Finite Group Databasebeta

← #18080604

Subgroups — #18080604

Order 4864.

482 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 89 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
1#14573583C211yesmaximal, characteristic
2#14566391C211yesmaximal, characteristic
3#14563712C211yesmaximal, characteristic
4#14562169C211yesmaximal, characteristic
5#14561544C211yesmaximal, characteristic
6#14561488C211yesmaximal, characteristic
7C19×#1826C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926885—22no—
10#11926879C412yescomplemented
11#11926874C412yescomplemented
12#11926587—21no—
13#11926552—21no—
14#11926508C2211yescharacteristic
15#11926448—21no—
16#11926438—21no—
17#11926432—21no—
18#11926429—21no—
19#11926428—21no—
20#11926407C2211yescharacteristic
21#11926407C2211yescharacteristic
22C4×Dic19⋊C4—21no—
23#11926311—21no—
24#11926311—21no—
25#11926282—22no—
26C2×C19×#117C2211yescharacteristic
27C19×#407C2211yescharacteristic
28C4×C22⋊C4×C19C2211yescharacteristic
29C19×#339—21no—
30C19×#339—21no—
31C23×C4×C19C2311yescharacteristic
32C22×Dic38D411yescharacteristic
33C2×M16×C19—21no—
34C19×#117—21no—
35C19×#117—21no—
36C19×#117—21no—
37C19×#117—21no—
38C2×C4⋊C4×C19C2×C411yescharacteristic
39C2×C4⋊C4×C19C2×C411yescharacteristic
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C42×C19—21no—
43C2×C42×C19D411yescharacteristic
44C2×C42×C19D411yescharacteristic
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19—21no—
47C2×C22⋊Dic19D411yescharacteristic
48C2×C22⋊Dic19D411yescharacteristic
49C2×C4⋊Dic19D411yescharacteristic
50#10597370—21no—
51#10597370—21no—
52#10597370C2×C412yes—
53#10597370D412yes—
54C2×Dic19⋊C4—21no—
55C2×Dic19⋊C4—21no—
56C2×Dic19⋊C4—21no—
57C2×C4×Dic19—21no—
58C2×C4×Dic19—21no—
59C2×#64520—21no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×#95—21no—
63C19⋊#95—21no—
64C19⋊#95—21no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)C2×C412yes—
73#10597267—22no—
74#10597267—22no—
75#10597265—22no—
76#10597264—22no—
77C24×C19C2×D411yescharacteristic
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—41no—
95C2×Dic38—21no—
96C2×Dic38—41no—
97C2×Dic38—41no—
98C2×Dic38C22⋊C412yes—
99M16×C19—41no—
100M16×C19—41no—
101C2×C8×C19—41no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C22⋊C4×C19—42no—
107C22⋊C4×C19—41no—
108C22⋊C4×C19—41no—
109C42×C19—41no—
110C42×C19—41no—
111C42×C19—41no—
112C42×C19—41no—
113C22⋊Dic19—22no—
114C22⋊Dic19—22no—
115C22⋊Dic19—41no—
116C22⋊Dic19—41no—
117C22⋊Dic19—41no—
118C22⋊Dic19—41no—
119C4⋊Dic19—21no—
120C4⋊Dic19C22⋊C412yes—
121Dic19⋊C4—22no—
122Dic19⋊C4—22no—
123Dic19⋊C4—42no—
124Dic19⋊C4—81no—
125C4×Dic19—42no—
126C4×Dic19—81no—
127#64520—41no—
128#64520—41no—
129C2×C19⋊C8—22no—
130#9526—191nomaximal, Sylow
131C23×C19—21no—
132C23×C19—21no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19C4×D411yescharacteristic
136C23×C19#12011yescharacteristic
137C23×C19#12111yescharacteristic
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—22no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—81no—
155C2×C4×C19—81no—
156C2×C4×C19C2×C22⋊C411yescharacteristic
157C2×C4×C19C4×D411yescharacteristic
158C2×C4×C19#12111yescharacteristic
159C2×C4×C19#12311yescharacteristic
160C2×Dic19—22no—
161C2×Dic19—22no—
162C2×Dic19—41no—
163C2×Dic19—41no—
164C2×Dic19—41no—
165C2×Dic19—41no—
166C2×Dic19—41no—
167C2×Dic19—41no—
168C2×Dic19—41no—
169C2×Dic19—41no—
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—81no—
173C2×Dic19—81no—
174C2×Dic19—81no—
175Dic38—42no—
176Dic38—81no—
177C8×C19—81no—
178C19⋊C8—42no—
179#3095—191no—
180#2332—191no—
181#1826D1911yescharacteristic
182#1820—191no—
183#1511—191no—
184#1306—191no—
185#1284—191no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—81no—
195C22×C19—81no—
196C22×C19#38611yescharacteristic
197C22×C19#45811yescharacteristic
198C22×C19#45811yescharacteristic
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—42no—
204C4×C19—81no—
205C4×C19—81no—
206C4×C19—81no—
207Dic19—42no—
208Dic19—42no—
