Finite Group Databasebeta

← #34047670

Subgroups — #34047670

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×#18011880C211yesmaximal, characteristic
2C2×C4×C22⋊D149C211yesmaximal, characteristic, complemented
3C2×#18011871C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic149C211yesmaximal, characteristic, complemented
5#23749525C211yesmaximal, characteristic, complemented
6#23749519C211yesmaximal, characteristic, complemented
7#23749513C211yesmaximal, characteristic, complemented
8#23749504C211yesmaximal, characteristic, complemented
9#23749502C211yesmaximal, characteristic, complemented
10#23749501C211yesmaximal, characteristic, complemented
11#23749498C211yesmaximal, characteristic, complemented
12#23749497C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic149C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic149C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149C2211yescharacteristic
17C22×C22⋊D149C2211yescharacteristic
18C22×C22⋊D149C2211yescharacteristic
19C23×Dic149C2211yescharacteristic
20C23×Dic149C2211yescharacteristic
21C22×C4×D149C2211yescharacteristic, complemented
22#18011880C418yescomplemented
23C4×C22⋊D149—24no—
24#18011871—24no—
25C2×#14558715C2211yescharacteristic, complemented
26C2×#14558715C2211yescharacteristic, complemented
27C2×#14558715C2211yescharacteristic, complemented
28C2×C22⋊Dic149—24no—
29C2×C22⋊Dic149C2211yescharacteristic
30C2×C22⋊Dic149C2211yescharacteristic
31C2×C22⋊Dic149C2211yescharacteristic
32C2×C22⋊Dic149C2211yescharacteristic
33C2×C22⋊Dic149C2211yescharacteristic
34C2×C22⋊Dic149C2211yescharacteristic
35C2×C22⋊Dic149C2211yescharacteristic
36C2×#14558713C2211yescharacteristic, complemented
37C2×#14558713C2211yescharacteristic, complemented
38C2×#14558713C2211yescharacteristic, complemented
39C2×C4×Dic149C2211yescharacteristic, complemented
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
48C25×C149C2211yescharacteristic
49C23×C4×C149C2211yescharacteristic
50C23×C4×C149C2211yescharacteristic
51C2×C22⋊C4×C149—24no—
52C2×C22⋊C4×C149C2211yescharacteristic
53C2×C22⋊C4×C149C2211yescharacteristic
54C2×C22⋊C4×C149C2211yescharacteristic
55C2×C22⋊C4×C149C2211yescharacteristic
56C23×D149C2311yescharacteristic
57C2×C22⋊D149—22no—
58C2×C22⋊D149—22no—
59C2×C22⋊D149—22no—
60C2×C22⋊D149—22no—
61C2×C22⋊D149—41no—
62C2×C22⋊D149—41no—
63C2×C22⋊D149C2×C414yescomplemented
64C2×C22⋊D149C2×C414yescomplemented
65C2×C22⋊D149C2×C414yescomplemented
66C22×Dic149—22no—
67C22×Dic149—22no—
68C22×Dic149—22no—
69C22×Dic149—22no—
70C22×Dic149—41no—
71C22×Dic149—41no—
72C22×Dic149C2311yescharacteristic
73C22×Dic149C2311yescharacteristic
74C22×Dic149C2311yescharacteristic
75C22×Dic149C2311yescharacteristic
76C22×Dic149C2311yescharacteristic
77C22×Dic149C2311yescharacteristic
78C22×Dic149C2311yescharacteristic
79C2×C4×D149—22no—
80C2×C4×D149—22no—
81C2×C4×D149—41no—
82#14558715—22no—
83#14558715—22no—
84#14558715—41no—
85C22⋊Dic149—22no—
86C22⋊Dic149—22no—
87C22⋊Dic149—22no—
88C22⋊Dic149C2×C414yescomplemented
89C22⋊Dic149C2×C414yescomplemented
90C22⋊Dic149C2×C414yescomplemented
91C22⋊Dic149D414yescomplemented
92#14558713—22no—
93#14558713—22no—
94#14558713—41no—
95C4×Dic149—22no—
96C4×Dic149—22no—
97C4×Dic149—41no—
98C24×C149—22no—
99C24×C149—22no—
100C24×C149—22no—
101C24×C149—22no—
102C24×C149—41no—
103C24×C149—41no—
104C24×C149C2×C414yescomplemented
105C24×C149C2311yescharacteristic
106C24×C149C2311yescharacteristic
107C24×C149C2311yescharacteristic
108C22×C4×C149—22no—
109C22×C4×C149—22no—
110C22×C4×C149—22no—
111C22×C4×C149—22no—
112C22×C4×C149—41no—
113C22×C4×C149—41no—
114C22×C4×C149C2311yescharacteristic
115C22×C4×C149C2311yescharacteristic
116C22×C4×C149C2311yescharacteristic
117C22×C4×C149C2311yescharacteristic
118C22⋊C4×C149—22no—
119C22⋊C4×C149—22no—
120C22⋊C4×C149—22no—
121C22⋊C4×C149D414yescomplemented
122C22×D149—21no—
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—21no—
126C22×D149—21no—
127C22×D149—21no—
128C22×D149C22×C412yes—
129C22⋊D149—28no—
130C22⋊D149—28no—
131C22⋊D149—44no—
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×Dic149—21no—
147C2×Dic149—21no—
148C2×Dic149—44no—
149C2×Dic149—44no—
150C2×Dic149C22×C412yes—
151C2×Dic149C22×C412yes—
152C2×Dic149C22×C412yes—
153C2×Dic149C2×D412yes—
154C2×Dic149C2×D412yes—
155C4×D149—44no—
156C23×C149—21no—
157C23×C149—21no—
158C23×C149—21no—
159C23×C149—21no—
160C23×C149—21no—
161C23×C149—21no—
162C23×C149—21no—
163C23×C149—21no—
164C23×C149—28no—
