Finite Group Databasebeta

← #18080360

Subgroups — #18080360

Order 4864.

726 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 93 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#14566235C211yesmaximal, characteristic, complemented
3#14563579C211yesmaximal, characteristic
4#14561964C211yesmaximal, characteristic, complemented
5#14561489C211yesmaximal, characteristic, complemented
6#14561488C211yesmaximal, characteristic, complemented
7C19×#1789C211yesmaximal, characteristic
8C2×#10597381—21no—
9C22×Dic19⋊C4C2211yescharacteristic
10C2×#10597294—22no—
11#11926508C2211yescharacteristic
12#11926463C412yescomplemented
13#11926458C412yescomplemented
14#11926428—22no—
15#11926426—22no—
16#11926424—21no—
17#11926417—22no—
18#11926407C2211yescharacteristic
19#11926405—21no—
20#11926402—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—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—22no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4C2×C412yes—
54C2×Dic19⋊C4D412yes—
55C2×C4×Dic19D412yes—
56C2×#64520—21no—
57C19×#104—44no—
58C19×C22⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×#95—21no—
61#10597294—44no—
62C19⋊#95—22no—
63C19⋊#95—24no—
64C19⋊#95—21no—
65C19⋊#95—21no—
66C19⋊#95—22no—
67C19⋊#95C2×C412yes—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)—21no—
70C24×C19—21no—
71C24×C19C2×D411yescharacteristic
72#41×C19—24no—
73#41×C19—24no—
74#41×C19—42no—
75#41×C19—42no—
76#41×C19—42no—
77#41×C19—42no—
78#41×C19—42no—
79#41×C19—42no—
80C2×Q8×C19—21no—
81C2×Q8×C19—21no—
82C2×Q8×C19—42no—
83C2×D4×C19—24no—
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—42no—
87C2×D4×C19—42no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C22×C4×C19—21no—
91C22×C4×C19—22no—
92C22×C4×C19—42no—
93C22×C4×C19—42no—
94C22×C4×C19—42no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19C22×C411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19#4111yescharacteristic
102C22×C4×C19#4111yescharacteristic
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—22no—
108C22×Dic19—22no—
109C22×Dic19—42no—
110C22×Dic19—42no—
111C22×Dic19C22⋊C412yes—
112C22×Dic19C22⋊C412yes—
113M16×C19—42no—
114C2×C8×C19—41no—
115C22⋊C4×C19—42no—
116C42×C19—42no—
117C22⋊Dic19—44no—
118C22⋊Dic19—44no—
119C22⋊Dic19—42no—
120C22⋊Dic19—42no—
121Dic19⋊C4—22no—
122Dic19⋊C4—22no—
123Dic19⋊C4—22no—
124Dic19⋊C4—22no—
125Dic19⋊C4—44no—
126Dic19⋊C4—82no—
127C4×Dic19—42no—
128#64520—42no—
129C2×C19⋊C8—41no—
130#9480—191nomaximal, Sylow
131C23×C19—22no—
132C23×C19—22no—
133C23×C19—22no—
134C23×C19—41no—
135C23×C19—41no—
136C23×C19—42no—
137C23×C19—41no—
138C23×C19—42no—
139C23×C19C2×C22⋊C411yescharacteristic
140C23×C19#12011yescharacteristic
141C23×C19#12311yescharacteristic
142Q8×C19—22no—
143Q8×C19—22no—
144Q8×C19—41no—
145Q8×C19—41no—
146D4×C19—22no—
147D4×C19—22no—
148D4×C19—41no—
149D4×C19—41no—
150D4×C19—44no—
151D4×C19—44no—
152C2×C4×C19—22no—
153C2×C4×C19—22no—
154C2×C4×C19—22no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—44no—
160C2×C4×C19—44no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—42no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19C4×D411yescharacteristic
167C2×C4×C19C4×D411yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12111yescharacteristic
170C2×Dic19—22no—
171C2×Dic19—22no—
172C2×Dic19—22no—
173C2×Dic19—22no—
174C2×Dic19—42no—
175C2×Dic19—42no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—42no—
181C2×Dic19—42no—
182C2×Dic19—42no—
183C2×Dic19—42no—
184C2×Dic19—81no—
185C8×C19—81no—
186C19⋊C8—81no—
187#2406—191no—
188#2313—191no—
189#1789—191no—
190#1789D1911yescharacteristic
191#1463—191no—
192#1284—191no—
193#1284—191no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—44no—
202C22×C19—44no—
203C22×C19—42no—
204C22×C19—82no—
205C22×C19—81no—
206C22×C19—81no—
207C22×C19#38611yescharacteristic
208C22×C19#42112yes—
209C22×C19B(4,𝔽2)12yes—
210C4×C19—21no—
211C4×C19—21no—
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—42no—
215C4×C19—82no—
216Dic19—42no—
217Dic19—42no—
218Dic19—82no—
219Dic19—82no—
220C22×#41C2×D1911yescharacteristic
