Finite Group Databasebeta

← #18083131

Subgroups — #18083131

Order 4864.

632 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11926874C211yesmaximal, characteristic
2#14569751C211yesmaximal, characteristic
3C2×#11926282C211yesmaximal, characteristic
4C2×#11926281C211yesmaximal, characteristic
5#14561903C211yesmaximal, characteristic
6#14561477C211yesmaximal, characteristic
7C2×C19×#483C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926874—22no—
10#11926874—22no—
11C2×#10597265—21no—
12C2×#10597267—21no—
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14#11926475—21no—
15#11926474—21no—
16#11926464—21no—
17#11926463—21no—
18#11926402—22no—
19C2×C19⋊#95—22no—
20C2×C19⋊#95C2211yescharacteristic
21C2×C19⋊#95C2211yescharacteristic
22#11926282—22no—
23#11926281—22no—
24C2×C19×C22⋊Q8C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C19×#483—22no—
27C19×#483—22no—
28C2×C19×#106—21no—
29C2×C19×#103—21no—
30C2×C19×C22⋊C8C2211yescharacteristic
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19—21no—
33C23×C4×C19C2311yescharacteristic
34C23×Dic19—21no—
35C23×Dic19D412yes—
36C22×Dic38D411yescharacteristic
37C22×C8×C19—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C4⋊C4×C19D412yes—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊Dic19—21no—
52C2×C4⋊Dic19D411yescharacteristic
53#10597370—21no—
54#10597370—21no—
55#10597370—21no—
56#10597370—21no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4—22no—
59C2×Dic19⋊C4—22no—
60C22×C19⋊C8—21no—
61C19×#106—24no—
62C19×#103—24no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8D412yes—
65C19⋊#95—22no—
66C19⋊#95—22no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—44no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)D412yes—
74#10597267—24no—
75#10597265—24no—
76C24×C19C2×D411yescharacteristic
77C2×Q8×C19—21no—
78C2×Q8×C19—21no—
79C2×Q8×C19—42no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—22no—
83C22×C4×C19—42no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—42no—
87C22×C4×C19—42no—
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C22×Dic19—22no—
95C22×Dic19—22no—
96C22×Dic19—22no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—42no—
100C22×Dic19—42no—
101C22×Dic19—41no—
102C22×Dic19—42no—
103C22×Dic19—41no—
104C22×Dic19—42no—
105C22×Dic19SD1614yes—
106C2×Dic38—21no—
107C2×Dic38—21no—
108C2×Dic38—42no—
109C2×C8×C19—22no—
110C2×C8×C19—42no—
111C4⋊C4×C19—22no—
112C4⋊C4×C19—22no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—41no—
116C4⋊C4×C19—41no—
117C4⋊C4×C19—41no—
118C4⋊C4×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊Dic19—41no—
122C22⋊Dic19—41no—
123C4⋊Dic19—21no—
124C4⋊Dic19—21no—
125Dic19⋊C4—41no—
126Dic19⋊C4—41no—
127Dic19⋊C4—82no—
128Dic19⋊C4—82no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—42no—
131#9973—191nomaximal, Sylow
132C23×C19—21no—
133C23×C19—21no—
134C23×C19—22no—
135C23×C19#12011yescharacteristic
136C23×C19#12111yescharacteristic
137C23×C19#12711yescharacteristic
138C23×C19C2×SD1612yes—
139C23×C19#13712yes—
140Q8×C19—42no—
141Q8×C19—81no—
142C2×C4×C19—22no—
143C2×C4×C19—22no—
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—42no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—44no—
155C2×C4×C19—82no—
156C2×C4×C19—81no—
157C2×C4×C19—81no—
158C2×C4×C19#12011yescharacteristic
159C2×C4×C19#12011yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C2×Dic19—24no—
163C2×Dic19—42no—
164C2×Dic19—42no—
165C2×Dic19—44no—
166C2×Dic19—44no—
167C2×Dic19—42no—
168C2×Dic19—41no—
169C2×Dic19—41no—
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—42no—
173C2×Dic19—82no—
174C2×Dic19—82no—
175C2×Dic19—81no—
176C2×Dic19—81no—
177Dic38—42no—
178Dic38—81no—
179C8×C19—42no—
180C19⋊C8—42no—
181C2×#483—191no—
182C2×#483D1911yescharacteristic
183#2659—191no—
184C2×#328—191no—
185C2×#328—191no—
186#1445—191no—
187#1280—191no—
188C22×C19—22no—
189C22×C19—22no—
190C22×C19—22no—
191C22×C19—22no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19#39211yescharacteristic
197C22×C19#44812yes—
198C22×C19#45511yescharacteristic
199C22×C19#45611yescharacteristic
200C22×C19#45812yes—
201C22×C19#46112yes—
202C22×C19#49211yescharacteristic
203C22×C19#49711yescharacteristic
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—81no—
