Finite Group Databasebeta

← #18078594

Subgroups — #18078594

Order 4864.

516 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 105 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#14569450C211yesmaximal, characteristic
2#14566237C211yesmaximal, characteristic
3#14562207C211yesmaximal, characteristic
4C2×#11926269C211yesmaximal, characteristic
5#14561503C211yesmaximal, characteristic
6#14561502C211yesmaximal, characteristic
7C19×#1520C211yesmaximal, characteristic
8C22×Dic19⋊C4C2211yescharacteristic
9C2×C22⋊(C19⋊C8)C2211yescharacteristic
10#11926482C412yescomplemented
11#11926477—22no—
12#11926463C412yescomplemented
13#11926431—22no—
14#11926425—22no—
15#11926416—21no—
16#11926405—21no—
17#11926405—21no—
18#11926404C2211yescharacteristic
19#11926404C2211yescharacteristic
20C22⋊C4×Dic19—21no—
21#11926281—22no—
22#11926269—22no—
23C2×C19×C22⋊Q8C2211yescharacteristic
24C2×C19×C22⋊C8C2211yescharacteristic
25C19×#380C2211yescharacteristic
26C19×#328—22no—
27C22×Q8×C19C2×C411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C23×Dic19D411yescharacteristic
30C23×Dic19D411yescharacteristic
31C22×C8×C19—21no—
32C19×C22⋊Q8—21no—
33C19×C22⋊Q8—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19C2×C411yescharacteristic
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—22no—
50C2×Dic19⋊C4C2×C412yes—
51C2×Dic19⋊C4D412yes—
52C2×C4×Dic19—22no—
53C22×C19⋊C8—21no—
54C19×C22⋊C8—21no—
55C19×C22⋊C8—21no—
56C19×#95D412yes—
57C19⋊#95—22no—
58C19⋊#95—24no—
59C19⋊#95—22no—
60C19⋊#95—22no—
61C19⋊#95—22no—
62C19⋊#95C2×C412yes—
63C19⋊#95D412yes—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)—21no—
66C24×C19C2×D411yescharacteristic
67C2×Q8×C19—21no—
68C2×Q8×C19—21no—
69C2×Q8×C19—81no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—22no—
73C22×C4×C19—81no—
74C22×C4×C19C22×C411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—22no—
89C22×Dic19—22no—
90C22×Dic19—81no—
91C22×Dic19C22⋊C412yes—
92C22×Dic19C22⋊C412yes—
93C2×C8×C19—41no—
94C2×C8×C19—81no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—81no—
100C22⋊C4×C19—41no—
101C22⋊C4×C19—41no—
102C22⋊C4×C19—41no—
103C22⋊C4×C19—41no—
104C22⋊Dic19—41no—
105C22⋊Dic19—41no—
106C22⋊Dic19—41no—
107C22⋊Dic19—41no—
108C4⋊Dic19—81no—
109C4⋊Dic19—81no—
110Dic19⋊C4—22no—
111Dic19⋊C4—22no—
112Dic19⋊C4—22no—
113Dic19⋊C4—22no—
114Dic19⋊C4—82no—
115C4×Dic19—82no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—81no—
118#9202—191nomaximal, Sylow
119C23×C19—41no—
120C23×C19—41no—
121C23×C19C2×C22⋊C411yescharacteristic
122C23×C19#12011yescharacteristic
123C23×C19#12311yescharacteristic
124C23×C19#13511yescharacteristic
125C23×C19#13511yescharacteristic
126C23×C19#13711yescharacteristic
127C23×C19#13711yescharacteristic
128Q8×C19—81no—
129Q8×C19—81no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19C4×D411yescharacteristic
144C2×C4×C19C4×D411yescharacteristic
145C2×C4×C19#12111yescharacteristic
146C2×C4×C19#12111yescharacteristic
147C2×Dic19—22no—
148C2×Dic19—22no—
149C2×Dic19—22no—
150C2×Dic19—22no—
151C2×Dic19—42no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—42no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—42no—
162C2×Dic19—42no—
163C2×Dic19—81no—
164C8×C19—81no—
165C19⋊C8—81no—
166#2627—191no—
167#2313—191no—
168#1520—191no—
169#1520D1911yescharacteristic
170C2×#324—191no—
171#1289—191no—
172#1289—191no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19#38611yescharacteristic
184C22×C19#41611yescharacteristic
185C22×C19#41911yescharacteristic
186C22×C19#45211yescharacteristic
187C22×C19#45211yescharacteristic
188C22×C19#48511yescharacteristic
189C22×C19#48511yescharacteristic
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—82no—
195C4×C19—81no—
196C4×C19—81no—
197Dic19—42no—
198Dic19—42no—
199Dic19—82no—
200Dic19—82no—
201C2×C22⋊Q8C2×D1911yescharacteristic
202C22×C4⋊C4—191no—
203C2×C22⋊C8—191no—
