Finite Group Databasebeta

← #18078625

Subgroups — #18078625

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#14573417C211yesmaximal, characteristic
2C8×#64541C211yesmaximal, characteristic
3#14563652C211yesmaximal, characteristic
4#14562134C211yesmaximal, characteristic, complemented
5#14561530C211yesmaximal, characteristic, complemented
6#14561475C211yesmaximal, characteristic, complemented
7C19×#1493C211yesmaximal, characteristic, complemented
8C4×#64541C2211yescharacteristic
9#11926848—21no—
10#11926841—21no—
11#11926836C411yescharacteristic, complemented
12#11926831C411yescharacteristic, complemented
13#11926826C411yescharacteristic, complemented
14#11926821C411yescharacteristic, complemented
15C8×Dic38—21no—
16C8×D76—21no—
17C8×C22⋊D19—22no—
18#11926597C2211yescharacteristic
19#11926595—21no—
20#11926580—21no—
21C2×C4⋊(C19⋊C8)C2211yescharacteristic
22C2×#10597282—21no—
23#11926538—21no—
24C4×C8×D19—21no—
25C4×C4⋊Dic19C2211yescharacteristic
26#11926305—21no—
27#11926281—22no—
28C19×#533C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C2×C4×C8×C19C2211yescharacteristic
31C19×Q8⋊C8—21no—
32C19×Q8⋊C8—21no—
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
48C2×C4⋊Dic19—21no—
49C2×C4×Dic19—21no—
50C22×C19⋊C8—21no—
51C2×C8×D19—22no—
52C4×D76C2×C411yescharacteristic
53C4×D76D411yescharacteristic
54#10597318—21no—
55C42×D19—21no—
56C4×Dic38C2×C411yescharacteristic
57C4×Dic38D411yescharacteristic
58C19×C4⋊C8—21no—
59C19×C4⋊C8—21no—
60C4×C8×C19—21no—
61C4×C8×C19D411yescharacteristic
62C4×C8×C19D411yescharacteristic
63C19⋊#95—21no—
64C22⋊(C19⋊C8)D412yes—
65#10597282—42no—
66(C2×D19)⋊C8—22no—
67Dic19⋊C8—22no—
68C8×Dic19—22no—
69#10597267—21no—
70#10597267—21no—
71#10597266—21no—
72#10597266—21no—
73#10597265—21no—
74#10597265—21no—
75#10597264—21no—
76#10597264—21no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)C2×C411yescharacteristic
80C4⋊(C19⋊C8)C2×C411yescharacteristic
81C4×C19⋊C8—21no—
82C2×Q8×C19—21no—
83C2×Q8×C19—21no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19#4111yescharacteristic
87C2×C22⋊D19—21no—
88C22×Dic19—41no—
89#64541—21no—
90#64541—21no—
91#64541SD1612yes—
92#64541Q1612yes—
93C2×D76C22⋊C411yescharacteristic
94C2×C4×D19—21no—
95C2×C4×D19—21no—
96C2×C4×D19—21no—
97C2×Dic38C22⋊C411yescharacteristic
98M16×C19—41no—
99M16×C19—41no—
100C2×C8×C19—21no—
101C2×C8×C19—21no—
102C2×C8×C19—42no—
103C2×C8×C19—41no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C42×C19—41no—
112C42×C19C22×C411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19#4111yescharacteristic
116C22⋊Dic19—21no—
117(C2×D19)⋊C4—21no—
118(C2×D19)⋊C4—21no—
119C4⋊Dic19—22no—
120C4⋊Dic19—41no—
121C4⋊Dic19C22⋊C411yescharacteristic
122C4⋊Dic19C22⋊C411yescharacteristic
123Dic19⋊C4—21no—
124Dic19⋊C4—21no—
125C4×Dic19—21no—
126C4×Dic19—21no—
127C4×Dic19—21no—
128C4×Dic19—41no—
129C4×Dic19—41no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—22no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135C8×D19—44no—
136#9207—191nomaximal, Sylow
137C23×C19#12111yescharacteristic
138C22×D19—21no—
139Q8×C19—41no—
140Q8×C19—41no—
141Q8×C19—81no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19C2×C22⋊C411yescharacteristic
148C2×C4×C19C4×D411yescharacteristic
149C2×C4×C19C4×D411yescharacteristic
150C2×C4×C19#12011yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19#12311yescharacteristic
153C2×C4×C19C2×SD1611yescharacteristic
154C2×C4×C19C2×Q1611yescharacteristic
155C2×C4×C19#13511yescharacteristic
156C2×C4×C19#13511yescharacteristic
157C22⋊D19—22no—
158C22⋊D19—22no—
159C2×Dic19—21no—
160C2×Dic19—21no—
161C2×Dic19—21no—
162C2×Dic19—42no—
163C2×Dic19—81no—
164C2×Dic19—81no—
165D76—21no—
166D76#10312yes—
167C4×D19—22no—
168C4×D19—22no—
169C4×D19—42no—
170C4×D19—41no—
171C4×D19—41no—
172Dic38—21no—
173Dic38#10312yes—
174C8×C19—22no—
175C8×C19—41no—
176C8×C19—81no—
177C19⋊C8—42no—
178C19⋊C8—41no—
179C19⋊C8—41no—
180#3076—191no—
181C8×#41—191no—
182#1806—191no—
183#1503—191no—
184#1493D1911yescharacteristic, complemented
185#1301—191no—
186#1279—191no—
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—81no—
199C4×C19—81no—
200C4×C19C2×#10311yescharacteristic
201C4×C19#41611yescharacteristic
202C4×C19#44311yescharacteristic
203C4×C19#44411yescharacteristic
204C4×C19#46511yescharacteristic
205C4×C19#46711yescharacteristic
206Dic19—22no—
207Dic19—41no—
