Finite Group Databasebeta

← #34047669

Subgroups — #34047669

Order 19072.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011881C211yesmaximal, characteristic
2C2×C4×D596C211yesmaximal, characteristic, complemented
3C2×#18011873C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D149C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D149C211yesmaximal, characteristic, complemented
6#23749525C211yesmaximal, characteristic, complemented
7#23749518C211yesmaximal, characteristic, complemented
8#23749503C211yesmaximal, characteristic, complemented
9#23749503C211yesmaximal, characteristic, complemented
10#23749501C211yesmaximal, characteristic, complemented
11#23749499C211yesmaximal, characteristic, complemented
12#23749496C211yesmaximal, characteristic, complemented
13C4×#14558713C211yesmaximal, characteristic, complemented
14#23749472C211yesmaximal, characteristic, complemented
15#388×C149C211yesmaximal, characteristic, complemented
16C24×D149C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C22×D596C2211yescharacteristic
19C22×C22⋊D149C2211yescharacteristic
20C22×C4×D149C2211yescharacteristic
21C22×C4×D149C2211yescharacteristic
22C22×C4×D149C2211yescharacteristic
23C22×C4×D149C2211yescharacteristic
24C22×C4×D149C2211yescharacteristic, complemented
25#18011881C418yescomplemented
26C4×D596—24no—
27#18011873—24no—
28C2×C4⋊Dic149C2211yescharacteristic, complemented
29C2×#14558715C2211yescharacteristic, complemented
30C2×C22⋊Dic149C2211yescharacteristic
31C2×C22⋊Dic149C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×#14558713C2211yescharacteristic
37C2×#14558713C2211yescharacteristic
38C2×#14558713C2211yescharacteristic, complemented
39C2×#14558713C2211yescharacteristic, complemented
40C2×#14558713C2211yescharacteristic, complemented
41C22⋊C4×D149—24no—
42C22⋊C4×D149—24no—
43C2×C4×Dic149C2211yescharacteristic, complemented
44C2×C4×Dic149C2211yescharacteristic, complemented
45#18011818C2211yescharacteristic, complemented
46#18011818C2211yescharacteristic, complemented
47#18011818C2211yescharacteristic, complemented
48#18011818C2211yescharacteristic, complemented
49C2×C4⋊C4×C149C2211yescharacteristic, complemented
50C2×C22⋊C4×C149C2211yescharacteristic
51C2×C22⋊C4×C149C2211yescharacteristic
52C2×C22⋊C4×C149C2211yescharacteristic
53C2×C42×C149C2211yescharacteristic, complemented
54#95×C149C2211yescharacteristic, complemented
55#95×C149C2211yescharacteristic, complemented
56C23×D149—22no—
57C23×D149—22no—
58C23×D149—22no—
59C23×D149—22no—
60C23×D149—41no—
61C23×D149—41no—
62C23×D149C2×C414yescomplemented
63C23×D149C2311yescharacteristic
64C23×D149C2311yescharacteristic
65C23×D149C2311yescharacteristic
66C2×D596—22no—
67C2×D596—22no—
68C2×D596—22no—
69C2×D596—22no—
70C2×D596C2×C414yescomplemented
71C2×D596C2×C414yescomplemented
72C2×C22⋊D149—41no—
73C2×C22⋊D149—41no—
74C2×C22⋊D149C2×C414yescomplemented
75C22×Dic149C2311yescharacteristic
76C22×Dic149C2311yescharacteristic
77C22×Dic149C2311yescharacteristic
78C22×Dic149C2311yescharacteristic
79C22×Dic149C2311yescharacteristic
80C2×C4×D149—22no—
81C2×C4×D149—22no—
82C2×C4×D149—22no—
83C2×C4×D149—22no—
84C2×C4×D149—22no—
85C2×C4×D149—22no—
86C2×C4×D149—22no—
87C2×C4×D149—22no—
88C2×C4×D149—22no—
89C2×C4×D149—22no—
90C2×C4×D149—41no—
91C2×C4×D149—41no—
92C2×C4×D149—41no—
93C2×C4×D149—41no—