209Dic19—81no—
210Dic19—81no—
211Dic19—161no—
212C2×C22⋊Q8—191no—
213C2×#117C2×D1911yescharacteristic
214#485—382no—
215#484—192no—
216#483—192no—
217#428—381no—
218#419—381no—
219#407—191no—
220#407C2×D1911yescharacteristic
221#391—381no—
222#388—381no—
223#388—381no—
224#387—381no—
225#387—381no—
226#381—191no—
227#381—191no—
228C4×C4⋊C4—381no—
229C4×C22⋊C4C2×D1911yescharacteristic
230#342—381no—
231#342—381no—
232#339—21no—
233#339—21no—
234#328—382no—
235C2×C19—21no—
236C2×C19—21no—
237C2×C19—41no—
238C2×C19—41no—
239C2×C19#189011yescharacteristic
240C2×C19#190511yescharacteristic
241C2×C19#190611yescharacteristic
242C22×Q8—191no—
243C23×C4C22×D1911yescharacteristic
244C2×M16—21no—
245C2×M16—381no—
246C22⋊Q8—192no—
247C22⋊Q8—192no—
248C22⋊Q8—381no—
249C22⋊Q8—381no—
250#117—21no—
251#117—21no—
252#117—21no—
253#117—21no—
254C2×C4⋊C4—191no—
255C2×C4⋊C4—381no—
256C2×C4⋊C4—381no—
257C2×C4⋊C4—381no—
258C2×C4⋊C4C4×D1911yescharacteristic
259C2×C4⋊C4C4×D1911yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—191no—
263C2×C22⋊C4—191no—
264C2×C22⋊C4—381no—
265C2×C22⋊C4—381no—
266C2×C42—21no—
267C2×C42—381no—
268C2×C42—381no—
269C2×C42C22⋊D1911yescharacteristic
270C2×C42C22⋊D1911yescharacteristic
271#107—382no—
272#106—382no—
273#103—382no—
274#103—382no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—192no—
278C22⋊C8—381no—
279#95—21no—
280#95—381no—
281#95—381no—
282#95—381no—
283#95—381no—
284#95—381no—
285#95—381no—
286#95—381no—
287#95—381no—
288C19#952611yescharacteristic, complemented, Sylow
289C24D4×D1911yescharacteristic
290C2×Q8—192no—
291C2×Q8—381no—
292C2×Q8—761no—
293C2×Q8—761no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—381no—
301C22×C4—381no—
302C22×C4—381no—
303C22×C4—381no—
304C22×C4—761no—
305C22×C4C2×C4×D1911yescharacteristic
306C22×C4#6454111yescharacteristic
307C22×C4D4×D1911yescharacteristic
308C22×C4D4×D1911yescharacteristic
309C22×C4#6454311yescharacteristic
310C22×C4C2×C22⋊D1911yescharacteristic
311M16—41no—
312M16—41no—
313M16—761no—
314M16—761no—
315C2×C8—41no—
316C2×C8—382no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—192no—
322C4⋊C4—382no—
323C4⋊C4—381no—
324C4⋊C4—382no—
325C4⋊C4—762no—
326C4⋊C4—1521no—
327C22⋊C4—42no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—382no—
331C22⋊C4—382no—
332C22⋊C4—761no—
333C22⋊C4—761no—
334C22⋊C4—761no—
335C22⋊C4—761no—
336C42—41no—
337C42—41no—
338C42—41no—
339C42—41no—
340C42—762no—
341C42—1521no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23(C22⋊D19)⋊C411yescharacteristic
347C23#1059733011yescharacteristic
348C23#1059738311yescharacteristic
349Q8—762no—
350Q8—1521no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—382no—
370C2×C4—382no—
371C2×C4—761no—
372C2×C4—761no—
373C2×C4—761no—
374C2×C4—761no—
375C2×C4—761no—
376C2×C4—761no—
377C2×C4—761no—
378C2×C4—761no—
379C2×C4—761no—
380C2×C4—761no—
381C2×C4—1521no—
382C2×C4—1521no—
383C2×C4—1521no—
384C2×C4C22⋊C4×D1911yescharacteristic
385C2×C4#1059732911yescharacteristic
386C2×C4C4×C22⋊D1911yescharacteristic
387C2×C4#1059738411yescharacteristic
388C8—81no—
389C8—762no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22#1192642011yescharacteristic
401C22#1192673311yescharacteristic
402C22#1192673311yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—42no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—3041no—
412C4—762no—
413C4—762no—
414C4—1521no—
415C4—1521no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2#1456404511yescharacteristic
421C2#1456412611yescharacteristic
422C2#1456413911yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1826C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1826D19
hypocenterC19#9526
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
10. #11926879C4semidirect
11. #11926874C4semidirect
288. C19#9526semidirect

Maximal subgroups

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

subgroupindex
#145735832
#145663912
#145637122
#145621692
#145615442
#145614882
C19×#18262
#952619