Finite Group Databasebeta

← #34047397

Subgroups — #34047397

Order 19072.

612 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011897C211yesmaximal, characteristic
2C2×#18011876C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D149C211yesmaximal, characteristic
4#23749529C211yesmaximal, characteristic, complemented
5#23749525C211yesmaximal, characteristic
6#23749519C211yesmaximal, characteristic, complemented
7#23749518C211yesmaximal, characteristic, complemented
8#23749515C211yesmaximal, characteristic, complemented
9#23749514C211yesmaximal, characteristic, complemented
10#23749499C211yesmaximal, characteristic, complemented
11#23749498C211yesmaximal, characteristic, complemented
12#23749496C211yesmaximal, characteristic, complemented
13#23749494C211yesmaximal, characteristic, complemented
14#23749470C211yesmaximal, characteristic, complemented
15#385×C149C211yesmaximal, characteristic, complemented
16C22×Dic298C2211yescharacteristic
17C22×C22⋊D149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19#18011897C418yescomplemented
20#18011876—24no—
21C4×C22⋊D149—24no—
22C2×C4⋊Dic149C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×#14558715C2211yescharacteristic
28C2×C22⋊Dic149C2211yescharacteristic
29C2×C22⋊Dic149C2211yescharacteristic
30C2×C22⋊Dic149C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×C4×Dic149C2211yescharacteristic
37C2×C4×Dic149C2211yescharacteristic
38C2×C4×Dic149C2211yescharacteristic
39C2×C4×Dic149C2211yescharacteristic
40C2×C4×Dic149C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45#18011818C2211yescharacteristic
46#18011818C2211yescharacteristic
47C23×C4×C149C2211yescharacteristic
48C2×C4⋊C4×C149C2211yescharacteristic
49C2×C4⋊C4×C149C2211yescharacteristic
50C2×C22⋊C4×C149C2211yescharacteristic
51C2×C22⋊C4×C149C2211yescharacteristic
52#95×C149C2211yescharacteristic
53#95×C149C2211yescharacteristic
54C23×D149C2311yescharacteristic
55C2×Dic298—22no—
56C2×Dic298—22no—
57C2×Dic298C2×C414yescomplemented
58C2×C22⋊D149—22no—
59C2×C22⋊D149—22no—
60C2×C22⋊D149C2×C414yes—
61C22×Dic149C2311yescharacteristic
62C22×Dic149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C22×Dic149C2311yescharacteristic
66C22×Dic149C2311yescharacteristic
67C22×Dic149C2311yescharacteristic
68C2×C4×D149—22no—
69C2×C4×D149—41no—
70C2×C4×D149—41no—
71C4⋊Dic149—41no—
72#14558715—22no—
73#14558715—22no—
74#14558715—22no—
75#14558715—41no—
76#14558715—41no—
77C22⋊Dic149—22no—
78C22⋊Dic149—41no—
79C22⋊Dic149C2×C414yescomplemented
80#14558713—22no—
81#14558713—41no—
82#14558713—41no—
83#14558713C2×C414yescomplemented
84#14558713C2×C414yescomplemented
85C4×Dic149—22no—
86C4×Dic149—22no—
87C4×Dic149—22no—
88C4×Dic149C2×C414yescomplemented
89C4×Dic149D414yes—
90C24×C149C2311yescharacteristic
91C22×C4×C149—22no—
92C22×C4×C149—41no—
93C22×C4×C149—41no—
94C22×C4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C22×C4×C149C2311yescharacteristic
97C22×C4×C149C2311yescharacteristic
98C22×C4×C149C2311yescharacteristic
99C22×C4×C149C2311yescharacteristic
100C4⋊C4×C149—22no—
101C4⋊C4×C149—41no—
102C22⋊C4×C149—41no—
103C22⋊C4×C149C2×C414yescomplemented
104C22×D149—21no—
105C22×D149—21no—
106C22×D149—21no—
107C22×D149—21no—
108C22×D149—21no—
109C22×D149—21no—
