Finite Group Databasebeta

← #34047673

Subgroups — #34047673

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×#18011871C211yesmaximal, characteristic, complemented
4C22×#14558713C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D149C211yesmaximal, characteristic, complemented
6#23749527C211yesmaximal, characteristic, complemented
7#23749517C211yesmaximal, characteristic, complemented
8#23749516C211yesmaximal, characteristic, complemented
9#23749504C211yesmaximal, characteristic, complemented
10#23749503C211yesmaximal, characteristic, complemented
11#23749503C211yesmaximal, characteristic, complemented
12#23749500C211yesmaximal, characteristic, complemented
13#23749499C211yesmaximal, characteristic, complemented
14C4×#14558713C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C149C211yesmaximal, characteristic, complemented
16C24×D149C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C22×D596C2211yescharacteristic
19C22×C22⋊D149C2211yescharacteristic
20C23×Dic149C2211yescharacteristic
21C22×C4×D149C2211yescharacteristic
22C22×C4×D149C2211yescharacteristic
23C22×C4×D149C2211yescharacteristic, complemented
24#18011881C418yescomplemented
25C4×D596—24no—
26#18011871—24no—
27C2×C4⋊Dic149C2211yescharacteristic, complemented
28C2×C4⋊Dic149C2211yescharacteristic, complemented
29C2×#14558715C2211yescharacteristic, complemented
30C2×C22⋊Dic149C2211yescharacteristic
31C2×#14558713—24no—
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×#14558713C2211yescharacteristic
37C2×#14558713C2211yescharacteristic
38C2×#14558713C2211yescharacteristic
39C2×#14558713C2211yescharacteristic
40C2×#14558713C2211yescharacteristic, complemented
41C2×#14558713C2211yescharacteristic, complemented
42C2×#14558713C2211yescharacteristic, complemented
43C22⋊C4×D149—24no—
44C2×C4×Dic149C2211yescharacteristic, complemented
45#18011818C2211yescharacteristic, complemented
46#18011818C2211yescharacteristic, complemented
47#18011818C2211yescharacteristic, complemented
48#18011818C2211yescharacteristic, complemented
49C23×C4×C149C2211yescharacteristic
50C2×C22⋊C4×C149C2211yescharacteristic
51C2×C22⋊C4×C149C2211yescharacteristic
52C2×C42×C149C2211yescharacteristic, complemented
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—41no—
69C2×D596—41no—
70C2×D596C2×C414yescomplemented
71C2×D596C2×C414yescomplemented
72C2×C22⋊D149—22no—
73C2×C22⋊D149—22no—
74C2×C22⋊D149C2×C414yescomplemented
75C22×Dic149—22no—
76C22×Dic149—22no—
77C22×Dic149—41no—
78C22×Dic149C2311yescharacteristic
79C22×Dic149C2311yescharacteristic
80C22×Dic149C2311yescharacteristic
81C22×Dic149C2311yescharacteristic
82C22×Dic149C2311yescharacteristic
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—41no—
90C2×C4×D149—41no—
91C2×C4×D149—41no—
92C4⋊Dic149—22no—
93C4⋊Dic149—41no—
94#14558715—22no—
95C22⋊Dic149—22no—
96#14558713—22no—
97#14558713—22no—
98#14558713—22no—
99#14558713—22no—
100#14558713—22no—
101#14558713—22no—
102#14558713—22no—
103#14558713—41no—
104#14558713C2×C414yescomplemented
105#14558713C2×C414yescomplemented
106#14558713D414yescomplemented
107C4×Dic149—22no—
108C24×C149C2311yescharacteristic
109C22×C4×C149—22no—
110C22×C4×C149—22no—
111C22×C4×C149—41no—
112C22×C4×C149C2311yescharacteristic
113C22×C4×C149C2311yescharacteristic
114C22×C4×C149C2311yescharacteristic
115C22×C4×C149C2311yescharacteristic
116C22×C4×C149C2311yescharacteristic
117C22×C4×C149C2311yescharacteristic
118C22⋊C4×C149C2×C414yescomplemented
119C22⋊C4×C149D414yescomplemented
120C42×C149—22no—
121C42×C149—41no—
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—21no—
134C22×D149—21no—
135C22×D149—21no—
136C22×D149—21no—
137C22×D149—21no—
138C22×D149—21no—
139C22×D149—28no—
140C22×D149—44no—
141C22×D149—44no—
142C22×D149—44no—
143C22×D149—44no—
144C22×D149—44no—
145C22×D149C22×C412yes—
146C22×D149C22×C412yes—
147C22×D149C22×C412yes—
148C22×D149C2×D412yes—
149C22×D149#4112yes—
150D596—28no—
151D596—44no—
152C22⋊D149—28no—
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×Dic149—21no—
166C2×Dic149—44no—
167C2×Dic149C22×C412yes—
168C2×Dic149C2×D412yes—
169C4×D149—44no—
170C4×D149—44no—
171C4×D149—44no—
172C23×C149—21no—
173C23×C149—21no—
174C23×C149—21no—
175C23×C149—21no—
176C23×C149C22×C412yes—
177C23×C149C2×D412yes—
178C23×C149#4112yes—
179C23×C149C2411yescharacteristic
180C2×C4×C149—21no—
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—44no—
194C2×C4×C149C22×C412yes—
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×C149C4×D414yescomplemented
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—416no—
226C2×D149—41no—
227C2×D149—41no—
228C2×D149—41no—
229C2×D149—41no—
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—22no—
240C4×C149—41no—
241Dic149—22no—
