Finite Group Databasebeta

← #18078933

Subgroups — #18078933

Order 4864.

528 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926821C211yesmaximal, characteristic
2M16×D76C211yesmaximal, characteristic
3#14562307C211yesmaximal, characteristic, complemented
4#14562059C211yesmaximal, characteristic
5#14561509C211yesmaximal, characteristic, complemented
6#14561486C211yesmaximal, characteristic, complemented
7C19×#1966C211yesmaximal, characteristic, complemented
8C2×M16×D19—21no—
9C2×C4×D76C2211yescharacteristic
10#11926821—21no—
11#11926821—21no—
12#11926821—21no—
13#11926821—21no—
14#11926623—21no—
15#11926617—22no—
16C8×D76—21no—
17#11926597C2211yescharacteristic
18C2×#10597264C412yes—
19#11926568C2211yescharacteristic
20C2×C4⋊(C19⋊C8)C2211yescharacteristic
21C2×#10597266C412yes—
22#11926507—21no—
23#11926290—22no—
24#11926271—21no—
25#11926271—21no—
26C2×C19×C4⋊Q8C2211yescharacteristic
27C19×#423C2211yescharacteristic
28C2×C19×#101—21no—
29C2×C19×#101—21no—
30C4×M16×C19C2211yescharacteristic
31C22×Q8×C19—21no—
32C22×D76C2×C411yescharacteristic
33C22×C4×D19—21no—
34C2×M16×C19—21no—
35C2×M16×C19D411yescharacteristic
36C2×M16×C19D411yescharacteristic
37C19×C4⋊Q8—21no—
38C19×C4⋊Q8—21no—
39C19×C4⋊Q8—21no—
40C19×C4⋊Q8—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19C2×C412yes—
43C2×C42×C19C2311yescharacteristic
44C2×(C2×D19)⋊C4—21no—
45C2×C4⋊Dic19C2×C411yescharacteristic
46C2×#64520—21no—
47C22×C19⋊C8C2×C412yes—
48M16×D19—42no—
49M16×D19—42no—
50C2×#64515—22no—
51C2×C8×D19—22no—
52C4×D76—21no—
53C4×D76—21no—
54C4×D76D411yescharacteristic
55C4×D76D411yescharacteristic
56C4×D76D411yescharacteristic
57C4×D76D411yescharacteristic
58C19×C4⋊C8—21no—
59C19×C4⋊C8—21no—
60C19×#101—42no—
61C19×#101—42no—
62C19×#97—21no—
63C4×C8×C19—21no—
64C22⋊(C19⋊C8)—21no—
65(C2×D19)⋊C8—22no—
66(C2×D19)⋊C8—22no—
67#10597266—22no—
68#10597266—22no—
69#10597264—22no—
70#10597264—22no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)D412yes—
76C4×C19⋊C8—21no—
77C23×D19—21no—
78C2×Q8×C19—41no—
79C2×Q8×C19—41no—
80C2×Q8×C19—41no—
81C2×Q8×C19—41no—
82C2×Q8×C19—41no—
83C2×Q8×C19—41no—
84C22×C4×C19—22no—
85C22×C4×C19C22×C411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19#4111yescharacteristic
88C22×Dic19—21no—
89C2×D76—22no—
90C2×D76—21no—
91C2×D76—41no—
92C2×D76C22⋊C411yescharacteristic
93C2×D76C22⋊C411yescharacteristic
94C2×C4×D19—21no—
95C2×C4×D19—21no—
96C2×C4×D19—21no—
97C2×C4×D19—21no—
98C2×C4×D19—41no—
99C2×C4×D19—41no—
100C2×C4×D19—41no—
101C2×C4×D19—41no—
102M16×C19—21no—
103M16×C19—21no—
104M16×C19—21no—
105M16×C19—41no—
106M16×C19—41no—
107M16×C19D812yes—
108C2×C8×C19—21no—
109C2×C8×C19—21no—
110C2×C8×C19—41no—
111C4⋊C4×C19—22no—
112C4⋊C4×C19—22no—
113C4⋊C4×C19—41no—
114C4⋊C4×C19—41no—
115C42×C19C2×D411yescharacteristic
116C42×C19C2×D411yescharacteristic
117C42×C19C2×D411yescharacteristic
118C42×C19#4111yescharacteristic
119(C2×D19)⋊C4—21no—
120(C2×D19)⋊C4—21no—
121(C2×D19)⋊C4—21no—
122(C2×D19)⋊C4—21no—
123C4⋊Dic19—21no—
124C4⋊Dic19C22⋊C411yescharacteristic
125C4⋊Dic19C22⋊C411yescharacteristic
126#64520—41no—
127#64520—41no—
128C2×C19⋊C8—22no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—42no—
131C2×C19⋊C8—41no—
