Finite Group Databasebeta

← #18078396

Subgroups — #18078396

Order 4864.

432 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#14573451C211yesmaximal, characteristic
2#14572300C211yesmaximal, characteristic
3#14562315C211yesmaximal, characteristic, complemented
4C2×#11926289C211yesmaximal, characteristic, complemented
5#14562023C211yesmaximal, characteristic
6#14561509C211yesmaximal, characteristic, complemented
7C19×#1301C211yesmaximal, characteristic, complemented
8C2×#10597315C2211yescharacteristic
9C4×#64541C2211yescharacteristic
10#11926840C412yes—
11#11926835C412yes—
12#11926830—21no—
13#11926825—21no—
14#11926604—22no—
15#11926600—21no—
16#11926596—21no—
17#11926586—21no—
18#11926568C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20#11926546—21no—
21#11926510—21no—
22#11926499—21no—
23#11926292—22no—
24#11926289—21no—
25#11926289—21no—
26#11926276—21no—
27#11926273—21no—
28C19×#431C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C2×C19×C4⋊C8C2211yescharacteristic
31C2×#64541D411yescharacteristic
32C22×Dic38—21no—
33C2×M16×C19—21no—
34C22×C8×C19—21no—
35C2×C42×C19C2311yescharacteristic
36C4×C22⋊D19—21no—
37C4×C22⋊D19—21no—
38#10597372D411yescharacteristic
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×#64520—21no—
42C22×C19⋊C8—21no—
43C4×D76C2×C411yescharacteristic
44C4×D76D411yescharacteristic
45#10597318—21no—
46C42×D19—21no—
47#10597315—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315C2×C412yes—
51C4×Dic38C2×C411yescharacteristic
52C4×Dic38D411yescharacteristic
53C19×C4⋊C8—21no—
54C19×C4⋊C8—21no—
55C19×C4⋊C8—21no—
56C19×C4⋊C8C2×C412yes—
57C19×C4⋊C8D411yescharacteristic
58C19×C4⋊C8D411yescharacteristic
59C19×C22⋊C8—21no—
60C4×C8×C19—21no—
61#10597278—22no—
62(C2×D19)⋊C8—22no—
63(C2×D19)⋊C8—22no—
64#10597275—22no—
65#10597274—22no—
66#10597273—22no—
67#10597272—22no—
68C8×Dic19—22no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)D412yes—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19#4111yescharacteristic
75C22×C4×C19#4111yescharacteristic
76C2×C22⋊D19—21no—
77C22×Dic19—41no—
78#64541—21no—
79#64541—21no—
80#64541—21no—
81#64541—21no—
82C2×D76C22⋊C411yescharacteristic
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19—21no—
86C2×Dic38—22no—
87C2×Dic38—41no—
88C2×Dic38—81no—
89C2×Dic38—81no—
90C2×Dic38C22⋊C411yescharacteristic
91M16×C19—41no—
92M16×C19—41no—
93C2×C8×C19—22no—
94C2×C8×C19—21no—
95C2×C8×C19—21no—
96C2×C8×C19—41no—
97C2×C8×C19—41no—
98C2×C8×C19—41no—
99C42×C19C22×C411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C22⋊Dic19—21no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106C4⋊Dic19—22no—
107C4⋊Dic19—22no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19C22⋊C411yescharacteristic
111C4⋊Dic19C22⋊C411yescharacteristic
112Dic19⋊C4—21no—
113Dic19⋊C4—21no—
114C4×Dic19—21no—
115C4×Dic19—21no—
116C4×Dic19—21no—
117#64520—41no—
118#64520—41no—
119C2×C19⋊C8—22no—
120C2×C19⋊C8—41no—
121C2×C19⋊C8—81no—
122#9168—191nomaximal, Sylow
123C23×C19#12311yescharacteristic
124C22×D19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—41no—
128C2×C4×C19C2×C22⋊C411yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19#12011yescharacteristic
132C2×C4×C19#12111yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×C4×C19#13511yescharacteristic
136C2×C4×C19#13711yescharacteristic
137C2×C4×C19#13711yescharacteristic
138C22⋊D19—41no—
139C22⋊D19—41no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—42no—
144C2×Dic19—82no—
145D76—21no—
146D76—21no—
147C4×D19—41no—
148C4×D19—41no—
149C4×D19—41no—
150C4×D19—41no—
151C4×D19—81no—
152Dic38—21no—
153Dic38—21no—
154Dic38—81no—
155Dic38—81no—
156Dic38—82no—
157C8×C19—42no—
158C8×C19—41no—
159C8×C19—41no—
160C8×C19—81no—
161C19⋊C8—42no—
162C19⋊C8—81no—
163#3079—191no—
164#2925—191no—
165#1548—191no—
166C2×#332—191no—
167#1477—191no—
168#1301D1911yescharacteristic, complemented
169#1292—191no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19#38611yescharacteristic
173C22×C19#48511yescharacteristic
174C22×C19#48511yescharacteristic
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19#41611yescharacteristic
182C4×C19#41911yescharacteristic
183C4×C19#45211yescharacteristic
184C4×C19#45211yescharacteristic
185C4×C19#47111yescharacteristic
