Finite Group Databasebeta

← #18086919

Subgroups — #18086919

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#14574456C211yesmaximal, characteristic
2#14564104C211yesmaximal, characteristic
3#14564066C211yesmaximal, characteristic
4#14563842C211yesmaximal, characteristic
5#14561998C211yesmaximal, characteristic
6#14561541C211yesmaximal, characteristic
7C19×#1520C211yesmaximal, characteristic
8C22×#64520C2211yescharacteristic
9C2×#10597370C2211yescharacteristic
10#11926874—21no—
11#11926872—21no—
12#11926800—21no—
13#11926800—21no—
14#11926700—21no—
15#11926699—21no—
16C2×#10597276—21no—
17C2×#10597267—21no—
18C2×#10597293—21no—
19#11926508C2211yescharacteristic
20#11926508C2211yescharacteristic
21#11926313—21no—
22#11926309—21no—
23#11926306—21no—
24#11926269—22no—
25C2×C19×C22⋊Q8C2211yescharacteristic
26C2×C19×C22⋊C8C2211yescharacteristic
27C19×#380C2211yescharacteristic
28C19×#328—22no—
29C22×Q8×C19D411yescharacteristic
30C23×C4×C19C2311yescharacteristic
31C22×Dic38D411yescharacteristic
32C22×C8×C19—21no—
33C19×C22⋊Q8—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C19×C22⋊Q8—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊Dic19—21no—
43C2×#64528—21no—
44C2×#64528—21no—
45C2×C4⋊Dic19D411yescharacteristic
46#10597370—21no—
47#10597370—21no—
48#10597370—21no—
49#10597370—21no—
50C2×Dic19⋊C4—21no—
51C2×#64520—21no—
52C2×#64520—21no—
53C2×#64520—21no—
54C2×#64520—42no—
55C2×#64520D411yescharacteristic
56C2×#64520D411yescharacteristic
57C22×C19⋊C8—21no—
58C19×C22⋊C8—21no—
59C19×C22⋊C8D412yes—
60C19×#95—21no—
61#10597293—42no—
62#10597292—21no—
63#10597292—21no—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)—21no—
68#10597276—42no—
69#10597267—21no—
70#10597267—21no—
71#10597267—42no—
72#10597265—21no—
73#10597265—21no—
74C24×C19#4111yescharacteristic
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19—41no—
78C2×Q8×C19—41no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×Dic19—21no—
91C22×Dic19—21no—
92C2×Dic38—21no—
93C2×Dic38—21no—
94C2×Dic38—41no—
95C2×Dic38—41no—
96C2×C8×C19—22no—
97C2×C8×C19—41no—
98C2×C8×C19—41no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19—41no—
103C4⋊C4×C19—41no—
104C4⋊C4×C19—41no—
105C22⋊C4×C19—41no—
106C22⋊C4×C19—41no—
107C22⋊C4×C19—81no—
108C22⋊Dic19—41no—
109C22⋊Dic19—41no—
110#64528—81no—
111#64528—81no—
112C4⋊Dic19—21no—
113C4⋊Dic19—21no—
114Dic19⋊C4—41no—
115Dic19⋊C4—41no—
116#64520—22no—
117#64520—22no—
118#64520—41no—
119#64520—41no—
120#64520—41no—
121#64520—41no—
122#64520—41no—
123#64520—41no—
124C2×C19⋊C8—22no—
125C2×C19⋊C8—21no—
126C2×C19⋊C8—21no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—41no—
129C2×C19⋊C8—41no—
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
138Q8×C19—41no—
139Q8×C19—41no—
140Q8×C19—81no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
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—81no—
154C2×C4×C19—81no—
155C2×C4×C19—81no—
156C2×C4×C19—81no—
157C2×C4×C19#12011yescharacteristic
158C2×C4×C19#12111yescharacteristic
159C2×C4×C19#12111yescharacteristic
160C2×C4×C19#12311yescharacteristic
161C2×Dic19—41no—
162C2×Dic19—41no—
163C2×Dic19—41no—
164C2×Dic19—41no—
165C2×Dic19—81no—
166Dic38—42no—
167Dic38—41no—
168Dic38—41no—
169C8×C19—42no—
170C19⋊C8—42no—
171C19⋊C8—41no—
172C19⋊C8—41no—
173C19⋊C8—81no—
174#3195—191no—
175#1901—191no—
176#1894—191no—
177#1855—191no—
178#1520D1911yescharacteristic
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×C19—81no—
198C4×C19—81no—
199C4×C19—161no—
200C4×C19B(4,𝔽2)11yescharacteristic
201C4×C19#45811yescharacteristic
