Finite Group Databasebeta

← #18082894

Subgroups — #18082894

Order 4864.

526 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 85 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#14573579C211yesmaximal, characteristic
2#14569433C211yesmaximal, characteristic
3#14564621C211yesmaximal, characteristic
4#14563732C211yesmaximal, characteristic
5#14562155C211yesmaximal, characteristic
6#14561540C211yesmaximal, characteristic
7C19×#3195C211yesmaximal, characteristic
8C2×#10597372C2211yescharacteristic
9#11926882—22no—
10#11926877—21no—
11#11926872—21no—
12#11926584—21no—
13#11926553—21no—
14#11926508C2211yescharacteristic
15#11926483—21no—
16#11926474—21no—
17#11926472—22no—
18#11926451—21no—
19#11926440—21no—
20#11926404C2211yescharacteristic
21C4×C22⋊Dic19C2211yescharacteristic
22#11926311—22no—
23#11926305—22no—
24#11926281—22no—
25C2×C19×C22⋊Q8C2211yescharacteristic
26C2×C19×C22⋊Q8C2211yescharacteristic
27C19×#483—21no—
28C19×#483—21no—
29C19×#470—22no—
30C19×#451—21no—
31C19×#451—21no—
32C19×#407C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C22×Q8×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C2×Q16×C19—22no—
37C2×M16×C19D412yes—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C19×C22⋊Q8—21no—
43C19×C22⋊Q8—21no—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊Dic19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19D412yes—
55#10597372—21no—
56#10597372—21no—
57#10597372—21no—
58#10597372—21no—
59C2×C4⋊Dic19—21no—
60C2×C4⋊Dic19D411yescharacteristic
61C2×C4⋊Dic19D411yescharacteristic
62C2×Dic19⋊C4—22no—
63C2×C4×Dic19—21no—
64C2×C4×Dic19—21no—
65C2×#64520—21no—
66C19×#106—22no—
67C19×#103—22no—
68C19×#103—22no—
69C19×C22⋊C8—21no—
70C19×C22⋊C8—21no—
71#10597292—22no—
72#10597292—22no—
73C19⋊#95—22no—
74C19⋊#95—22no—
75C19⋊#95—22no—
76C19⋊#95—21no—
77C19⋊#95—21no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)D412yes—
80#10597265—22no—
81#10597264—22no—
82C24×C19C2×D411yescharacteristic
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—21no—
87C2×Q8×C19—42no—
88C2×Q8×C19—42no—
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—42no—
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19#4111yescharacteristic
100C22×Dic19—21no—
101C22×Dic19—21no—
102C22×Dic19—22no—
103C22×Dic19—41no—
104Q16×C19—82no—
105M16×C19—42no—
106C2×C8×C19—22no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C4⋊C4×C19—41no—
114C4⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C22⋊C4×C19—41no—
119C22⋊Dic19—22no—
120C22⋊Dic19—41no—
121C22⋊Dic19—41no—
122C22⋊Dic19—41no—
123C22⋊Dic19—42no—
124C4⋊Dic19—21no—
125C4⋊Dic19—21no—
126C4⋊Dic19—21no—
127C4⋊Dic19—21no—
128C4⋊Dic19—42no—
129Dic19⋊C4—82no—
130C4×Dic19—41no—
131C4×Dic19—41no—
132C4×Dic19—42no—
133#64520—42no—
134C2×C19⋊C8—22no—
135#9937—191nomaximal, Sylow
136C23×C19—21no—
137C23×C19—21no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19#12011yescharacteristic
141C23×C19#12111yescharacteristic
142C23×C19#12711yescharacteristic
143Q8×C19—42no—
144Q8×C19—42no—
145Q8×C19—42no—
146Q8×C19—81no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—22no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—81no—
161C2×C4×C19—81no—
162C2×C4×C19#12011yescharacteristic
163C2×C4×C19#12011yescharacteristic
164C2×C4×C19#12111yescharacteristic
165C2×C4×C19#12111yescharacteristic
166C2×Dic19—42no—
167C2×Dic19—42no—
168C2×Dic19—42no—
169C2×Dic19—42no—
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—41no—
173C2×Dic19—42no—
174C2×Dic19—41no—
175C2×Dic19—81no—
176C2×Dic19—81no—
177C8×C19—42no—
178C19⋊C8—42no—
179#3195D1911yescharacteristic
180#3095—191no—
181#2625—191no—
182#1996—191no—
183#1826—191no—
184#1508—191no—
185#1305—191no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—81no—
195C22×C19—81no—
196C22×C19#39211yescharacteristic
197C22×C19#45511yescharacteristic
198C22×C19#45611yescharacteristic
