Finite Group Databasebeta

← #14568648

Subgroups — #14568648

Order 2432.

544 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597370C211yesmaximal, characteristic
2C2×#10597324C211yesmaximal, characteristic
3#11926478C211yesmaximal, characteristic, complemented
4#11926477C211yesmaximal, characteristic, complemented
5#11926465C211yesmaximal, characteristic, complemented
6#11926464C211yesmaximal, characteristic, complemented
7#11926448C211yesmaximal, characteristic, complemented
8#11926448C211yesmaximal, characteristic, complemented
9#11926443C211yesmaximal, characteristic, complemented
10#11926440C211yesmaximal, characteristic, complemented
11#11926419C211yesmaximal, characteristic
12#11926402C211yesmaximal, characteristic
13C22⋊C4×Dic19C211yesmaximal, characteristic
14C2×C19⋊#95C211yesmaximal, characteristic
15C19×#385C211yesmaximal, characteristic
16C23×C4×C19C2211yescharacteristic
17C23×Dic19C2211yescharacteristic
18C23×Dic19C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C22×Dic38C2211yescharacteristic
21C2×C4⋊C4×C19C2211yescharacteristic
22C2×C4⋊C4×C19C2211yescharacteristic
23C2×C22⋊C4×C19C2211yescharacteristic
24C2×C22⋊C4×C19C2211yescharacteristic
25C2×C22⋊Dic19C2211yescharacteristic
26C2×C22⋊Dic19C2211yescharacteristic
27C2×C4⋊Dic19C2211yescharacteristic
28C2×C4⋊Dic19C2211yescharacteristic
29C2×C4⋊Dic19C2211yescharacteristic
30C2×C4⋊Dic19C2211yescharacteristic
31#10597370—24no—
32C2×Dic19⋊C4C2211yescharacteristic
33C2×Dic19⋊C4C2211yescharacteristic
34C2×Dic19⋊C4C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×Dic19⋊C4C2211yescharacteristic
37C2×Dic19⋊C4C2211yescharacteristic
38C2×C4×Dic19C2211yescharacteristic
39C2×C4×Dic19C2211yescharacteristic
40#10597324—24no—
41C19×#95C2211yescharacteristic
42C19×#95C2211yescharacteristic
43C19⋊#95C2211yescharacteristic
44C19⋊#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C19⋊#95C2211yescharacteristic
53C24×C19C2311yescharacteristic
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—41no—
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C22×Dic19—22no—
64C22×Dic19—22no—
65C22×Dic19—41no—
66C22×Dic19—41no—
67C22×Dic19—41no—
68C22×Dic19Q814yescomplemented
69C22×Dic19C2311yescharacteristic
70C22×Dic19C2311yescharacteristic
71C22×Dic19C2311yescharacteristic
72C22×Dic19C2311yescharacteristic
73C22×Dic19C2311yescharacteristic
74C22×Dic19C2311yescharacteristic
75C22×Dic19C2311yescharacteristic
76C22×Dic19C2311yescharacteristic
77C2×Dic38—22no—
78C2×Dic38—22no—
79C2×Dic38—22no—
80C2×Dic38—22no—
81C2×Dic38—41no—
82C2×Dic38—41no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—41no—
85C22⋊C4×C19—22no—
86C22⋊C4×C19Q814yescomplemented
87C22⋊Dic19—22no—
88C22⋊Dic19D414yes—
89C4⋊Dic19—22no—
90C4⋊Dic19—22no—
91C4⋊Dic19—22no—
92C4⋊Dic19—41no—
93Dic19⋊C4—22no—
94Dic19⋊C4—22no—
95Dic19⋊C4—22no—
96Dic19⋊C4—22no—
97Dic19⋊C4—41no—
98Dic19⋊C4—41no—
99C4×Dic19—41no—
100C4×Dic19—41no—
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19—21no—
105C23×C19C2×D412yes—
106C23×C19C2×Q812yes—
107C23×C19C2×Q812yes—
108C23×C19C2411yescharacteristic
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—44no—
125C2×C4×C19C2×Q812yes—
126C2×C4×C19C2×Q812yes—
127C2×C4×C19#4112yes—
128C2×Dic19—21no—
129C2×Dic19—21no—
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—44no—
148C2×Dic19—44no—
149C2×Dic19C2×D412yes—
150C2×Dic19C2×D412yes—
151C2×Dic19C2×Q812yes—
152C2×Dic19C2×Q812yes—
153C2×Dic19#4112yes—
154Dic38—44no—
155Dic38—44no—
156#2549—191nomaximal, Sylow
157C22×C19—22no—
158C22×C19—22no—
159C22×C19—22no—
160C22×C19—22no—
161C22×C19—22no—
162C22×C19—22no—
163C22×C19C4⋊Q814yes—
164C22×C19C22×D411yescharacteristic
165C22×C19C22×Q811yescharacteristic
166C22×C19C22×Q811yescharacteristic
167C22×C19C2×#4111yescharacteristic
168C22×C19C2×#4111yescharacteristic
169C22×C19H(5,𝔽2)11yescharacteristic
170C22×C19H(5,𝔽2)11yescharacteristic
171C4×C19—22no—
172C4×C19—22no—
173C4×C19—22no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19—41no—
177Dic19—22no—
178Dic19—22no—
179Dic19—22no—
180Dic19—22no—
181Dic19—22no—
182Dic19—41no—
183Dic19—41no—
184Dic19—41no—
185C2×C22⋊Q8—191no—
186C2×C22⋊Q8—191no—
187#398—191no—
