Finite Group Databasebeta

← #34047668

Subgroups — #34047668

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×#18011879C211yesmaximal, characteristic
2C2×C4×C22⋊D149C211yesmaximal, characteristic, complemented
3C22×#14558713C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D149C211yesmaximal, characteristic, complemented
5#23749525C211yesmaximal, characteristic, complemented
6#23749516C211yesmaximal, characteristic, complemented
7#23749515C211yesmaximal, characteristic, complemented
8#23749505C211yesmaximal, characteristic, complemented
9#23749504C211yesmaximal, characteristic, complemented
10#23749501C211yesmaximal, characteristic, complemented
11#23749498C211yesmaximal, characteristic, complemented
12#23749496C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic149C211yesmaximal, characteristic, complemented
14C4×#14558713C211yesmaximal, characteristic, complemented
15C2×C4×D4×C149C211yesmaximal, characteristic, complemented
16C24×D149C2211yescharacteristic
17C22×C22⋊D149C2211yescharacteristic
18C22×C22⋊D149C2211yescharacteristic
19C23×Dic149C2211yescharacteristic
20C22×C4×D149C2211yescharacteristic
21C22×C4×D149C2211yescharacteristic
22#18011879C418yescomplemented
23C4×C22⋊D149—24no—
24C2×#14558715C2211yescharacteristic, complemented
25C2×#14558715C2211yescharacteristic, complemented
26C2×C22⋊Dic149C2211yescharacteristic
27C2×C22⋊Dic149C2211yescharacteristic
28C2×C22⋊Dic149C2211yescharacteristic, complemented
29C2×C22⋊Dic149C2211yescharacteristic, complemented
30C2×#14558713—24no—
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×#14558713C2211yescharacteristic
37C2×#14558713C2211yescharacteristic
38C2×#14558713C2211yescharacteristic
39C22⋊C4×D149—24no—
40C2×C4×Dic149C2211yescharacteristic, complemented
41C2×C4×Dic149C2211yescharacteristic, complemented
42#18011818C2211yescharacteristic, complemented
43#18011818C2211yescharacteristic, complemented
44#18011818C2211yescharacteristic, complemented
45#18011818C2211yescharacteristic, complemented
46#18011818C2211yescharacteristic, complemented
47#18011818C2211yescharacteristic, complemented
48C22×D4×C149C2211yescharacteristic
49C23×C4×C149C2211yescharacteristic
50C23×C4×C149C2211yescharacteristic, complemented
51C4×D4×C149—24no—
52C2×C4⋊C4×C149C2211yescharacteristic, complemented
53C2×C22⋊C4×C149C2211yescharacteristic
54C2×C22⋊C4×C149C2211yescharacteristic, complemented
55C2×C42×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
65C2×C22⋊D149—22no—
66C2×C22⋊D149—22no—
67C2×C22⋊D149—41no—
68C2×C22⋊D149—41no—
69C2×C22⋊D149C2×C414yescomplemented
70C2×C22⋊D149C2×C414yescomplemented
71C22×Dic149—22no—
72C22×Dic149—22no—
73C22×Dic149—41no—
74C22×Dic149C2311yescharacteristic
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—41no—
85C2×C4×D149—41no—
86#14558715—22no—
87#14558715—41no—
88C22⋊Dic149—22no—
89C22⋊Dic149—22no—
90C22⋊Dic149—41no—
91C22⋊Dic149C2×C414yescomplemented
92#14558713—22no—
93#14558713—22no—
94#14558713—22no—
95#14558713—22no—
96#14558713—22no—
97#14558713C2×C414yescomplemented
98#14558713C2×C414yescomplemented
99#14558713D414yescomplemented
100C4×Dic149—22no—
101C4×Dic149—41no—
102C24×C149C2311yescharacteristic
103C24×C149C2311yescharacteristic
104C2×D4×C149—22no—
105C2×D4×C149—22no—
106C2×D4×C149C2×C414yescomplemented
107C22×C4×C149—22no—
108C22×C4×C149—22no—
109C22×C4×C149—22no—
110C22×C4×C149—22no—
111C22×C4×C149—41no—
112C22×C4×C149—41no—
113C22×C4×C149C2311yescharacteristic
114C22×C4×C149C2311yescharacteristic
115C22×C4×C149C2311yescharacteristic
116C22×C4×C149C2311yescharacteristic
117C22×C4×C149C2311yescharacteristic
118C4⋊C4×C149—22no—
119C22⋊C4×C149—22no—
120C22⋊C4×C149D414yescomplemented
121C42×C149—22no—
122C22×D149—21no—
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—21no—
126C22×D149—28no—
127C22×D149—21no—
128C22×D149—21no—
