Finite Group Databasebeta

← #14569559

Subgroups — #14569559

Order 2432.

520 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597342C211yesmaximal, characteristic, complemented
2C2×C4×D76C211yesmaximal, characteristic
3#11926477C211yesmaximal, characteristic, complemented
4#11926473C211yesmaximal, characteristic, complemented
5#11926473C211yesmaximal, characteristic, complemented
6#11926471C211yesmaximal, characteristic, complemented
7#11926465C211yesmaximal, characteristic, complemented
8#11926462C211yesmaximal, characteristic
9#11926461C211yesmaximal, characteristic
10#11926457C211yesmaximal, characteristic, complemented
11#11926428C211yesmaximal, characteristic, complemented
12#11926418C211yesmaximal, characteristic, complemented
13#11926415C211yesmaximal, characteristic, complemented
14#11926406C211yesmaximal, characteristic, complemented
15C19×#387C211yesmaximal, characteristic, complemented
16C22×D76C2211yescharacteristic
17C22×C4×D19C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C2×C4⋊C4×C19C2211yescharacteristic
21C2×C4⋊C4×C19C2211yescharacteristic
22C2×C42×C19C2211yescharacteristic
23C2×(C2×D19)⋊C4C2211yescharacteristic
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2211yescharacteristic
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×(C2×D19)⋊C4C2211yescharacteristic
32C2×(C2×D19)⋊C4C2211yescharacteristic
33C2×C4⋊Dic19C2211yescharacteristic
34C2×C4⋊Dic19C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×Dic19⋊C4C2211yescharacteristic
37C2×Dic19⋊C4C2211yescharacteristic
38C2×Dic19⋊C4C2211yescharacteristic
39#10597342—24no—
40C4×D76—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
53C23×D19C2311yescharacteristic
54C23×D19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C2×D76—22no—
69C2×D76—22no—
70C2×D76—22no—
71C2×C4×D19—22no—
72C2×C4×D19—41no—
73C2×C4×D19—41no—
74C2×C4×D19—41no—
75C2×C4×D19—41no—
76C2×C4×D19D414yes—
77C2×Dic38—22no—
78C2×Dic38—41no—
79C2×Dic38—41no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—22no—
82C42×C19—22no—
83(C2×D19)⋊C4—22no—
84(C2×D19)⋊C4—22no—
85(C2×D19)⋊C4—22no—
86(C2×D19)⋊C4—22no—
87(C2×D19)⋊C4—22no—
88(C2×D19)⋊C4—22no—
89(C2×D19)⋊C4—41no—
90(C2×D19)⋊C4—41no—
91(C2×D19)⋊C4—41no—
92(C2×D19)⋊C4—41no—
93C4⋊Dic19—22no—
94C4⋊Dic19—41no—
95Dic19⋊C4—22no—
96Dic19⋊C4—22no—
97Dic19⋊C4—22no—
98Dic19⋊C4—41no—
99C23×C19C2411yescharacteristic
100C22×D19—21no—
101C22×D19—21no—
102C22×D19—21no—
103C22×D19—21no—
104C22×D19—21no—
105C22×D19—21no—
106C22×D19—21no—
107C22×D19—21no—
108C22×D19—21no—
109C22×D19—21no—
110C22×D19—21no—
111C22×D19—21no—
112C22×D19C2×D412yes—
113C22×D19#4112yes—
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—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19C2×D412yes—
134C2×C4×C19#4112yes—
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—21no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19C2×D412yes—
153D76—28no—
154C4×D19—44no—
155C4×D19—44no—
156Dic38—44no—
157#2638—191nomaximal, Sylow
158C22×C19C22×D411yescharacteristic
159C22×C19C2×#4111yescharacteristic
160C22×C19C2×#4111yescharacteristic
161C22×C19H(5,𝔽2)11yescharacteristic
162C22×C19H(5,𝔽2)11yescharacteristic
163C22×C192−1+411yescharacteristic
164C22×C192−1+411yescharacteristic
165C2×D19—22no—
166C2×D19—22no—
167C2×D19—22no—
168C2×D19—22no—
169C2×D19—22no—
170C2×D19—22no—
171C2×D19—41no—
172C2×D19—41no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—41no—
179C4×C19—22no—
180C4×C19—22no—
181C4×C19—41no—
182C4×C19—41no—
183C4×C19—41no—
184C4×C19—41no—
185C4×C19—41no—
186Dic19—22no—
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190Dic19—41no—
191Dic19—41no—
192C2×C22⋊Q8—191no—
193C2×C4×D4—191no—
194#398—191no—
195#397—191no—
196#397—191no—
197#397—191no—
198#395—191no—
199#394—191no—
200#394—191no—
201#393—191no—
202#387—191no—
203#387D1911yescharacteristic, complemented
204#385—191no—
205#385—191no—
206#381—191no—
207C2×C19#52511yescharacteristic
208C2×C19#53411yescharacteristic
209C2×C19#53611yescharacteristic
210C2×C19#53911yescharacteristic
211C2×C19#53911yescharacteristic
