Finite Group Databasebeta

← #34047735

Subgroups — #34047735

Order 19072.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011884C211yesmaximal, characteristic
2C2×#18011873C211yesmaximal, characteristic, complemented
3C2×#18011871C211yesmaximal, characteristic, complemented
4#23749514C211yesmaximal, characteristic, complemented
5#23749507C211yesmaximal, characteristic, complemented
6#23749506C211yesmaximal, characteristic, complemented
7#23749503C211yesmaximal, characteristic, complemented
8#23749502C211yesmaximal, characteristic, complemented
9#23749501C211yesmaximal, characteristic, complemented
10#23749501C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic149C211yesmaximal, characteristic, complemented
12C4×#14558713C211yesmaximal, characteristic, complemented
13C4×#14558713C211yesmaximal, characteristic, complemented
14#95×D149C211yesmaximal, characteristic, complemented
15#388×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C22×C22⋊D149C2211yescharacteristic
18C22×C22⋊D149C2211yescharacteristic
19C23×Dic149C2211yescharacteristic
20C22×C4×D149C2211yescharacteristic
21C22×C4×D149C2211yescharacteristic
22C22×C4×D149C2211yescharacteristic
23C22×C4×D149C2211yescharacteristic
24#18011884C418yescomplemented
25#18011873—24no—
26#18011871—24no—
27C2×#14558715C2211yescharacteristic
28C2×#14558715C2211yescharacteristic
29C2×C22⋊Dic149C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×C4×Dic149C2211yescharacteristic
37C2×C4×Dic149C2211yescharacteristic
38C2×C4×Dic149C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45#18011818C2211yescharacteristic
46#18011818C2211yescharacteristic
47C2×C4⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C22⋊C4×C149C2211yescharacteristic
50C2×C22⋊C4×C149C2211yescharacteristic
51C2×C42×C149C2211yescharacteristic
52#95×C149C2211yescharacteristic
53#95×C149C2211yescharacteristic
54C23×D149C2311yescharacteristic
55C23×D149C2311yescharacteristic
56C2×D596—22no—
57C2×D596—22no—
58C2×D596C2×C414yescomplemented
59C2×C22⋊D149—22no—
60C2×C22⋊D149—22no—
61C2×C22⋊D149—41no—
62C2×C22⋊D149—41no—
63C2×C22⋊D149C2×C414yescomplemented
64C2×C22⋊D149C2×C414yescomplemented
65C22×Dic149—22no—
66C22×Dic149—22no—
67C22×Dic149—41no—
68C22×Dic149C2311yescharacteristic
69C22×Dic149C2311yescharacteristic
70C22×Dic149C2311yescharacteristic
71C22×Dic149C2311yescharacteristic
72C22×Dic149C2311yescharacteristic
73C22×Dic149C2311yescharacteristic
74C2×C4×D149—22no—
75C2×C4×D149—22no—
76C2×C4×D149—22no—
77C2×C4×D149—22no—
78C2×C4×D149—22no—
79C2×C4×D149—22no—
80C2×C4×D149—41no—
81C2×C4×D149—41no—
82C2×C4×D149—41no—
83C2×C4×D149—41no—
84C2×C4×D149—41no—
85C2×C4×D149C2×C414yescomplemented
86#14558715—22no—
87#14558715C2×C414yescomplemented
88C22⋊Dic149—22no—
89#14558713—22no—
90#14558713—22no—
91#14558713—22no—
92#14558713—41no—
93#14558713C2×C414yescomplemented
94#14558713D414yescomplemented
95C4×Dic149—22no—
96C4×Dic149—22no—
97C4×Dic149—41no—
98C24×C149C2311yescharacteristic
99C22×C4×C149C2311yescharacteristic
100C22×C4×C149C2311yescharacteristic
101C22×C4×C149C2311yescharacteristic
102C22×C4×C149C2311yescharacteristic
103C22×C4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105C4⋊C4×C149—22no—
106C22⋊C4×C149—22no—
107C22⋊C4×C149—41no—
108C22⋊C4×C149C2×C414yescomplemented
109C42×C149—41no—
110C22×D149—21no—
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—21no—
117C22×D149—21no—
118C22×D149—21no—
119C22×D149—21no—
120C22×D149C22×C412yes—
121C22×D149C22×C412yes—
122C22×D149C2×D412yes—
123C22×D149#4112yes—
124D596—28no—
