Finite Group Databasebeta

← #18086920

Subgroups — #18086920

Order 4864.

438 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 79 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#14574459C211yesmaximal, characteristic
2#14564103C211yesmaximal, characteristic
3#14564068C211yesmaximal, characteristic
4#14562208C211yesmaximal, characteristic
5#14561998C211yesmaximal, characteristic
6#14561540C211yesmaximal, characteristic
7C19×#1855C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C2×#10597370C2211yescharacteristic
10#11926875—21no—
11#11926875—21no—
12#11926802—21no—
13#11926802—21no—
14#11926702—21no—
15#11926702—21no—
16C2×#10597273—21no—
17C2×#10597281—21no—
18#11926508C2211yescharacteristic
19#11926404C2211yescharacteristic
20#11926312—21no—
21#11926307—21no—
22#11926282—22no—
23#11926269—22no—
24C22×M16×C19C2211yescharacteristic
25C2×C19×#108—21no—
26C19×#407C2211yescharacteristic
27C2×C19×C22⋊C8C2211yescharacteristic
28C19×#341—21no—
29C23×C4×C19C2311yescharacteristic
30C22×Dic38D411yescharacteristic
31C22×Dic38D411yescharacteristic
32C2×M16×C19—21no—
33C2×M16×C19—21no—
34C2×M16×C19—42no—
35C2×M16×C19D411yescharacteristic
36C2×M16×C19D411yescharacteristic
37C22×C8×C19—21no—
38C22×C8×C19—21no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19D411yescharacteristic
44C2×C4⋊Dic19D411yescharacteristic
45#10597370—21no—
46#10597370—21no—
47#10597370—21no—
48#10597370—21no—
49#10597370—21no—
50#10597370—21no—
51#10597370—21no—
52#10597370—21no—
53C2×Dic19⋊C4—21no—
54C2×Dic19⋊C4—21no—
55C2×#64520—21no—
56C2×Dic76—21no—
57C2×Dic76—21no—
58C19×#108—42no—
59C19×C22⋊C8—21no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8D412yes—
63C19⋊#95—21no—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66#10597281—42no—
67#10597274—21no—
68#10597274—21no—
69#10597273—21no—
70#10597273—21no—
71#10597273—21no—
72#10597273—21no—
73#10597273—42no—
74C24×C19#4111yescharacteristic
75C22×C4×C19—41no—
76C22×C4×C19—41no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19#4111yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—41no—
88C2×Dic38—21no—
89C2×Dic38—21no—
90C2×Dic38—21no—
91C2×Dic38—21no—
92C2×Dic38—41no—
93C2×Dic38—41no—
94C2×Dic38—41no—
95C2×Dic38—41no—
96M16×C19—22no—
97M16×C19—22no—
98M16×C19—41no—
99M16×C19—41no—
100M16×C19—41no—
101M16×C19—41no—
102C2×C8×C19—22no—
103C2×C8×C19—21no—
104C2×C8×C19—21no—
105C2×C8×C19—22no—
106C2×C8×C19—41no—
107C2×C8×C19—41no—
108C2×C8×C19—41no—
109C2×C8×C19—41no—
110C22⋊Dic19—41no—
111C22⋊Dic19—41no—
112C22⋊Dic19—41no—
113C22⋊Dic19—41no—
114C22⋊Dic19—81no—
115C4⋊Dic19—21no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119C4⋊Dic19—41no—
120C4⋊Dic19—41no—
121Dic19⋊C4—41no—
122Dic19⋊C4—41no—
123Dic19⋊C4—41no—
124Dic19⋊C4—41no—
125#64520—41no—
126#64520—41no—
127C2×C19⋊C8—41no—
128Dic76—81no—
129Dic76—81no—
130#10563—191nomaximal, Sylow
131C23×C19—21no—
132C23×C19—21no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19#12111yescharacteristic
136C23×C19#12311yescharacteristic
137C23×C19#12411yescharacteristic
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19#12011yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12311yescharacteristic
151C2×Dic19—42no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—81no—
159C2×Dic19—81no—
160C2×Dic19—81no—
161C2×Dic19—81no—
162C2×Dic19—81no—
163Dic38—42no—
164Dic38—41no—
165Dic38—41no—
166Dic38—41no—
167Dic38—41no—
168Dic38—81no—
169C8×C19—42no—
170C8×C19—41no—
171C8×C19—42no—
172C8×C19—41no—
173C19⋊C8—81no—
174#3195—191no—
175#1901—191no—
176#1894—191no—
177#1855D1911yescharacteristic
178#1520—191no—
179#1472—191no—
180#1305—191no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—81no—
190C22×C19—81no—
191C22×C19#39411yescharacteristic
192C22×C19#47111yescharacteristic
193C22×C19#47311yescharacteristic
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19B(4,𝔽2)11yescharacteristic
198C4×C19#45811yescharacteristic
199Dic19—81no—
200Dic19—81no—
201Dic19—81no—
