharacteristic
22#11926276C411yescharacteristic
23#11926274—21no—
24#11926274—21no—
25C19×#423C2211yescharacteristic
26C19×#423C2211yescharacteristic
27C2×C4×C8×C19C2211yescharacteristic
28C19×#334—22no—
29C22×Dic38Q811yescharacteristic
30C2×M16×C19—21no—
31C2×M16×C19—21no—
32C22×C8×C19—21no—
33C2×C42×C19C2311yescharacteristic
34C2×C4⋊Dic19Q811yescharacteristic
35C2×Dic19⋊C4—21no—
36C2×C4×Dic19—21no—
37C2×#64520D411yescharacteristic
38C2×#64520D411yescharacteristic
39C22×C19⋊C8—21no—
40C4×Dic38—21no—
41C4×Dic38—21no—
42C4×Dic38C2×C411yescharacteristic
43C4×Dic38C2×C411yescharacteristic
44C4×Dic38D411yescharacteristic
45C4×Dic38D411yescharacteristic
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8—21no—
49C19×C4⋊C8D412yes—
50C4×C8×C19—21no—
51C4×C8×C19C2×C411yescharacteristic
52C4×C8×C19C2×C411yescharacteristic
53C22⋊(C19⋊C8)—21no—
54#10597279—42no—
55#10597272—22no—
56Dic19⋊C8—22no—
57Dic19⋊C8—22no—
58C8×Dic19—22no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)C2×C411yescharacteristic
62C4⋊(C19⋊C8)C2×C411yescharacteristic
63#10597260—21no—
64C4×C19⋊C8—21no—
65C4×C19⋊C8—21no—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×Q811yescharacteristic
68C22×C4×C19#4111yescharacteristic
69C22×Dic19—21no—
70C22×Dic19—21no—
71C2×Dic38—22no—
72C2×Dic38—21no—
73C2×Dic38—41no—
74C2×Dic38C4⋊C411yescharacteristic
75C2×Dic38C4⋊C411yescharacteristic
76M16×C19—41no—
77M16×C19—41no—
78M16×C19—41no—
79M16×C19—41no—
80C2×C8×C19—21no—
81C2×C8×C19—21no—
82C2×C8×C19—22no—
83C2×C8×C19—42no—
84C2×C8×C19—41no—
85C42×C19C22×C411yescharacteristic
86C42×C19C2×D411yescharacteristic
87C42×C19C2×D411yescharacteristic
88C42×C19#4111yescharacteristic
89C4⋊Dic19—21no—
90C4⋊Dic19C4⋊C411yescharacteristic
91C4⋊Dic19C4⋊C411yescharacteristic
92Dic19⋊C4—21no—
93Dic19⋊C4—21no—
94Dic19⋊C4—21no—
95Dic19⋊C4—21no—
96C4×Dic19—21no—
97C4×Dic19—21no—
98C4×Dic19—21no—
99C4×Dic19—21no—
100#64520—21no—
101#64520—21no—
102#64520—21no—
103#64520SD1612yes—
104C2×C19⋊C8—21no—
105C2×C19⋊C8—21no—
106C2×C19⋊C8—21no—
107C2×C19⋊C8—21no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—41no—
111#8909—191nomaximal, Sylow
112C23×C19C22⋊Q811yescharacteristic
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—41no—
116C2×C4×C19C2×C4⋊C411yescharacteristic
117C2×C4×C19C4×D411yescharacteristic
118C2×C4×C19C4×D411yescharacteristic
119C2×C4×C19#12011yescharacteristic
120C2×C4×C19C22⋊Q811yescharacteristic
121C2×C4×C19#12311yescharacteristic
122C2×C4×C19C2×SD1611yescharacteristic
123C2×C4×C19#13511yescharacteristic
124C2×C4×C19#13711yescharacteristic
125C2×C4×C19#13711yescharacteristic
126C2×Dic19—21no—
127C2×Dic19—21no—
128C2×Dic19—21no—
129C2×Dic19—21no—
130C2×Dic19—42no—
131C2×Dic19—81no—
132Dic38—21no—
133Dic38—21no—
134Dic38—21no—
135Dic38—42no—
136Dic38#10812yescomplemented
137C8×C19—22no—
138C8×C19—41no—
139C8×C19—42no—
140C8×C19—81no—
141C19⋊C8—22no—
142C19⋊C8—41no—
143C19⋊C8—41no—
144C19⋊C8—41no—
145C19⋊C8—81no—
146Q8×M16—191no—
147#1950—191no—
148#1566D1911yescharacteristic
149#1487—191no—
150C2×Q8⋊C8—191no—
151#1301—191no—
152#1278—191no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19#38511yescharacteristic
156C22×C19#47511yescharacteristic
157C22×C19#47911yescharacteristic
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19C2×#10811yescharacteristic
162C4×C19#43011yescharacteristic
163C4×C19C4×SD1611yescharacteristic
164C4×C19#44111yescharacteristic
165C4×C19#44811yescharacteristic
166C4×C19#45211yescharacteristic
167Dic19—22no—
168Dic19—41no—
169Dic19—41no—
170Dic19—41no—
171C2×C4×Q8—191no—
172#446—381no—
173#446—382no—
174C8×Q8—381no—
175#431—191no—
176C2×#108—381no—
177#423—381no—
