Finite Group Databasebeta

← #18072349

Subgroups — #18072349

Order 4864.

544 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572265C211yesmaximal, characteristic
2D19×#432C211yesmaximal, characteristic
3D19×#431C211yesmaximal, characteristic
4#14561498C211yesmaximal, characteristic, complemented
5#14561497C211yesmaximal, characteristic, complemented
6#14561496C211yesmaximal, characteristic, complemented
7C19×#1287C211yesmaximal, characteristic, complemented
8C2×C42×D19C2211yescharacteristic
9#11926601C2211yescharacteristic
10#11926601C2211yescharacteristic
11#11926600—21no—
12#11926599—21no—
13#11926599C412yes—
14#11926598—21no—
15#11926597C2211yescharacteristic
16#11926596—21no—
17#11926596—21no—
18#11926595C412yes—
19#11926594—21no—
20#11926594C412yes—
21#11926566—21no—
22C4⋊C8×D19—21no—
23C4⋊C8×D19—21no—
24#11926506C412yes—
25C22⋊C8×D19—21no—
26C22⋊C8×D19—21no—
27#11926496—21no—
28#97×D19C412yes—
29C4×C8×D19C412yes—
30C19×#432C2211yescharacteristic
31C19×#432C2211yescharacteristic
32C19×#431C2211yescharacteristic
33C22×C4×D19C2×C411yescharacteristic
34C22×C4×D19D411yescharacteristic
35C22×C4×D19Q811yescharacteristic
36C2×C42×C19C2311yescharacteristic
37C2×C4×Dic19C2×C411yescharacteristic
38C2×C4×Dic19D411yescharacteristic
39C2×C4×Dic19Q811yescharacteristic
40C2×#64515—22no—
41C2×C8×D19—22no—
42C2×C8×D19—22no—
43C42×D19C2×C411yescharacteristic
44C42×D19C2×C411yescharacteristic
45C42×D19C2×C411yescharacteristic
46C42×D19C2×C411yescharacteristic
47C42×D19D411yescharacteristic
48C42×D19D411yescharacteristic
49C42×D19D411yescharacteristic
50C42×D19D411yescharacteristic
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C22⋊C8—21no—
55C19×C22⋊C8—21no—
56C19×C22⋊C8C2×C412yes—
57C19×#97—21no—
58C19×#97C2×C412yes—
59C4×C8×C19C2×C412yes—
60C22⋊(C19⋊C8)—21no—
61C22⋊(C19⋊C8)—21no—
62C22⋊(C19⋊C8)C2×C412yes—
63(C2×D19)⋊C8—22no—
64(C2×D19)⋊C8—22no—
65(C2×D19)⋊C8—22no—
66#10597272—22no—
67Dic19⋊C8—22no—
68Dic19⋊C8—22no—
69Dic19⋊C8—22no—
70C8×Dic19—22no—
71C8×Dic19—22no—
72C4⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)—21no—
75#10597260—21no—
76#10597260C2×C412yes—
77C4×C19⋊C8C2×C412yes—
78C23×D19C4⋊C411yescharacteristic
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×Q811yescharacteristic
82C22×Dic19C4⋊C411yescharacteristic
83C22×Dic19C4⋊C411yescharacteristic
84C22×Dic19C4⋊C411yescharacteristic
85C2×C4×D19—24no—
86C2×C4×D19—42no—
87C2×C4×D19—42no—
88C2×C4×D19C4211yescharacteristic
89C2×C4×D19C4211yescharacteristic
90C2×C4×D19C22⋊C411yescharacteristic
91C2×C4×D19C22⋊C411yescharacteristic
92C2×C4×D19C22⋊C411yescharacteristic
93C2×C4×D19C22⋊C411yescharacteristic
94C2×C4×D19C22⋊C411yescharacteristic
95C2×C4×D19C22⋊C411yescharacteristic
96C2×C4×D19C4⋊C411yescharacteristic
97C2×C4×D19C4⋊C411yescharacteristic
98C2×C4×D19C4⋊C411yescharacteristic
99C2×C4×D19C4⋊C411yescharacteristic
100C2×C8×C19—22no—
101C2×C8×C19—22no—
102C2×C8×C19—22no—
103C42×C19C22×C411yescharacteristic
104C42×C19C22×C411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C4×Dic19C4211yescharacteristic
108C4×Dic19C4211yescharacteristic
