Finite Group Databasebeta

← #18080340

Subgroups — #18080340

Order 4864.

818 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 97 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#14566966C211yesmaximal, characteristic
2#14565990C211yesmaximal, characteristic, complemented
3#14563579C211yesmaximal, characteristic
4#14561964C211yesmaximal, characteristic, complemented
5#14561489C211yesmaximal, characteristic, complemented
6#14561488C211yesmaximal, characteristic, complemented
7C19×#1789C211yesmaximal, characteristic
8C2×#10597381—21no—
9C2×#10597323—21no—
10C22×Dic19⋊C4C2211yescharacteristic
11C2×#10597294—22no—
12#11926508C2211yescharacteristic
13#11926463C412yescomplemented
14#11926458C412yescomplemented
15#11926424—21no—
16#11926417—22no—
17#11926407C2211yescharacteristic
18C4×Dic19⋊C4—22no—
19#11926395—22no—
20C22⋊C4×Dic19—21no—
21C4×C22⋊Dic19C2211yescharacteristic
22#11926269—22no—
23C22×#41×C19C2211yescharacteristic
24C2×C19×#104—22no—
25C19×#407C2211yescharacteristic
26C4×C22⋊C4×C19C2211yescharacteristic
27C2×#41×C19—21no—
28C2×#41×C19—21no—
29C2×#41×C19—21no—
30C2×#41×C19—21no—
31C2×#41×C19—44no—
32C22×Q8×C19C2×C411yescharacteristic
33C22×D4×C19—21no—
34C22×D4×C19C2×C411yescharacteristic
35C23×C4×C19—21no—
36C23×C4×C19C2311yescharacteristic
37C23×Dic19D411yescharacteristic
38C23×Dic19D411yescharacteristic
39C2×M16×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C42×C19D412yes—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—21no—
44C2×C22⋊Dic19—22no—
45C2×C22⋊Dic19—22no—
46#10597381—44no—
47C2×Dic19⋊C4—22no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4C2×C412yes—
54C2×Dic19⋊C4D412yes—
55C2×C4×Dic19—22no—
56C2×C4×Dic19—22no—
57C2×C4×Dic19D412yes—
58C2×#64520—21no—
59#10597323—28no—
60C19×#104—44no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×#95—21no—
64#10597294—44no—
65C19⋊#95—22no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—22no—
69C19⋊#95C2×C412yes—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C24×C19—21no—
73C24×C19C2×D411yescharacteristic
74#41×C19—24no—
75#41×C19—24no—
76#41×C19—42no—
77#41×C19—42no—
78#41×C19—42no—
79#41×C19—42no—
80#41×C19—42no—
81#41×C19—42no—
82C2×Q8×C19—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—42no—
85C2×D4×C19—24no—
86C2×D4×C19—21no—
87C2×D4×C19—21no—
88C2×D4×C19—42no—
89C2×D4×C19—42no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C22×C4×C19—21no—
93C22×C4×C19—22no—
94C22×C4×C19—42no—
95C22×C4×C19—42no—
96C22×C4×C19—42no—
97C22×C4×C19—41no—
98C22×C4×C19—41no—
99C22×C4×C19C22×C411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19#4111yescharacteristic
104C22×C4×C19#4111yescharacteristic
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—24no—
108C22×Dic19—22no—
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—22no—
112C22×Dic19—42no—
113C22×Dic19C22⋊C412yes—
114C22×Dic19C22⋊C412yes—
115M16×C19—42no—
116C2×C8×C19—41no—
117C22⋊C4×C19—24no—
118C42×C19—42no—
119C22⋊Dic19—24no—
120C22⋊Dic19—44no—
121C22⋊Dic19—42no—
122C22⋊Dic19—44no—
123Dic19⋊C4—28no—
124Dic19⋊C4—22no—
125Dic19⋊C4—22no—