178#423C2×D1911yescharacteristic
179#423C2×D1911yescharacteristic
180C2×C4⋊C8—191no—
181C4×M16—191no—
182C4×M16—381no—
183C2×C4×C8C2×D1911yescharacteristic
184#341—381no—
185#334—22no—
186Q8⋊C8—191no—
187Q8⋊C8—191no—
188Q8⋊C8—191no—
189Q8⋊C8—191no—
190Q8⋊C8—381no—
191Q8⋊C8—381no—
192C2×C19—21no—
193C2×C19—21no—
194C2×C19#185511yescharacteristic
195C2×C19#186111yescharacteristic
196C2×C19#186511yescharacteristic
197C22×Q8—191no—
198C2×M16—21no—
199C2×M16—21no—
200C2×M16—191no—
201C2×M16—191no—
202C22×C8—21no—
203C22×C8—381no—
204C4×Q8—191no—
205C4×Q8—191no—
206C4×Q8—191no—
207C4×Q8—191no—
208C4×Q8—381no—
209C4×Q8—381no—
210C2×C4⋊C4—191no—
211C2×C4⋊C4—381no—
212C2×C42—381no—
213C2×C42C22×D1911yescharacteristic
214#108—762no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—191no—
219C4⋊C8—191no—
220C4⋊C8—382no—
221C4⋊C8—382no—
222C4⋊C8—381no—
223C4⋊C8—381no—
224C4⋊C8C22⋊D1912yes—
225C22⋊C8—381no—
226#97—382no—
227#97—381no—
228C4×C8—21no—
229C4×C8—382no—
230C4×C8—381no—
231C4×C8—381no—
232C4×C8C4×D1911yescharacteristic
233C4×C8C4×D1911yescharacteristic
234C19#890911yescharacteristic, complemented, Sylow
235C2×Q8—191no—
236C2×Q8—191no—
237C2×Q8—382no—
238C2×Q8—381no—
239C2×Q8—761no—
240C22×C4—381no—
241C22×C4—381no—
242C22×C4#6454111yescharacteristic
243C22×C4D4×D1911yescharacteristic
244C22×C4Q8×D1911yescharacteristic
245M16—41no—
246M16—41no—
247M16—41no—
248M16—41no—
249M16—192no—
250M16—381no—
251M16—381no—
252M16—381no—
253C2×C8—21no—
254C2×C8—22no—
255C2×C8—21no—
256C2×C8—42no—
257C2×C8—41no—
258C2×C8—381no—
259C2×C8—381no—
260C2×C8—381no—
261C2×C8—381no—
262C2×C8—761no—
263C2×C8—761no—
264C2×C8—761no—
265C4⋊C4—191no—
266C4⋊C4—191no—
267C4⋊C4—381no—
268C4⋊C4—381no—
269C4⋊C4—381no—
270C4⋊C4—381no—
271C4⋊C4—381no—
272C42—381no—
273C42—381no—
274C42—381no—
275C42—381no—
276C42C2×C4×D1911yescharacteristic
277C42D4×D1911yescharacteristic
278C42#6454511yescharacteristic
279C42C2×C22⋊D1911yescharacteristic
280C23#1059734211yescharacteristic
281Q8—192no—
282Q8—381no—
283Q8—381no—
284Q8—381no—
285Q8—762no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—381no—
290C2×C4—381no—
291C2×C4—381no—
292C2×C4—381no—
293C2×C4—762no—
294C2×C4—1521no—
295C2×C4C4⋊C4×D1911yescharacteristic
296C2×C4#1059733911yescharacteristic
297C2×C4#1059734011yescharacteristic
298C2×C4SD16×D1911yescharacteristic
299C2×C4#1059736111yescharacteristic
300C2×C4#1059736111yescharacteristic
301C2×C4#1059736211yescharacteristic
302C2×C4C4×C22⋊D1911yescharacteristic
303C2×C4#1059738311yescharacteristic
304C2×C4#1059739211yescharacteristic
305C8—22no—
306C8—41no—
307C8—42no—
308C8—81no—
309C8—382no—
310C8—761no—
311C8—761no—
312C8—761no—
313C8—1521no—
314C22—21no—
315C22—21no—
316C22#1192641511yescharacteristic
317C22#1192682811yescharacteristic
318C22#1192685411yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—382no—
323C4—761no—
324C4—761no—
325C4—761no—
326C4#108×D1911yescharacteristic
327C4#1192659111yescharacteristic
328C4#1192663111yescharacteristic
329C4#1192665011yescharacteristic
330C4#1192668111yescharacteristic
331C4#1192670311yescharacteristic
332C2—21no—
333C2—21no—
334C2#1456383811yescharacteristic
335C2#1456387411yescharacteristic
336C2#1456390011yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1566C2
socleC22×C19#385
prime radicalC23×C19C22⋊Q8
cosocleC2×C42×C19C23
hypercenter#1566D19
hypocenterC19#8909
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
136. Dic38#108semidirect
234. C19#8909semidirect

Maximal subgroups

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

subgroupindex
#145725862
#145644082
#145620632
C2×#119262762
#145615302
#145614722
C19×#15662
#890919