Finite Group Databasebeta

← #18078621

Subgroups — #18078621

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573425C211yesmaximal, characteristic
2C8×#64541C211yesmaximal, characteristic
3#14563656C211yesmaximal, characteristic
4#14562133C211yesmaximal, characteristic, complemented
5#14562091C211yesmaximal, characteristic, complemented
6#14561532C211yesmaximal, characteristic, complemented
7C19×#1279C211yesmaximal, characteristic, complemented
8#11927101C2211yescharacteristic
9C4×#64541C2211yescharacteristic
10#11926852—21no—
11#11926845—21no—
12#11926840C411yescharacteristic, complemented
13#11926835C411yescharacteristic, complemented
14#11926830C411yescharacteristic, complemented
15#11926825C411yescharacteristic, complemented
16C8×Dic38—21no—
17C8×D76—21no—
18C8×C22⋊D19—22no—
19#11926597C2211yescharacteristic
20#11926595—21no—
21#11926582—21no—
22#11926568C2211yescharacteristic
23C2×#10597262—21no—
24#11926541—21no—
25C4×C8×D19—21no—
26#11926304—21no—
27#11926280—22no—
28#11926276—21no—
29#11926276—21no—
30C2×C19×C4⋊C8C2211yescharacteristic
31C2×C4×C8×C19C2211yescharacteristic
32C4×C4⋊C4×C19C2211yescharacteristic
33C2×#64541D411yescharacteristic
34C22×C8×C19—21no—
35C22×C8×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C42×C19—21no—
38C2×C42×C19C2311yescharacteristic
39C4×C22⋊D19—21no—
40C4×C22⋊D19—21no—
41#10597372—21no—
42#10597372D411yescharacteristic
43#10597370—21no—
44#10597370—21no—
45C2×#64520—21no—
46C2×C8×D19—22no—
47C4×D76C2×C411yescharacteristic
48C4×D76D411yescharacteristic
49#10597318—21no—
50C42×D19—21no—
51#10597316—21no—
52#10597315C2×C411yescharacteristic
53#10597315C2×C411yescharacteristic
54C4×Dic38—21no—
55C4×Dic38—21no—
56C4×Dic38C2×C411yescharacteristic
57C4×Dic38D411yescharacteristic
58C19×C4⋊C8—21no—
59C19×C4⋊C8C2×C411yescharacteristic
60C19×C4⋊C8C2×C411yescharacteristic
61C4×C8×C19—21no—
62C4×C8×C19D411yescharacteristic
63C4×C8×C19D411yescharacteristic
64C19×#95—21no—
65C22⋊(C19⋊C8)D412yes—
66#10597278—21no—
67#10597278—21no—
68(C2×D19)⋊C8—22no—
69#10597275—21no—
70#10597275—21no—
71#10597274—21no—
72#10597274—21no—
73#10597273—21no—
74#10597273—21no—
75Dic19⋊C8—22no—
76C8×Dic19—22no—
77#10597262—42no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)—21no—
81C4×C19⋊C8—21no—
82C22×C4×C19—41no—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19#4111yescharacteristic
86C2×C22⋊D19—21no—
87#64541—21no—
88#64541—21no—
89#64541SD1612yes—
90#64541Q1612yes—
91C2×D76C22⋊C411yescharacteristic
92C2×C4×D19—21no—
93C2×C4×D19—21no—
94C2×C4×D19—21no—
95C2×Dic38—21no—
96C2×Dic38—21no—
97C2×Dic38C22⋊C411yescharacteristic
98C2×C8×C19—21no—
99C2×C8×C19—21no—
100C2×C8×C19—21no—
101C2×C8×C19—21no—
102C2×C8×C19—42no—
103C2×C8×C19—41no—
104C2×C8×C19—41no—
105C4⋊C4×C19—22no—
106C4⋊C4×C19—41no—
107C42×C19—41no—
108C42×C19—41no—
109C42×C19C22×C411yescharacteristic
110C42×C19C2×D411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19#4111yescharacteristic
113C22⋊Dic19—21no—
114C22⋊Dic19—41no—
115(C2×D19)⋊C4—21no—
116(C2×D19)⋊C4—21no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121C4⋊Dic19C22⋊C411yescharacteristic
122C4⋊Dic19C22⋊C411yescharacteristic
123Dic19⋊C4—21no—
124Dic19⋊C4—21no—
125Dic19⋊C4—41no—