209C4×C19—82no—
210C4×C19—81no—
211Dic19—44no—
212Dic19—82no—
213Dic19—81no—
214Dic19—81no—
215C2×C22⋊Q8—191no—
216C2×C22⋊Q8C2×D1911yescharacteristic
217C22×C4⋊C4C2×D1911yescharacteristic
218#483—22no—
219#483—22no—
220#483—382no—
221#483—382no—
222C2×#106—21no—
223C2×#106—381no—
224C2×#103—21no—
225C2×#103—381no—
226C2×C22⋊C8—191no—
227C2×C22⋊C8C2×D1911yescharacteristic
228#398—381no—
229#398—381no—
230#395—381no—
231#395—381no—
232#380—382no—
233C2×#95—191no—
234C2×#95—191no—
235C2×#95—382no—
236#328—382no—
237#328—382no—
238C2×C19—21no—
239C2×C19—22no—
240C2×C19—21no—
241C2×C19#160812yes—
242C2×C19#161112yes—
243C2×C19#200711yescharacteristic
244C2×C19#201311yescharacteristic
245C2×C19#202211yescharacteristic
246C22×Q8—191no—
247C22×Q8C22⋊D1911yescharacteristic
248C23×C4—21no—
249C23×C4—192no—
250C23×C4—381no—
251C23×C4C22×D1911yescharacteristic
252C22×C8—21no—
253C22×C8—381no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—381no—
259C22⋊Q8—381no—
260C22⋊Q8—381no—
261C22⋊Q8—381no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—191no—
269C2×C4⋊C4—381no—
270C2×C4⋊C4—382no—
271C2×C4⋊C4—382no—
272C2×C4⋊C4C22⋊D1912yes—
273C2×C4⋊C4C22⋊D1911yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—381no—
276#106—24no—
277#106—384no—
278#103—24no—
279#103—384no—
280C22⋊C8—21no—
281C22⋊C8—192no—
282C22⋊C8—381no—
283C22⋊C8C22⋊D1912yes—
284#95—382no—
285#95—382no—
286#95—381no—
287#95—381no—
288#95—381no—
289#95—381no—
290#95—764no—
291C19#997311yescharacteristic, complemented, Sylow
292C24D4×D1911yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—42no—
296C2×Q8—381no—
297C2×Q8—381no—
298C2×Q8—762no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—42no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—194no—
308C22×C4—382no—
309C22×C4—382no—
310C22×C4—382no—
311C22×C4—381no—
312C22×C4—381no—
313C22×C4—762no—
314C22×C4—762no—
315C22×C4—761no—
316C22×C4—762no—
317C22×C4—761no—
318C22×C4—762no—
319C22×C4D4×D1911yescharacteristic
320C22×C4D4×D1911yescharacteristic
321C22×C4#6454311yescharacteristic
322C22×C4C2×C22⋊D1911yescharacteristic
323C22×C4C2×C22⋊D1911yescharacteristic
324C22×C4C2×C22⋊D1911yescharacteristic
325C2×C8—22no—
326C2×C8—42no—
327C2×C8—382no—
328C2×C8—762no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—381no—
338C4⋊C4—381no—
339C4⋊C4—761no—
340C4⋊C4—761no—
341C4⋊C4—1522no—
342C4⋊C4—1522no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—761no—
346C22⋊C4—761no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23SD16×D1912yes—
351C23#1059736112yes—
352C23#1059738311yescharacteristic
353C23#1059738511yescharacteristic
354C23#1059738611yescharacteristic
355Q8—42no—
356Q8—81no—
357Q8—762no—
358Q8—1521no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—82no—
375C2×C4—384no—
376C2×C4—762no—
377C2×C4—762no—
378C2×C4—764no—
379C2×C4—762no—
380C2×C4—764no—
381C2×C4—761no—
382C2×C4—761no—
383C2×C4—761no—
384C2×C4—761no—
385C2×C4—762no—
386C2×C4—1522no—
387C2×C4—1522no—
388C2×C4—1521no—
389C2×C4—1521no—
390C2×C4#1059738311yescharacteristic
391C2×C4#1059738411yescharacteristic
392C2×C4#1059738511yescharacteristic
393C2×C4#1059739911yescharacteristic
394C8—42no—
395C8—762no—
396C22—22no—
397C22—22no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—22no—
402C22—21no—
403C22—21no—
404C22#1192645211yescharacteristic
405C22#1192668112yes—
406C22#1192672011yescharacteristic
407C22#1192672511yescharacteristic
408C22#1192673312yes—
409C22#1192674712yes—
410C22#1192691511yescharacteristic
411C22#1192693511yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—81no—
417C4—82no—
418C4—81no—
419C4—764no—
420C4—1522no—
421C4—1521no—
422C4—1521no—
423C2—21no—
424C2—21no—
425C2—22no—
426C2#1456262412yes—
427C2#1456264112yes—
428C2#1456468011yescharacteristic
429C2#1456471611yescharacteristic
430C2#1456476311yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#483C2
socleC23×C19#120
prime radicalC24×C19C2×D4
hypercenterC2×#483D19
hypocenterC19#9973
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
291. C19#9973semidirect

Maximal subgroups

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

subgroupindex
C2×#119268742
#145697512
C2×#119262822
C2×#119262812
#145619032
#145614772
C2×C19×#4832
#997319