Finite Group Databasebeta

← #18083053

Subgroups — #18083053

Order 4864.

568 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 109 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#14574410C211yesmaximal, characteristic
2C2×#11926880C211yesmaximal, characteristic
3#14568113C211yesmaximal, characteristic
4#14564620C211yesmaximal, characteristic
5#14563726C211yesmaximal, characteristic
6#14562208C211yesmaximal, characteristic
7C19×#1282C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C2×#10597370C2211yescharacteristic
10C22×C4⋊Dic19C2211yescharacteristic
11#11926880—21no—
12#11926880—21no—
13#11926880—22no—
14#11926880—22no—
15#11926785—22no—
16#11926702—21no—
17#11926702—21no—
18C2×#10597275—21no—
19C2×#10597273—21no—
20#11926476—22no—
21#11926450—21no—
22#11926419—22no—
23#11926414—21no—
24#11926404C2211yescharacteristic
25#11926310—22no—
26#11926307—22no—
27#11926282—22no—
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×C22⋊C8C2211yescharacteristic
30C4×C22⋊C4×C19C2211yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C23×Dic19—21no—
33C22×Dic38D411yescharacteristic
34C22×Dic38D411yescharacteristic
35C22×C8×C19—21no—
36C22×C8×C19D412yes—
37C2×C22⋊C4×C19D412yes—
38C2×C42×C19—21no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—24no—
49C2×C4⋊Dic19D411yescharacteristic
50C2×C4⋊Dic19D411yescharacteristic
51C2×C4⋊Dic19D412yes—
52#10597370—21no—
53#10597370—21no—
54#10597370—21no—
55#10597370—21no—
56#10597370—21no—
57#10597370—21no—
58#10597370—21no—
59#10597370—21no—
60C2×Dic19⋊C4—21no—
61C2×Dic19⋊C4—21no—
62C2×Dic76—22no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8D412yes—
67C19×#95—21no—
68C19⋊#95—24no—
69C19⋊#95—21no—
70#10597275—22no—
71#10597275—24no—
72#10597273—22no—
73#10597273—22no—
74#10597273—24no—
75C24×C19C2×D411yescharacteristic
76C22×C4×C19—22no—
77C22×C4×C19—42no—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—22no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—41no—
90C22×Dic19—41no—
91C22×Dic19—41no—
92C22×Dic19—82no—
93C2×Dic38—21no—
94C2×Dic38—21no—
95C2×Dic38—21no—
96C2×Dic38—21no—
97C2×Dic38—42no—
98C2×Dic38—42no—
99C2×C8×C19—22no—
100C2×C8×C19—22no—
101C2×C8×C19—42no—
102C2×C8×C19—42no—
103C22⋊C4×C19—22no—
104C22⋊C4×C19Q1614yescomplemented
105C42×C19—42no—
106C22⋊Dic19—41no—
107C22⋊Dic19—41no—
108C22⋊Dic19—41no—
109C22⋊Dic19—41no—
110C22⋊Dic19—42no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—22no—
114C4⋊Dic19—21no—
115C4⋊Dic19—21no—
116C4⋊Dic19—22no—
117C4⋊Dic19—41no—
118C4⋊Dic19—41no—
119C4⋊Dic19—42no—
120C4⋊Dic19—84no—
121Dic19⋊C4—41no—
122Dic19⋊C4—41no—
123Dic19⋊C4—41no—
124Dic19⋊C4—41no—
125Dic76—82no—
126#9959—191nomaximal, Sylow
127C23×C19—41no—
128C23×C19—41no—
129C23×C19#12011yescharacteristic
130C23×C19#12111yescharacteristic
131C23×C19#12711yescharacteristic
132C23×C19C2×Q1612yes—
133C23×C19#13712yes—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—24no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19#12011yescharacteristic
144C2×C4×C19#12011yescharacteristic
145C2×C4×C19#12111yescharacteristic
146C2×C4×C19#12111yescharacteristic
147C2×Dic19—42no—
148C2×Dic19—44no—
149C2×Dic19—42no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—42no—
155C2×Dic19—82no—
156C2×Dic19—82no—
157C2×Dic19—81no—
158C2×Dic19—81no—
159C2×Dic19—81no—
160C2×Dic19—81no—
161C2×Dic19—81no—
162Dic38—42no—
163Dic38—42no—
164Dic38—42no—
165Dic38—81no—
166C8×C19—42no—
167C8×C19—42no—
168#3189—191no—
169C2×#484—191no—
170#2502—191no—
171#1996—191no—
172#1824—191no—
173#1520—191no—
174#1282D1911yescharacteristic
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—42no—
182C22×C19—42no—
183C22×C19#39211yescharacteristic
184C22×C19#45112yes—
185C22×C19#46212yes—
186C22×C19#49411yescharacteristic
187C22×C19#49711yescharacteristic
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—44no—
192C4×C19#45812yes—
193Dic19—81no—
194Dic19—82no—
195Dic19—81no—
196Dic19—81no—
197Dic19—81no—
198Dic19—161no—
199C2×C22⋊Q8—191no—
200C2×C22⋊Q8—191no—
201C22×C4⋊C4—191no—
202#484—382no—