129C22×D149—21no—
130C22×D149—21no—
131C22×D149—21no—
132C22×D149—21no—
133C22×D149—28no—
134C22×D149—44no—
135C22×D149—44no—
136C22×D149—44no—
137C22×D149—44no—
138C22×D149—44no—
139C22×D149C22×C412yes—
140C22×D149C22×C412yes—
141C22×D149C2×D412yes—
142C22×D149#4112yes—
143C22⋊D149—28no—
144C22⋊D149—44no—
145C2×Dic149—21no—
146C2×Dic149—21no—
147C2×Dic149—21no—
148C2×Dic149—21no—
149C2×Dic149—21no—
150C2×Dic149—21no—
151C2×Dic149—21no—
152C2×Dic149—21no—
153C2×Dic149—21no—
154C2×Dic149—21no—
155C2×Dic149—21no—
156C2×Dic149—21no—
157C2×Dic149—21no—
158C2×Dic149—21no—
159C2×Dic149—21no—
160C2×Dic149—44no—
161C2×Dic149C22×C412yes—
162C2×Dic149C22×C412yes—
163C2×Dic149C2×D412yes—
164C4×D149—44no—
165C4×D149—44no—
166C23×C149—21no—
167C23×C149—21no—
168C23×C149—21no—
169C23×C149—21no—
170C23×C149—21no—
171C23×C149—21no—
172C23×C149—21no—
173C23×C149—21no—
174C23×C149—21no—
175C23×C149—21no—
176C23×C149C22×C412yes—
177C23×C149C22×C412yes—
178C23×C149C2×D412yes—
179C23×C149#4112yes—
180C23×C149C2411yescharacteristic
181D4×C149—28no—
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—44no—
194C2×C4×C149—44no—
195C2×C4×C149C22×C412yes—
196C2×C4×C149C2×D412yes—
197C2×C4×C149C2×D412yes—
198C2×C4×C149C2×D412yes—
199C22×C149—22no—
200C22×C149—22no—
201C22×C149—22no—
202C22×C149—22no—
203C22×C149—22no—
204C22×C149—22no—
205C22×C149—22no—
206C22×C149—22no—
207C22×C149—22no—
208C22×C149—41no—
209C22×C149—41no—
210C22×C149—41no—
211C22×C149—41no—
212C22×C149C4×D414yescomplemented
213C22×C149C23×C411yescharacteristic
214C22×C149C22×D411yescharacteristic
215C22×C149C22×D411yescharacteristic
216C22×C149C2×#4111yescharacteristic
217C22×C149C2×#4111yescharacteristic
218C22×C149H(5,𝔽2)11yescharacteristic
219C22×C149H(5,𝔽2)11yescharacteristic
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—22no—
229C2×D149—416no—
230C2×D149—41no—
231C2×D149—41no—
232C2×D149—41no—
233C2×D149—41no—
234C2×D149C4×D414yescomplemented
235C4×C149—22no—
236C4×C149—22no—
237C4×C149—22no—
238C4×C149—22no—
239C4×C149—41no—
240Dic149—22no—
241Dic149—22no—
242Dic149—22no—
243Dic149—41no—
244Dic149—41no—
245Dic149—41no—
246C2×C149—24no—
247C2×C149—42no—
248C2×C149C2×C4×D411yescharacteristic
249C2×C149C2×C4×D411yescharacteristic
250C2×C149#51811yescharacteristic
251C2×C149D4211yescharacteristic
252C2×C149#54611yescharacteristic
253C2×C149#54611yescharacteristic
254C2×C149#55111yescharacteristic
255D149—24no—
256D149—42no—
257C149#235811yescharacteristic, complemented, Sylow
258#2358—1491nomaximal, Sylow
259C2×#120—1491no—
260C2×C4×D4—1491no—
261C2×C4×D4D14911yescharacteristic, complemented
262C22×C22⋊C4—1491no—
263C22×C22⋊C4—1491no—
264#390—1491no—
265#388—1491no—
266#388—1491no—
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×D4C2×D14911yescharacteristic
278C23×C4—1491no—
279C23×C4—1491no—
280C23×C4—1491no—
281C23×C4C2×D14911yescharacteristic
282C23×C4C2×D14911yescharacteristic, complemented
283#120—1498no—
284C4×D4—24no—
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⋊C4—1491no—
303C2×C22⋊C4C2×D14911yescharacteristic
304C2×C22⋊C4C2×D14911yescharacteristic, complemented
305C2×C42—1491no—
306C2×C42—1491no—
307C2×C42C2×D14911yescharacteristic, complemented
308#95—1491no—
309#95—1491no—
310#95—1491no—
311#95—1491no—
312#95—1491no—
313#95—1491no—
314C24—2982no—
315C24—2982no—
316C24—2982no—
317C24—2982no—
318C24—5961no—
319C24—5961no—
320C24—1491no—
321C24—1494no—
322C24—1491no—
323C24C22×D14911yescharacteristic
324C24C22×D14911yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—2982no—
328C2×D4—2982no—
329C2×D4—5961no—
330C2×D4—5961no—
331C2×D4—1494no—
332C2×D4—1494no—
333C2×D4C4×D14914yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—2982no—
341C22×C4—2982no—
342C22×C4—2982no—
343C22×C4—2982no—
344C22×C4—2982no—
345C22×C4—2982no—