110C22×D149C22×C412yes—
111Dic298—28no—
112C22⋊D149—28no—
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×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149C22×C412yes—
129C2×Dic149C22×C412yes—
130C2×Dic149C22×C412yes—
131C2×Dic149C2×D412yes—
132C2×Dic149C2×D412yes—
133C2×Dic149#4112yes—
134C4×D149—44no—
135C23×C149—21no—
136C23×C149—21no—
137C23×C149—21no—
138C23×C149—21no—
139C23×C149—21no—
140C23×C149—21no—
141C23×C149C22×C412yes—
142C23×C149C2411yescharacteristic
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—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—44no—
159C2×C4×C149C22×C412yes—
160C2×C4×C149C22×C412yes—
161C2×C4×C149C2×D412yes—
162C22×C149—22no—
163C22×C149—22no—
164C22×C149—22no—
165C22×C149—41no—
166C22×C149—41no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149C23×C411yescharacteristic
170C22×C149C22×D411yescharacteristic
171C22×C149C2×#4111yescharacteristic
172C22×C149H(5,𝔽2)11yescharacteristic
173C22×C149H(5,𝔽2)11yescharacteristic
174C22×C1492−1+411yescharacteristic
175C22×C1492−1+411yescharacteristic
176C2×D149—22no—
177C2×D149—22no—
178C2×D149—22no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C4×C149—22no—
184C4×C149—22no—
185C4×C149—22no—
186C4×C149—41no—
187C4×C149—41no—
188C4×C149—41no—
189Dic149—22no—
190Dic149—22no—
191Dic149—22no—
192Dic149—41no—
193Dic149—41no—
194Dic149—41no—
195Dic149C4×D414yes—
196C2×C149—42no—
197C2×C149C2×C4×D411yescharacteristic
198C2×C149#52011yescharacteristic
199C2×C149#52011yescharacteristic
200C2×C149#53511yescharacteristic
201C2×C149#53611yescharacteristic
202C2×C149#54211yescharacteristic
203C2×C149#54211yescharacteristic
204D149—42no—
205C149#232611yescharacteristic, complemented, Sylow
206#2326—1491nomaximal, Sylow
207C2×#124—1491no—
208C2×C4×Q8—1491no—
209C2×C4×D4—1491no—
210#391—1491no—
211#390—1491no—
212#388—1491no—
213#388—1491no—
214#388—1491no—
215#388—1491no—
216#385—1491no—
217#385—1491no—
218#385—1491no—
219#385D14911yescharacteristic, complemented
220#384—1491no—
221#376—1491no—
222C22×Q8—1491no—
223C22×D4—1491no—
224C23×C4—1491no—
225C23×C4C2×D14911yescharacteristic
226#124—1498no—
227C4×Q8—2984no—
228C4×D4—2984no—
229C2×C4⋊C4—1491no—
230C2×C4⋊C4—1491no—
231C2×C4⋊C4—1491no—
232C2×C4⋊C4—1491no—
233C2×C4⋊C4—1491no—
234C2×C4⋊C4—1491no—
235C2×C4⋊C4C2×D14911yescharacteristic
236C2×C4⋊C4C2×D14911yescharacteristic
237C2×C22⋊C4—1491no—
238C2×C22⋊C4—1491no—
239C2×C22⋊C4—1491no—
240C2×C22⋊C4—1491no—
241C2×C22⋊C4—1491no—
242C2×C22⋊C4—1491no—
243C2×C22⋊C4—1491no—
244C2×C22⋊C4—1491no—
245C2×C22⋊C4C2×D14911yescharacteristic
246C2×C22⋊C4C2×D14911yescharacteristic
247C2×C42—1491no—
248C2×C42—1491no—
249C2×C42—1491no—
250C2×C42—1491no—
251C2×C42—1491no—
252#95—1491no—
253#95—1491no—
254#95—1491no—
255#95—1491no—
256#95—1491no—
257#95—1491no—
258#95C2×D14911yescharacteristic
259#95C2×D14911yescharacteristic
260C24—1491no—
261C24C22×D14911yescharacteristic
262C2×Q8—2982no—
263C2×Q8—2982no—
264C2×Q8—1494no—
265C2×D4—2982no—
266C2×D4—2982no—
267C2×D4—1494no—
268C22×C4—22no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—2982no—
272C22×C4—5961no—
273C22×C4—5961no—
274C22×C4—1491no—
275C22×C4—1491no—
276C22×C4—1491no—
277C22×C4—1491no—
278C22×C4—1491no—
