Finite Group Databasebeta

← #18083199

Subgroups — #18083199

Order 4864.

502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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#14571670C211yesmaximal, characteristic
3#14563712C211yesmaximal, characteristic
4#14562169C211yesmaximal, characteristic
5#14562168C211yesmaximal, characteristic
6#14561544C211yesmaximal, characteristic
7C19×#3095C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926885—22no—
10#11926879—21no—
11#11926874—21no—
12#11926587—21no—
13#11926552—21no—
14#11926508C2211yescharacteristic
15#11926483—21no—
16#11926482—21no—
17#11926472—22no—
18#11926464—21no—
19#11926463—21no—
20#11926407C2211yescharacteristic
21#11926407C2211yescharacteristic
22#11926311—22no—
23#11926282—22no—
24#11926281—22no—
25C2×C19×C22⋊Q8C2211yescharacteristic
26C2×C19×#117C2211yescharacteristic
27C19×#485—22no—
28C19×#484—21no—
29C19×#483—21no—
30C19×#428—21no—
31C19×#419—21no—
32C19×#407C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C22×Dic38D411yescharacteristic
36C2×M16×C19—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×#117—21no—
42C19×#117—21no—
43C19×#117—21no—
44C19×#117—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19D411yescharacteristic
47C2×C4⋊C4×C19D411yescharacteristic
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—21no—
51C2×C42×C19—21no—
52C2×C22⋊Dic19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19D412yes—
55C2×C4⋊Dic19D411yescharacteristic
56#10597370—21no—
57#10597370—21no—
58#10597370—21no—
59#10597370—21no—
60C2×Dic19⋊C4—21no—
61C2×Dic19⋊C4—22no—
62C2×#64520—21no—
63C19×#107—22no—
64C19×#106—22no—
65C19×#103—22no—
66C19×#103—22no—
67C19×C22⋊C8—21no—
68C19×C22⋊C8D412yes—
69C19⋊#95—22no—
70C19⋊#95—22no—
71C19⋊#95—22no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C19⋊#95—21no—
75C19⋊#95—21no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)D412yes—
78#10597267—22no—
79#10597267—22no—
80#10597265—22no—
81#10597264—22no—
82C24×C19C2×D411yescharacteristic
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—42no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—42no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—22no—
100C22×Dic19—41no—
101C2×Dic38—21no—
102C2×Dic38—21no—
103C2×Dic38—42no—
104M16×C19—42no—
105C2×C8×C19—22no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—41no—
113C4⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C42×C19—41no—
119C42×C19—41no—
120C22⋊Dic19—41no—
121C22⋊Dic19—41no—
122C22⋊Dic19—42no—
123C22⋊Dic19—42no—
124C4⋊Dic19—21no—
125C4⋊Dic19—21no—
126Dic19⋊C4—41no—
127Dic19⋊C4—41no—
128Dic19⋊C4—82no—
129#64520—42no—
130C2×C19⋊C8—22no—
131#9985—191nomaximal, Sylow
132C23×C19—22no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19#12011yescharacteristic
136C23×C19#12111yescharacteristic
137C23×C19#12711yescharacteristic
138Q8×C19—42no—
139Q8×C19—81no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—42no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—81no—
153C2×C4×C19—81no—
154C2×C4×C19#12011yescharacteristic
155C2×C4×C19#12011yescharacteristic
156C2×C4×C19#12111yescharacteristic
157C2×C4×C19#12111yescharacteristic
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—41no—
162C2×Dic19—41no—
163C2×Dic19—42no—
164C2×Dic19—42no—
165C2×Dic19—81no—
166C2×Dic19—81no—
167C2×Dic19—81no—
168Dic38—42no—
169Dic38—81no—
170C8×C19—42no—
171C19⋊C8—42no—
172#3095—191no—
173#3095D1911yescharacteristic
174#2817—191no—
175#1820—191no—
176#1511—191no—
177#1511—191no—
178#1306—191no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—82no—
188C22×C19#39211yescharacteristic
189C22×C19#45812yes—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—81no—
195C4×C19—81no—
