Finite Group Databasebeta

← #34077479

Subgroups — #34077479

Order 19328.

524 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012729C211yesmaximal, characteristic, complemented
2C2×#18012725C211yesmaximal, characteristic
3#23752116C211yesmaximal, characteristic, complemented
4#23752116C211yesmaximal, characteristic, complemented
5#23752112C211yesmaximal, characteristic
6#23752112C211yesmaximal, characteristic
7#23752106C211yesmaximal, characteristic, complemented
8#23752105C211yesmaximal, characteristic, complemented
9#23752104C211yesmaximal, characteristic, complemented
10#23752103C211yesmaximal, characteristic, complemented
11#23752102C211yesmaximal, characteristic, complemented
12#23752101C211yesmaximal, characteristic, complemented
13#23752100C211yesmaximal, characteristic, complemented
14C42×Dic151C211yesmaximal, characteristic, complemented
15#388×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C22×C22⋊D151C2211yescharacteristic
18#18012729—24no—
19#18012725—24no—
20C2×C4⋊Dic151C2211yescharacteristic
21C2×Dic151⋊C4C2211yescharacteristic
22C2×Dic151⋊C4C2211yescharacteristic
23C2×Dic151⋊C4C2211yescharacteristic
24C2×Dic151⋊C4C2211yescharacteristic
25C2×C22⋊Dic151C2211yescharacteristic
26C2×C22⋊Dic151C2211yescharacteristic
27C2×C22⋊Dic151C2211yescharacteristic
28C2×(C2×D151)⋊C4C2211yescharacteristic
29C2×(C2×D151)⋊C4C2211yescharacteristic
30C2×(C2×D151)⋊C4C2211yescharacteristic
31C2×(C2×D151)⋊C4C2211yescharacteristic
32C2×(C2×D151)⋊C4C2211yescharacteristic
33C2×(C2×D151)⋊C4C2211yescharacteristic
34C2×C4×Dic151C2211yescharacteristic
35C2×C4×Dic151C2211yescharacteristic
36C2×C4×Dic151C2211yescharacteristic
37C2×C4×Dic151C2211yescharacteristic
38C2×C4×Dic151C2211yescharacteristic
39C2×C4×Dic151C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C151⋊#95C2211yescharacteristic
46C2×C4⋊C4×C151C2211yescharacteristic
47C2×C22⋊C4×C151C2211yescharacteristic
48C2×C22⋊C4×C151C2211yescharacteristic
49C2×C22⋊C4×C151C2211yescharacteristic
50C2×C42×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52#95×C151C2211yescharacteristic
53C23×D151C2311yescharacteristic
54C2×Dic302—22no—
55C2×Dic302—22no—
56C2×Dic302—22no—
57C2×C22⋊D151—22no—
58C2×C22⋊D151—22no—
59C2×C22⋊D151—22no—
60C22×Dic151C2311yescharacteristic
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C22×Dic151C2311yescharacteristic
64C22×Dic151C2311yescharacteristic
65C22×Dic151C2311yescharacteristic
66C22×Dic151C2311yescharacteristic
67C4⋊Dic151—22no—
68Dic151⋊C4—22no—
69Dic151⋊C4—22no—
70Dic151⋊C4—22no—
71Dic151⋊C4—22no—
72C22⋊Dic151—22no—
73C22⋊Dic151—22no—
74C22⋊Dic151—22no—
75(C2×D151)⋊C4—22no—
76(C2×D151)⋊C4—22no—
77(C2×D151)⋊C4—22no—
78(C2×D151)⋊C4—22no—
79(C2×D151)⋊C4—22no—
80(C2×D151)⋊C4—22no—
81C4×Dic151—22no—
82C4×Dic151—22no—
83C4×Dic151—22no—
84C4×Dic151—22no—
85C4×Dic151—22no—
86C4×Dic151D414yes—
87C24×C151C2311yescharacteristic
88C22×C4×C151C2311yescharacteristic
89C22×C4×C151C2311yescharacteristic
90C22×C4×C151C2311yescharacteristic
91C22×C4×C151C2311yescharacteristic
92C22×C4×C151C2311yescharacteristic
93C22×C4×C151C2311yescharacteristic
94C4⋊C4×C151—22no—
95C22⋊C4×C151—22no—
96C22⋊C4×C151—22no—
97C22⋊C4×C151—22no—
98C42×C151—22no—
99C22×D151—21no—
100C22×D151—21no—
101C22×D151—21no—
102C22×D151—21no—
103C22×D151—21no—
104C22×D151—21no—
105C22×D151—21no—
106Dic302—44no—
107C22⋊D151—44no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151C2×D412yes—
124C2×Dic151C2×D412yes—
125C2×Dic151#4112yes—
126C2×Dic151#4112yes—
127C2×Dic151#4112yes—
128C2×Dic151#4112yes—
129C23×C151—21no—
130C23×C151—21no—
131C23×C151—21no—
132C23×C151—21no—
133C23×C151—21no—
134C23×C151—21no—
135C23×C151—21no—
136C23×C151C2411yescharacteristic
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151C2×D412yes—
153C2×C4×C151#4112yes—
154C2×C4×C151#4112yes—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151C22×D411yescharacteristic
163C22×C151C2×#4111yescharacteristic
164C22×C151C2×#4111yescharacteristic
165C22×C151C2×#4111yescharacteristic
166C22×C151C2×#4111yescharacteristic
167C22×C151C2×#4111yescharacteristic
168C22×C151C2×#4111yescharacteristic
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C4×C151—22no—
177C4×C151—22no—
178C4×C151—22no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182Dic151—22no—
183Dic151—22no—
184Dic151—22no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188Dic151#12414yes—
189C2×C151—81no—
190C2×C151C2×#12411yescharacteristic
