Finite Group Databasebeta

← #18078856

Subgroups — #18078856

Order 4864.

452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926882C211yesmaximal, characteristic
2#14572289C211yesmaximal, characteristic
3#14563732C211yesmaximal, characteristic
4#14562155C211yesmaximal, characteristic
5#14561511C211yesmaximal, characteristic
6#14561481C211yesmaximal, characteristic
7C19×#1472C211yesmaximal, characteristic
8C2×#10597372C2211yescharacteristic
9#11926882—21no—
10#11926882—21no—
11#11926882—21no—
12#11926882—21no—
13#11926602—22no—
14#11926598—21no—
15#11926594—21no—
16C2×#10597264C411yescharacteristic, complemented
17C2×#10597265C411yescharacteristic, complemented
18#11926570—21no—
19C2×#10597292C411yescharacteristic, complemented
20C2×#10597292C411yescharacteristic, complemented
21#11926508C2211yescharacteristic
22C2×C22⋊(C19⋊C8)C2211yescharacteristic
23#11926499—21no—
24C4×C22⋊Dic19C2211yescharacteristic
25#11926305—21no—
26#11926305—21no—
27#11926281—22no—
28C2×C19×C22⋊Q8C2211yescharacteristic
29C19×#407C2211yescharacteristic
30C2×C19×C22⋊C8C2211yescharacteristic
31C19×#324—21no—
32C19×#324—21no—
33C22×Q8×C19C2×C411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C2×M16×C19—21no—
36C22×C8×C19—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19C2×C411yescharacteristic
43C2×C22⋊C4×C19—21no—
44C2×C22⋊Dic19—21no—
45C2×C22⋊Dic19—21no—
46#10597372—21no—
47#10597372—21no—
48#10597372D411yescharacteristic
49#10597372D411yescharacteristic
50#10597372D411yescharacteristic
51#10597372D411yescharacteristic
52C2×C4⋊Dic19C2×C411yescharacteristic
53C2×C4⋊Dic19C2×C411yescharacteristic
54C2×C4×Dic19—21no—
55C2×C4×Dic19—21no—
56C2×#64520—21no—
57C22×C19⋊C8C2×C411yescharacteristic
58C22×C19⋊C8C2×C411yescharacteristic
59C19×C22⋊C8—21no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8D411yescharacteristic
63C19×C22⋊C8D411yescharacteristic
64#10597292—21no—
65#10597292—21no—
66#10597292—21no—
67#10597292—21no—
68C19⋊#95—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)D412yes—
73#10597272—22no—
74Dic19⋊C8—22no—
75Dic19⋊C8—22no—
76C8×Dic19—22no—
77#10597265—21no—
78#10597265—21no—
79#10597264—21no—
80#10597264—21no—
81C24×C19#4111yescharacteristic
82C2×Q8×C19—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—41no—
85C2×Q8×C19—41no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19C22×C411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—41no—
99M16×C19—41no—
100M16×C19—41no—
101C2×C8×C19—21no—
102C2×C8×C19—21no—
103C2×C8×C19—41no—
104C2×C8×C19—41no—
105C2×C8×C19—41no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C22⋊Dic19—21no—
113C22⋊Dic19—21no—
114C22⋊Dic19—21no—
115C22⋊Dic19—21no—
116C22⋊Dic19—22no—
117C22⋊Dic19—41no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19C22⋊C411yescharacteristic
121C4⋊Dic19C22⋊C411yescharacteristic
122C4⋊Dic19C22⋊C411yescharacteristic
123C4⋊Dic19C22⋊C411yescharacteristic
124C4×Dic19—21no—
125C4×Dic19—21no—
126C4×Dic19—21no—
127C4×Dic19—21no—
128C4×Dic19—41no—
129C4×Dic19—41no—
130#64520—41no—
131#64520—41no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—22no—
135C2×C19⋊C8—41no—
136C2×C19⋊C8—41no—
137#9240—191nomaximal, Sylow
138C23×C19—21no—
139C23×C19—21no—
140C23×C19—41no—
141C23×C19—41no—
142C23×C19C4×D411yescharacteristic
143C23×C19#12111yescharacteristic
144C23×C19#12311yescharacteristic
145Q8×C19—41no—
146Q8×C19—41no—
147Q8×C19—81no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—81no—
162C2×C4×C19C2×C22⋊C411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19#12011yescharacteristic
165C2×C4×C19#12111yescharacteristic
166C2×Dic19—21no—
167C2×Dic19—21no—
168C2×Dic19—21no—
169C2×Dic19—21no—
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—42no—
173C2×Dic19—81no—
174C2×Dic19—81no—
175C2×Dic19—81no—
176C8×C19—41no—
177C8×C19—41no—
178C8×C19—81no—
179C19⋊C8—42no—
180C19⋊C8—41no—
181C19⋊C8—41no—
182C2×#485—191no—
183#2924—191no—
184#1826—191no—
185#1508—191no—
186#1472D1911yescharacteristic
187#1293—191no—
188#1282—191no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19#38611yescharacteristic
200C22×C19#44311yescharacteristic
201C22×C19#44411yescharacteristic
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—81no—