94C2×C4×D149—41no—
95C4⋊Dic149—22no—
96#14558715—41no—
97C22⋊Dic149—22no—
98C22⋊Dic149—22no—
99#14558713—22no—
100#14558713—22no—
101#14558713—22no—
102#14558713—22no—
103#14558713—41no—
104#14558713C2×C414yescomplemented
105#14558713C2×C414yescomplemented
106#14558713D414yescomplemented
107#14558713D414yescomplemented
108C4×Dic149—22no—
109C4×Dic149—41no—
110C24×C149C2311yescharacteristic
111C22×C4×C149C2311yescharacteristic
112C22×C4×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114C22×C4×C149C2311yescharacteristic
115C22×C4×C149C2311yescharacteristic
116C22×C4×C149C2311yescharacteristic
117C4⋊C4×C149—22no—
118C22⋊C4×C149—22no—
119C22⋊C4×C149—22no—
120C22⋊C4×C149C2×C414yescomplemented
121C42×C149—22no—
122C22×D149—21no—
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—21no—
126C22×D149—21no—
127C22×D149—21no—
128C22×D149—21no—
129C22×D149—21no—
130C22×D149—21no—
131C22×D149—21no—
132C22×D149—21no—
133C22×D149—21no—
134C22×D149—21no—
135C22×D149—21no—
136C22×D149—28no—
137C22×D149—28no—
138C22×D149—44no—
139C22×D149—44no—
140C22×D149—44no—
141C22×D149—44no—
142C22×D149—44no—
143C22×D149C22×C412yes—
144C22×D149C22×C412yes—
145C22×D149C22×C412yes—
146C22×D149C2×D412yes—
147C22×D149C2×D412yes—
148C22×D149#4112yes—
149C22×D149#4112yes—
150D596—28no—
151D596—28no—
152C22⋊D149—44no—
153C2×Dic149—21no—
154C2×Dic149—21no—
155C2×Dic149—21no—
156C2×Dic149—21no—
157C2×Dic149—21no—
158C2×Dic149—21no—
159C2×Dic149—21no—
160C2×Dic149—21no—
161C2×Dic149—21no—
162C2×Dic149—21no—
163C2×Dic149—21no—
164C2×Dic149—21no—
165C2×Dic149C22×C412yes—
166C2×Dic149C2×D412yes—
167C2×Dic149C2×D412yes—
168C4×D149—44no—
169C4×D149—44no—
170C4×D149—44no—
171C4×D149—44no—
172C4×D149—44no—
173C23×C149—21no—
174C23×C149—21no—
175C23×C149—21no—
176C23×C149—21no—
177C23×C149—21no—
178C23×C149—21no—
179C23×C149C22×C412yes—
180C23×C149C2411yescharacteristic
181C2×C4×C149—21no—
182C2×C4×C149—21no—
183C2×C4×C149—21no—
184C2×C4×C149—21no—
185C2×C4×C149—21no—
186C2×C4×C149—21no—
187C2×C4×C149—21no—
188C2×C4×C149—21no—
189C2×C4×C149—21no—
190C2×C4×C149—21no—
191C2×C4×C149—21no—
192C2×C4×C149—21no—
193C2×C4×C149—21no—
194C2×C4×C149—21no—
195C2×C4×C149C22×C412yes—
196C2×C4×C149C22×C412yes—
197C2×C4×C149C2×D412yes—
198C2×C4×C149C2×D412yes—
199C22×C149—22no—
200C22×C149—22no—
201C22×C149—22no—
202C22×C149—41no—
203C22×C149—41no—
204C22×C149—41no—
205C22×C149—41no—
206C22×C149C23×C411yescharacteristic
207C22×C149C22×D411yescharacteristic
208C22×C149C22×D411yescharacteristic
209C22×C149C2×#4111yescharacteristic
210C22×C149C2×#4111yescharacteristic
211C22×C149H(5,𝔽2)11yescharacteristic
212C22×C149H(5,𝔽2)11yescharacteristic
213C2×D149—22no—
214C2×D149—22no—
215C2×D149—22no—
216C2×D149—22no—
217C2×D149—22no—
218C2×D149—22no—
219C2×D149—22no—
220C2×D149—22no—
221C2×D149—22no—
222C2×D149—22no—
223C2×D149—22no—
224C2×D149—22no—
225C2×D149—22no—
226C2×D149—22no—
227C2×D149—22no—
228C2×D149—416no—
229C2×D149—41no—
230C2×D149—41no—
231C2×D149—41no—
232C2×D149—41no—
233C2×D149C4×D414yescomplemented
234C2×D149C4×D414yescomplemented
235C4×C149—22no—
236C4×C149—22no—
237C4×C149—22no—
238C4×C149—22no—
239C4×C149—41no—
240C4×C149—41no—
241Dic149—22no—
242Dic149—22no—
243Dic149—22no—
244Dic149—41no—
245Dic149—41no—
246C2×C149—42no—
247C2×C149C2×C4×D411yescharacteristic
248C2×C149C2×C4×D411yescharacteristic
