Finite Group Databasebeta

← #18077416

Subgroups — #18077416

Order 4864.

430 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573417C211yesmaximal, characteristic
2#14572303C211yesmaximal, characteristic
3#14562038C211yesmaximal, characteristic, complemented
4#14562018C211yesmaximal, characteristic
5#14561530C211yesmaximal, characteristic, complemented
6#14561470C211yesmaximal, characteristic, complemented
7C19×#1493C211yesmaximal, characteristic, complemented
8C4×#64541C2211yescharacteristic
9#11926848—21no—
10#11926841—21no—
11#11926836C411yescharacteristic
12#11926831C411yescharacteristic
13#11926826C411yescharacteristic
14#11926821C411yescharacteristic
15#11926604—22no—
16#11926600—21no—
17#11926597C2211yescharacteristic
18#11926596—21no—
19#11926580—21no—
20C2×C4⋊(C19⋊C8)C2211yescharacteristic
21C2×C4⋊(C19⋊C8)C2211yescharacteristic
22#11926538—21no—
23#11926512—21no—
24#11926502—21no—
25#11926276—21no—
26Q8⋊(C19⋊C8)—21no—
27Q8⋊(C19⋊C8)—21no—
28#11926273—21no—
29C19×#533C2211yescharacteristic
30C19×#423C2211yescharacteristic
31C2×C4×C8×C19C2211yescharacteristic
32C19×Q8⋊C8—22no—
33C2×#64541D411yescharacteristic
34C2×M16×C19—21no—
35C22×C8×C19—21no—
36C19×C4⋊Q8C2×C411yescharacteristic
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×#125—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C4×Q8×C19—21no—
42C4×Q8×C19—21no—
43C19×#117—21no—
44C2×C42×C19C2311yescharacteristic
45C4×C22⋊D19—21no—
46C4×C22⋊D19—21no—
47#10597372D411yescharacteristic
48C22×C19⋊C8—21no—
49C22×C19⋊C8—21no—
50C4×D76C2×C411yescharacteristic
51C4×D76D411yescharacteristic
52#10597318—21no—
53C42×D19—21no—
54C4×Dic38C2×C411yescharacteristic
55C4×Dic38D411yescharacteristic
56C19×C4⋊C8—21no—
57C19×C4⋊C8D412yes—
58C4×C8×C19—21no—
59C4×C8×C19—21no—
60C22⋊(C19⋊C8)—21no—
61(C2×D19)⋊C8—22no—
62(C2×D19)⋊C8—22no—
63#10597272—22no—
64C8×Dic19—22no—
65#10597267—21no—
66#10597267—21no—
67#10597266—21no—
68#10597266—21no—
69#10597265—21no—
70#10597265—21no—
71#10597264—21no—
72#10597264—21no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)C2×C411yescharacteristic
77C4⋊(C19⋊C8)C2×C411yescharacteristic
78C4⋊(C19⋊C8)D411yescharacteristic
79C4⋊(C19⋊C8)D411yescharacteristic
80C4×C19⋊C8—21no—
81C2×Q8×C19—21no—
82C2×Q8×C19—21no—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19#4111yescharacteristic
85C22×C4×C19#4111yescharacteristic
86C2×C22⋊D19—21no—
87#64541—21no—
88#64541—21no—
89#64541—21no—
90#64541—21no—
91C2×D76C22⋊C411yescharacteristic
92C2×C4×D19—21no—
93C2×C4×D19—21no—
94C2×C4×D19—21no—
95C2×Dic38C22⋊C411yescharacteristic
96M16×C19—41no—
97M16×C19—41no—
98C2×C8×C19—22no—
99C2×C8×C19—22no—
100C2×C8×C19—41no—
101C2×C8×C19—41no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C22⋊C4×C19—41no—
109C42×C19—41no—
110C42×C19C22×C411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C22⋊Dic19—21no—
115(C2×D19)⋊C4—21no—
116(C2×D19)⋊C4—21no—
117C4⋊Dic19C22⋊C411yescharacteristic
118C4⋊Dic19C22⋊C411yescharacteristic
119Dic19⋊C4—21no—
