Finite Group Databasebeta

← #34047539

Subgroups — #34047539

Order 19072.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011869C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D149C211yesmaximal, characteristic
3C2×C22⋊C4×D149C211yesmaximal, characteristic
4#23749519C211yesmaximal, characteristic, complemented
5#23749518C211yesmaximal, characteristic, complemented
6#23749513C211yesmaximal, characteristic, complemented
7#23749499C211yesmaximal, characteristic, complemented
8#23749496C211yesmaximal, characteristic, complemented
9#23749487C211yesmaximal, characteristic, complemented
10#23749484C211yesmaximal, characteristic, complemented
11#23749480C211yesmaximal, characteristic
12C4×#14558713C211yesmaximal, characteristic, complemented
13C4×#14558713C211yesmaximal, characteristic, complemented
14#23749472C211yesmaximal, characteristic, complemented
15#388×C149C211yesmaximal, characteristic, complemented
16C24×D149C2211yescharacteristic
17C22×C4×D149C2211yescharacteristic
18C22×C4×D149C2211yescharacteristic
19C22×C4×D149C2211yescharacteristic
20C22×C4×D149C2211yescharacteristic
21#18011869—24no—
22C2×C4⋊Dic149C2211yescharacteristic, complemented
23C2×#14558715C2211yescharacteristic, complemented
24C2×#14558715C2211yescharacteristic, complemented
25C2×C22⋊Dic149C2211yescharacteristic
26C2×C22⋊Dic149C2211yescharacteristic
27C2×C22⋊Dic149C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C22⋊C4×D149—24no—
37C22⋊C4×D149C418yescomplemented
38C2×C4×Dic149C2211yescharacteristic, complemented
39C2×C4×Dic149C2211yescharacteristic, complemented
40C2×C4×Dic149C2211yescharacteristic, complemented
41#18011818C2211yescharacteristic, complemented
42#18011818C2211yescharacteristic, complemented
43#18011818C2211yescharacteristic, complemented
44#18011818C2211yescharacteristic, complemented
45#18011818C2211yescharacteristic, complemented
46#18011818C2211yescharacteristic, complemented
47C2×C4⋊C4×C149C2211yescharacteristic, complemented
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C22⋊C4×C149C2211yescharacteristic
50C2×C22⋊C4×C149C2211yescharacteristic
51C2×C42×C149C2211yescharacteristic, complemented
52#95×C149C2211yescharacteristic, complemented
53#95×C149C2211yescharacteristic, complemented
54C23×D149—22no—
55C23×D149—22no—
56C23×D149—22no—
57C23×D149—22no—
58C23×D149—41no—
59C23×D149—41no—
60C23×D149C2×C414yes—
61C23×D149C2311yescharacteristic
62C23×D149C2311yescharacteristic
63C22×Dic149C2311yescharacteristic
64C22×Dic149C2311yescharacteristic
65C22×Dic149C2311yescharacteristic
66C22×Dic149C2311yescharacteristic
67C22×Dic149C2311yescharacteristic
68C22×Dic149C2311yescharacteristic
69C2×C4×D149—22no—
70C2×C4×D149—22no—
71C2×C4×D149—22no—
72C2×C4×D149—22no—
73C2×C4×D149—22no—
74C2×C4×D149—22no—
75C2×C4×D149—41no—
76C2×C4×D149—41no—
77C2×C4×D149—41no—
78C2×C4×D149—41no—
79C2×C4×D149C2×C414yescomplemented
80C2×C4×D149C2×C414yescomplemented
81C4⋊Dic149—22no—
82#14558715—41no—
83#14558715—41no—
84C22⋊Dic149—22no—
85C22⋊Dic149—41no—
86C22⋊Dic149C2×C414yescomplemented
87#14558713—22no—
88#14558713—22no—
89#14558713—22no—
90#14558713—22no—
91#14558713—22no—
92#14558713C2×C414yes—
93#14558713C2×C414yes—
94#14558713D414yes—
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—28no—
119C22×D149—28no—
120C22×D149—44no—
121C22×D149—44no—
122C22×D149—44no—
123C22×D149—44no—
124C22×D149—44no—
125C22×D149C22×C412yes—
126C22×D149C22×C412yes—
127C22×D149C2×D412yes—
128C22×D149#4112yes—
129C22×D149#4112yes—
130C22×D149#4112yes—
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—21no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149—21no—