249C2×C149#51811yescharacteristic
250C2×C149D4211yescharacteristic
251C2×C149#54611yescharacteristic
252C2×C149#54611yescharacteristic
253C2×C149#55111yescharacteristic
254D149—24no—
255D149—24no—
256D149—42no—
257C149#235811yescharacteristic, complemented, Sylow
258#2358—1491nomaximal, Sylow
259C2×#120—1491no—
260C2×C4×D4—1491no—
261C2×C4×D4—1491no—
262C22×C22⋊C4—1491no—
263C22×C22⋊C4—1491no—
264#390—1491no—
265#388—1491no—
266#388D14911yescharacteristic, complemented
267#386—1491no—
268#386—1491no—
269#386—1491no—
270#385—1491no—
271#385—1491no—
272C4×C22⋊C4—1491no—
273C4×C22⋊C4—1491no—
274C25—1491no—
275C22×D4—1491no—
276C22×D4—1491no—
277C22×D4—1491no—
278C23×C4—1491no—
279C23×C4—1491no—
280C23×C4—1491no—
281C23×C4—1491no—
282C23×C4—1491no—
283#120—1498no—
284C4×D4—2984no—
285C4×D4—2984no—
286C2×C4⋊C4—1491no—
287C2×C4⋊C4—1491no—
288C2×C4⋊C4C2×D14911yescharacteristic, complemented
289C2×C22⋊C4—2984no—
290C2×C22⋊C4—2984no—
291C2×C22⋊C4—1491no—
292C2×C22⋊C4—1491no—
293C2×C22⋊C4—1491no—
294C2×C22⋊C4—1491no—
295C2×C22⋊C4—1491no—
296C2×C22⋊C4—1491no—
297C2×C22⋊C4—1491no—
298C2×C22⋊C4—1491no—
299C2×C22⋊C4—1491no—
300C2×C22⋊C4—1491no—
301C2×C22⋊C4—1491no—
302C2×C22⋊C4C2×D14911yescharacteristic
303C2×C22⋊C4C2×D14911yescharacteristic
304C2×C22⋊C4C2×D14911yescharacteristic
305C2×C42—1491no—
306C2×C42—1491no—
307C2×C42C2×D14911yescharacteristic, complemented
308#95—1491no—
309#95—1491no—
310#95—1491no—
311#95—1491no—
312#95C2×D14911yescharacteristic, complemented
313#95C2×D14911yescharacteristic, complemented
314C24—2982no—
315C24—2982no—
316C24—2982no—
317C24—2982no—
318C24—5961no—
319C24—5961no—
320C24—1491no—
321C24—1494no—
322C24—1491no—
323C24—1491no—
324C24C22×D14911yescharacteristic
325C2×D4—2982no—
326C2×D4—2982no—
327C2×D4—2982no—
328C2×D4—2982no—
329C2×D4—5961no—
330C2×D4—5961no—
331C2×D4—1494no—
332C2×D4—1494no—
333C2×D4—1494no—
334C22×C4—2982no—
335C22×C4—2982no—
336C22×C4—2982no—
337C22×C4—2982no—
338C22×C4—2982no—
339C22×C4—2982no—
340C22×C4—2982no—
341C22×C4—2982no—
342C22×C4—2982no—
343C22×C4—2982no—
344C22×C4—5961no—
345C22×C4—5961no—
346C22×C4—5961no—
347C22×C4—5961no—
348C22×C4—5961no—
349C22×C4—1491no—
350C22×C4—1491no—
351C22×C4—1491no—
352C22×C4—1491no—
353C22×C4—1491no—
354C22×C4C22×D14911yescharacteristic
355C22×C4C22×D14911yescharacteristic
356C22×C4C22×D14911yescharacteristic
357C22×C4C22×D14911yescharacteristic
358C22×C4C22×D14911yescharacteristic
359C22×C4C22×D14911yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—2982no—
362C4⋊C4—5961no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—2982no—
366C22⋊C4—2982no—
367C22⋊C4—2982no—
368C22⋊C4—2982no—
369C22⋊C4—2982no—
370C22⋊C4—2982no—
371C22⋊C4—5961no—
372C22⋊C4—1494no—
373C22⋊C4—1494no—
374C22⋊C4—1494no—
375C22⋊C4—1494no—
376C22⋊C4C4×D14914yescomplemented
377C42—22no—
378C42—2982no—
379C42—5961no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—2988no—
387C23—2988no—
388C23—2981no—
389C23—2981no—
390C23—2981no—
391C23—2981no—
392C23—2981no—
393C23—2981no—
394C23—2981no—
395C23—2981no—
396C23—2981no—
397C23—2981no—
398C23—2981no—
399C23—2981no—
400C23—2981no—
401C23—2981no—
402C23—5964no—
403C23—5964no—
404C23—5964no—
405C23—5964no—
406C23—5964no—
407C23—1492no—
408C23—1492no—
409C23—1492no—
410C23—1492no—
411C23—1492no—
412C23—1492no—
413C23—1492no—
414C23C2×C4×D14912yes—