120Dic19⋊C4—21no—
121C4×Dic19—21no—
122C4×Dic19—21no—
123C4×Dic19—21no—
124C2×C19⋊C8—21no—
125C2×C19⋊C8—21no—
126C2×C19⋊C8—21no—
127C2×C19⋊C8—21no—
128C2×C19⋊C8—41no—
129C2×C19⋊C8—41no—
130C2×C19⋊C8—41no—
131C2×C19⋊C8—41no—
132C2×C19⋊C8—41no—
133#8994—191nomaximal, Sylow
134C23×C19#12311yescharacteristic
135C22×D19—21no—
136Q8×C19—42no—
137Q8×C19—41no—
138Q8×C19—41no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19C2×C22⋊C411yescharacteristic
145C2×C4×C19C4×D411yescharacteristic
146C2×C4×C19C4×D411yescharacteristic
147C2×C4×C19#12011yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#13511yescharacteristic
151C2×C4×C19#13511yescharacteristic
152C2×C4×C19#13711yescharacteristic
153C2×C4×C19#13711yescharacteristic
154C22⋊D19—41no—
155C22⋊D19—41no—
156C2×Dic19—21no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159D76—21no—
160D76—21no—
161C4×D19—41no—
162C4×D19—41no—
163C4×D19—41no—
164C4×D19—41no—
165C4×D19—81no—
166Dic38—21no—
167Dic38—21no—
168C8×C19—42no—
169C8×C19—42no—
170C19⋊C8—41no—
171C19⋊C8—41no—
172C19⋊C8—41no—
173C19⋊C8—41no—
174C19⋊C8—81no—
175#3076—191no—
176#2925—191no—
177#1493D1911yescharacteristic, complemented
178#1481—191no—
179#1476—191no—
180#1301—191no—
181#1277—191no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19#38611yescharacteristic
185C22×C19#48511yescharacteristic
186C22×C19#48511yescharacteristic
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—41no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—81no—
194C4×C19—81no—
195C4×C19#41611yescharacteristic
196C4×C19#41911yescharacteristic
197C4×C19#44311yescharacteristic
198C4×C19#44411yescharacteristic
199C4×C19#45211yescharacteristic
200C4×C19#45211yescharacteristic
201Dic19—41no—
202Dic19—41no—
203Dic19—41no—
204#533C2×D1911yescharacteristic
205C4×#41—191no—
206#479—381no—
207#478—381no—
208#477—191no—
209#476—191no—
210#475—191no—
211#474—191no—
212#433—382no—
213#432—381no—
214#431—191no—
215#431—381no—
216#427—381no—
217#423C2×D1911yescharacteristic
218C2×C4⋊C8—191no—
219C2×C4⋊C8—191no—
220#416—381no—
221#408—381no—
222#405—381no—
223C2×C4×C8C2×D1911yescharacteristic
224Q8⋊C8—22no—
225Q8⋊C8—381no—
226Q8⋊C8—381no—
227Q8⋊C8—381no—
228D4⋊C8—381no—
229C2×C19—21no—
230C2×C19—21no—
231C2×C19#187311yescharacteristic
232C2×C19#187611yescharacteristic
233C2×C19#188111yescharacteristic
234D19—81no—
235C2×#41—191no—
236C2×M16—21no—
237C22×C8—21no—
238C22×C8—381no—
239C22×C8—381no—
240C4⋊Q8C4×D1911yescharacteristic
241C4⋊Q8C4×D1911yescharacteristic
242#125—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—191no—
248C4×Q8—191no—
249C4×D4—191no—
250C4×D4—191no—
251C4×D4—381no—
252C4×D4—381no—
253#117—21no—
254#117—191no—
255#117—381no—
256C2×C42—381no—
257C2×C42C22×D1911yescharacteristic
258#107—381no—
259#107—381no—
260#106—381no—
261#106—381no—
262C4⋊C8—21no—
263C4⋊C8—191no—
264C4⋊C8—191no—
265C4⋊C8—191no—
266C4⋊C8—191no—
267C4⋊C8—381no—
268C4⋊C8—381no—
269C4⋊C8—381no—
270C4⋊C8C22⋊D1912yes—
271#103—381no—
272#103—381no—