208Dic19—41no—
209Dic19—82no—
210#533C2×D1911yescharacteristic
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#423C2×D1911yescharacteristic
225C2×C4⋊C8—191no—
226C2×#104—381no—
227#416—381no—
228C2×C4×C8—381no—
229C2×C4×C8C2×D1911yescharacteristic
230C4×C4⋊C4—191no—
231#339—381no—
232#328—382no—
233Q8⋊C8—21no—
234Q8⋊C8—21no—
235C2×C19—21no—
236C2×C19—21no—
237C2×C19#187611yescharacteristic
238C2×C19#189211yescharacteristic
239C2×C19#190611yescharacteristic
240D19—42no—
241C2×#41—191no—
242C2×M16—21no—
243C22×C8—21no—
244C22×C8—382no—
245C22×C8—381no—
246C4⋊Q8C4×D1911yescharacteristic
247C4⋊Q8C4×D1911yescharacteristic
248#125—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—191no—
254C4×Q8—191no—
255C4×D4—191no—
256C4×D4—191no—
257C4×D4—381no—
258C4×D4—381no—
259#117—21no—
260#117—191no—
261#117—381no—
262C2×C4⋊C4—381no—
263C2×C42—381no—
264C2×C42—381no—
265C2×C42C22×D1911yescharacteristic
266#107—381no—
267#107—381no—
268#106—381no—
269#106—381no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—191no—
273C4⋊C8—191no—
274C4⋊C8—382no—
275C4⋊C8—381no—
276C4⋊C8—381no—
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×C8C22⋊D1911yescharacteristic
288C4×C8C22⋊D1911yescharacteristic
289#95—381no—
290C19#920711yescharacteristic, complemented, Sylow
291#41—192no—
292#41—192no—
293#41—381no—
294#41—381no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—191no—
298C2×D4—191no—
299C2×D4—381no—
300C22×C4—381no—
301C22×C4—381no—
302C22×C4—381no—
303C22×C4—761no—
304C22×C4#6454111yescharacteristic
305C22×C4D4×D1911yescharacteristic
306C22×C4D4×D1911yescharacteristic
307M16—41no—
308M16—41no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—42no—
312C2×C8—41no—
313C2×C8—382no—
314C2×C8—381no—
315C2×C8—381no—
316C2×C8—764no—
317C2×C8—761no—
318C2×C8—761no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—191no—
326C4⋊C4—191no—
327C4⋊C4—382no—
328C4⋊C4—381no—
329C4⋊C4—381no—
330C4⋊C4—761no—
331C22⋊C4—41no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C22⋊C4—381no—
335C42—41no—
336C42—381no—
337C42—381no—
338C42—381no—
339C42—761no—
340C42—761no—
341C42C2×C4×D1911yescharacteristic
342C42D4×D1911yescharacteristic
343C42#6454311yescharacteristic
344C42C2×C22⋊D1911yescharacteristic
345C23—381no—
346C23#1059733011yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—81no—
350Q8—192no—
351Q8—381no—
352D4—192no—
353D4—382no—
354D4—382no—
355D4—381no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—381no—
362C2×C4—382no—
363C2×C4—382no—
364C2×C4—381no—
365C2×C4—381no—
366C2×C4—762no—
367C2×C4—761no—
368C2×C4—761no—
369C2×C4—762no—
370C2×C4—1521no—
371C2×C4—1521no—
372C2×C4C22⋊C4×D1911yescharacteristic
373C2×C4(C22⋊D19)⋊C411yescharacteristic
374C2×C4#1059732911yescharacteristic
375C2×C4SD16×D1911yescharacteristic
376C2×C4#1059736211yescharacteristic
377C2×C4Q16×D1911yescharacteristic
378C2×C4#1059736511yescharacteristic
379C2×C4C4×C22⋊D1911yescharacteristic
380C2×C4#1059738311yescharacteristic
381C2×C4#1059738411yescharacteristic
382C8—22no—
383C8—41no—
384C8—81no—
385C8—762no—
386C8—761no—
387C8—761no—
388C22—21no—
389C22—21no—
390C22—382no—
391C22—761no—
392C22—761no—
393C22#1192642011yescharacteristic
394C22#1192677611yescharacteristic
395C22#1192678411yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—81no—
401C4—382no—
402C4—761no—
403C4—761no—
404C4—1522no—
405C4#103×D1911yescharacteristic
406C4#1192653911yescharacteristic
407C4#1192665911yescharacteristic
408C4#1192666411yescharacteristic
409C4#1192677011yescharacteristic
410C4#1192678211yescharacteristic
411C2—21no—
412C2—21no—
413C2—762no—
414C2#1456396511yescharacteristic
415C2#1456405511yescharacteristic
416C2#1456413911yescharacteristic
subgroupG/H
centerC2×C4#10597384
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1493C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1493D19
hypocenterC19#9207
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
4. #14562134C2semidirect
5. #14561530C2semidirect
6. #14561475C2semidirect
7. C19×#1493C2semidirect
11. #11926836C4semidirect
12. #11926831C4semidirect
13. #11926826C4semidirect
14. #11926821C4semidirect
184. #1493D19semidirect
290. C19#9207semidirect

Maximal subgroups

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

subgroupindex
#145734172
C8×#645412
#145636522
#145621342
#145615302
#145614752
C19×#14932
#920719