196C4×C19—81no—
197C4×C19—81no—
198Dic19—82no—
199Dic19—81no—
200Dic19—81no—
201Dic19—161no—
202C2×C22⋊Q8—191no—
203C2×C22⋊Q8C2×D1911yescharacteristic
204C2×#117C2×D1911yescharacteristic
205#485—22no—
206#485—382no—
207#484—21no—
208#484—381no—
209#483—21no—
210#483—381no—
211#428—21no—
212#428—381no—
213#419—21no—
214#419—381no—
215#407—191no—
216#407C2×D1911yescharacteristic
217#400—381no—
218#400—381no—
219#397—382no—
220#395—381no—
221#395—381no—
222#381—191no—
223#381—191no—
224#342—382no—
225#328—382no—
226#328—382no—
227C2×C19—22no—
228C2×C19—41no—
229C2×C19—41no—
230C2×C19#200911yescharacteristic
231C2×C19#200911yescharacteristic
232C2×C19#202211yescharacteristic
233C22×Q8—191no—
234C22×Q8C22⋊D1911yescharacteristic
235C23×C4C22×D1911yescharacteristic
236C2×M16—21no—
237C2×M16—381no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—381no—
243C22⋊Q8—381no—
244C22⋊Q8—381no—
245C22⋊Q8—381no—
246#117—21no—
247#117—21no—
248#117—21no—
249#117—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—191no—
252C2×C4⋊C4—381no—
253C2×C4⋊C4—382no—
254C2×C4⋊C4C22⋊D1911yescharacteristic
255C2×C4⋊C4C22⋊D1911yescharacteristic
256C2×C4⋊C4C22⋊D1911yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—192no—
260C2×C22⋊C4—381no—
261C2×C22⋊C4—381no—
262C2×C42—21no—
263#107—22no—
264#107—382no—
265#106—22no—
266#106—382no—
267#103—22no—
268#103—22no—
269#103—382no—
270#103—382no—
271C22⋊C8—21no—
272C22⋊C8—192no—
273C22⋊C8—381no—
274C22⋊C8C22⋊D1912yes—
275#95—382no—
276#95—382no—
277#95—382no—
278#95—381no—
279#95—381no—
280#95—381no—
281#95—381no—
282C19#998511yescharacteristic, complemented, Sylow
283C24D4×D1911yescharacteristic
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—42no—
287C2×Q8—381no—
288C2×Q8—381no—
289C2×Q8—762no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—382no—
296C22×C4—381no—
297C22×C4—381no—
298C22×C4—761no—
299C22×C4D4×D1911yescharacteristic
300C22×C4D4×D1911yescharacteristic
301C22×C4#6454311yescharacteristic
302C22×C4C2×C22⋊D1911yescharacteristic
303C22×C4C2×C22⋊D1911yescharacteristic
304C22×C4C2×C22⋊D1911yescharacteristic
305M16—42no—
306M16—762no—
307C2×C8—22no—
308C2×C8—382no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C4⋊C4—761no—
320C4⋊C4—761no—
321C4⋊C4—1522no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—761no—
327C22⋊C4—761no—
328C22⋊C4—762no—
329C22⋊C4—762no—
330C42—41no—
331C42—41no—
332C23—22no—
333C23—41no—
334C23—41no—
335C23#1059738311yescharacteristic
336C23#1059738511yescharacteristic
337C23#1059738611yescharacteristic
338Q8—42no—
339Q8—81no—
340Q8—762no—
341Q8—1521no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—762no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—761no—
360C2×C4—761no—
361C2×C4—762no—
362C2×C4—762no—
363C2×C4—1521no—
364C2×C4—1521no—
365C2×C4—1521no—
366C2×C4#1059738311yescharacteristic
367C2×C4#1059738411yescharacteristic
368C2×C4#1059738511yescharacteristic
369C2×C4#1059739911yescharacteristic
370C8—42no—
371C8—762no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—82no—
381C22#1192645211yescharacteristic
382C22#1192673312yes—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—3041no—
392C4—1522no—
393C4—1521no—
394C4—1521no—
395C2—22no—
396C2—41no—
397C2—41no—
398C2#1456469211yescharacteristic
399C2#1456469311yescharacteristic
400C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3095C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#3095D19
hypocenterC19#9985
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
282. C19#9985semidirect

Maximal subgroups

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

subgroupindex
#145735832
#145716702
#145637122
#145621692
#145621682
#145615442
C19×#30952
#998519