126Dic19⋊C4—22no—
127Dic19⋊C4—22no—
128Dic19⋊C4—44no—
129C4×Dic19—28no—
130C4×Dic19—42no—
131C4×Dic19—82no—
132#64520—42no—
133C2×C19⋊C8—41no—
134#9476—191nomaximal, Sylow
135C23×C19—22no—
136C23×C19—22no—
137C23×C19—22no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19—42no—
141C23×C19—41no—
142C23×C19—42no—
143C23×C19C2×C22⋊C411yescharacteristic
144C23×C19#12011yescharacteristic
145C23×C19#12311yescharacteristic
146Q8×C19—22no—
147Q8×C19—22no—
148Q8×C19—41no—
149Q8×C19—41no—
150D4×C19—22no—
151D4×C19—22no—
152D4×C19—41no—
153D4×C19—41no—
154D4×C19—44no—
155D4×C19—44no—
156C2×C4×C19—22no—
157C2×C4×C19—22no—
158C2×C4×C19—24no—
159C2×C4×C19—22no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—44no—
165C2×C4×C19—44no—
166C2×C4×C19—42no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—42no—
170C2×C4×C19C4×D411yescharacteristic
171C2×C4×C19C4×D411yescharacteristic
172C2×C4×C19#12111yescharacteristic
173C2×C4×C19#12111yescharacteristic
174C2×Dic19—22no—
175C2×Dic19—22no—
176C2×Dic19—24no—
177C2×Dic19—22no—
178C2×Dic19—22no—
179C2×Dic19—24no—
180C2×Dic19—22no—
181C2×Dic19—42no—
182C2×Dic19—42no—
183C2×Dic19—42no—
184C2×Dic19—42no—
185C2×Dic19—42no—
186C2×Dic19—42no—
187C2×Dic19—42no—
188C2×Dic19—81no—
189C2×Dic19#10414yescomplemented
190C8×C19—81no—
191C19⋊C8—81no—
192#2406—191no—
193#2274—191no—
194#1789—191no—
195#1789D1911yescharacteristic
196#1463—191no—
197#1284—191no—
198#1284—191no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—44no—
207C22×C19—44no—
208C22×C19—42no—
209C22×C19—82no—
210C22×C19—81no—
211C22×C19—81no—
212C22×C19#38611yescharacteristic
213C22×C19C2×#10412yes—
214C22×C19B(4,𝔽2)12yes—
215C4×C19—21no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—44no—
220C4×C19—42no—
221Dic19—24no—
222Dic19—44no—
223Dic19—42no—
224Dic19—82no—
225C22×#41C2×D1911yescharacteristic
226C2×#123—381no—
227C2×#117—381no—
228C22×C4⋊C4—191no—
229C2×#104—22no—
230C2×#104—382no—
231#407—191no—
232#407C2×D1911yescharacteristic
233#395—192no—
234#394—192no—
235#386—381no—
236#385—382no—
237#381—191no—
238C4×C4⋊C4—382no—
239C4×C4⋊C4—382no—
240C4×C22⋊C4—191no—
241C4×C22⋊C4—381no—
242C4×C22⋊C4C2×D1911yescharacteristic
243#324—382no—
244C2×C19—22no—
245C2×C19—22no—
246C2×C19—41no—
247C2×C19—82no—
248C2×C19#188911yescharacteristic
249C2×C19#189611yescharacteristic
250C2×C19#191211yescharacteristic
251C2×#41—21no—
252C2×#41—21no—
253C2×#41—21no—
254C2×#41—21no—
255C2×#41—44no—
256C22×Q8C4×D1911yescharacteristic
257C22×D4—21no—
258C22×D4C4×D1911yescharacteristic
259C23×C4—21no—
260C23×C4—191no—
261C23×C4—191no—
262C23×C4C22×D1911yescharacteristic
263C2×M16—21no—
264C2×M16—381no—
265#123—764no—
266#117—388no—
267C2×C4⋊C4—192no—
268C2×C4⋊C4—192no—
269C2×C4⋊C4—382no—
270C2×C4⋊C4—381no—
271C2×C4⋊C4—381no—
272C2×C4⋊C4—381no—
273C2×C4⋊C4—381no—
274C2×C4⋊C4—382no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—381no—
277C2×C22⋊C4—382no—
278C2×C22⋊C4—382no—
279C2×C22⋊C4—381no—
280C2×C42—192no—
281C2×C42—382no—
282C2×C42—382no—
283C2×C42C22⋊D1912yes—
284#104—44no—
285#104—764no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—381no—