273#102—381no—
274#102—381no—
275C22⋊C8—382no—
276C22⋊C8—382no—
277C22⋊C8—381no—
278#97—382no—
279C4×C8—21no—
280C4×C8—21no—
281C4×C8—382no—
282C4×C8—381no—
283C19#899411yescharacteristic, complemented, Sylow
284#41—381no—
285#41—381no—
286#41—381no—
287#41—381no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—191no—
291C2×D4—191no—
292C2×D4—381no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4#6454111yescharacteristic
297C22×C4D4×D1911yescharacteristic
298C22×C4#6454311yescharacteristic
299M16—41no—
300M16—41no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—381no—
306C2×C8—381no—
307C2×C8—381no—
308C2×C8—381no—
309C2×C8—761no—
310C2×C8—761no—
311C2×C8—761no—
312C2×C8—761no—
313C2×C8—761no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—191no—
321C4⋊C4—191no—
322C4⋊C4—381no—
323C4⋊C4—381no—
324C22⋊C4—41no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C42—41no—
329C42—381no—
330C42—381no—
331C42—381no—
332C42C2×C4×D1911yescharacteristic
333C42D4×D1911yescharacteristic
334C42D4×D1911yescharacteristic
335C42C2×C22⋊D1911yescharacteristic
336C23—381no—
337C23#1059732911yescharacteristic
338Q8—42no—
339Q8—41no—
340Q8—41no—
341Q8—381no—
342Q8—381no—
343D4—381no—
344D4—381no—
345D4—761no—
346D4—761no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—381no—
353C2×C4—381no—
354C2×C4—381no—
355C2×C4—761no—
356C2×C4—761no—
357C2×C4—761no—
358C2×C4—761no—
359C2×C4—1521no—
360C2×C4C22⋊C4×D1911yescharacteristic
361C2×C4(C22⋊D19)⋊C411yescharacteristic
362C2×C4#1059733011yescharacteristic
363C2×C4#1059736111yescharacteristic
364C2×C4#1059736211yescharacteristic
365C2×C4#1059736411yescharacteristic
366C2×C4#1059736511yescharacteristic
367C2×C4C4×C22⋊D1911yescharacteristic
368C2×C4#1059738311yescharacteristic
369C2×C4#1059738411yescharacteristic
370C8—42no—
371C8—42no—
372C8—761no—
373C8—761no—
374C8—761no—
375C8—761no—
376C8—1521no—
377C22—21no—
378C22—21no—
379C22—761no—
380C22—761no—
381C22—761no—
382C22#1192642011yescharacteristic
383C22#1192688311yescharacteristic
384C22#1192688411yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—81no—
390C4—761no—
391C4—761no—
392C4—761no—
393C4#1192653911yescharacteristic
394C4#1192655111yescharacteristic
395C4#1192665811yescharacteristic
396C4#1192666311yescharacteristic
397C4#1192670311yescharacteristic
398C4#1192670511yescharacteristic
399C2—21no—
400C2—21no—
401C2—1521no—
402C2#1456394411yescharacteristic
403C2#1456395911yescharacteristic
404C2#1456400011yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1493C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1493D19
hypocenterC19#8994
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #14562038C2semidirect
5. #14561530C2semidirect
6. #14561470C2semidirect
7. C19×#1493C2semidirect
177. #1493D19semidirect
283. C19#8994semidirect

Maximal subgroups

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

subgroupindex
#145734172
#145723032
#145620382
#145620182
#145615302
#145614702
C19×#14932
#899419