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—81no—
203C4×C19—81no—
204C4×C19—81no—
205C4×C19—81no—
206C4×C19#45812yes—
207Dic19—82no—
208Dic19—82no—
209Dic19—81no—
210Dic19—81no—
211C2×C22⋊Q8C2×D1911yescharacteristic
212C2×C22⋊Q8C2×D1911yescharacteristic
213C2×#117—191no—
214#485—382no—
215#484—381no—
216#483—21no—
217#483—21no—
218#483—381no—
219#470—22no—
220#451—21no—
221#451—21no—
222#428—381no—
223#419—381no—
224#407—191no—
225#407C2×D1911yescharacteristic
226#400—381no—
227#398—381no—
228#397—382no—
229#391—381no—
230#389—381no—
231#380—191no—
232C4×C22⋊C4—191no—
233#342—382no—
234#339—382no—
235#328—382no—
236C2×C19—21no—
237C2×C19—21no—
238C2×C19—41no—
239C2×C19—41no—
240C2×C19#200711yescharacteristic
241C2×C19#200911yescharacteristic
242C2×C19#202211yescharacteristic
243C22×Q8C22⋊D1911yescharacteristic
244C22×Q8C22⋊D1911yescharacteristic
245C23×C4C22×D1911yescharacteristic
246C2×Q16—22no—
247C2×M16—381no—
248C2×M16C22⋊D1912yes—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257#117—381no—
258#117—381no—
259#117—381no—
260#117—381no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—191no—
264C2×C4⋊C4—191no—
265C2×C4⋊C4—381no—
266C2×C4⋊C4—382no—
267C2×C4⋊C4C22⋊D1911yescharacteristic
268C2×C4⋊C4C22⋊D1911yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—192no—
272C2×C22⋊C4—381no—
273C2×C22⋊C4—381no—
274C2×C42—381no—
275C2×C42—381no—
276#107—382no—
277#106—22no—
278#106—382no—
279#103—22no—
280#103—22no—
281#103—382no—
282#103—382no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—192no—
286C22⋊C8—381no—
287#95—382no—
288#95—382no—
289#95—382no—
290#95—381no—
291#95—381no—
292C19#993711yescharacteristic, complemented, Sylow
293C24D4×D1911yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—42no—
299C2×Q8—42no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—381no—
306C22×C4—382no—
307C22×C4—381no—
308C22×C4—761no—
309C22×C4D4×D1911yescharacteristic
310C22×C4D4×D1911yescharacteristic
311C22×C4#6454311yescharacteristic
312C22×C4C2×C22⋊D1911yescharacteristic
313C22×C4C2×C22⋊D1911yescharacteristic
314C22×C4C2×C22⋊D1911yescharacteristic
315Q16—82no—
316M16—42no—
317M16—762no—
318C2×C8—22no—
319C2×C8—382no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—381no—
329C4⋊C4—381no—
330C4⋊C4—381no—
331C4⋊C4—381no—
332C4⋊C4—762no—
333C4⋊C4—1522no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—382no—
339C22⋊C4—761no—
340C22⋊C4—761no—
341C22⋊C4—761no—
342C22⋊C4—762no—
343C42—762no—
344C42—761no—
345C42—761no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23#1059738311yescharacteristic
351C23#1059738511yescharacteristic
352C23#1059738611yescharacteristic
353Q8—42no—
354Q8—42no—
355Q8—42no—
356Q8—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—762no—
373C2×C4—762no—
374C2×C4—762no—
375C2×C4—762no—
376C2×C4—761no—
377C2×C4—761no—
378C2×C4—762no—
379C2×C4—761no—
380C2×C4—761no—
381C2×C4—1521no—
382C2×C4—1521no—
383C2×C4#1059738311yescharacteristic
384C2×C4#1059738411yescharacteristic
385C2×C4#1059738511yescharacteristic
386C2×C4#1059739911yescharacteristic
387C8—42no—
388C8—762no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—81no—
398C22—81no—
399C22#1192645211yescharacteristic
400C22#1192672011yescharacteristic
401C22#1192672511yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—1522no—
410C4—1522no—
411C4—1521no—
412C4—1521no—
413C4#1192673412yes—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2#1456468011yescharacteristic
419C2#1456469311yescharacteristic
420C2#1456476411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3195C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#3195D19
hypocenterC19#9937
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
292. C19#9937semidirect

Maximal subgroups

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

subgroupindex
#145735792
#145694332
#145646212
#145637322
#145621552
#145615402
C19×#31952
#993719