126Dic19⋊C4—41no—
127C4×Dic19—21no—
128C4×Dic19—21no—
129C4×Dic19—21no—
130C4×Dic19—41no—
131#64520—41no—
132#64520—41no—
133C2×C19⋊C8—22no—
134C2×C19⋊C8—41no—
135C8×D19—44no—
136#9207—191nomaximal, Sylow
137C23×C19#12111yescharacteristic
138C22×D19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19—81no—
144C2×C4×C19—81no—
145C2×C4×C19C2×C22⋊C411yescharacteristic
146C2×C4×C19C4×D411yescharacteristic
147C2×C4×C19C4×D411yescharacteristic
148C2×C4×C19#12011yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12311yescharacteristic
151C2×C4×C19C2×SD1611yescharacteristic
152C2×C4×C19C2×Q1611yescharacteristic
153C2×C4×C19#13511yescharacteristic
154C2×C4×C19#13511yescharacteristic
155C22⋊D19—22no—
156C22⋊D19—22no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159C2×Dic19—21no—
160C2×Dic19—41no—
161C2×Dic19—41no—
162D76—21no—
163D76#10312yes—
164C4×D19—22no—
165C4×D19—22no—
166C4×D19—42no—
167C4×D19—41no—
168C4×D19—41no—
169Dic38—21no—
170Dic38—41no—
171Dic38—41no—
172Dic38—81no—
173Dic38#10312yes—
174C8×C19—22no—
175C8×C19—41no—
176C8×C19—41no—
177C8×C19—41no—
178C19⋊C8—42no—
179C19⋊C8—81no—
180#3076—191no—
181C8×#41—191no—
182#1806—191no—
183#1503—191no—
184#1493—191no—
185#1301—191no—
186#1279D1911yescharacteristic, complemented
187C22×C19—21no—
188C22×C19—21no—
189C22×C19#38611yescharacteristic
190C22×C19#46511yescharacteristic
191C22×C19#46711yescharacteristic
192C2×D19—22no—
193C2×D19—41no—
194C2×D19—41no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—82no—
199C4×C19C2×#10311yescharacteristic
200C4×C19#41611yescharacteristic
201C4×C19#44311yescharacteristic
202C4×C19#44411yescharacteristic
203C4×C19#46511yescharacteristic
204C4×C19#46711yescharacteristic
205Dic19—22no—
206Dic19—41no—
207Dic19—41no—
208Dic19—81no—
209Dic19—81no—
210#533—191no—
211C4×#41—191no—
212#479—381no—
213#478—381no—
214#477—191no—
215#476—191no—
216#475—191no—
217#474—191no—
218C8×Q8—381no—
219C8×D4—381no—
220C8×D4—382no—
221#431—191no—
222#431—381no—
223#427—381no—
224#423—191no—
225C2×C4⋊C8C2×D1911yescharacteristic
226C2×#104—381no—
227#416—381no—
228C2×C4×C8—381no—
229C2×C4×C8C2×D1911yescharacteristic
230C4×C4⋊C4C2×D1911yescharacteristic
231#339—381no—
232#328—382no—
233Q8⋊C8—381no—
234Q8⋊C8—381no—
235C2×C19—21no—
236C2×C19—21no—
237C2×C19#187611yescharacteristic
238C2×C19#189211yescharacteristic
239C2×C19#190611yescharacteristic
240D19—42no—
241C2×#41—191no—
242C2×M16—381no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—382no—
246C4⋊Q8—191no—
247C4⋊Q8—191no—
248#125—381no—
249C22⋊Q8—381no—
250C22⋊Q8—381no—
251C4×Q8—191no—
252C4×Q8—191no—
253C4×Q8—381no—
254C4×Q8—381no—
255C4×D4—191no—
256C4×D4—191no—
257C4×D4—381no—
258C4×D4—381no—
259#117—191no—
260#117—381no—
261#117—381no—
262C2×C4⋊C4—21no—
263C2×C42—21no—
264C2×C42—381no—
265C2×C42C22×D1911yescharacteristic
266#107—381no—
267#107—381no—
268#106—381no—
269#106—381no—
270C4⋊C8—21no—
271C4⋊C8—382no—
272C4⋊C8—381no—
273C4⋊C8—381no—
274C4⋊C8—381no—
275C4⋊C8C4×D1911yescharacteristic
276C4⋊C8C4×D1911yescharacteristic
277#104—762no—
278#103—381no—
279#103—381no—
280#102—381no—
281#102—381no—
282C22⋊C8—192no—
283C22⋊C8—382no—
284C4×C8—21no—
285C4×C8—382no—
286C4×C8—381no—