125C22⋊D149—28no—
126C22⋊D149—44no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—21no—
140C2×Dic149—44no—
141C2×Dic149C22×C412yes—
142C2×Dic149C22×C412yes—
143C2×Dic149C2×D412yes—
144C2×Dic149#4112yes—
145C2×Dic149#4112yes—
146C4×D149—44no—
147C4×D149—44no—
148C4×D149—44no—
149C4×D149—44no—
150C23×C149—21no—
151C23×C149—21no—
152C23×C149—21no—
153C23×C149—21no—
154C23×C149—21no—
155C23×C149—21no—
156C23×C149C22×C412yes—
157C23×C149C2411yescharacteristic
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
167C2×C4×C149—21no—
168C2×C4×C149—21no—
169C2×C4×C149—21no—
170C2×C4×C149—21no—
171C2×C4×C149—21no—
172C2×C4×C149—21no—
173C2×C4×C149C22×C412yes—
174C2×C4×C149C22×C412yes—
175C2×C4×C149C2×D412yes—
176C22×C149—22no—
177C22×C149—22no—
178C22×C149—22no—
179C22×C149—41no—
180C22×C149—41no—
181C22×C149—41no—
182C22×C149—41no—
183C22×C149C23×C411yescharacteristic
184C22×C149C22×D411yescharacteristic
185C22×C149C2×#4111yescharacteristic
186C22×C149C2×#4111yescharacteristic
187C22×C149C2×#4111yescharacteristic
188C22×C149H(5,𝔽2)11yescharacteristic
189C22×C149H(5,𝔽2)11yescharacteristic
190C2×D149—22no—
191C2×D149—22no—
192C2×D149—22no—
193C2×D149—22no—
194C2×D149—22no—
195C2×D149—22no—
196C2×D149—22no—
197C2×D149—22no—
198C2×D149—22no—
199C2×D149—41no—
200C2×D149—41no—
201C2×D149—41no—
202C2×D149—41no—
203C2×D149C4×D414yes—
204C4×C149—22no—
205C4×C149—22no—
206C4×C149—22no—
207C4×C149—41no—
208C4×C149—41no—
209C4×C149—41no—
210Dic149—22no—
211Dic149—22no—
212Dic149—22no—
213Dic149—22no—
214Dic149—22no—
215Dic149—41no—
216C2×C149—42no—
217C2×C149C2×C4×D411yescharacteristic
218C2×C149C4×#4111yescharacteristic
219C2×C149#51811yescharacteristic
220C2×C149#54611yescharacteristic
221C2×C149#54611yescharacteristic
222C2×C149#55311yescharacteristic
223C2×C149#55311yescharacteristic
224D149—24no—
225D149—42no—
226C149#236411yescharacteristic, complemented, Sylow
227#2364—1491nomaximal, Sylow
228C2×#121—1491no—
229C2×C4×D4—1491no—
230C2×C4×D4—1491no—
231#388—1491no—
232#388D14911yescharacteristic, complemented
233#387—1491no—
234#387—1491no—
235#386—1491no—
236#386—1491no—
237#386—1491no—
238#386—1491no—
239C4×C22⋊C4—1491no—
240C4×C22⋊C4—1491no—
241C4×C22⋊C4—1491no—
242C2×#95—1491no—
243C22×D4—1491no—
244C22×D4—1491no—
245C22×D4—1491no—
246C23×C4—1491no—
247C23×C4—1491no—
248C23×C4—1491no—
249C23×C4—1491no—
250C23×C4—1491no—
251#121—1498no—
252C4×D4—2984no—
253C4×D4—2984no—
254C2×C4⋊C4—1491no—
255C2×C4⋊C4—1491no—
256C2×C4⋊C4C2×D14911yescharacteristic
257C2×C22⋊C4—1491no—
258C2×C22⋊C4—1491no—
259C2×C22⋊C4—1491no—
260C2×C22⋊C4—1491no—
261C2×C22⋊C4—1491no—
262C2×C22⋊C4—1491no—
263C2×C22⋊C4—1491no—
264C2×C22⋊C4C2×D14911yescharacteristic
265C2×C22⋊C4C2×D14911yescharacteristic
266C2×C22⋊C4C2×D14911yescharacteristic
267C2×C42—1491no—
268C2×C42—1491no—
269C2×C42—1491no—
270C2×C42C2×D14911yescharacteristic
271#95—1491no—
272#95—1491no—
273#95—1491no—
274#95—1491no—
275#95—1491no—
276#95—1491no—
277#95—1491no—
278#95—1491no—
279#95C2×D14911yescharacteristic
280#95C2×D14911yescharacteristic
281C24—1491no—
282C24—1491no—
283C24C22×D14911yescharacteristic
284C2×D4—2982no—
285C2×D4—2982no—
286C2×D4—2982no—
287C2×D4—2982no—
288C2×D4—5961no—
289C2×D4—5961no—
290C2×D4—1494no—
291C2×D4—1494no—
292C2×D4—1494no—
293C22×C4—2982no—
294C22×C4—2982no—
295C22×C4—2982no—
296C22×C4—2982no—
297C22×C4—2982no—
298C22×C4—2982no—
299C22×C4—2982no—
300C22×C4—2982no—
301C22×C4—5961no—
302C22×C4—5961no—
303C22×C4—5961no—
304C22×C4—5961no—
305C22×C4—5961no—
306C22×C4—5961no—