415C23C23×D14911yescharacteristic
416D4—2988no—
417D4—2988no—
418D4—5964no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—2981no—
434C2×C4—2981no—
435C2×C4—2981no—
436C2×C4—2981no—
437C2×C4—2981no—
438C2×C4—2981no—
439C2×C4—2981no—
440C2×C4—2981no—
441C2×C4—2981no—
442C2×C4—2981no—
443C2×C4—2981no—
444C2×C4—2981no—
445C2×C4—5964no—
446C2×C4—5964no—
447C2×C4—5964no—
448C2×C4—5964no—
449C2×C4—5964no—
450C2×C4—1492no—
451C2×C4—1492no—
452C2×C4—1492no—
453C2×C4C2×C4×D14912yes—
454C2×C4C2×C4×D14912yes—
455C2×C4D4×D14912yes—
456C2×C4D4×D14912yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—2982no—
465C22—2982no—
466C22—2982no—
467C22—2982no—
468C22—2982no—
469C22—2982no—
470C22—2982no—
471C22—2982no—
472C22—2982no—
473C22—2982no—
474C22—2982no—
475C22—2982no—
476C22—2982no—
477C22—2982no—
478C22—2982no—
479C22—59616no—
480C22—5961no—
481C22—5961no—
482C22—5961no—
483C22—5961no—
484C22—1494no—
485C22—1494no—
486C22C22×C4×D14911yescharacteristic
487C22C2×D4×D14911yescharacteristic
488C22C2×D4×D14911yescharacteristic
489C22#41×D14911yescharacteristic
490C22#41×D14911yescharacteristic
491C22#1801195711yescharacteristic
492C22#1801195711yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—2982no—
500C4—2982no—
501C4—2982no—
502C4—5961no—
503C4—5961no—
504C2—42no—
505C2—2984no—
506C2—2984no—
507C2—5962no—
508C2C4×D4×D14911yescharacteristic
509C2C4×D4×D14911yescharacteristic
510C2#2375009911yescharacteristic
511C2#2375025911yescharacteristic
512C2#2375026711yescharacteristic
513C2#2375026811yescharacteristic
514C2#2375030011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#388×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011881C2
hypercenter#388D149
hypocenterC149#2358
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D596C2semidirect
3. C2×#18011873C2semidirect
4. C2×C22⋊C4×D149C2semidirect
5. C2×C22⋊C4×D149C2semidirect
6. #23749525C2semidirect
7. #23749518C2semidirect
8. #23749503C2semidirect
9. #23749503C2semidirect
10. #23749501C2semidirect
11. #23749499C2semidirect
12. #23749496C2semidirect
13. C4×#14558713C2semidirect
14. #23749472C2semidirect
15. #388×C149C2semidirect
24. C22×C4×D149C22semidirect
25. #18011881C4semidirect
28. C2×C4⋊Dic149C22semidirect
29. C2×#14558715C22semidirect
38. C2×#14558713C22semidirect
39. C2×#14558713C22semidirect
40. C2×#14558713C22semidirect
43. C2×C4×Dic149C22semidirect
44. C2×C4×Dic149C22semidirect
45. #18011818C22semidirect
46. #18011818C22semidirect
47. #18011818C22semidirect
48. #18011818C22semidirect
49. C2×C4⋊C4×C149C22semidirect
53. C2×C42×C149C22semidirect
54. #95×C149C22semidirect
55. #95×C149C22semidirect
62. C23×D149C2×C4semidirect
70. C2×D596C2×C4semidirect
71. C2×D596C2×C4semidirect
74. C2×C22⋊D149C2×C4semidirect
104. #14558713C2×C4semidirect
105. #14558713C2×C4semidirect
106. #14558713D4semidirect
107. #14558713D4semidirect
120. C22⋊C4×C149C2×C4semidirect
233. C2×D149C4×D4semidirect
234. C2×D149C4×D4semidirect
257. C149#2358semidirect
266. #388D149semidirect
288. C2×C4⋊C4C2×D149semidirect
307. C2×C42C2×D149semidirect
312. #95C2×D149semidirect
313. #95C2×D149semidirect
376. C22⋊C4C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118812
C2×C4×D5962
C2×#180118732
C2×C22⋊C4×D1492
#237495252
#237495182
#237495032
#237495012
#237494992
#237494962
C4×#145587132
#237494722
#388×C1492
#2358149