109C4×Dic19C22⋊C411yescharacteristic
110C4×Dic19C22⋊C411yescharacteristic
111C4×Dic19C22⋊C411yescharacteristic
112C4×Dic19C22⋊C411yescharacteristic
113C4×Dic19C22⋊C411yescharacteristic
114C4×Dic19C22⋊C411yescharacteristic
115C4×Dic19C4⋊C411yescharacteristic
116C4×Dic19C4⋊C411yescharacteristic
117C4×Dic19C4⋊C411yescharacteristic
118C4×Dic19C4⋊C411yescharacteristic
119C2×C19⋊C8—22no—
120C2×C19⋊C8—22no—
121C2×C19⋊C8—22no—
122#64515—44no—
123C8×D19—44no—
124C8×D19—44no—
125#7964—191nomaximal, Sylow
126C23×C19C2×C4⋊C411yescharacteristic
127C22×D19—22no—
128C22×D19—22no—
129C22×D19—41no—
130C22×D19#9511yescharacteristic
131C22×D19#9511yescharacteristic
132C2×C4×C19—22no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19C2×C4211yescharacteristic
136C2×C4×C19C2×C22⋊C411yescharacteristic
137C2×C4×C19C2×C22⋊C411yescharacteristic
138C2×C4×C19C2×C22⋊C411yescharacteristic
139C2×C4×C19C2×C4⋊C411yescharacteristic
140C2×C4×C19C2×C4⋊C411yescharacteristic
141C2×Dic19—22no—
142C2×Dic19—22no—
143C2×Dic19—41no—
144C2×Dic19#9511yescharacteristic
145C2×Dic19#9511yescharacteristic
146C2×Dic19#9511yescharacteristic
147C2×Dic19#9511yescharacteristic
148C2×Dic19#9511yescharacteristic
149C2×Dic19#9511yescharacteristic
150C4×D19—22no—
151C4×D19—22no—
152C4×D19—22no—
153C4×D19—22no—
154C4×D19—22no—
155C4×D19—22no—
156C4×D19—22no—
157C4×D19—41no—
158C4×D19—41no—
159C4×D19—41no—
160C4×D19—41no—
161C4×D19#10814yes—
162C8×C19—42no—
163C8×C19—42no—
164C8×C19—42no—
165C19⋊C8—42no—
166C19⋊C8—42no—
167C19⋊C8—42no—
168#2920—191no—
169C2×#432—191no—
170C2×#431—191no—
171#1287—191no—
172#1287—191no—
173#1287—191no—
174#1287D1911yescharacteristic, complemented
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19C2×#9511yescharacteristic
179C2×D19—21no—
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—21no—
183C2×D19—44no—
184C2×D19#34112yes—
185C2×D19#34412yes—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19C2×#10812yes—
192Dic19—21no—
193Dic19—21no—
194Dic19—21no—
195Dic19—21no—
196Dic19H(3,ℤ/4)12yes—
197Dic19#34112yes—
198C22×C42—191no—
199#432—191no—
200#432—192no—
201#432—191no—
202#432—381no—
203#432—381no—
204#432—381no—
205#432C2×D1911yescharacteristic
206#432C2×D1911yescharacteristic
207#431—191no—
208#431—192no—
209#431—192no—
210#431—381no—
211#431—381no—
212#431—381no—
213#431C2×D1911yescharacteristic
214#423—381no—
215C2×C4⋊C8—381no—
216C2×C4⋊C8—381no—
217#407—192no—
218C2×C22⋊C8—381no—
219C2×C22⋊C8—381no—
220C4×M16—381no—
221C2×#97—192no—
222C2×C4×C8—192no—
223C2×C19—41no—
224C2×C19C2×H(3,ℤ/4)11yescharacteristic
225C2×C19C2×#34111yescharacteristic
226C2×C19C2×#34411yescharacteristic
227D19—22no—
228D19—22no—
229C23×C4—191no—
230C23×C4—191no—
231C23×C4—191no—
232C2×M16—382no—
233C22×C8—382no—
234C22×C8—382no—
235C2×C42—191no—
236C2×C42—191no—
237C2×C42—191no—
238C2×C42—191no—
239C2×C42—191no—
240C2×C42—191no—
241C2×C42—191no—
242C2×C42—191no—
243C2×C42—191no—
244C2×C42—191no—
245C2×C42—191no—
246C2×C42C22×D1911yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—382no—
251C4⋊C8—382no—
252C4⋊C8—382no—