289C22⋊C8—381no—
290#95—21no—
291#95—192no—
292#95—382no—
293#95—382no—
294#95—381no—
295#95—381no—
296C19#947611yescharacteristic, complemented, Sylow
297C24—21no—
298C24D4×D1911yescharacteristic
299#41—24no—
300#41—24no—
301#41—42no—
302#41—42no—
303#41—42no—
304#41—42no—
305#41—42no—
306#41—42no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—42no—
310C2×D4—24no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—41no—
316C2×D4—41no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—192no—
325C22×C4—192no—
326C22×C4—384no—
327C22×C4—381no—
328C22×C4—381no—
329C22×C4—382no—
330C22×C4—381no—
331C22×C4—381no—
332C22×C4—382no—
333C22×C4—762no—
334C22×C4C2×C4×D1911yescharacteristic
335C22×C4#6454111yescharacteristic
336C22×C4D4×D1911yescharacteristic
337C22×C4D4×D1911yescharacteristic
338C22×C4#6454311yescharacteristic
339C22×C4C2×C22⋊D1911yescharacteristic
340M16—42no—
341M16—762no—
342C2×C8—41no—
343C2×C8—761no—
344C4⋊C4—388no—
345C4⋊C4—382no—
346C4⋊C4—382no—
347C4⋊C4—382no—
348C4⋊C4—382no—
349C4⋊C4—764no—
350C22⋊C4—24no—
351C22⋊C4—384no—
352C22⋊C4—764no—
353C22⋊C4—764no—
354C22⋊C4—762no—
355C42—42no—
356C42—388no—
357C42—762no—
358C42—1522no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—41no—
363C23—41no—
364C23—42no—
365C23—42no—
366C23—41no—
367C23C22⋊C4×D1911yescharacteristic
368C23#1059732911yescharacteristic
369C23#1059738311yescharacteristic
370Q8—22no—
371Q8—22no—
372Q8—41no—
373Q8—41no—
374D4—22no—
375D4—22no—
376D4—41no—
377D4—41no—
378D4—44no—
379D4—44no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—194no—
395C2×C4—382no—
396C2×C4—382no—
397C2×C4—384no—
398C2×C4—382no—
399C2×C4—382no—
400C2×C4—384no—
401C2×C4—382no—
402C2×C4—762no—
403C2×C4—762no—
404C2×C4—762no—
405C2×C4—762no—
406C2×C4—762no—
407C2×C4—762no—
408C2×C4—762no—
409C2×C4—1521no—
410C2×C4(C22⋊D19)⋊C411yescharacteristic
411C2×C4#1059733011yescharacteristic
412C2×C4C4×C22⋊D1911yescharacteristic
413C2×C4#1059738411yescharacteristic
414C8—81no—
415C8—1521no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—44no—
424C22—44no—
425C22—42no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22#1192642011yescharacteristic
430C22#104×D1912yes—
431C22#1192673012yes—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—44no—
437C4—42no—
438C4—384no—
439C4—764no—
440C4—762no—
441C4—1522no—
442C2—22no—
443C2—22no—
444C2—41no—
445C2—82no—
446C2#1456404011yescharacteristic
447C2#1456407511yescharacteristic
448C2#1456416911yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1789C2
socleC22×C19#386
prime radicalC22×#41×C19C22
cosocleC23×C4×C19C23
hypercenter#1789D19
hypocenterC19#9476
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #14565990C2semidirect
4. #14561964C2semidirect
5. #14561489C2semidirect
6. #14561488C2semidirect
13. #11926463C4semidirect
14. #11926458C4semidirect
189. C2×Dic19#104semidirect
296. C19#9476semidirect

Maximal subgroups

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

subgroupindex
#145669662
#145659902
#145635792
#145619642
#145614892
#145614882
C19×#17892
#947619