144C2×Dic149—21no—
145C2×Dic149—21no—
146C2×Dic149C22×C412yes—
147C2×Dic149C22×C412yes—
148C2×Dic149C2×D412yes—
149C4×D149—28no—
150C4×D149—44no—
151C4×D149—44no—
152C4×D149—44no—
153C23×C149—21no—
154C23×C149—21no—
155C23×C149—21no—
156C23×C149—21no—
157C23×C149—21no—
158C23×C149—21no—
159C23×C149C22×C412yes—
160C23×C149C2411yescharacteristic
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×C149—21no—
174C2×C4×C149—21no—
175C2×C4×C149—21no—
176C2×C4×C149C22×C412yes—
177C2×C4×C149C22×C412yes—
178C2×C4×C149C2×D412yes—
179C22×C149—22no—
180C22×C149—22no—
181C22×C149—22no—
182C22×C149—41no—
183C22×C149—41no—
184C22×C149—41no—
185C22×C149—41no—
186C22×C149C23×C411yescharacteristic
187C22×C149C22×D411yescharacteristic
188C22×C149C2×#4111yescharacteristic
189C22×C149C2×#4111yescharacteristic
190C22×C149C2×#4111yescharacteristic
191C22×C149H(5,𝔽2)11yescharacteristic
192C22×C149H(5,𝔽2)11yescharacteristic
193C2×D149—22no—
194C2×D149—22no—
195C2×D149—22no—
196C2×D149—22no—
197C2×D149—22no—
198C2×D149—22no—
199C2×D149—22no—
200C2×D149—22no—
201C2×D149—22no—
202C2×D149—22no—
203C2×D149—22no—
204C2×D149—22no—
205C2×D149—416no—
206C2×D149#11714yescomplemented
207C2×D149C4×D414yes—
208C4×C149—22no—
209C4×C149—22no—
210C4×C149—22no—
211C4×C149—41no—
212C4×C149—41no—
213C4×C149—41no—
214Dic149—22no—
215Dic149—22no—
216Dic149—22no—
217Dic149—41no—
218Dic149—41no—
219Dic149—41no—
220C2×C149—42no—
221C2×C149C2×#11711yescharacteristic
222C2×C149C2×C4×D411yescharacteristic
223C2×C149#51811yescharacteristic
224C2×C149#54611yescharacteristic
225C2×C149#54611yescharacteristic
226C2×C149#55111yescharacteristic
227C2×C149#55111yescharacteristic
228D149—24no—
229D149—24no—
230C149#234211yescharacteristic, complemented, Sylow
231#2342—1491nomaximal, Sylow
232C2×#117—1491no—
233C22×C22⋊C4—1491no—
234C22×C22⋊C4—1491no—
235#388—1491no—
236#388—1491no—
237#388—1491no—
238#388D14911yescharacteristic, complemented
239#385—1491no—
240#385—1491no—
241#381—1491no—
242#380—1491no—
243#379—1491no—
244C4×C22⋊C4—1491no—
245C4×C22⋊C4—1491no—
246C4×C22⋊C4—1491no—
247C25—1491no—
248C23×C4—1491no—
249C23×C4—1491no—
250C23×C4—1491no—
251C23×C4—1491no—
252#117—2984no—
253C2×C4⋊C4—1491no—
254C2×C4⋊C4—1491no—
255C2×C4⋊C4—1491no—
256C2×C4⋊C4C2×D14911yescharacteristic, complemented
257C2×C22⋊C4—2984no—
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⋊C4—1491no—
265C2×C22⋊C4—1491no—
266C2×C22⋊C4—1491no—
267C2×C22⋊C4—1491no—
268C2×C22⋊C4—1491no—
269C2×C22⋊C4—1498no—
270C2×C22⋊C4C2×D14911yescharacteristic
271C2×C22⋊C4C2×D14911yescharacteristic
272C2×C22⋊C4C2×D14911yescharacteristic
273C2×C42—1491no—
274C2×C42—1491no—
275C2×C42—1491no—
276C2×C42C2×D14911yescharacteristic, complemented
277#95—1491no—
278#95—1491no—
279#95—1491no—
280#95—1491no—
281#95—1491no—
282#95—1491no—
283#95C2×D14911yescharacteristic, complemented
284#95C2×D14911yescharacteristic, complemented
285C24—2982no—
286C24—2982no—
287C24—2982no—
288C24—2982no—
289C24—5961no—
290C24—5961no—
291C24—1494no—
292C24—1491no—
293C24—1491no—
294C24C22×D14911yescharacteristic
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—1491no—
306C22×C4—1491no—
307C22×C4—1491no—
308C22×C4—1491no—
309C22×C4—1491no—
310C22×C4—1491no—
311C22×C4—1494no—
312C22×C4—1494no—
313C22×C4C22×D14911yescharacteristic
314C22×C4C22×D14911yescharacteristic
315C22×C4C22×D14911yescharacteristic
316C22×C4C22×D14911yescharacteristic
317C22×C4C22×D14911yescharacteristic
318C22×C4C22×D14911yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—2982no—
321C4⋊C4—5961no—
322C4⋊C4—5961no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—2982no—