206C4×C19—81no—
207C4×C19#41011yescharacteristic
208C4×C19#41011yescharacteristic
209Dic19—41no—
210Dic19—41no—
211Dic19—41no—
212Dic19—41no—
213Dic19—82no—
214C2×C22⋊Q8C2×D1911yescharacteristic
215C2×#117—191no—
216#485—381no—
217#485—381no—
218#485—381no—
219#485—381no—
220#433—382no—
221#432—381no—
222#431—381no—
223C2×#107—191no—
224C2×#106—191no—
225#424—381no—
226C2×#103—191no—
227C2×#103—191no—
228#407—191no—
229#407C2×D1911yescharacteristic
230C2×C22⋊C8—191no—
231C2×C22⋊C8C2×D1911yescharacteristic
232#405—381no—
233C4×C22⋊C4—191no—
234#339—381no—
235#339—381no—
236#328—382no—
237#324—21no—
238#324—21no—
239C2×C19—21no—
240C2×C19—21no—
241C2×C19—41no—
242C2×C19—41no—
243C2×C19#187611yescharacteristic
244C2×C19#189911yescharacteristic
245C2×C19#190211yescharacteristic
246C22×Q8C4×D1911yescharacteristic
247C23×C4C22×D1911yescharacteristic
248C2×M16—21no—
249C2×M16—381no—
250C22×C8—21no—
251C22×C8—191no—
252C22×C8—191no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257#117—191no—
258#117—191no—
259#117—191no—
260#117—191no—
261#117—381no—
262#117—381no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—191no—
265C2×C4⋊C4—191no—
266C2×C4⋊C4C4×D1911yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—381no—
269C2×C22⋊C4—381no—
270C2×C42—381no—
271C2×C42—381no—
272#107—381no—
273#107—381no—
274#106—381no—
275#106—381no—
276C4⋊C8—382no—
277C4⋊C8—382no—
278#103—381no—
279#103—381no—
280#103—381no—
281#103—381no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—192no—
286C22⋊C8—381no—
287C22⋊C8—381no—
288C22⋊C8—381no—
289C22⋊C8C22⋊D1911yescharacteristic
290C22⋊C8C22⋊D1911yescharacteristic
291#97—382no—
292C4×C8—382no—
293#95—381no—
294C19#924011yescharacteristic, complemented, Sylow
295C24#6454111yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—381no—
305C22×C4—381no—
306C22×C4—761no—
307C22×C4C2×C4×D1911yescharacteristic
308C22×C4D4×D1911yescharacteristic
309C22×C4D4×D1911yescharacteristic
310C22×C4D4×D1911yescharacteristic
311C22×C4#6454311yescharacteristic
312C22×C4C2×C22⋊D1911yescharacteristic
313M16—41no—
314M16—41no—
315M16—761no—
316M16—761no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—382no—
323C2×C8—381no—
324C2×C8—381no—
325C2×C8—761no—
326C2×C8—761no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—191no—
332C4⋊C4—191no—
333C4⋊C4—191no—
334C4⋊C4—191no—
335C4⋊C4—381no—
336C4⋊C4—381no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—381no—
340C22⋊C4—381no—
341C22⋊C4—381no—
342C22⋊C4—381no—
343C22⋊C4—382no—
344C22⋊C4—761no—
345C42—381no—
346C42—381no—
347C42—381no—
348C42—381no—
349C42—761no—
350C42—761no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23#1059732911yescharacteristic
356C23#1059733011yescharacteristic
357C23C4×C22⋊D1911yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—381no—
376C2×C4—381no—
377C2×C4—381no—
378C2×C4—381no—
379C2×C4—761no—
380C2×C4—761no—
381C2×C4—762no—
382C2×C4—1521no—
383C2×C4—1521no—
384C2×C4—1521no—
385C2×C4C22⋊C4×D1911yescharacteristic
386C2×C4(C22⋊D19)⋊C411yescharacteristic
387C2×C4#1059738311yescharacteristic
388C2×C4#1059738411yescharacteristic
389C8—41no—
390C8—41no—
391C8—81no—
392C8—762no—
393C8—761no—
394C8—761no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22#1192642011yescharacteristic
406C22#1192665911yescharacteristic
407C22#1192666411yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—81no—
413C4—761no—
414C4—761no—
415C4—761no—
416C4—761no—
417C4—1522no—
418C4#1192651611yescharacteristic
419C4#1192651611yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2#1456396511yescharacteristic
425C2#1456409011yescharacteristic
426C2#1456411111yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1472C2
socleC22×C19#386
prime radicalC24×C19#41
cosocleC23×C4×C19C23
hypercenter#1472D19
hypocenterC19#9240
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
16. C2×#10597264C4semidirect
17. C2×#10597265C4semidirect
19. C2×#10597292C4semidirect
20. C2×#10597292C4semidirect
294. C19#9240semidirect

Maximal subgroups

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

subgroupindex
C2×#119268822
#145722892
#145637322
#145621552
#145615112
#145614812
C19×#14722
#924019