Finite Group Databasebeta

← #34047477

Subgroups — #34047477

Order 19072.

532 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×#18011894C211yesmaximal, characteristic
2#23749525C211yesmaximal, characteristic
3#23749520C211yesmaximal, characteristic, complemented
4#23749519C211yesmaximal, characteristic, complemented
5#23749515C211yesmaximal, characteristic, complemented
6#23749514C211yesmaximal, characteristic, complemented
7#23749513C211yesmaximal, characteristic, complemented
8#23749507C211yesmaximal, characteristic, complemented
9#23749506C211yesmaximal, characteristic, complemented
10#23749501C211yesmaximal, characteristic
11#23749496C211yesmaximal, characteristic, complemented
12#23749476C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic149C211yesmaximal, characteristic, complemented
14#23749472C211yesmaximal, characteristic, complemented
15#380×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18#18011894C418yescomplemented
19C2×#14558715C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×C22⋊Dic149C2211yescharacteristic
25C2×C22⋊Dic149C2211yescharacteristic
26C2×C22⋊Dic149C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×C4×Dic149C2211yescharacteristic
33C2×C4×Dic149C2211yescharacteristic
34C2×C4×Dic149C2211yescharacteristic
35C2×C4×Dic149C2211yescharacteristic
36C2×C4×Dic149C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45C23×C4×C149C2211yescharacteristic
46C2×C4⋊C4×C149C2211yescharacteristic
47C2×C4⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C22⋊C4×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52C23×D149C2311yescharacteristic
53C2×C22⋊D149—41no—
54C2×C22⋊D149—41no—
55C2×C22⋊D149C2×C414yes—
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C22×Dic149C2311yescharacteristic
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C2×C4×D149—22no—
64C2×C4×D149—41no—
65C2×C4×D149—41no—
66#14558715—22no—
67#14558715—41no—
68#14558715—41no—
69#14558715C2×C414yescomplemented
70#14558715C2×C414yescomplemented
71C22⋊Dic149—22no—
72C22⋊Dic149—22no—
73C22⋊Dic149C2×C414yescomplemented
74#14558713—22no—
75#14558713—41no—
76#14558713—41no—
77#14558713C2×C414yes—
78#14558713C2×C414yes—
79C4×Dic149—22no—
80C4×Dic149—41no—
81C4×Dic149—41no—
82C4×Dic149—41no—
83C4×Dic149—41no—
84C24×C149C2311yescharacteristic
85C22×C4×C149—41no—
86C22×C4×C149—41no—
87C22×C4×C149C2×C414yescomplemented
88C22×C4×C149C2311yescharacteristic
89C22×C4×C149C2311yescharacteristic
90C22×C4×C149C2311yescharacteristic
91C22×C4×C149C2311yescharacteristic
92C22×C4×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C4⋊C4×C149—41no—
95C4⋊C4×C149—41no—
96C22⋊C4×C149—41no—
97C22⋊C4×C149—41no—
98C22×D149—21no—
99C22×D149—21no—
100C22×D149—21no—
101C22×D149—21no—
102C22×D149—21no—
103C22×D149—21no—
104C22×D149C22×C412yes—
105C22⋊D149—44no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149C22×C412yes—
123C2×Dic149C22×C412yes—
124C2×Dic149C22×C412yes—
125C2×Dic149#4112yes—
126C2×Dic149#4112yes—
127C4×D149—44no—
128C23×C149—21no—
129C23×C149—21no—
130C23×C149—21no—
131C23×C149—21no—
132C23×C149—21no—
133C23×C149—21no—
134C23×C149C22×C412yes—
135C23×C149C2411yescharacteristic
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—44no—
153C2×C4×C149C22×C412yes—
154C2×C4×C149C22×C412yes—
155C22×C149—22no—
156C22×C149—22no—
157C22×C149—22no—
158C22×C149—41no—
159C22×C149—41no—
160C22×C149—41no—
161C22×C149—41no—
162C22×C149C23×C411yescharacteristic
163C22×C149C2×#4111yescharacteristic
164C22×C149C2×#4111yescharacteristic
165C22×C149H(5,𝔽2)11yescharacteristic
166C22×C149H(5,𝔽2)11yescharacteristic
167C22×C149H(5,𝔽2)11yescharacteristic
168C22×C1492−1+411yescharacteristic
169C2×D149—22no—
170C2×D149—22no—
171C2×D149—22no—
172C2×D149—41no—
173C2×D149—41no—
174C2×D149—41no—
175C2×D149—41no—
176C4×C149—22no—
177C4×C149—22no—
178C4×C149—41no—
179C4×C149—41no—
180C4×C149—41no—
181C4×C149—41no—
182Dic149—22no—
183Dic149—22no—
184Dic149—22no—
185Dic149—22no—
186Dic149—22no—
187Dic149—41no—
188Dic149—41no—
189C2×C149—42no—
190C2×C149C4×#4111yescharacteristic
191C2×C149#51811yescharacteristic
192C2×C149#52011yescharacteristic
193C2×C149#53811yescharacteristic
194C2×C149#53911yescharacteristic
195C2×C149#54011yescharacteristic
196C2×C149#54211yescharacteristic
197D149—42no—
198C149#233511yescharacteristic, complemented, Sylow
199#2335—1491nomaximal, Sylow
200C2×#123—1491no—