221C2×#123—381no—
222C22×C4⋊C4—191no—
223C2×#104—22no—
224C2×#104—382no—
225#407—191no—
226#407C2×D1911yescharacteristic
227#395—192no—
228#394—192no—
229#387—382no—
230#387—382no—
231#386—381no—
232#385—382no—
233#381—191no—
234#381—381no—
235#380—381no—
236C4×C22⋊C4—191no—
237C4×C22⋊C4C2×D1911yescharacteristic
238#324—382no—
239C2×C19—22no—
240C2×C19—22no—
241C2×C19—41no—
242C2×C19—82no—
243C2×C19#188911yescharacteristic
244C2×C19#189711yescharacteristic
245C2×C19#191211yescharacteristic
246C2×#41—21no—
247C2×#41—21no—
248C2×#41—21no—
249C2×#41—21no—
250C2×#41—44no—
251C22×Q8C4×D1911yescharacteristic
252C22×D4—21no—
253C22×D4C4×D1911yescharacteristic
254C23×C4—21no—
255C23×C4—191no—
256C23×C4—191no—
257C23×C4C22×D1911yescharacteristic
258C2×M16—21no—
259C2×M16—381no—
260#123—764no—
261C2×C4⋊C4—192no—
262C2×C4⋊C4—192no—
263C2×C4⋊C4—381no—
264C2×C4⋊C4—381no—
265C2×C4⋊C4—381no—
266C2×C4⋊C4—381no—
267C2×C4⋊C4—382no—
268C2×C4⋊C4—382no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—382no—
271C2×C22⋊C4—382no—
272C2×C22⋊C4—381no—
273C2×C22⋊C4—381no—
274C2×C42—192no—
275C2×C42C22⋊D1912yes—
276#104—44no—
277#104—764no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—381no—
281C22⋊C8—381no—
282#95—21no—
283#95—192no—
284#95—382no—
285#95—382no—
286#95—384no—
287#95—381no—
288#95—381no—
289C19#948011yescharacteristic, complemented, Sylow
290C24—21no—
291C24D4×D1911yescharacteristic
292#41—24no—
293#41—24no—
294#41—42no—
295#41—42no—
296#41—42no—
297#41—42no—
298#41—42no—
299#41—42no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—42no—
303C2×D4—24no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—41no—
309C2×D4—41no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—192no—
318C22×C4—192no—
319C22×C4—381no—
320C22×C4—381no—
321C22×C4—381no—
322C22×C4—381no—
323C22×C4—382no—
324C22×C4—382no—
325C22×C4—762no—
326C22×C4—762no—
327C22×C4C2×C4×D1911yescharacteristic
328C22×C4#6454111yescharacteristic
329C22×C4D4×D1911yescharacteristic
330C22×C4D4×D1911yescharacteristic
331C22×C4#6454311yescharacteristic
332C22×C4C2×C22⋊D1911yescharacteristic
333M16—42no—
334M16—762no—
335C2×C8—41no—
336C2×C8—761no—
337C4⋊C4—382no—
338C4⋊C4—382no—
339C4⋊C4—382no—
340C4⋊C4—382no—
341C4⋊C4—764no—
342C4⋊C4—1522no—
343C22⋊C4—42no—
344C22⋊C4—764no—
345C22⋊C4—762no—
346C22⋊C4—764no—
347C22⋊C4—762no—
348C42—42no—
349C42—762no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—41no—
354C23—41no—
355C23—42no—
356C23—42no—
357C23—41no—
358C23C22⋊C4×D1911yescharacteristic
359C23#1059732911yescharacteristic
360C23#1059738311yescharacteristic
361Q8—22no—
362Q8—22no—
363Q8—41no—
364Q8—41no—
365D4—22no—
366D4—22no—
367D4—41no—
368D4—41no—
369D4—44no—
370D4—44no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—382no—
386C2×C4—382no—
387C2×C4—382no—
388C2×C4—382no—
389C2×C4—762no—
390C2×C4—762no—
391C2×C4—762no—
392C2×C4—762no—
393C2×C4—762no—
394C2×C4—762no—
395C2×C4—762no—
396C2×C4—762no—
397C2×C4—762no—
398C2×C4—762no—
399C2×C4—1521no—
400C2×C4(C22⋊D19)⋊C411yescharacteristic
401C2×C4#1059733011yescharacteristic
402C2×C4C4×C22⋊D1911yescharacteristic
403C2×C4#1059738411yescharacteristic
404C8—81no—
405C8—1521no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—44no—
414C22—44no—
415C22—42no—
416C22—82no—
417C22—81no—
418C22—81no—
419C22#1192642011yescharacteristic
420C22#1192655912yes—
421C22#1192673012yes—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—42no—
427C4—82no—
428C4—762no—
429C4—762no—
430C4—1522no—
431C4—1522no—
432C2—22no—
433C2—22no—
434C2—41no—
435C2—82no—
436C2#1456404011yescharacteristic
437C2#1456408011yescharacteristic
438C2#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#9480
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. #14566235C2semidirect
4. #14561964C2semidirect
5. #14561489C2semidirect
6. #14561488C2semidirect
12. #11926463C4semidirect
13. #11926458C4semidirect
289. C19#9480semidirect

Maximal subgroups

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

subgroupindex
#145669662
#145662352
#145635792
#145619642
#145614892
#145614882
C19×#17892
#948019