132#64515—44no—
133C8×D19—44no—
134#9251—191nomaximal, Sylow
135C23×C19C4×D411yescharacteristic
136C22×D19—21no—
137C22×D19—21no—
138C22×D19—42no—
139C22×D19—41no—
140C22×D19—41no—
141C22×D19—81no—
142Q8×C19—81no—
143Q8×C19—81no—
144Q8×C19—81no—
145Q8×C19—81no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—41no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19C2×C22⋊C411yescharacteristic
153C2×C4×C19C4×D411yescharacteristic
154C2×C4×C19#12011yescharacteristic
155C2×C4×C19#12111yescharacteristic
156C2×C4×C19#12111yescharacteristic
157C2×C4×C19#12311yescharacteristic
158C2×C4×C19C2×D811yescharacteristic
159C2×C4×C19#13511yescharacteristic
160C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
162C2×Dic19—21no—
163C2×Dic19—21no—
164C2×Dic19—41no—
165C2×Dic19—41no—
166D76—21no—
167D76—21no—
168D76—21no—
169D76—42no—
170D76#10112yescomplemented
171C4×D19—41no—
172C4×D19—41no—
173C4×D19—41no—
174C4×D19—41no—
175C4×D19—41no—
176C4×D19—41no—
177C4×D19—41no—
178C4×D19—41no—
179C8×C19—22no—
180C8×C19—41no—
181C8×C19—81no—
182C19⋊C8—42no—
183C19⋊C8—42no—
184C19⋊C8—81no—
185C2×#474—191no—
186D4×M16—191no—
187#1966D1911yescharacteristic, complemented
188#1546—191no—
189#1486—191no—
190#1292—191no—
191#1283—191no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19#38611yescharacteristic
195C22×C19C4×D811yescharacteristic
196C22×C19#44211yescharacteristic
197C2×D19—22no—
198C2×D19—41no—
199C2×D19—41no—
200C2×D19—41no—
201C2×D19—41no—
202C2×D19—41no—
203C2×D19—82no—
204C2×D19—82no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—82no—
209C4×C19C2×#10111yescharacteristic
210C4×C19#41311yescharacteristic
211C4×C19#44711yescharacteristic
212C4×C19#44911yescharacteristic
213C4×C19#45911yescharacteristic
214C4×C19#46311yescharacteristic
215Dic19—41no—
216Dic19—41no—
217C22×M16—381no—
218C2×C4⋊Q8C2×D1911yescharacteristic
219C2×C4×D4—191no—
220#474—381no—
221#474—381no—
222#474—381no—
223#474—381no—
224#436—381no—
225#435—382no—
226C8×D4—381no—
227#431—191no—
228C2×#107—192no—
229#423—191no—
230#423C2×D1911yescharacteristic
231C2×C4⋊C8—191no—
232C2×#102—192no—
233C2×#101—21no—
234C2×#101—21no—
235#407—381no—
236C4×M16C2×D1911yescharacteristic
237#332—382no—
238D4⋊C8—381no—
239D4⋊C8—381no—
240C2×C19—21no—
241C2×C19—21no—
242C2×C19#187911yescharacteristic
243C2×C19#190111yescharacteristic
244C2×C19#190211yescharacteristic
245D19—42no—
246D19—81no—
247C22×Q8—21no—
248C22×D4—191no—
249C23×C4—381no—
250C2×M16—21no—
251C2×M16—382no—
252C2×M16—381no—
253C2×M16—762no—
254C2×M16—762no—
255C2×M16C22⋊D1911yescharacteristic
256C2×M16C22⋊D1911yescharacteristic
257C22×C8—192no—
258C22×C8—382no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4×D4—191no—
264C4×D4—191no—
265C4×D4—191no—
266C4×D4—191no—
267C4×D4—381no—
268C4×D4—381no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—191no—
271C2×C4⋊C4C4×D1912yes—
272C2×C22⋊C4—381no—
273C2×C42C22×D1911yescharacteristic
274#107—382no—
275#107—382no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—192no—
279C4⋊C8—381no—
280C4⋊C8—381no—
281C4⋊C8—381no—
282C4⋊C8—381no—
283#102—382no—
284#102—382no—
285#101—42no—
286#101—42no—
287C22⋊C8—382no—
288C22⋊C8—382no—
289C22⋊C8—381no—
290#97—21no—
