Finite Group Databasebeta

← #18080607

Subgroups — #18080607

Order 4864.

482 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 99 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#14573579C211yesmaximal, characteristic
2#14563735C211yesmaximal, characteristic
3#14563710C211yesmaximal, characteristic
4#14562168C211yesmaximal, characteristic
5#14561543C211yesmaximal, characteristic
6#14561488C211yesmaximal, characteristic
7C19×#2332C211yesmaximal, characteristic
8C2×#10597372C2211yescharacteristic
9#11926882—22no—
10#11926877C412yescomplemented
11#11926872C412yescomplemented
12#11926584—21no—
13#11926553—21no—
14#11926508C2211yescharacteristic
15#11926508C2211yescharacteristic
16#11926407C2211yescharacteristic
17#11926310—21no—
18#11926310—21no—
19#11926304—21no—
20#11926304—21no—
21#11926281—22no—
22C2×C19×C22⋊Q8C2211yescharacteristic
23C19×#391—21no—
24C19×#388—21no—
25C19×#388—21no—
26C19×#387—21no—
27C19×#387—21no—
28C19×#381C2211yescharacteristic
29C4×C4⋊C4×C19—21no—
30C4×C22⋊C4×C19C2211yescharacteristic
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C19×C22⋊Q8—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8C2×C412yes—
36C19×C22⋊Q8D412yes—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19D411yescharacteristic
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19D411yescharacteristic
44C2×C22⋊C4×C19D411yescharacteristic
45C2×C42×C19—21no—
46C2×C42×C19—21no—
47C2×C42×C19D411yescharacteristic
48C2×C42×C19D411yescharacteristic
49C2×C22⋊Dic19—21no—
50C2×C22⋊Dic19—21no—
51#10597372—21no—
52#10597372—21no—
53#10597372—21no—
54#10597372—21no—
55C2×C4⋊Dic19C2×C411yescharacteristic
56C2×C4⋊Dic19C2×C411yescharacteristic
57C2×C4×Dic19—21no—
58C2×#64520—21no—
59C2×#64520—21no—
60C19×#95—21no—
61C19×#95—21no—
62C19×#95—21no—
63C19×#95—21no—
64C19×#95—21no—
65C19×#95—21no—
66C19×#95—21no—
67#10597292—22no—
68#10597292—22no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)C2×C412yes—
75#10597265—22no—
76#10597264—22no—
77C24×C19C2×D411yescharacteristic
78C2×Q8×C19—21no—
79C2×Q8×C19—41no—
80C2×Q8×C19—41no—
81C2×Q8×C19C22⋊C412yes—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
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×C19#4111yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—41no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—42no—
103C4⋊C4×C19—81no—
104C4⋊C4×C19C22⋊C412yes—
105C22⋊C4×C19—22no—
106C22⋊C4×C19—22no—
107C22⋊C4×C19—42no—
108C22⋊C4×C19—41no—
109C22⋊C4×C19—41no—
110C42×C19—41no—
111C42×C19—41no—
112C42×C19—42no—
113C42×C19—81no—
114C22⋊Dic19—41no—
115C22⋊Dic19—41no—
116C22⋊Dic19—41no—
117C22⋊Dic19—41no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121C4⋊Dic19—21no—
122C4×Dic19—41no—
123C4×Dic19—41no—
124#64520—41no—
125#64520—41no—
126#64520—41no—
127#64520—41no—
128C2×C19⋊C8—22no—
129C2×C19⋊C8—41no—
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
138Q8×C19—42no—
139Q8×C19—81no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—22no—
145C2×C4×C19—22no—
146C2×C4×C19—22no—
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—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—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19C2×C22⋊C411yescharacteristic
167C2×C4×C19C4×D411yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12311yescharacteristic
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—81no—
173C2×Dic19—81no—
174C2×Dic19—81no—
175C2×Dic19—81no—
176C2×Dic19—81no—
177C19⋊C8—42no—
178C19⋊C8—81no—
179#3095—191no—
180#2332D1911yescharacteristic
181#1826—191no—
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—42no—
205C4×C19—42no—
206C4×C19—81no—
207C4×C19—81no—
208C4×C19—81no—
209Dic19—81no—
210Dic19—81no—
211Dic19—161no—
212C2×C22⋊Q8C2×D1911yescharacteristic
213C2×#117—191no—