201#390—1491no—
202#389—1491no—
203#388—1491no—
204#388—1491no—
205#388—1491no—
206#388—1491no—
207#387—1491no—
208#387—1491no—
209#386—1491no—
210#385—1491no—
211#380D14911yescharacteristic, complemented
212C4×C4⋊C4—1491no—
213C4×C22⋊C4—1491no—
214C4×C22⋊C4—1491no—
215C22×D4—1491no—
216C23×C4—1491no—
217C23×C4C2×D14911yescharacteristic
218#123—1498no—
219C2×C4⋊C4—1491no—
220C2×C4⋊C4—1491no—
221C2×C4⋊C4—1491no—
222C2×C4⋊C4—1491no—
223C2×C4⋊C4—1491no—
224C2×C4⋊C4C2×D14911yescharacteristic
225C2×C4⋊C4C2×D14911yescharacteristic
226C2×C22⋊C4—1491no—
227C2×C22⋊C4—1491no—
228C2×C22⋊C4—1491no—
229C2×C22⋊C4—1491no—
230C2×C22⋊C4—1491no—
231C2×C22⋊C4—1491no—
232C2×C22⋊C4—1491no—
233C2×C22⋊C4—1491no—
234C2×C22⋊C4C2×D14911yescharacteristic
235C2×C22⋊C4C2×D14911yescharacteristic
236C2×C42—1491no—
237C2×C42—1491no—
238C2×C42—1491no—
239C2×C42—1491no—
240C2×C42—1491no—
241#95—1491no—
242#95—1491no—
243#95—1491no—
244#95—1491no—
245#95—1491no—
246#95—1491no—
247#95—1491no—
248#95—1491no—
249#95C2×D14911yescharacteristic
250#95C2×D14911yescharacteristic
251C24—1491no—
252C24C22×D14911yescharacteristic
253C2×D4—5961no—
254C2×D4—5961no—
255C2×D4—1494no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—2982no—
259C22×C4—5961no—
260C22×C4—5961no—
261C22×C4—1491no—
262C22×C4—1491no—
263C22×C4—1491no—
264C22×C4—1491no—
265C22×C4—1491no—
266C22×C4—1491no—
267C22×C4—1491no—
268C22×C4C4×D14914yescomplemented
269C22×C4C22×D14911yescharacteristic
270C22×C4C22×D14911yescharacteristic
271C22×C4C22×D14911yescharacteristic
272C22×C4C22×D14911yescharacteristic
273C22×C4C22×D14911yescharacteristic
274C22×C4C22×D14911yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—2982no—
278C4⋊C4—5961no—
279C4⋊C4—5961no—
280C4⋊C4—1494no—
281C4⋊C4—1494no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—2982no—
285C22⋊C4—2982no—
286C22⋊C4—2982no—
287C22⋊C4—5961no—
288C22⋊C4—5961no—
289C22⋊C4—1494no—
290C22⋊C4—1494no—
291C22⋊C4—1494no—
292C42—2982no—
293C42—5961no—
294C42—5961no—
295C42—5961no—
296C42—5961no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—2981no—
304C23—2981no—
305C23—2981no—
306C23—2981no—
307C23—2981no—
308C23—2981no—
309C23—1492no—
310C23C2×C4×D14912yes—
311C23C23×D14911yescharacteristic
312D4—5964no—
313C2×C4—21no—
314C2×C4—21no—
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—44no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—2981no—
339C2×C4—2981no—
340C2×C4—2981no—
341C2×C4—2981no—
342C2×C4—2981no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—5964no—
347C2×C4—1492no—
348C2×C4—1492no—
349C2×C4—1492no—
350C2×C4—1492no—
351C2×C4—1492no—
352C2×C4C2×C4×D14912yes—
353C2×C4C2×C4×D14912yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—2982no—
362C22—2982no—
363C22—2982no—
364C22—5961no—
365C22—5961no—
366C22—5961no—
367C22—5961no—
368C22C22×C4×D14911yescharacteristic
369C22#41×D14911yescharacteristic
370C22#41×D14911yescharacteristic
371C22#1801195611yescharacteristic
372C22#1801195611yescharacteristic
373C22#1801195611yescharacteristic
374C22#1801195911yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—2982no—
382C4—2982no—
383C4—2982no—
384C4—2982no—
385C4—2982no—
386C4—5961no—
387C4—5961no—
388C2—42no—
389C2—5962no—
390C2#2375009311yescharacteristic
391C2#2375009811yescharacteristic
392C2#2375010611yescharacteristic
393C2#2375020711yescharacteristic
394C2#2375022111yescharacteristic
395C2#2375022511yescharacteristic
396C2#2375024511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#380×C149C2
socle, cosocleC23×C149C24
prime radicalC22×C22⋊D149C22
hypercenter#380D149
hypocenterC149#2335
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #23749520C2semidirect
4. #23749519C2semidirect
5. #23749515C2semidirect
6. #23749514C2semidirect
7. #23749513C2semidirect
8. #23749507C2semidirect
9. #23749506C2semidirect
11. #23749496C2semidirect
12. #23749476C2semidirect
13. C4×C22⋊Dic149C2semidirect
14. #23749472C2semidirect
15. #380×C149C2semidirect
18. #18011894C4semidirect
69. #14558715C2×C4semidirect
70. #14558715C2×C4semidirect
73. C22⋊Dic149C2×C4semidirect
87. C22×C4×C149C2×C4semidirect
198. C149#2335semidirect
211. #380D149semidirect
268. C22×C4C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118942
#237495252
#237495202
#237495192
#237495152
#237495142
#237495132
#237495072
#237495062
#237495012
#237494962
#237494762
C4×C22⋊Dic1492
#237494722
#380×C1492
#2335149