186C4×C19#47211yescharacteristic
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190Dic19—82no—
191C2×C4⋊Q8—191no—
192C4×#41—191no—
193#477—192no—
194#476—192no—
195#475—381no—
196#474—381no—
197#433—382no—
198#432—381no—
199#431—381no—
200#431C2×D1911yescharacteristic
201#428—381no—
202#423—191no—
203#423C2×D1911yescharacteristic
204C2×C4⋊C8—191no—
205C2×C4⋊C8C2×D1911yescharacteristic
206#417—381no—
207#408—381no—
208#405—381no—
209#333—382no—
210#332—381no—
211#332—381no—
212Q8⋊C8—381no—
213D4⋊C8—381no—
214C2×C19—21no—
215C2×C19—21no—
216C2×C19#187311yescharacteristic
217C2×C19#190211yescharacteristic
218C2×C19#190711yescharacteristic
219D19—81no—
220C2×#41—191no—
221C22×Q8—381no—
222C2×M16—21no—
223C2×M16—381no—
224C22×C8—21no—
225C22×C8—381no—
226C4⋊Q8—192no—
227C4⋊Q8—381no—
228C4⋊Q8—381no—
229C4⋊Q8—381no—
230C4×Q8—191no—
231C4×Q8—191no—
232C4×D4—191no—
233C4×D4—191no—
234C4×D4—381no—
235C4×D4—381no—
236#117—191no—
237#117—381no—
238C2×C4⋊C4—381no—
239C2×C4⋊C4—381no—
240C2×C42—381no—
241C2×C42C22×D1911yescharacteristic
242#107—382no—
243#106—382no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—192no—
248C4⋊C8—381no—
249C4⋊C8—381no—
250C4⋊C8—381no—
251C4⋊C8C4×D1912yes—
252C4⋊C8D7611yescharacteristic
253C4⋊C8D7611yescharacteristic
254#103—382no—
255#102—382no—
256C22⋊C8—21no—
257C22⋊C8—382no—
258C22⋊C8—382no—
259#97—382no—
260C4×C8—21no—
261C4×C8—382no—
262C19#916811yescharacteristic, complemented, Sylow
263#41—381no—
264#41—381no—
265#41—381no—
266#41—381no—
267C2×Q8—191no—
268C2×Q8—382no—
269C2×Q8—761no—
270C2×Q8—1521no—
271C2×Q8—1521no—
272C2×D4—191no—
273C2×D4—381no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4—761no—
278C22×C4#6454111yescharacteristic
279C22×C4D4×D1911yescharacteristic
280C22×C4#6454511yescharacteristic
281M16—41no—
282M16—41no—
283M16—761no—
284M16—761no—
285C2×C8—22no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—382no—
292C2×C8—761no—
293C2×C8—1521no—
294C4⋊C4—191no—
295C4⋊C4—191no—
296C4⋊C4—381no—
297C4⋊C4—381no—
298C4⋊C4—382no—
299C4⋊C4—382no—
300C4⋊C4—761no—
301C4⋊C4—761no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C22⋊C4—381no—
305C42—381no—
306C42—381no—
307C42—381no—
308C42C2×C4×D1911yescharacteristic
309C42C2×D7611yescharacteristic
310C42D4×D1911yescharacteristic
311C42D4×D1911yescharacteristic
312C23—381no—
313C23#1059734011yescharacteristic
314Q8—381no—
315Q8—381no—
316Q8—1522no—
317Q8—1521no—
318Q8—1521no—
319D4—381no—
320D4—381no—
321D4—761no—
322D4—761no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—381no—
327C2×C4—381no—
328C2×C4—381no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4—762no—
334C2×C4—1521no—
335C2×C4—1522no—
336C2×C4C4×D7611yescharacteristic
337C2×C4C22⋊C4×D1911yescharacteristic
338C2×C4#1059732811yescharacteristic
339C2×C4#1059733011yescharacteristic
340C2×C4#1059733911yescharacteristic
341C2×C4#1059734111yescharacteristic
342C2×C4#1059735811yescharacteristic
343C2×C4#1059736111yescharacteristic
344C2×C4#1059736211yescharacteristic
345C2×C4#1059736411yescharacteristic
346C8—42no—
347C8—41no—
348C8—41no—
349C8—81no—
350C8—762no—
351C8—1521no—
352C22—21no—
353C22—21no—
354C22—761no—
355C22—761no—
356C22—761no—
357C22#1192642211yescharacteristic
358C22#1192688711yescharacteristic
359C22#1192688811yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—761no—
364C4—761no—
365C4—761no—
366C4—1522no—
367C4#1192653711yescharacteristic
368C4#1192655111yescharacteristic
369C4#1192670711yescharacteristic
370C4#1192670911yescharacteristic
371C4#1192680811yescharacteristic
372C4#1192681511yescharacteristic
373C2—21no—
374C2—21no—
375C2—1521no—
376C2#1456394611yescharacteristic
377C2#1456410711yescharacteristic
378C2#1456414211yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1301C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1301D19
hypocenterC19#9168
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
3. #14562315C2semidirect
4. C2×#11926289C2semidirect
6. #14561509C2semidirect
7. C19×#1301C2semidirect
168. #1301D19semidirect
262. C19#9168semidirect

Maximal subgroups

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

subgroupindex
#145734512
#145723002
#145623152
C2×#119262892
#145620232
#145615092
C19×#13012
#916819