191C2×C151#52911yescharacteristic
192C2×C151#52911yescharacteristic
193C2×C151#52911yescharacteristic
194C2×C151#52911yescharacteristic
195C2×C151#53211yescharacteristic
196C2×C151#53211yescharacteristic
197D151—81no—
198C151#286111yescharacteristic, complemented, Sylow
199#2861—1511nomaximal, Sylow
200C2×#125—1511no—
201C2×#124—1511no—
202#391—1511no—
203#391—1511no—
204#390—1511no—
205#390—1511no—
206#388—1511no—
207#388—1511no—
208#388—1511no—
209#388—1511no—
210#388—1511no—
211#388—1511no—
212#388—1511no—
213#388D15111yescharacteristic, complemented
214C43—1511no—
215C22×Q8—1511no—
216C22×D4—1511no—
217#125—3024no—
218#124—3024no—
219C2×C4⋊C4—1511no—
220C2×C4⋊C4—1511no—
221C2×C4⋊C4—1511no—
222C2×C4⋊C4—1511no—
223C2×C4⋊C4—1511no—
224C2×C4⋊C4C2×D15111yescharacteristic
225C2×C22⋊C4—1511no—
226C2×C22⋊C4—1511no—
227C2×C22⋊C4—1511no—
228C2×C22⋊C4—1511no—
229C2×C22⋊C4—1511no—
230C2×C22⋊C4—1511no—
231C2×C22⋊C4—1511no—
232C2×C22⋊C4—1511no—
233C2×C22⋊C4—1511no—
234C2×C22⋊C4C2×D15111yescharacteristic
235C2×C22⋊C4C2×D15111yescharacteristic
236C2×C22⋊C4C2×D15111yescharacteristic
237C2×C42—1511no—
238C2×C42—1511no—
239C2×C42—1511no—
240C2×C42—1511no—
241C2×C42—1511no—
242C2×C42—1511no—
243C2×C42C2×D15111yescharacteristic
244#95—1511no—
245#95—1511no—
246#95—1511no—
247#95—1511no—
248#95—1511no—
249#95—1511no—
250#95C2×D15111yescharacteristic
251#95C2×D15111yescharacteristic
252C24—1511no—
253C24C22×D15111yescharacteristic
254C2×Q8—3022no—
255C2×Q8—3022no—
256C2×Q8—3022no—
257C2×D4—3022no—
258C2×D4—3022no—
259C2×D4—3022no—
260C22×C4—1511no—
261C22×C4—1511no—
262C22×C4—1511no—
263C22×C4—1511no—
264C22×C4—1511no—
265C22×C4—1511no—
266C22×C4—1511no—
267C22×C4C22×D15111yescharacteristic
268C22×C4C22×D15111yescharacteristic
269C22×C4C22×D15111yescharacteristic
270C22×C4C22×D15111yescharacteristic
271C22×C4C22×D15111yescharacteristic
272C22×C4C22×D15111yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—3022no—
275C4⋊C4—3022no—
276C4⋊C4—3022no—
277C4⋊C4—3022no—
278C4⋊C4—3022no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—3022no—
283C22⋊C4—3022no—
284C22⋊C4—3022no—
285C22⋊C4—3022no—
286C22⋊C4—3022no—
287C22⋊C4—3022no—
288C22⋊C4—3022no—
289C22⋊C4—3022no—
290C22⋊C4—3022no—
291C42—22no—
292C42—3022no—
293C42—3022no—
294C42—3022no—
295C42—3022no—
296C42—3022no—
297C42—1514no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—3021no—
306C23—3021no—
307C23—3021no—
308C23—3021no—
309C23—3021no—
310C23—3021no—
311C23—3021no—
312C23C23×D15111yescharacteristic
313Q8—6044no—
314D4—6044no—
315C2×C4—21no—
316C2×C4—21no—
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—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—3021no—
340C2×C4—3021no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—1512no—
346C2×C4—1512no—
347C2×C4—1512no—
348C2×C4—1512no—
349C2×C4—1512no—
350C2×C4—1512no—
351C2×C4D4×D15112yes—
352C2×C4#1455900312yes—
353C2×C4#1455900412yes—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—6041no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—6041no—
367C22—6041no—
368C22C2×D4×D15111yescharacteristic
369C22#41×D15111yescharacteristic
370C22#41×D15111yescharacteristic
371C22#41×D15111yescharacteristic
372C22#41×D15111yescharacteristic
373C22C2×#1455900311yescharacteristic
374C22C2×#1455900411yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—3022no—
382C4—3022no—
383C4—3022no—
384C4—6041no—
385C4—6041no—
386C4—6041no—
387C4—1514no—
388C2—81no—
389C2—12081no—
390C2#124×D15111yescharacteristic
391C2#2375273911yescharacteristic
392C2#2375274011yescharacteristic
393C2#2375274211yescharacteristic
394C2#2375274511yescharacteristic
395C2#2375275711yescharacteristic
396C2#2375275911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#388×C151C2
prime radicalC22×C22⋊D151C22
hypercenter#388D151
hypocenterC151#2861
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#18012729C2semidirect
3. #23752116C2semidirect
4. #23752116C2semidirect
7. #23752106C2semidirect
8. #23752105C2semidirect
9. #23752104C2semidirect
10. #23752103C2semidirect
11. #23752102C2semidirect
12. #23752101C2semidirect
13. #23752100C2semidirect
14. C42×Dic151C2semidirect
15. #388×C151C2semidirect
198. C151#2861semidirect
213. #388D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127292
C2×#180127252
#237521162
#237521122
#237521062
#237521052
#237521042
#237521032
#237521022
#237521012
#237521002
C42×Dic1512
#388×C1512
#2861151