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×C4—1491no—
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—2982no—
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⋊C4C22⋊D14914yescomplemented
377C42—22no—
378C42—2982no—
379C42—5961no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—2988no—
391C23—2981no—
392C23—2981no—
393C23—2981no—
394C23—2981no—
395C23—2981no—
396C23—2981no—
397C23—2981no—
398C23—2981no—
399C23—2981no—
400C23—2981no—
401C23—2988no—
402C23—5964no—
403C23—5964no—
404C23—5964no—
405C23—5964no—
406C23—5964no—
407C23—1492no—
408C23—1492no—
409C23—1492no—
410C23—1492no—
411C23C2×C4×D14912yes—
412C23C2×C4×D14912yes—
413C23C2×C22⋊D14912yes—
414C23#1455873612yes—
415C23C23×D14911yescharacteristic
416D4—28no—
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—44no—
431C2×C4—44no—
432C2×C4—2981no—
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—2981no—
446C2×C4—2981no—
447C2×C4—5964no—
448C2×C4—5964no—
449C2×C4—5964no—
450C2×C4—1492no—
451C2×C4—1492no—
452C2×C4—1492no—
453C2×C4C2×C4×D14912yes—
454C2×C4D4×D14912yes—
455C2×C4C2×C22⋊D14912yes—
456C2×C4C2×C22⋊D14912yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
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—
485C22C4×C22⋊D14914yescomplemented
486C22C22×C4×D14911yescharacteristic
487C22C2×D4×D14911yescharacteristic
488C22C22×C22⋊D14911yescharacteristic
489C22#41×D14911yescharacteristic
490C22C2×#1455873611yescharacteristic
491C22#1801195611yescharacteristic
492C22#1801195711yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—2982no—
499C4—2982no—
500C4—2982no—
501C4—5961no—
502C4—5961no—
503C4—5961no—
504C2—24no—
505C2—42no—
506C2—2984no—
507C2—5962no—
508C2C4×D4×D14911yescharacteristic
509C2C2×C4×C22⋊D14911yescharacteristic
510C2#2375009711yescharacteristic
511C2D4×C22⋊D14911yescharacteristic
512C2#2375026311yescharacteristic
513C2#2375027111yescharacteristic
514C2#2375030411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC2×C4×D4×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011879C2
hypercenterC2×C4×D4D149
hypocenterC149#2358
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D149C2semidirect
3. C22×#14558713C2semidirect
4. C2×C22⋊C4×D149C2semidirect
5. #23749525C2semidirect
6. #23749516C2semidirect
7. #23749515C2semidirect
8. #23749505C2semidirect
9. #23749504C2semidirect
10. #23749501C2semidirect
11. #23749498C2semidirect
12. #23749496C2semidirect
13. C22⋊C4×Dic149C2semidirect
14. C4×#14558713C2semidirect
15. C2×C4×D4×C149C2semidirect
22. #18011879C4semidirect
24. C2×#14558715C22semidirect
25. C2×#14558715C22semidirect
28. C2×C22⋊Dic149C22semidirect
29. C2×C22⋊Dic149C22semidirect
40. C2×C4×Dic149C22semidirect
41. C2×C4×Dic149C22semidirect
42. #18011818C22semidirect
43. #18011818C22semidirect
44. #18011818C22semidirect
45. #18011818C22semidirect
46. #18011818C22semidirect
47. #18011818C22semidirect
50. C23×C4×C149C22semidirect
52. C2×C4⋊C4×C149C22semidirect
54. C2×C22⋊C4×C149C22semidirect
55. C2×C42×C149C22semidirect
62. C23×D149C2×C4semidirect
69. C2×C22⋊D149C2×C4semidirect
70. C2×C22⋊D149C2×C4semidirect
91. C22⋊Dic149C2×C4semidirect
97. #14558713C2×C4semidirect
98. #14558713C2×C4semidirect
99. #14558713D4semidirect
106. C2×D4×C149C2×C4semidirect
120. C22⋊C4×C149D4semidirect
212. C22×C149C4×D4semidirect
234. C2×D149C4×D4semidirect
257. C149#2358semidirect
261. C2×C4×D4D149semidirect
282. C23×C4C2×D149semidirect
288. C2×C4⋊C4C2×D149semidirect
304. C2×C22⋊C4C2×D149semidirect
307. C2×C42C2×D149semidirect
333. C2×D4C4×D149semidirect
376. C22⋊C4C22⋊D149semidirect
485. C22C4×C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118792
C2×C4×C22⋊D1492
C22×#145587132
C2×C22⋊C4×D1492
#237495252
#237495162
#237495152
#237495052
#237495042
#237495012
#237494982
#237494962
C22⋊C4×Dic1492
C4×#145587132
C2×C4×D4×C1492
#2358149