202Dic19—81no—
203Dic19—161no—
204C22×M16C2×D1911yescharacteristic
205C2×C22⋊Q8—191no—
206C2×C22⋊Q8—191no—
207#483—381no—
208#483—381no—
209#470—381no—
210#470—381no—
211#451—381no—
212#451—381no—
213C2×#108—21no—
214C2×#103—381no—
215C2×#101—381no—
216#407—191no—
217#407C2×D1911yescharacteristic
218C2×C22⋊C8C2×D1911yescharacteristic
219#380—191no—
220#343—381no—
221#341—21no—
222#340—381no—
223#328—382no—
224#324—382no—
225C2×C19—21no—
226C2×C19—21no—
227C2×C19—41no—
228C2×C19—41no—
229C2×C19#204411yescharacteristic
230C2×C19#204911yescharacteristic
231C2×C19#205211yescharacteristic
232C22×Q8—191no—
233C22×Q8—191no—
234C23×C4C22×D1911yescharacteristic
235C2×Q16—381no—
236C2×Q16—381no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—42no—
240C2×M16—381no—
241C2×M16C22⋊D1911yescharacteristic
242C2×M16C22⋊D1911yescharacteristic
243C22×C8—21no—
244C22×C8—21no—
245C22⋊Q8—381no—
246C22⋊Q8—381no—
247C22⋊Q8—381no—
248C22⋊Q8—381no—
249C22⋊Q8—381no—
250C22⋊Q8—381no—
251C22⋊Q8—381no—
252C22⋊Q8—381no—
253C2×C4⋊C4—191no—
254C2×C4⋊C4—191no—
255C2×C4⋊C4—381no—
256C2×C4⋊C4—381no—
257C2×C4⋊C4—381no—
258C2×C22⋊C4—381no—
259C2×C22⋊C4—381no—
260C2×C22⋊C4—381no—
261#108—42no—
262#106—381no—
263#106—381no—
264#103—381no—
265#103—381no—
266#103—381no—
267#103—381no—
268#103—762no—
269#101—762no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—381no—
274C22⋊C8—381no—
275C22⋊C8D7612yes—
276#95—381no—
277C19#1056311yescharacteristic, complemented, Sylow
278C24#6454511yescharacteristic
279C2×Q8—381no—
280C2×Q8—381no—
281C2×Q8—381no—
282C2×Q8—381no—
283C2×Q8—761no—
284C2×Q8—761no—
285C2×Q8—761no—
286C2×Q8—761no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—381no—
292C22×C4—381no—
293C22×C4—761no—
294C22×C4C2×D7611yescharacteristic
295C22×C4#6454111yescharacteristic
296C22×C4D4×D1911yescharacteristic
297C22×C4D4×D1911yescharacteristic
298C22×C4#6454511yescharacteristic
299C22×C4C2×C22⋊D1911yescharacteristic
300Q16—1521no—
301Q16—1521no—
302M16—22no—
303M16—22no—
304M16—41no—
305M16—41no—
306M16—41no—
307M16—41no—
308M16—761no—
309M16—761no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—761no—
319C4⋊C4—381no—
320C4⋊C4—381no—
321C4⋊C4—381no—
322C4⋊C4—381no—
323C4⋊C4—761no—
324C4⋊C4—761no—
325C4⋊C4—761no—
326C4⋊C4—761no—
327C4⋊C4—761no—
328C4⋊C4—761no—
329C22⋊C4—761no—
330C22⋊C4—761no—
331C22⋊C4—761no—
332C22⋊C4—761no—
333C22⋊C4—1521no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23#1059734011yescharacteristic
339C23#1059734111yescharacteristic
340C23#1059739311yescharacteristic
341Q8—762no—
342Q8—761no—
343Q8—761no—
344Q8—761no—
345Q8—761no—
346Q8—1521no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—762no—
357C2×C4—761no—
358C2×C4—761no—
359C2×C4—761no—
360C2×C4—761no—
361C2×C4—761no—
362C2×C4—761no—
363C2×C4—1521no—
364C2×C4—1521no—
365C2×C4—1521no—
366C2×C4—1521no—
367C2×C4—1521no—
368C2×C4#1059734011yescharacteristic
369C2×C4#1059734111yescharacteristic
370C2×C4#1059737611yescharacteristic
371C2×C4#1059738311yescharacteristic
372C8—42no—
373C8—42no—
374C8—41no—
375C8—41no—
376C8—1521no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22#1192646111yescharacteristic
388C22#1192680811yescharacteristic
389C22#1192682011yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—3041no—
394C4—1521no—
395C4—1521no—
396C4—1521no—
397C4—1521no—
398C4#1192673011yescharacteristic
399C4#1192673311yescharacteristic
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#1456488611yescharacteristic
405C2#1456491711yescharacteristic
406C2#1456493611yescharacteristic
subgroupG/H
centerC22#11926461
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1855C2
socleC22×C19#394
prime radicalC24×C19#41
hypercenter#1855D19
hypocenterC19#10563
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
277. C19#10563semidirect

Maximal subgroups

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

subgroupindex
#145744592
#145641032
#145640682
#145622082
#145619982
#145615402
C19×#18552
#1056319