Finite Group Databasebeta

← #18078024

Subgroups — #18078024

Order 4864.

488 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572596C211yesmaximal, characteristic
2C4×#10597388C211yesmaximal, characteristic
3#14562023C211yesmaximal, characteristic
4C2×Q8⋊(C19⋊C8)C211yesmaximal, characteristic, complemented
5#14561484C211yesmaximal, characteristic, complemented
6#14561471C211yesmaximal, characteristic, complemented
7C19×#1461C211yesmaximal, characteristic, complemented
8C2×#10597388C411yescharacteristic
9C4×#64541C2211yescharacteristic
10#11926671—21no—
11#11926649—21no—
12#11926642—21no—
13C4×#64528—21no—
14C4×#64527—21no—
15#11926621—21no—
16#11926612—22no—
17#11926595—21no—
18#11926584C411yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20#11926553C411yescharacteristic
21#11926543C411yescharacteristic
22C4×#64520C2211yescharacteristic
23C4×#64515—21no—
24C2×C4×C19⋊C8C2211yescharacteristic
25#11926276—21no—
26Q8⋊(C19⋊C8)—21no—
27Q8⋊(C19⋊C8)—21no—
28#11926273—21no—
29C2×C4×Q8×C19C2211yescharacteristic
30C19×#431C2211yescharacteristic
31C19×#431C2211yescharacteristic
32C19×#324—22no—
33C22×Q8×C19C2×C411yescharacteristic
34C2×#64541C2×C411yescharacteristic
35C4×Q8×C19—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19C2×C411yescharacteristic
41C2×C42×C19—21no—
42C2×C42×C19C2311yescharacteristic
43C2×#64528—21no—
44#10597388—22no—
45#10597388—22no—
46C2×#64527—21no—
47C4×C22⋊D19—21no—
48C4×C22⋊D19—21no—
49#10597372C2×C411yescharacteristic
50C2×#64520C2×C411yescharacteristic
51C2×#64520C2×C411yescharacteristic
52C22×C19⋊C8—21no—
53C22×C19⋊C8—21no—
54C2×#64515—22no—
55C4×D76D411yescharacteristic
56C4×D76D411yescharacteristic
57#10597318—21no—
58C42×D19—21no—
59C4×Dic38D411yescharacteristic
60C4×Dic38D411yescharacteristic
61C19×C4⋊C8—21no—
62C19×C4⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8D412yes—
65C4×C8×C19—21no—
66C4×C8×C19—21no—
67#10597292—21no—
68#10597292—21no—
69(C2×D19)⋊C8—22no—
70#10597272—22no—
71Dic19⋊C8—22no—
72#10597267—21no—
73#10597266—21no—
74#10597265—21no—
75#10597264—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78#10597260—21no—
79C4×C19⋊C8—21no—
80C4×C19⋊C8—21no—
81C4×C19⋊C8D411yescharacteristic
82C4×C19⋊C8D411yescharacteristic
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—21no—
87C2×Q8×C19—21no—
88C2×Q8×C19M1612yescomplemented
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19C22×C411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C2×C22⋊D19—21no—
95#64541—21no—
96#64541—21no—
97#64541—21no—
98#64541—21no—
99C2×D76C22⋊C411yescharacteristic
100C2×C4×D19—21no—
101C2×C4×D19—21no—
102C2×C4×D19—21no—
103C2×Dic38C22⋊C411yescharacteristic
104C2×C8×C19—22no—
105C2×C8×C19—41no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C42×C19—41no—
111C42×C19—41no—
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19#4111yescharacteristic
116C22⋊Dic19—21no—
117#64528—24no—
118#64527—24no—
119(C2×D19)⋊C4—21no—
120(C2×D19)⋊C4—21no—
121C4⋊Dic19C22⋊C411yescharacteristic
122C4⋊Dic19C22⋊C411yescharacteristic
123Dic19⋊C4—21no—
124Dic19⋊C4—21no—
125C4×Dic19—21no—
126C4×Dic19—21no—
127C4×Dic19—21no—
128#64520—21no—
129#64520—21no—
130#64520—21no—
131#64520M1612yescomplemented