253C4⋊C8—381no—
254C4⋊C8—381no—
255C4⋊C8—381no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—192no—
259C22⋊C8—382no—
260C22⋊C8—382no—
261C22⋊C8—382no—
262C22⋊C8—381no—
263C22⋊C8—381no—
264C22⋊C8C4×D1912yes—
265#97—21no—
266#97—192no—
267#97—382no—
268#97—381no—
269#97C4×D1912yes—
270C4×C8—192no—
271C4×C8—382no—
272C4×C8—382no—
273C4×C8C4×D1912yes—
274C19#796411yescharacteristic, complemented, Sylow
275C24—191no—
276C22×C4—191no—
277C22×C4—191no—
278C22×C4—191no—
279C22×C4—191no—
280C22×C4—191no—
281C22×C4—191no—
282C22×C4—191no—
283C22×C4—191no—
284C22×C4—191no—
285C22×C4—191no—
286C22×C4—191no—
287C22×C4—191no—
288C22×C4—191no—
289C22×C4—191no—
290C22×C4—191no—
291C22×C4—384no—
292C22×C4—762no—
293C22×C4—762no—
294C22×C4C2×C4×D1911yescharacteristic
295C22×C4D4×D1911yescharacteristic
296C22×C4Q8×D1911yescharacteristic
297M16—764no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—382no—
302C2×C8—382no—
303C2×C8—382no—
304C2×C8—764no—
305C2×C8—764no—
306C42—191no—
307C42—191no—
308C42—191no—
309C42—191no—
310C42—191no—
311C42—191no—
312C42—191no—
313C42—191no—
314C42—191no—
315C42—191no—
316C42—191no—
317C42—191no—
318C42C2×C4×D1911yescharacteristic
319C42C2×C4×D1911yescharacteristic
320C42D4×D1911yescharacteristic
321C42D4×D1911yescharacteristic
322C23—191no—
323C23—191no—
324C23—382no—
325C23—382no—
326C23—761no—
327C23C4⋊C4×D1911yescharacteristic
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—191no—
332C2×C4—191no—
333C2×C4—194no—
334C2×C4—191no—
335C2×C4—191no—
336C2×C4—191no—
337C2×C4—191no—
338C2×C4—382no—
339C2×C4—382no—
340C2×C4—382no—
341C2×C4—382no—
342C2×C4—382no—
343C2×C4—382no—
344C2×C4—382no—
345C2×C4—382no—
346C2×C4—382no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4—761no—
351C2×C4—761no—
352C2×C4C42×D1911yescharacteristic
353C2×C4C22⋊C4×D1911yescharacteristic
354C2×C4C22⋊C4×D1911yescharacteristic
355C2×C4C22⋊C4×D1911yescharacteristic
356C2×C4C4⋊C4×D1911yescharacteristic
357C2×C4C4⋊C4×D1911yescharacteristic
358C8—42no—
359C8—42no—
360C8—42no—
361C8—762no—
362C8—762no—
363C8—762no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—192no—
368C22—192no—
369C22—381no—
370C22—381no—
371C22—381no—
372C22—381no—
373C22—764no—
374C22#95×D1911yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—192no—
381C4—192no—
382C4—381no—
383C4—381no—
384C4—381no—
385C4—381no—
386C4#108×D1912yes—
387C2—41no—
388C2—382no—
389C2—382no—
390C2D19×H(3,ℤ/4)11yescharacteristic
391C2D19×#34111yescharacteristic
392C2D19×#34411yescharacteristic
subgroupG/H
centerC22#95×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#1287C2
socleC22×C19C2×#95
prime radicalC23×D19C4⋊C4
cosocleC2×C42×C19C23
hypercenter#1287D19
hypocenterC19#7964
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
4. #14561498C2semidirect
5. #14561497C2semidirect
6. #14561496C2semidirect
7. C19×#1287C2semidirect
174. #1287D19semidirect
274. C19#7964semidirect

Maximal subgroups

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

subgroupindex
#145722652
D19×#4322
D19×#4312
#145614982
#145614972
#145614962
C19×#12872
#796419