188#398—191no—
189#395—191no—
190#395—191no—
191#391—191no—
192#391—191no—
193#389—191no—
194#389—191no—
195#385—191no—
196#385D1911yescharacteristic
197#380—191no—
198C4×C22⋊C4—191no—
199C2×#95—191no—
200C2×C19—24no—
201C2×C19C2×C4⋊Q811yescharacteristic
202C2×C19#53311yescharacteristic
203C2×C19#54311yescharacteristic
204C2×C19#54611yescharacteristic
205C2×C19#54611yescharacteristic
206C2×C19#55411yescharacteristic
207C2×C19#55411yescharacteristic
208C22×Q8—191no—
209C22×Q8—191no—
210C23×C4—191no—
211C23×C4—191no—
212C23×C4C2×D1911yescharacteristic
213C22⋊Q8—384no—
214C22⋊Q8—384no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—191no—
217C2×C4⋊C4—191no—
218C2×C4⋊C4—191no—
219C2×C4⋊C4—191no—
220C2×C4⋊C4—191no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4C2×D1911yescharacteristic
226C2×C4⋊C4C2×D1911yescharacteristic
227C2×C22⋊C4—191no—
228C2×C22⋊C4—191no—
229C2×C22⋊C4C2×D1911yescharacteristic
230C2×C22⋊C4C2×D1911yescharacteristic
231C2×C42—191no—
232C2×C42—191no—
233#95—191no—
234#95—191no—
235#95—191no—
236#95—191no—
237#95—191no—
238#95—191no—
239#95—191no—
240#95—191no—
241#95—191no—
242#95—191no—
243#95C2×D1911yescharacteristic
244#95C2×D1911yescharacteristic
245C19#254911yescharacteristic, complemented, Sylow
246C24C22×D1911yescharacteristic
247C2×Q8—382no—
248C2×Q8—382no—
249C2×Q8—382no—
250C2×Q8—382no—
251C2×Q8—761no—
252C2×Q8—761no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4—191no—
257C22×C4—191no—
258C22×C4—191no—
259C22×C4—191no—
260C22×C4—191no—
261C22×C4—194no—
262C22×C4—191no—
263C22×C4—191no—
264C22×C4—191no—
265C22×C4—382no—
266C22×C4—382no—
267C22×C4—761no—
268C22×C4—761no—
269C22×C4—761no—
270C22×C4C22×D1911yescharacteristic
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273C22×C4C22×D1911yescharacteristic
274C22×C4C22×D1911yescharacteristic
275C22×C4C22×D1911yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—382no—
279C4⋊C4—382no—
280C4⋊C4—382no—
281C4⋊C4—382no—
282C4⋊C4—382no—
283C4⋊C4—382no—
284C4⋊C4—382no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C4⋊C4—761no—
288C22⋊C4—22no—
289C22⋊C4—194no—
290C22⋊C4—382no—
291C22⋊C4Dic3814yescomplemented
292C42—761no—
293C42—761no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23C2×Dic3812yes—
299C23D4×D1912yes—
300C23Q8×D1912yes—
301C23C23×D1911yescharacteristic
302Q8—764no—
303Q8—764no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—44no—
320C2×C4—192no—
321C2×C4—192no—
322C2×C4—192no—
323C2×C4—192no—
324C2×C4—192no—
325C2×C4—381no—
326C2×C4—381no—
327C2×C4—381no—
328C2×C4—381no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—381no—
343C2×C4—381no—
344C2×C4—764no—
345C2×C4—764no—
346C2×C4C2×Dic3812yes—
347C2×C4C2×Dic3812yes—
348C2×C4#6454312yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22#1059733414yes—
356C22C22×Dic3811yescharacteristic
357C22C2×D4×D1911yescharacteristic
358C22C2×#6454311yescharacteristic
359C22#1059743011yescharacteristic
360C22C2×Q8×D1911yescharacteristic
361C22#41×D1911yescharacteristic
362C22#1059743511yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—382no—
370C4—382no—
371C4—382no—
372C4—382no—
373C4—382no—
374C4—761no—
375C4—761no—
376C4—761no—
377C2—24no—
378C2C2×#1059733411yescharacteristic
379C2#1192709611yescharacteristic
380C2#1192716911yescharacteristic
381C2#1192718111yescharacteristic
382C2#1192718611yescharacteristic
383C2#1192725111yescharacteristic
384C2#1192725311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#385C2
prime radicalC24×C19C23
hypercenter#385D19
hypocenterC19#2549
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #11926478C2semidirect
4. #11926477C2semidirect
5. #11926465C2semidirect
6. #11926464C2semidirect
7. #11926448C2semidirect
8. #11926448C2semidirect
9. #11926443C2semidirect
10. #11926440C2semidirect
68. C22×Dic19Q8semidirect
86. C22⋊C4×C19Q8semidirect
245. C19#2549semidirect
291. C22⋊C4Dic38semidirect

Maximal subgroups

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

subgroupindex
C2×#105973702
C2×#105973242
#119264782
#119264772
#119264652
#119264642
#119264482
#119264432
#119264402
#119264192
#119264022
C22⋊C4×Dic192
C2×C19⋊#952
C19×#3852
#254919