132C2×C19⋊C8—21no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—21no—
136C2×C19⋊C8—42no—
137C2×C19⋊C8—41no—
138C2×C19⋊C8—81no—
139#64515—44no—
140#9098—191nomaximal, Sylow
141C23×C19C4×D411yescharacteristic
142C22×D19—21no—
143Q8×C19—22no—
144Q8×C19—22no—
145Q8×C19—41no—
146Q8×C19—41no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—22no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—81no—
155C2×C4×C19C2×C22⋊C411yescharacteristic
156C2×C4×C19C4×D411yescharacteristic
157C2×C4×C19#12011yescharacteristic
158C2×C4×C19#12111yescharacteristic
159C2×C4×C19#12111yescharacteristic
160C2×C4×C19#12311yescharacteristic
161C2×C4×C19C2×M1611yescharacteristic
162C2×C4×C19C2×M1611yescharacteristic
163C2×C4×C19#13111yescharacteristic
164C2×C4×C19#13111yescharacteristic
165C22⋊D19—41no—
166C22⋊D19—41no—
167C2×Dic19—21no—
168C2×Dic19—21no—
169C2×Dic19—21no—
170D76—21no—
171D76—21no—
172C4×D19—42no—
173C4×D19—41no—
174C4×D19—41no—
175C4×D19—41no—
176C4×D19—41no—
177Dic38—21no—
178Dic38—21no—
179C8×C19—42no—
180C8×C19—81no—
181C19⋊C8—22no—
182C19⋊C8—22no—
183C19⋊C8—41no—
184C19⋊C8—41no—
185C19⋊C8—81no—
186#2965—191no—
187C4×#137—191no—
188#1477—191no—
189C2×Q8⋊C8—191no—
190#1461D1911yescharacteristic, complemented
191#1283—191no—
192#1278—191no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19#38611yescharacteristic
196C22×C19#43511yescharacteristic
197C22×C19#43611yescharacteristic
198C2×D19—41no—
199C2×D19—41no—
200C2×D19—41no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—42no—
205C4×C19—81no—
206C4×C19#40711yescharacteristic
207C4×C19#40811yescharacteristic
208C4×C19#43511yescharacteristic
209C4×C19#43611yescharacteristic
210C4×C19#47111yescharacteristic
211C4×C19#47311yescharacteristic
212Dic19—41no—
213Dic19—41no—
214Dic19—41no—
215C2×#137—191no—
216C4×#41—191no—
217C2×C4×Q8C2×D1911yescharacteristic
218#446—381no—
219#441—381no—
220#440—381no—
221C4×Q16—381no—
222C4×SD16—381no—
223#436—381no—
224#435—382no—
225#431—381no—
226#431C2×D1911yescharacteristic
227#431C2×D1911yescharacteristic
228#428—191no—
229C2×C4⋊C8—191no—
230#419—191no—
231#417—191no—
232C4×M16—191no—
233C4×M16—381no—
234C2×C4×C8—191no—
235Q8⋊C8—381no—
236Q8⋊C8—381no—
237Q8⋊C8—381no—
238D4⋊C8—381no—
239#324—22no—
240C2×C19—21no—
241C2×C19—21no—
242C2×C19#187011yescharacteristic
243C2×C19#190611yescharacteristic
244C2×C19#190811yescharacteristic
245D19—81no—
246C2×#41—191no—
247C22×Q8C4×D1911yescharacteristic
248#137—382no—
249#137—382no—
250C2×Q16—381no—
251C2×SD16—381no—
252C2×M16—191no—
253C2×M16—191no—
254C2×M16—382no—
255C22×C8—381no—
256C22×C8—381no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—191no—
262C4×Q8—191no—
263C4×D4—191no—
264C4×D4—191no—
265C4×D4—381no—
266C4×D4—381no—
267#117—191no—
268#117—381no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4C4×D1911yescharacteristic
271C2×C42—21no—
272C2×C42—381no—
273C2×C42C22×D1911yescharacteristic
274#107—381no—
275#106—381no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—382no—
279C4⋊C8—381no—
280C4⋊C8—381no—
281#103—381no—
282#103—381no—
283#103—381no—
284#102—381no—
285C22⋊C8—21no—
286C22⋊C8—382no—
287C22⋊C8C22⋊D1912yes—
288#97—382no—
289#97—381no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—191no—