214#485—382no—
215#484—192no—
216#483—192no—
217#428—381no—
218#419—381no—
219#407—191no—
220#407—191no—
221#391—21no—
222#388—21no—
223#388—21no—
224#387—21no—
225#387—21no—
226#381—191no—
227#381C2×D1911yescharacteristic
228C4×C4⋊C4—21no—
229C4×C22⋊C4C2×D1911yescharacteristic
230#342—381no—
231#342—381no—
232#339—381no—
233#339—381no—
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×Q8C22⋊D1911yescharacteristic
243C23×C4C22×D1911yescharacteristic
244C2×M16—381no—
245C2×M16—381no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8C4×D1912yes—
249C22⋊Q8D7612yes—
250#117—381no—
251#117—381no—
252#117—381no—
253#117—381no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—191no—
258C2×C4⋊C4—191no—
259C2×C4⋊C4C22⋊D1911yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—381no—
263C2×C22⋊C4—381no—
264C2×C22⋊C4C22⋊D1911yescharacteristic
265C2×C22⋊C4C22⋊D1911yescharacteristic
266C2×C42—21no—
267C2×C42—21no—
268C2×C42—381no—
269C2×C42C22⋊D1911yescharacteristic
270C2×C42C22⋊D1911yescharacteristic
271#107—382no—
272#106—382no—
273#103—382no—
274#103—382no—
275C22⋊C8—192no—
276C22⋊C8—381no—
277C22⋊C8—381no—
278C22⋊C8—381no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—381no—
287#95—381no—
288C19#952611yescharacteristic, complemented, Sylow
289C24C2×C22⋊D1911yescharacteristic
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8(C2×D19)⋊C412yes—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—381no—
303C22×C4—381no—
304C22×C4—761no—
305C22×C4C2×C4×D1911yescharacteristic
306C22×C4C2×D7611yescharacteristic
307C22×C4#6454111yescharacteristic
308C22×C4#6454111yescharacteristic
309C22×C4C2×C22⋊D1911yescharacteristic
310C22×C4C2×C22⋊D1911yescharacteristic
311M16—761no—
312M16—761no—
313M16—761no—
314M16—761no—
315C2×C8—382no—
316C2×C8—761no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—21no—
320C4⋊C4—42no—
321C4⋊C4—81no—
322C4⋊C4—381no—
323C4⋊C4—381no—
324C4⋊C4—381no—
325C4⋊C4—381no—
326C4⋊C4(C2×D19)⋊C412yes—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—761no—
333C22⋊C4—761no—
334C22⋊C4—761no—
335C22⋊C4—761no—
336C42—41no—
337C42—41no—
338C42—42no—
339C42—81no—
340C42—761no—
341C42—761no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23C4×C22⋊D1911yescharacteristic
347C23#1059737611yescharacteristic
348C23#1059739911yescharacteristic
349Q8—42no—
350Q8—81no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
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—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—761no—
378C2×C4—761no—
379C2×C4—1521no—
380C2×C4—1521no—
381C2×C4—1521no—
382C2×C4—1521no—
383C2×C4—1521no—
384C2×C4C2×(C2×D19)⋊C411yescharacteristic
385C2×C4C4×C22⋊D1911yescharacteristic
386C2×C4#1059737511yescharacteristic
387C2×C4#1059737611yescharacteristic
388C8—762no—
389C8—1521no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22#1192642311yescharacteristic
401C22#1192673411yescharacteristic
402C22#1192673411yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—42no—
408C4—42no—
409C4—42no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4—3041no—
414C4—1521no—
415C4—1521no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2#1456404811yescharacteristic
421C2#1456412911yescharacteristic
422C2#1456413611yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2332C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2332D19
hypocenterC19#9526
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2332

Complements

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

NH ≅ G/Ntype
10. #11926877C4semidirect
11. #11926872C4semidirect
288. C19#9526semidirect

Maximal subgroups

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

subgroupindex
#145735792
#145637352
#145637102
#145621682
#145615432
#145614882
C19×#23322
#952619