287C4×C8D7611yescharacteristic
288C4×C8D7611yescharacteristic
289#95—21no—
290C19#920711yescharacteristic, complemented, Sylow
291#41—192no—
292#41—192no—
293#41—381no—
294#41—381no—
295C2×Q8—191no—
296C2×Q8—381no—
297C2×Q8—381no—
298C2×D4—191no—
299C2×D4—381no—
300C22×C4—41no—
301C22×C4—381no—
302C22×C4—381no—
303C22×C4—381no—
304C22×C4#6454111yescharacteristic
305C22×C4D4×D1911yescharacteristic
306C22×C4D4×D1911yescharacteristic
307M16—761no—
308M16—761no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—42no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—382no—
317C2×C8—764no—
318C2×C8—761no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—191no—
322C4⋊C4—191no—
323C4⋊C4—381no—
324C4⋊C4—381no—
325C4⋊C4—381no—
326C4⋊C4—381no—
327C4⋊C4—381no—
328C4⋊C4—381no—
329C4⋊C4—761no—
330C4⋊C4—761no—
331C22⋊C4—381no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C22⋊C4—761no—
335C42—41no—
336C42—41no—
337C42—381no—
338C42—381no—
339C42—381no—
340C42—761no—
341C42C2×C4×D1911yescharacteristic
342C42C2×D7611yescharacteristic
343C42D4×D1911yescharacteristic
344C42#6454511yescharacteristic
345C23—381no—
346C23#1059733011yescharacteristic
347Q8—192no—
348Q8—381no—
349Q8—761no—
350Q8—761no—
351Q8—1521no—
352D4—192no—
353D4—382no—
354D4—382no—
355D4—381no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—381no—
363C2×C4—382no—
364C2×C4—382no—
365C2×C4—381no—
366C2×C4—381no—
367C2×C4—762no—
368C2×C4—761no—
369C2×C4—761no—
370C2×C4—761no—
371C2×C4—761no—
372C2×C4C4×D7611yescharacteristic
373C2×C4C22⋊C4×D1911yescharacteristic
374C2×C4#1059732811yescharacteristic
375C2×C4#1059733911yescharacteristic
376C2×C4#1059734011yescharacteristic
377C2×C4#1059734111yescharacteristic
378C2×C4#1059735811yescharacteristic
379C2×C4SD16×D1911yescharacteristic
380C2×C4#1059736211yescharacteristic
381C2×C4Q16×D1911yescharacteristic
382C8—22no—
383C8—41no—
384C8—41no—
385C8—41no—
386C8—762no—
387C8—1521no—
388C22—21no—
389C22—21no—
390C22—382no—
391C22—761no—
392C22—761no—
393C22#1192642211yescharacteristic
394C22#1192677211yescharacteristic
395C22#1192678411yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—82no—
400C4—382no—
401C4—761no—
402C4—761no—
403C4—1521no—
404C4—1521no—
405C4#103×D1911yescharacteristic
406C4#1192653711yescharacteristic
407C4#1192666211yescharacteristic
408C4#1192666711yescharacteristic
409C4#1192677411yescharacteristic
410C4#1192678611yescharacteristic
411C2—21no—
412C2—21no—
413C2—762no—
414C2#1456396111yescharacteristic
415C2#1456405711yescharacteristic
416C2#1456413511yescharacteristic
subgroupG/H
centerC2×C4#10597341
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1279C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1279D19
hypocenterC19#9207
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #14562133C2semidirect
5. #14562091C2semidirect
6. #14561532C2semidirect
7. C19×#1279C2semidirect
12. #11926840C4semidirect
13. #11926835C4semidirect
14. #11926830C4semidirect
15. #11926825C4semidirect
186. #1279D19semidirect
290. C19#9207semidirect

Maximal subgroups

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

subgroupindex
#145734252
C8×#645412
#145636562
#145621332
#145620912
#145615322
C19×#12792
#920719