293C4×C8—191no—
294C4×C8—381no—
295C4×C8—381no—
296C19#909811yescharacteristic, complemented, Sylow
297#41—381no—
298#41—381no—
299#41—381no—
300#41—381no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—191no—
307C2×Q8#6451512yescomplemented
308C2×D4—191no—
309C2×D4—381no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—381no—
313C22×C4—381no—
314C22×C4—381no—
315C22×C4C2×C4×D1911yescharacteristic
316C22×C4#6454111yescharacteristic
317C22×C4C2×C22⋊D1911yescharacteristic
318Q16—384no—
319SD16—384no—
320M16—192no—
321M16—381no—
322M16—381no—
323M16—381no—
324M16—764no—
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—381no—
328C2×C8—381no—
329C2×C8—381no—
330C2×C8—381no—
331C2×C8—762no—
332C2×C8—761no—
333C2×C8—1521no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—191no—
339C4⋊C4—191no—
340C4⋊C4—381no—
341C4⋊C4—381no—
342C22⋊C4—381no—
343C22⋊C4—381no—
344C22⋊C4—381no—
345C42—41no—
346C42—41no—
347C42—381no—
348C42—381no—
349C42—381no—
350C42D4×D1911yescharacteristic
351C42D4×D1911yescharacteristic
352C42D4×D1911yescharacteristic
353C42#6454311yescharacteristic
354C23—381no—
355C23C4×C22⋊D1911yescharacteristic
356Q8—22no—
357Q8—22no—
358Q8—41no—
359Q8—41no—
360Q8—381no—
361Q8—381no—
362D4—381no—
363D4—381no—
364D4—761no—
365D4—761no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—381no—
375C2×C4—381no—
376C2×C4—381no—
377C2×C4—762no—
378C2×C4—761no—
379C2×C4—761no—
380C2×C4—761no—
381C2×C4—761no—
382C2×C4C22⋊C4×D1911yescharacteristic
383C2×C4(C22⋊D19)⋊C411yescharacteristic
384C2×C4#1059732911yescharacteristic
385C2×C4#1059733011yescharacteristic
386C2×C4C2×#6451511yescharacteristic
387C2×C4#1059734711yescharacteristic
388C2×C4M16×D1911yescharacteristic
389C2×C4#1059735311yescharacteristic
390C2×C4#1059738311yescharacteristic
391C2×C4#1059738411yescharacteristic
392C8—42no—
393C8—81no—
394C8—382no—
395C8—382no—
396C8—761no—
397C8—761no—
398C8—1521no—
399C22—21no—
400C22—21no—
401C22—761no—
402C22—761no—
403C22—761no—
404C22#1192642011yescharacteristic
405C22#1192661511yescharacteristic
406C22#1192662011yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—42no—
411C4—81no—
412C4—761no—
413C4—761no—
414C4—761no—
415C4#1192650611yescharacteristic
416C4#1192650911yescharacteristic
417C4#1192661211yescharacteristic
418C4#1192661911yescharacteristic
419C4#1192681011yescharacteristic
420C4#1192681811yescharacteristic
421C2—21no—
422C2—21no—
423C2—1521no—
424C2#1456392911yescharacteristic
425C2#1456413311yescharacteristic
426C2#1456414711yescharacteristic
subgroupG/H
centerC2×C4#10597330
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1461C2
socleC22×C19#386
prime radicalC2×#64541C2×C4
cosocleC2×C42×C19C23
hypercenter#1461D19
hypocenterC19#9098
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊(C19⋊C8)C2semidirect
5. #14561484C2semidirect
6. #14561471C2semidirect
7. C19×#1461C2semidirect
88. C2×Q8×C19M16semidirect
131. #64520M16semidirect
190. #1461D19semidirect
296. C19#9098semidirect
307. C2×Q8#64515semidirect

Maximal subgroups

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

subgroupindex
#145725962
C4×#105973882
#145620232
C2×Q8⋊(C19⋊C8)2
#145614842
#145614712
C19×#14612
#909819