326C22⋊C4—2982no—
327C22⋊C4—2982no—
328C22⋊C4—2982no—
329C22⋊C4—2982no—
330C22⋊C4—2982no—
331C22⋊C4—5961no—
332C22⋊C4—1494no—
333C22⋊C4—1494no—
334C22⋊C4—1494no—
335C22⋊C4—1494no—
336C22⋊C4C4×D14914yescomplemented
337C42—41no—
338C42—2982no—
339C42—2982no—
340C42—5961no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—2988no—
348C23—2988no—
349C23—2981no—
350C23—2981no—
351C23—2981no—
352C23—2981no—
353C23—2981no—
354C23—2981no—
355C23—2981no—
356C23—2981no—
357C23—5964no—
358C23—5964no—
359C23—5964no—
360C23—5964no—
361C23—5964no—
362C23—1492no—
363C23—1492no—
364C23—1492no—
365C23—1492no—
366C23—1492no—
367C23—1492no—
368C23C2×C4×D14912yes—
369C23C23×D14911yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—2988no—
386C2×C4—2981no—
387C2×C4—2981no—
388C2×C4—2981no—
389C2×C4—2981no—
390C2×C4—2981no—
391C2×C4—2981no—
392C2×C4—2981no—
393C2×C4—2981no—
394C2×C4—2981no—
395C2×C4—2981no—
396C2×C4—2981no—
397C2×C4—2981no—
398C2×C4—2981no—
399C2×C4—2981no—
400C2×C4—2981no—
401C2×C4—5964no—
402C2×C4—5964no—
403C2×C4—5964no—
404C2×C4—1492no—
405C2×C4—1492no—
406C2×C4—1492no—
407C2×C4C2×C4×D14912yes—
408C2×C4C2×C4×D14912yes—
409C2×C4D4×D14912yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—2982no—
418C22—2982no—
419C22—2982no—
420C22—2982no—
421C22—2982no—
422C22—2982no—
423C22—2982no—
424C22—2982no—
425C22—2982no—
426C22—2982no—
427C22—2982no—
428C22—2982no—
429C22—59616no—
430C22—1494no—
431C22—1494no—
432C22C22×C4×D14911yescharacteristic
433C22C2×D4×D14911yescharacteristic
434C22#41×D14911yescharacteristic
435C22#41×D14911yescharacteristic
436C22#41×D14911yescharacteristic
437C22#1801195611yescharacteristic
438C22#1801195711yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—2982no—
446C4—2982no—
447C4—2982no—
448C4—5961no—
449C4—5961no—
450C4—5961no—
451C2—42no—
452C2—2984no—
453C2—2984no—
454C2#117×D14911yescharacteristic
455C2C4×D4×D14911yescharacteristic
456C2#2375009711yescharacteristic
457C2#2375026411yescharacteristic
458C2#2375026811yescharacteristic
459C2#2375030011yescharacteristic
460C2#2375030311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#388×C149C2
socle, cosocleC23×C149C24
prime radicalC24×D149C22
hypercenter#388D149
hypocenterC149#2342
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#18011869C2semidirect
4. #23749519C2semidirect
5. #23749518C2semidirect
6. #23749513C2semidirect
7. #23749499C2semidirect
8. #23749496C2semidirect
9. #23749487C2semidirect
10. #23749484C2semidirect
12. C4×#14558713C2semidirect
13. C4×#14558713C2semidirect
14. #23749472C2semidirect
15. #388×C149C2semidirect
22. C2×C4⋊Dic149C22semidirect
23. C2×#14558715C22semidirect
24. C2×#14558715C22semidirect
37. C22⋊C4×D149C4semidirect
38. C2×C4×Dic149C22semidirect
39. C2×C4×Dic149C22semidirect
40. C2×C4×Dic149C22semidirect
41. #18011818C22semidirect
42. #18011818C22semidirect
43. #18011818C22semidirect
44. #18011818C22semidirect
45. #18011818C22semidirect
46. #18011818C22semidirect
47. C2×C4⋊C4×C149C22semidirect
51. C2×C42×C149C22semidirect
52. #95×C149C22semidirect
53. #95×C149C22semidirect
79. C2×C4×D149C2×C4semidirect
80. C2×C4×D149C2×C4semidirect
86. C22⋊Dic149C2×C4semidirect
108. C22⋊C4×C149C2×C4semidirect
206. C2×D149#117semidirect
230. C149#2342semidirect
238. #388D149semidirect
256. C2×C4⋊C4C2×D149semidirect
276. C2×C42C2×D149semidirect
283. #95C2×D149semidirect
284. #95C2×D149semidirect
336. C22⋊C4C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118692
C2×C22⋊C4×D1492
#237495192
#237495182
#237495132
#237494992
#237494962
#237494872
#237494842
#237494802
C4×#145587132
#237494722
#388×C1492
#2342149