242Dic149—22no—
243Dic149—41no—
244Dic149—41no—
245Dic149—41no—
246C2×C149—24no—
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—42no—
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#388—1491no—
267#386—1491no—
268#386—1491no—
269#386—1491no—
270#385—1491no—
271#385—1491no—
272C4×C22⋊C4—1491no—
273C4×C22⋊C4D14911yescharacteristic, complemented
274C25—1491no—
275C22×D4—1491no—
276C22×D4—1491no—
277C22×D4—1491no—
278C23×C4—1491no—
279C23×C4—1491no—
280C23×C4—1491no—
281C23×C4—1491no—
282C23×C4C2×D14911yescharacteristic
283#120—1498no—
284C4×D4—2984no—
285C4×D4—2984no—
286C2×C4⋊C4—1491no—
287C2×C4⋊C4—1491no—
288C2×C4⋊C4—1491no—
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
305C2×C42—1491no—
306C2×C42C2×D14911yescharacteristic, complemented
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—1491no—
322C24—1494no—
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—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—2982no—
338C22×C4—2982no—
339C22×C4—2982no—
340C22×C4—2982no—
341C22×C4—2982no—
342C22×C4—2982no—
343C22×C4—2982no—
344C22×C4—2982no—
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—2982no—
361C4⋊C4—2982no—
362C4⋊C4—5961no—
363C22⋊C4—2982no—
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⋊C4C4×D14914yescomplemented
376C22⋊C4D59614yescomplemented
377C42—22no—
378C42—41no—
379C42—2982no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—2988no—
385C23—2981no—
386C23—2981no—
387C23—2981no—
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—2988no—
402C23—5964no—
403C23—5964no—
404C23—5964no—
405C23—5964no—
406C23—5964no—
407C23—1492no—
408C23—1492no—
409C23—1492no—
410C23—1492no—
411C23—1492no—
412C23C2×C4×D14912yes—
413C23C2×D59612yes—
414C23#1455873612yes—
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—44no—
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—5964no—
447C2×C4—5964no—
448C2×C4—5964no—
449C2×C4—5964no—
450C2×C4—1492no—
451C2×C4—1492no—
452C2×C4C2×C4×D14912yes—
453C2×C4C2×C4×D14912yes—
454C2×C4D4×D14912yes—
455C2×C4C2×D59612yes—
456C2×C4C2×D59612yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—2982no—
464C22—2982no—
465C22—2982no—
466C22—2982no—
467C22—2982no—
468C22—2982no—
469C22—2982no—
470C22—2982no—
471C22—2982no—
472C22—2982no—
473C22—2982no—
474C22—2982no—
475C22—59616no—
476C22—5961no—
477C22—5961no—
478C22—5961no—
479C22—5961no—
480C22—5961no—
481C22—5961no—
482C22—5961no—
483C22—5961no—
484C22—1494no—
485C22C4×D59614yescomplemented
486C22C22×C4×D14911yescharacteristic
487C22C2×D4×D14911yescharacteristic
488C22C22×D59611yescharacteristic
489C22#41×D14911yescharacteristic
490C22C2×#1455873611yescharacteristic
491C22#1801195611yescharacteristic
492C22#1801195711yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—2982no—
500C4—2982no—
501C4—5961no—
502C4—5961no—
503C4—5961no—
504C2—24no—
505C2—2984no—
506C2—5962no—
507C2—5962no—
508C2C4×D4×D14911yescharacteristic
509C2C2×C4×D59611yescharacteristic
510C2#2375009711yescharacteristic
511C2D4×D59611yescharacteristic
512C2#2375026511yescharacteristic
513C2#2375027011yescharacteristic
514C2#2375029911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC4×C22⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011881C2
hypercenterC4×C22⋊C4D149
hypocenterC149#2358
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D596C2semidirect
3. C2×#18011871C2semidirect
4. C22×#14558713C2semidirect
5. C2×C22⋊C4×D149C2semidirect
6. #23749527C2semidirect
7. #23749517C2semidirect
8. #23749516C2semidirect
9. #23749504C2semidirect
10. #23749503C2semidirect
11. #23749503C2semidirect
12. #23749500C2semidirect
13. #23749499C2semidirect
14. C4×#14558713C2semidirect
15. C4×C22⋊C4×C149C2semidirect
23. C22×C4×D149C22semidirect
24. #18011881C4semidirect
27. C2×C4⋊Dic149C22semidirect
28. C2×C4⋊Dic149C22semidirect
29. C2×#14558715C22semidirect
40. C2×#14558713C22semidirect
41. C2×#14558713C22semidirect
42. C2×#14558713C22semidirect
44. C2×C4×Dic149C22semidirect
45. #18011818C22semidirect
46. #18011818C22semidirect
47. #18011818C22semidirect
48. #18011818C22semidirect
52. C2×C42×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
118. C22⋊C4×C149C2×C4semidirect
119. C22⋊C4×C149D4semidirect
205. C22×C149C4×D4semidirect
234. C2×D149C4×D4semidirect
257. C149#2358semidirect
273. C4×C22⋊C4D149semidirect
306. C2×C42C2×D149semidirect
307. C2×C42C2×D149semidirect
312. #95C2×D149semidirect
313. #95C2×D149semidirect
375. C22⋊C4C4×D149semidirect
376. C22⋊C4D596semidirect
485. C22C4×D596semidirect

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×#180118712
C22×#145587132
C2×C22⋊C4×D1492
#237495272
#237495172
#237495162
#237495042
#237495032
#237495002
#237494992
C4×#145587132
C4×C22⋊C4×C1492
#2358149