307C22×C4—1491no—
308C22×C4—1491no—
309C22×C4—1491no—
310C22×C4—1491no—
311C22×C4—1491no—
312C22×C4—1491no—
313C22×C4—1494no—
314C22×C4C22×D14911yescharacteristic
315C22×C4C22×D14911yescharacteristic
316C22×C4C22×D14911yescharacteristic
317C22×C4C22×D14911yescharacteristic
318C22×C4C22×D14911yescharacteristic
319C22×C4C22×D14911yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—2982no—
322C4⋊C4—1494no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—2982no—
326C22⋊C4—2982no—
327C22⋊C4—2982no—
328C22⋊C4—2982no—
329C22⋊C4—5961no—
330C22⋊C4—1494no—
331C22⋊C4—1494no—
332C22⋊C4C4×D14914yescomplemented
333C42—41no—
334C42—2982no—
335C42—2982no—
336C42—5961no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—2981no—
344C23—2981no—
345C23—2981no—
346C23—2981no—
347C23—2981no—
348C23—2981no—
349C23—2981no—
350C23—2981no—
351C23—2981no—
352C23—2981no—
353C23—1492no—
354C23—1492no—
355C23—1492no—
356C23—1492no—
357C23C2×C4×D14912yes—
358C23C23×D14911yescharacteristic
359D4—2988no—
360D4—2988no—
361D4—5964no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—2981no—
378C2×C4—2981no—
379C2×C4—2981no—
380C2×C4—2981no—
381C2×C4—2981no—
382C2×C4—2981no—
383C2×C4—2981no—
384C2×C4—2981no—
385C2×C4—2981no—
386C2×C4—2981no—
387C2×C4—2981no—
388C2×C4—2981no—
389C2×C4—2981no—
390C2×C4—5964no—
391C2×C4—5964no—
392C2×C4—5964no—
393C2×C4—5964no—
394C2×C4—5964no—
395C2×C4—1492no—
396C2×C4—1492no—
397C2×C4—1492no—
398C2×C4—1492no—
399C2×C4—1492no—
400C2×C4C2×C4×D14912yes—
401C2×C4C2×C4×D14912yes—
402C2×C4D4×D14912yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—2982no—
411C22—2982no—
412C22—2982no—
413C22—2982no—
414C22—2982no—
415C22—2982no—
416C22—2982no—
417C22—2982no—
418C22—2982no—
419C22—5961no—
420C22—5961no—
421C22—5961no—
422C22—5961no—
423C22—1494no—
424C22C22×C4×D14911yescharacteristic
425C22C2×D4×D14911yescharacteristic
426C22#41×D14911yescharacteristic
427C22#41×D14911yescharacteristic
428C22#41×D14911yescharacteristic
429C22#1801195611yescharacteristic
430C22#1801195711yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—2982no—
438C4—2982no—
439C4—2982no—
440C4—2982no—
441C4—2982no—
442C4—5961no—
443C2—42no—
444C2—2984no—
445C2—5962no—
446C2C4×D4×D14911yescharacteristic
447C2#2375009311yescharacteristic
448C2#2375009711yescharacteristic
449C2#2375026411yescharacteristic
450C2#2375026811yescharacteristic
451C2#2375032011yescharacteristic
452C2#2375032611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#388×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011884C2
hypercenter#388D149
hypocenterC149#2364
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#18011873C2semidirect
3. C2×#18011871C2semidirect
4. #23749514C2semidirect
5. #23749507C2semidirect
6. #23749506C2semidirect
7. #23749503C2semidirect
8. #23749502C2semidirect
9. #23749501C2semidirect
10. #23749501C2semidirect
11. C22⋊C4×Dic149C2semidirect
12. C4×#14558713C2semidirect
13. C4×#14558713C2semidirect
14. #95×D149C2semidirect
15. #388×C149C2semidirect
24. #18011884C4semidirect
58. C2×D596C2×C4semidirect
63. C2×C22⋊D149C2×C4semidirect
64. C2×C22⋊D149C2×C4semidirect
85. C2×C4×D149C2×C4semidirect
87. #14558715C2×C4semidirect
93. #14558713C2×C4semidirect
94. #14558713D4semidirect
108. C22⋊C4×C149C2×C4semidirect
226. C149#2364semidirect
232. #388D149semidirect
332. C22⋊C4C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118842
C2×#180118732
C2×#180118712
#237495142
#237495072
#237495062
#237495032
#237495022
#237495012
C22⋊C4×Dic1492
C4×#145587132
#95×D1492
#388×C1492
#2364149