Finite Group Databasebeta

← #18085691

Subgroups — #18085691

Order 4864.

466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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#14564620C211yesmaximal, characteristic
2#14562206C211yesmaximal, characteristic
3C2×#11926280C211yesmaximal, characteristic
4#14561514C211yesmaximal, characteristic
5#14561502C211yesmaximal, characteristic
6#14561483C211yesmaximal, characteristic
7C19×#2549C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C2×C22⋊(C19⋊C8)C2211yescharacteristic
10C2×C22⋊(C19⋊C8)C2211yescharacteristic
11#11926404C2211yescharacteristic
12#11926310—21no—
13#11926310—21no—
14#11926280—21no—
15#11926280—21no—
16#11926280—21no—
17#11926280—21no—
18C2×C19×C22⋊Q8—21no—
19C19×#398—21no—
20C19×#395—21no—
21C19×#391—21no—
22C19×#389—21no—
23C19×#385—21no—
24C19×#380C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C2×C19×#95C2211yescharacteristic
27C22×Q8×C19—21no—
28C23×C4×C19—21no—
29C23×C4×C19C2311yescharacteristic
30C22×Dic38Q811yescharacteristic, complemented
31C19×C22⋊Q8—42no—
32C19×C22⋊Q8—42no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19D411yescharacteristic
41C2×C22⋊C4×C19D411yescharacteristic
42C2×C42×C19—21no—
43C2×C22⋊Dic19—21no—
44C2×C22⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19Q811yescharacteristic, complemented
47#10597370—21no—
48#10597370—21no—
49#10597370—21no—
50#10597370—21no—
51C2×Dic19⋊C4—21no—
52C22×C19⋊C8—21no—
53C22×C19⋊C8—21no—
54C19×#95—21no—
55C19×#95—21no—
56C19×#95—21no—
57C19×#95—21no—
58C19×#95D411yescharacteristic
59C19×#95D411yescharacteristic
60C19×#95D411yescharacteristic
61C19×#95D411yescharacteristic
62C19⋊#95—21no—
63C22⋊(C19⋊C8)—21no—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66C22⋊(C19⋊C8)—21no—
67C24×C19C2×D411yescharacteristic
68C2×Q8×C19—42no—
69C2×Q8×C19—42no—
70C2×Q8×C19—81no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—42no—
78C22×C4×C19—41no—
79C22×C4×C19—41no—
80C22×C4×C19—81no—
81C22×C4×C19—81no—
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×Q811yescharacteristic
85C22×C4×C19#4111yescharacteristic
86C22×C4×C19#4111yescharacteristic
87C22×C4×C19#4111yescharacteristic
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—41no—
91C2×Dic38—21no—
92C2×Dic38—21no—
93C2×Dic38—81no—
94C4⋊C4×C19—42no—
95C4⋊C4×C19—42no—
96C4⋊C4×C19—42no—
97C4⋊C4×C19—42no—
98C4⋊C4×C19—81no—
99C4⋊C4×C19—81no—
100C22⋊C4×C19—21no—
101C22⋊C4×C19—21no—
102C22⋊C4×C19—41no—
103C22⋊C4×C19—41no—
104C22⋊C4×C19SD1612yes—
105C22⋊C4×C19Q1612yes—
106C42×C19—81no—
107C22⋊Dic19—41no—
108C22⋊Dic19—41no—
109C22⋊Dic19—41no—
110C22⋊Dic19—41no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—81no—
114Dic19⋊C4—41no—
115Dic19⋊C4—41no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—81no—
119C2×C19⋊C8—81no—
120#10375—191nomaximal, Sylow
121C23×C19—41no—
122C23×C19—41no—
123C23×C19#12011yescharacteristic
124C23×C19C22⋊Q811yescharacteristic
125C23×C19#12411yescharacteristic
126C23×C19C2×SD1611yescharacteristic
127C23×C19C2×Q1611yescharacteristic
128C23×C19AGL(1,ℤ/8)11yescharacteristic
129C23×C19#13711yescharacteristic
130Q8×C19—84no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—22no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
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—41no—
155C2×C4×C19—82no—
156C2×C4×C19—82no—
157C2×C4×C19C22⋊Q811yescharacteristic
158C2×C4×C19C22⋊Q811yescharacteristic
159C2×C4×C19#12411yescharacteristic
160C2×C4×C19#12411yescharacteristic
161C2×Dic19—41no—
162C2×Dic19—41no—
163C2×Dic19—81no—
164C2×Dic19—81no—
165C2×Dic19—81no—
166C2×Dic19—81no—
167C2×Dic19—81no—
168Dic38—81no—
169Dic38—81no—
170C19⋊C8—81no—
171C19⋊C8—81no—
172#2549D1911yescharacteristic
173#1996—191no—
174#1520—191no—
175C2×#328—191no—
176#1294—191no—
177#1289—191no—
178#1282—191no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—41no—
186C22×C19—41no—
187C22×C19—41no—
188C22×C19—41no—
189C22×C19#39311yescharacteristic
190C22×C19#45011yescharacteristic
191C22×C19#45111yescharacteristic
192C22×C19#47511yescharacteristic
193C22×C19#47711yescharacteristic
194C22×C19#48711yescharacteristic
195C22×C19#48911yescharacteristic
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—21no—
200C4×C19—42no—
201C4×C19—42no—