291C4×C8—21no—
292C4×C8—381no—
293C19#925111yescharacteristic, complemented, Sylow
294C24—381no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×D4—191no—
302C2×D4—191no—
303C2×D4—382no—
304C2×D4—381no—
305C2×D4—761no—
306C22×C4—22no—
307C22×C4—381no—
308C22×C4—381no—
309C22×C4—381no—
310C22×C4—381no—
311C22×C4—381no—
312C22×C4—761no—
313C22×C4—761no—
314C22×C4—761no—
315C22×C4—761no—
316C22×C4C2×C4×D1911yescharacteristic
317C22×C4#6454111yescharacteristic
318C22×C4C2×C22⋊D1911yescharacteristic
319M16—21no—
320M16—21no—
321M16—21no—
322M16—41no—
323M16—41no—
324M16—764no—
325M16—761no—
326M16—761no—
327M16#6452512yes—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—41no—
331C2×C8—382no—
332C2×C8—382no—
333C2×C8—764no—
334C2×C8—762no—
335C2×C8—761no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—191no—
341C4⋊C4—191no—
342C4⋊C4—381no—
343C22⋊C4—381no—
344C22⋊C4—381no—
345C22⋊C4—381no—
346C22⋊C4—381no—
347C42D4×D1911yescharacteristic
348C42D4×D1911yescharacteristic
349C42D4×D1911yescharacteristic
350C42#6454311yescharacteristic
351C23—381no—
352C23—381no—
353C23—762no—
354C23—761no—
355C23—761no—
356C23—1521no—
357C23C4×C22⋊D1911yescharacteristic
358Q8—81no—
359Q8—81no—
360Q8—81no—
361Q8—81no—
362D4—192no—
363D4—381no—
364D4—381no—
365D4—381no—
366D4—762no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—381no—
374C2×C4—381no—
375C2×C4—761no—
376C2×C4—761no—
377C2×C4—761no—
378C2×C4—761no—
379C2×C4—761no—
380C2×C4—761no—
381C2×C4—761no—
382C2×C4—761no—
383C2×C4—761no—
384C2×C4—761no—
385C2×C4C22⋊C4×D1911yescharacteristic
386C2×C4(C22⋊D19)⋊C411yescharacteristic
387C2×C4#1059732911yescharacteristic
388C2×C4#1059733011yescharacteristic
389C2×C4C2×#6452511yescharacteristic
390C2×C4#1059737811yescharacteristic
391C2×C4#1059738311yescharacteristic
392C2×C4#1059738411yescharacteristic
393C2×C4#1059739511yescharacteristic
394C2×C4#1059739611yescharacteristic
395C8—22no—
396C8—41no—
397C8—81no—
398C8—762no—
399C8—762no—
400C8—1521no—
401C22—21no—
402C22—21no—
403C22—382no—
404C22—761no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22—761no—
409C22—1522no—
410C22—1522no—
411C22#1192642011yescharacteristic
412C22C4×#6452511yescharacteristic
413C22#1192665411yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—82no—
418C4—761no—
419C4—761no—
420C4#101×D1911yescharacteristic
421C4#1192652711yescharacteristic
422C4#1192667711yescharacteristic
423C4#1192668711yescharacteristic
424C4#1192673611yescharacteristic
425C4#1192675611yescharacteristic
426C2—21no—
427C2—21no—
428C2—762no—
429C2—1521no—
430C2#1456398611yescharacteristic
431C2#1456410011yescharacteristic
432C2#1456411111yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1966C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1966D19
hypocenterC19#9251
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
3. #14562307C2semidirect
5. #14561509C2semidirect
6. #14561486C2semidirect
7. C19×#1966C2semidirect
170. D76#101semidirect
187. #1966D19semidirect
293. C19#9251semidirect

Maximal subgroups

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

subgroupindex
C2×#119268212
M16×D762
#145623072
#145620592
#145615092
#145614862
C19×#19662
#925119