212C2×C19#54211yescharacteristic
213C2×C19#54211yescharacteristic
214D19—42no—
215D19—42no—
216C22×Q8—191no—
217C22×D4—191no—
218C23×C4—191no—
219C23×C4—191no—
220C22⋊Q8—384no—
221C4×D4—384no—
222C2×C4⋊C4—191no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—191no—
226C2×C4⋊C4—191no—
227C2×C4⋊C4—191no—
228C2×C4⋊C4C2×D1911yescharacteristic
229C2×C4⋊C4C2×D1911yescharacteristic
230C2×C22⋊C4—191no—
231C2×C22⋊C4—191no—
232C2×C22⋊C4—191no—
233C2×C22⋊C4—191no—
234C2×C22⋊C4—191no—
235C2×C22⋊C4—191no—
236C2×C22⋊C4—191no—
237C2×C22⋊C4—191no—
238C2×C22⋊C4—191no—
239C2×C22⋊C4—191no—
240C2×C42C2×D1911yescharacteristic
241#95—191no—
242#95—191no—
243#95—191no—
244#95—191no—
245#95—191no—
246#95—191no—
247#95—191no—
248#95—191no—
249#95C2×D1911yescharacteristic
250#95C2×D1911yescharacteristic
251#95C2×D1911yescharacteristic
252#95C2×D1911yescharacteristic
253C19#263811yescharacteristic, complemented, Sylow
254C24—191no—
255C24—191no—
256C2×Q8—382no—
257C2×Q8—761no—
258C2×Q8—761no—
259C2×D4—382no—
260C2×D4—382no—
261C2×D4—382no—
262C22×C4—191no—
263C22×C4—194no—
264C22×C4—191no—
265C22×C4—191no—
266C22×C4—191no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—382no—
270C22×C4—761no—
271C22×C4—761no—
272C22×C4—761no—
273C22×C4—761no—
274C22×C4C22×D1911yescharacteristic
275C22×C4C22×D1911yescharacteristic
276C22×C4C22×D1911yescharacteristic
277C22×C4C22×D1911yescharacteristic
278C22×C4C22×D1911yescharacteristic
279C22×C4C22×D1911yescharacteristic
280C22×C4C22×D1911yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—382no—
284C4⋊C4—382no—
285C4⋊C4—382no—
286C4⋊C4—382no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C22⋊C4—382no—
290C22⋊C4—382no—
291C22⋊C4—382no—
292C22⋊C4—382no—
293C22⋊C4—382no—
294C22⋊C4—382no—
295C22⋊C4—761no—
296C22⋊C4—761no—
297C22⋊C4—761no—
298C22⋊C4—761no—
299C42—22no—
300C23—192no—
301C23—192no—
302C23—381no—
303C23—381no—
304C23—381no—
305C23—381no—
306C23—381no—
307C23—381no—
308C23—381no—
309C23—381no—
310C23—381no—
311C23—381no—
312C23—381no—
313C23—381no—
314C23C23×D1911yescharacteristic
315Q8—764no—
316D4—388no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—192no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—381no—
342C2×C4—381no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—381no—
349C2×C4—381no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—381no—
354C2×C4—764no—
355C2×C4—764no—
356C2×C4#6454112yes—
357C2×C4D4×D1912yes—
358C22—382no—
359C22—382no—
360C22—382no—
361C22—382no—
362C22—382no—
363C22—382no—
364C22—761no—
365C22—761no—
366C22—761no—
367C22—761no—
368C22—761no—
369C22—761no—
370C22—761no—
371C22—761no—
372C22C2×#6454111yescharacteristic
373C22C2×D4×D1911yescharacteristic
374C22#1059743311yescharacteristic
375C22#41×D1911yescharacteristic
376C22#1059743511yescharacteristic
377C22#1059743511yescharacteristic
378C22#1059743611yescharacteristic
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—382no—
387C4—761no—
388C4—761no—
389C4—761no—
390C4—761no—
391C4—761no—
392C2—762no—
393C2—762no—
394C2#1192705311yescharacteristic
395C2#1192710511yescharacteristic
396C2#1192711711yescharacteristic
397C2#1192713511yescharacteristic
398C2#1192714211yescharacteristic
399C2#1192716511yescharacteristic
400C2#1192716611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#387C2
prime radicalC22×D76C22
hypercenter#387D19
hypocenterC19#2638
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#10597342C2semidirect
3. #11926477C2semidirect
4. #11926473C2semidirect
5. #11926473C2semidirect
6. #11926471C2semidirect
7. #11926465C2semidirect
10. #11926457C2semidirect
11. #11926428C2semidirect
12. #11926418C2semidirect
13. #11926415C2semidirect
14. #11926406C2semidirect
15. C19×#387C2semidirect
203. #387D19semidirect
253. C19#2638semidirect

Maximal subgroups

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

subgroupindex
C2×#105973422
C2×C4×D762
#119264772
#119264732
#119264712
#119264652
#119264622
#119264612
#119264572
#119264282
#119264182
#119264152
#119264062
C19×#3872
#263819