204C2×C22⋊C8C2×D1911yescharacteristic
205#400—192no—
206#398—382no—
207#395—192no—
208#387—382no—
209#387—382no—
210#385—381no—
211#381—381no—
212#381—381no—
213#380—191no—
214#380—191no—
215#380C2×D1911yescharacteristic
216C4×C22⋊C4—381no—
217#328—22no—
218#328—382no—
219#324—382no—
220C2×C19—21no—
221C2×C19—21no—
222C2×C19—21no—
223C2×C19—21no—
224C2×C19—21no—
225C2×C19—21no—
226C2×C19#187311yescharacteristic
227C2×C19#191211yescharacteristic
228C2×C19#191311yescharacteristic
229C22×Q8C4×D1911yescharacteristic
230C23×C4—191no—
231C23×C4—191no—
232C23×C4C22×D1911yescharacteristic
233C22×C8—21no—
234C22×C8—381no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—192no—
242C2×C4⋊C4—192no—
243C2×C4⋊C4—381no—
244C2×C4⋊C4—381no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4—381no—
247C2×C4⋊C4—382no—
248C2×C4⋊C4—381no—
249C2×C4⋊C4—381no—
250C2×C4⋊C4C4×D1911yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—381no—
254C2×C22⋊C4—381no—
255C2×C42—382no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—381no—
259C22⋊C8—381no—
260#95—192no—
261#95—192no—
262#95—382no—
263#95—382no—
264#95—382no—
265#95—382no—
266#95—384no—
267#95C22⋊D1912yes—
268C19#920211yescharacteristic, complemented, Sylow
269C24D4×D1911yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—81no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—81no—
277C22×C4—192no—
278C22×C4—192no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—381no—
282C22×C4—381no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—382no—
288C22×C4—382no—
289C22×C4—1521no—
290C22×C4C2×C4×D1911yescharacteristic
291C22×C4#6454111yescharacteristic
292C22×C4D4×D1911yescharacteristic
293C22×C4D4×D1911yescharacteristic
294C22×C4#6454311yescharacteristic
295C22×C4C2×C22⋊D1911yescharacteristic
296C2×C8—41no—
297C2×C8—81no—
298C2×C8—761no—
299C2×C8—1521no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—81no—
305C4⋊C4—382no—
306C4⋊C4—382no—
307C4⋊C4—382no—
308C4⋊C4—382no—
309C4⋊C4—1522no—
310C4⋊C4—1521no—
311C4⋊C4—1521no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—761no—
317C22⋊C4—761no—
318C22⋊C4—761no—
319C22⋊C4—761no—
320C42—1522no—
321C23—41no—
322C23—41no—
323C23C22⋊C4×D1911yescharacteristic
324C23#1059732911yescharacteristic
325C23#1059736111yescharacteristic
326C23#1059736211yescharacteristic
327C23#1059736411yescharacteristic
328C23#1059736511yescharacteristic
329C23#1059738311yescharacteristic
330Q8—81no—
331Q8—81no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—382no—
346C2×C4—382no—
347C2×C4—382no—
348C2×C4—382no—
349C2×C4—762no—
350C2×C4—761no—
351C2×C4—761no—
352C2×C4—761no—
353C2×C4—761no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—762no—
360C2×C4—762no—
361C2×C4—1521no—
362C2×C4(C22⋊D19)⋊C411yescharacteristic
363C2×C4#1059733011yescharacteristic
364C2×C4C4×C22⋊D1911yescharacteristic
365C2×C4#1059738411yescharacteristic
366C8—81no—
367C8—1521no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1192642011yescharacteristic
379C22#1192653911yescharacteristic
380C22#1192655111yescharacteristic
381C22#1192670311yescharacteristic
382C22#1192670511yescharacteristic
383C22#1192688311yescharacteristic
384C22#1192688411yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—81no—
391C4—81no—
392C4—762no—
393C4—762no—
394C4—1522no—
395C4—1522no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#1456394411yescharacteristic
403C2#1456416911yescharacteristic
404C2#1456417411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1520C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#1520D19
hypocenterC19#9202
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
10. #11926482C4semidirect
12. #11926463C4semidirect
268. C19#9202semidirect

Maximal subgroups

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

subgroupindex
#145694502
#145662372
#145622072
C2×#119262692
#145615032
#145615022
C19×#15202
#920219