203#484—381no—
204#484—381no—
205#484—382no—
206#467—382no—
207#451—381no—
208#451—381no—
209C2×#107—381no—
210C2×#103—381no—
211C2×C22⋊C8C2×D1911yescharacteristic
212C2×C22⋊C8C2×D1911yescharacteristic
213#398—382no—
214#391—381no—
215#385—382no—
216#384—381no—
217#380—191no—
218C4×C22⋊C4C2×D1911yescharacteristic
219#342—382no—
220#340—382no—
221#328—382no—
222C2×C19—21no—
223C2×C19—22no—
224C2×C19—22no—
225C2×C19—21no—
226C2×C19#200811yescharacteristic
227C2×C19#201611yescharacteristic
228C2×C19#202211yescharacteristic
229C22×Q8—191no—
230C22×Q8—191no—
231C23×C4—381no—
232C23×C4C22×D1911yescharacteristic
233C2×Q16—382no—
234C22×C8—21no—
235C22×C8D7612yes—
236C22⋊Q8—381no—
237C22⋊Q8—381no—
238C22⋊Q8—381no—
239C22⋊Q8—381no—
240C22⋊Q8—381no—
241C22⋊Q8—381no—
242C22⋊Q8—381no—
243C22⋊Q8—381no—
244C2×C4⋊C4—192no—
245C2×C4⋊C4—191no—
246C2×C4⋊C4—191no—
247C2×C4⋊C4—381no—
248C2×C4⋊C4—381no—
249C2×C4⋊C4—381no—
250C2×C4⋊C4—381no—
251C2×C4⋊C4—381no—
252C2×C4⋊C4—381no—
253C2×C4⋊C4—381no—
254C2×C4⋊C4—381no—
255C2×C4⋊C4—384no—
256C2×C22⋊C4—381no—
257C2×C22⋊C4—381no—
258C2×C22⋊C4—381no—
259C2×C22⋊C4D7612yes—
260C2×C42—21no—
261#107—384no—
262#107—382no—
263#103—384no—
264#103—382no—
265#103—382no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8D7612yes—
270#95—21no—
271#95—384no—
272#95—381no—
273C19#995911yescharacteristic, complemented, Sylow
274C24C2×D7611yescharacteristic
275C2×Q8—381no—
276C2×Q8—381no—
277C2×Q8—381no—
278C2×Q8—381no—
279C2×Q8—762no—
280C2×Q8—762no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—381no—
284C22×C4—382no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4—761no—
289C22×C4—761no—
290C22×C4—761no—
291C22×C4—1522no—
292C22×C4C2×D7611yescharacteristic
293C22×C4C2×D7611yescharacteristic
294C22×C4D4×D1911yescharacteristic
295C22×C4D4×D1911yescharacteristic
296C22×C4D4×D1911yescharacteristic
297C22×C4#6454511yescharacteristic
298Q16—1522no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—42no—
303C4⋊C4—382no—
304C4⋊C4—381no—
305C4⋊C4—381no—
306C4⋊C4—381no—
307C4⋊C4—382no—
308C4⋊C4—381no—
309C4⋊C4—762no—
310C4⋊C4—761no—
311C4⋊C4—761no—
312C4⋊C4—761no—
313C4⋊C4—761no—
314C4⋊C4—761no—
315C4⋊C4—761no—
316C4⋊C4—1524no—
317C22⋊C4—22no—
318C22⋊C4—761no—
319C22⋊C4—761no—
320C22⋊C4—761no—
321C22⋊C4—761no—
322C22⋊C4—762no—
323C22⋊C4Dic7614yescomplemented
324C42—42no—
325C23—41no—
326C23—41no—
327C23#1059732011yescharacteristic
328C23#1059732811yescharacteristic
329C23#1059734111yescharacteristic
330C23C2×Dic7612yes—
331C23#1059735512yes—
332Q8—762no—
333Q8—762no—
334Q8—762no—
335Q8—1521no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—762no—
346C2×C4—764no—
347C2×C4—762no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4—761no—
351C2×C4—761no—
352C2×C4—762no—
353C2×C4—1521no—
354C2×C4—1521no—
355C2×C4—1521no—
356C2×C4—1522no—
357C2×C4—1522no—
358C2×C4—1521no—
359C2×C4—1521no—
360C2×C4#1059732811yescharacteristic
361C2×C4#1059732811yescharacteristic
362C2×C4#1059734111yescharacteristic
363C2×C4#1059734111yescharacteristic
364C8—42no—
365C8—42no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22#1192645411yescharacteristic
375C22#1192670212yes—
376C22#1192675512yes—
377C22#1192692411yescharacteristic
378C22#1192693811yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—3041no—
384C4—1522no—
385C4—1521no—
386C4—1521no—
387C4—1521no—
388C4—1521no—
389C4#1192673512yes—
390C2—22no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2#1456469111yescharacteristic
395C2#1456473711yescharacteristic
396C2#1456476711yescharacteristic
subgroupG/H
centerC22#11926454
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1282C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#1282D19
hypocenterC19#9959
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
104. C22⋊C4×C19Q16semidirect
273. C19#9959semidirect
323. C22⋊C4Dic76semidirect

Maximal subgroups

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

subgroupindex
#145744102
C2×#119268802
#145681132
#145646202
#145637262
#145622082
C19×#12822
#995919