279C22×C4—1491no—
280C22×C4—1491no—
281C22×C4C22×D14911yescharacteristic
282C22×C4C22×D14911yescharacteristic
283C22×C4C22×D14911yescharacteristic
284C22×C4C22×D14911yescharacteristic
285C22×C4C22×D14911yescharacteristic
286C22×C4C22×D14911yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4—2982no—
290C4⋊C4—2982no—
291C4⋊C4—2982no—
292C4⋊C4—5961no—
293C4⋊C4—5961no—
294C4⋊C4—5961no—
295C22⋊C4—41no—
296C22⋊C4—2982no—
297C22⋊C4—2982no—
298C22⋊C4—5961no—
299C22⋊C4—5961no—
300C22⋊C4—5961no—
301C22⋊C4—1494no—
302C22⋊C4—1494no—
303C22⋊C4—1494no—
304C22⋊C4C4×D14914yescomplemented
305C42—2982no—
306C42—2982no—
307C42—2982no—
308C42—1494no—
309C42—1494no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—2981no—
317C23—2981no—
318C23—2981no—
319C23—2981no—
320C23—2981no—
321C23—2981no—
322C23—1492no—
323C23C2×C4×D14912yes—
324C23C23×D14911yescharacteristic
325Q8—2988no—
326D4—2988no—
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—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—2981no—
344C2×C4—2981no—
345C2×C4—2981no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—2981no—
350C2×C4—2981no—
351C2×C4—2981no—
352C2×C4—2981no—
353C2×C4—2981no—
354C2×C4—2981no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—2981no—
358C2×C4—5964no—
359C2×C4—1492no—
360C2×C4—1492no—
361C2×C4—1492no—
362C2×C4—1492no—
363C2×C4—1492no—
364C2×C4—1492no—
365C2×C4C2×C4×D14912yes—
366C2×C4C2×C4×D14912yes—
367C2×C4D4×D14912yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—2982no—
376C22—2982no—
377C22—2982no—
378C22—5961no—
379C22—5961no—
380C22—5961no—
381C22—5961no—
382C22C22×C4×D14911yescharacteristic
383C22C2×D4×D14911yescharacteristic
384C22#41×D14911yescharacteristic
385C22#1801195611yescharacteristic
386C22#1801195611yescharacteristic
387C22#1801195811yescharacteristic
388C22#1801195911yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—2982no—
396C4—2982no—
397C4—2982no—
398C4—5961no—
399C4—5961no—
400C4—5961no—
401C4—1494no—
402C2—42no—
403C2—5962no—
404C2C4×D4×D14911yescharacteristic
405C2#2375010411yescharacteristic
406C2#2375010611yescharacteristic
407C2#2375019011yescharacteristic
408C2#2375019811yescharacteristic
409C2#2375024311yescharacteristic
410C2#2375024511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#385×C149C2
socle, cosocleC23×C149C24
prime radicalC22×C22⋊D149C22
hypercenter#385D149
hypocenterC149#2326
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#18011876C2semidirect
4. #23749529C2semidirect
6. #23749519C2semidirect
7. #23749518C2semidirect
8. #23749515C2semidirect
9. #23749514C2semidirect
10. #23749499C2semidirect
11. #23749498C2semidirect
12. #23749496C2semidirect
13. #23749494C2semidirect
14. #23749470C2semidirect
15. #385×C149C2semidirect
19. #18011897C4semidirect
57. C2×Dic298C2×C4semidirect
79. C22⋊Dic149C2×C4semidirect
83. #14558713C2×C4semidirect
84. #14558713C2×C4semidirect
88. C4×Dic149C2×C4semidirect
103. C22⋊C4×C149C2×C4semidirect
205. C149#2326semidirect
219. #385D149semidirect
304. C22⋊C4C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118972
C2×#180118762
C2×C4×C22⋊D1492
#237495292
#237495252
#237495192
#237495182
#237495152
#237495142
#237494992
#237494982
#237494962
#237494942
#237494702
#385×C1492
#2326149