202C4×C19—42no—
203C4×C19—81no—
204C4×C19—81no—
205C4×C19—81no—
206Dic19—81no—
207Dic19—81no—
208Dic19—161no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8—191no—
211C2×C22⋊C8—191no—
212C2×C22⋊C8—191no—
213#398—21no—
214#395—21no—
215#391—21no—
216#389—21no—
217#385—21no—
218#380—191no—
219#380C2×D1911yescharacteristic
220C4×C22⋊C4C2×D1911yescharacteristic
221C2×#95C2×D1911yescharacteristic
222#342—381no—
223#342—381no—
224#328—381no—
225#328—381no—
226#328—381no—
227#328—381no—
228C2×C19—21no—
229C2×C19—21no—
230C2×C19—21no—
231C2×C19—21no—
232C2×C19—21no—
233C2×C19—21no—
234C2×C19#202411yescharacteristic
235C2×C19#203111yescharacteristic
236C2×C19#203211yescharacteristic
237C22×Q8—21no—
238C22×Q8—191no—
239C23×C4—21no—
240C23×C4C22×D1911yescharacteristic
241C22×C8—381no—
242C22×C8—381no—
243C22⋊Q8—42no—
244C22⋊Q8—42no—
245C22⋊Q8—381no—
246C22⋊Q8—381no—
247C22⋊Q8—381no—
248C22⋊Q8—381no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—191no—
256C2×C4⋊C4—381no—
257C2×C4⋊C4—381no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—381no—
260C2×C22⋊C4—381no—
261C2×C22⋊C4C22⋊D1911yescharacteristic
262C2×C22⋊C4C22⋊D1911yescharacteristic
263C2×C42—21no—
264C22⋊C8—381no—
265C22⋊C8—381no—
266C22⋊C8—381no—
267C22⋊C8—381no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—381no—
273#95C22⋊D1911yescharacteristic
274#95C22⋊D1911yescharacteristic
275#95C22⋊D1911yescharacteristic
276#95C22⋊D1911yescharacteristic
277C19#1037511yescharacteristic, complemented, Sylow
278C24C2×C22⋊D1911yescharacteristic
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—81no—
282C2×Q8—381no—
283C2×Q8—381no—
284C2×Q8—1521no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4—381no—
297C22×C4—381no—
298C22×C4—761no—
299C22×C4Q8×D1911yescharacteristic
300C22×C4#6454511yescharacteristic
301C22×C4#6454511yescharacteristic
302C22×C4#6454511yescharacteristic
303C22×C4C2×C22⋊D1911yescharacteristic
304C22×C4C2×C22⋊D1911yescharacteristic
305C2×C8—761no—
306C2×C8—761no—
307C2×C8—1521no—
308C2×C8—1521no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—81no—
314C4⋊C4—81no—
315C4⋊C4—381no—
316C4⋊C4—381no—
317C4⋊C4—761no—
318C4⋊C4—761no—
319C4⋊C4—1521no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—761no—
325C22⋊C4—761no—
326C22⋊C4—761no—
327C22⋊C4—761no—
328C22⋊C4#6452612yes—
329C22⋊C4#6452812yes—
330C42—81no—
331C23—41no—
332C23—41no—
333C23#1059737811yescharacteristic
334C23C2×#6452611yescharacteristic
335C23#1059738811yescharacteristic
336C23C2×#6452811yescharacteristic
337C23#1059739211yescharacteristic
338C23#1059739311yescharacteristic
339C23#1059739911yescharacteristic
340Q8—84no—
341Q8—1521no—
342Q8—1521no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
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—82no—
368C2×C4—82no—
369C2×C4—761no—
370C2×C4—761no—
371C2×C4—1521no—
372C2×C4—1521no—
373C2×C4—1521no—
374C2×C4—1521no—
375C2×C4—1521no—
376C2×C4#1059739211yescharacteristic
377C2×C4#1059739211yescharacteristic
378C2×C4#1059739311yescharacteristic
379C2×C4#1059739311yescharacteristic
380C8—1521no—
381C8—1521no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#1192645511yescharacteristic
393C22#1192669511yescharacteristic
394C22#1192670011yescharacteristic
395C22#1192682611yescharacteristic
396C22#1192683611yescharacteristic
397C22#1192689611yescharacteristic
398C22#1192690611yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—42no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—3041no—
410C4—1521no—
411C4—1521no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2—21no—
417C2—21no—
418C2#1456477311yescharacteristic
419C2#1456480411yescharacteristic
420C2#1456481111yescharacteristic
subgroupG/H
centerC22#11926455
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2549C2
socleC22×C19#393
prime radicalC24×C19C2×D4
hypercenter#2549D19
hypocenterC19#10375
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2549

Complements

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

NH ≅ G/Ntype
30. C22×Dic38Q8semidirect
46. C2×C4⋊Dic19Q8semidirect
277. C19#10375semidirect

Maximal subgroups

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

subgroupindex
#145646202
#145622062
C2×#119262802
#145615142
#145615022
#145614832
C19×#25492
#1037519