202Dic19—81no—
203Dic19—81no—
204C22×M16—191no—
205C2×C22⋊Q8—191no—
206C2×C22⋊Q8C2×D1911yescharacteristic
207#483—381no—
208#483—381no—
209#470—381no—
210#470—381no—
211#451—381no—
212#451—381no—
213C2×#108—381no—
214C2×#103—381no—
215C2×#101—381no—
216#407—191no—
217#407—191no—
218C2×C22⋊C8C2×D1911yescharacteristic
219#380C2×D1911yescharacteristic
220#343—381no—
221#341—381no—
222#340—381no—
223#328—22no—
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×Q8D7611yescharacteristic
234C23×C4C22×D1911yescharacteristic
235C2×Q16—381no—
236C2×Q16—381no—
237C2×M16—191no—
238C2×M16—191no—
239C2×M16—381no—
240C2×M16—381no—
241C2×M16—381no—
242C2×M16—762no—
243C22×C8—21no—
244C22×C8—381no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—381no—
250C22⋊Q8—381no—
251C22⋊Q8—381no—
252C22⋊Q8—381no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—191no—
256C2×C4⋊C4—381no—
257C2×C4⋊C4D7611yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—381no—
261#108—762no—
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—381no—
272C22⋊C8—381no—
273C22⋊C8—381no—
274C22⋊C8—381no—
275C22⋊C8C22⋊D1912yes—
276#95—21no—
277C19#1056311yescharacteristic, complemented, Sylow
278C24#6454311yescharacteristic
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—381no—
284C2×Q8—381no—
285C2×Q8—761no—
286C2×Q8—761no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—381no—
293C22×C4—381no—
294C22×C4C2×D7611yescharacteristic
295C22×C4#6454111yescharacteristic
296C22×C4D4×D1911yescharacteristic
297C22×C4D4×D1911yescharacteristic
298C22×C4#6454311yescharacteristic
299C22×C4C2×C22⋊D1911yescharacteristic
300Q16—1521no—
301Q16—1521no—
302M16—382no—
303M16—382no—
304M16—761no—
305M16—761no—
306M16—761no—
307M16—761no—
308M16—761no—
309M16—761no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—382no—
314C2×C8—381no—
315C2×C8—381no—
316C2×C8—761no—
317C2×C8—761no—
318C2×C8—761no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—381no—
326C4⋊C4—381no—
327C4⋊C4—761no—
328C4⋊C4—761no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—761no—
333C22⋊C4—761no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23#1059733111yescharacteristic
339C23#1059733211yescharacteristic
340C23#1059738411yescharacteristic
341Q8—41no—
342Q8—41no—
343Q8—81no—
344Q8—762no—
345Q8—761no—
346Q8—761no—
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—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—761no—
364C2×C4—761no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4—1521no—
368C2×C4#1059732811yescharacteristic
369C2×C4#1059732911yescharacteristic
370C2×C4#1059737611yescharacteristic
371C2×C4#1059738511yescharacteristic
372C8—42no—
373C8—762no—
374C8—761no—
375C8—761no—
376C8—1521no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22#1192646011yescharacteristic
388C22#1192680411yescharacteristic
389C22#1192681611yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—81no—
395C4—161no—
396C4—1521no—
397C4—1521no—
398C4#1192673211yescharacteristic
399C4#1192673511yescharacteristic
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#1456488511yescharacteristic
405C2#1456491611yescharacteristic
406C2#1456493511yescharacteristic
subgroupG/H
centerC22#11926460
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1520C2
socleC22×C19#394
prime radicalC24×C19#41
hypercenter#1520D19
hypocenterC19#10563
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

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
#145744562
#145641042
#145640662
#145638422
#145619982
#145615412
C19×#15202
#1056319