165C23×C149—28no—
166C23×C149—21no—
167C23×C149—21no—
168C23×C149—21no—
169C23×C149—21no—
170C23×C149—21no—
171C23×C149—21no—
172C23×C149—44no—
173C23×C149—44no—
174C23×C149—44no—
175C23×C149—44no—
176C23×C149—44no—
177C23×C149C22×C412yes—
178C23×C149C22×C412yes—
179C23×C149C22×C412yes—
180C23×C149C2×D412yes—
181C23×C149C2×D412yes—
182C23×C149#4112yes—
183C23×C149#4112yes—
184C23×C149C2411yescharacteristic
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×C149—44no—
196C2×C4×C149—44no—
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—22no—
209C22×C149—22no—
210C22×C149—22no—
211C22×C149—22no—
212C22×C149—22no—
213C22×C149—22no—
214C22×C149—416no—
215C22×C149—41no—
216C22×C149—41no—
217C22×C149—41no—
218C22×C149—41no—
219C22×C149C4×D414yescomplemented
220C22×C149C4×D414yescomplemented
221C22×C149C23×C411yescharacteristic
222C22×C149C22×D411yescharacteristic
223C22×C149C22×D411yescharacteristic
224C22×C149C2×#4111yescharacteristic
225C22×C149C2×#4111yescharacteristic
226C22×C149H(5,𝔽2)11yescharacteristic
227C22×C149H(5,𝔽2)11yescharacteristic
228C2×D149—22no—
229C2×D149—22no—
230C2×D149—22no—
231C2×D149—41no—
232C2×D149—41no—
233C2×D149—41no—
234C2×D149—41no—
235C4×C149—22no—
236C4×C149—22no—
237C4×C149—41no—
238C4×C149—41no—
239Dic149—22no—
240Dic149—22no—
241Dic149—22no—
242Dic149—22no—
243Dic149—22no—
244Dic149—41no—
245Dic149—41no—
246C2×C149—24no—
247C2×C149—24no—
248C2×C149—42no—
249C2×C149C2×C4×D411yescharacteristic
250C2×C149C2×C4×D411yescharacteristic
251C2×C149#51811yescharacteristic
252C2×C149D4211yescharacteristic
253C2×C149#54611yescharacteristic
254C2×C149#54611yescharacteristic
255C2×C149#55111yescharacteristic
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⋊C4D14911yescharacteristic, complemented
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—
274C25C2×D14911yescharacteristic
275C22×D4—1491no—
276C22×D4—1491no—
277C22×D4—1491no—
278C23×C4—1491no—
279C23×C4—1491no—
280C23×C4—1491no—
281C23×C4C2×D14911yescharacteristic
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—24no—
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⋊C4C2×D14911yescharacteristic
302C2×C22⋊C4C2×D14911yescharacteristic
303C2×C22⋊C4C2×D14911yescharacteristic
304C2×C22⋊C4C2×D14911yescharacteristic
305C2×C42—1491no—
306C2×C42—1491no—
307C2×C42—1491no—
308#95—1491no—
309#95—1491no—
310#95—1491no—
311#95—1491no—
312#95—1491no—
313#95—1491no—
314C24—22no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—1491no—
321C24C4×D14914yescomplemented
322C24C22×D14911yescharacteristic
323C24C22×D14911yescharacteristic
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—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×C4—1491no—
356C22×C4C22×D14911yescharacteristic
357C22×C4C22×D14911yescharacteristic
358C22×C4C22×D14911yescharacteristic
359C22×C4C22×D14911yescharacteristic
360C4⋊C4—2982no—
361C4⋊C4—2982no—
362C4⋊C4—5961no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
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—2982no—
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—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—28no—
395C23—28no—
396C23—44no—
397C23—44no—
398C23—44no—
399C23—44no—
400C23—44no—
401C23—2981no—
402C23—2981no—
403C23—2981no—
404C23—2981no—
405C23—2981no—
406C23—2981no—
407C23—1492no—
408C23C2×C4×D14912yes—
409C23C2×C4×D14912yes—
410C23C2×C4×D14912yes—
411C23D4×D14912yes—
412C23C2×C22⋊D14912yes—
413C23#1455873512yes—
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—44no—
430C2×C4—44no—
431C2×C4—2981no—
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×C4—1492no—
454C2×C4—1492no—
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—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—416no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—2982no—
478C22—2982no—
479C22—2982no—
480C22—5961no—
481C22—5961no—
482C22—5961no—
483C22—5961no—
484C22#1801187114yescomplemented
485C22C4×C22⋊D14914yescomplemented
486C22C22×C4×D14911yescharacteristic
487C22C2×D4×D14911yescharacteristic
488C22C22×C22⋊D14911yescharacteristic
489C22C2×#1455873511yescharacteristic
490C22C2×#1455873611yescharacteristic
491C22#1801195611yescharacteristic
492C22#1801195611yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—2982no—
498C4—2982no—
499C4—2982no—
500C4—2982no—
501C4—2982no—
502C4—5961no—
503C4—5961no—
504C2—24no—
505C2—24no—
506C2—42no—
507C2—5962no—
508C2C2×#1801187111yescharacteristic
509C2C2×C4×C22⋊D14911yescharacteristic
510C2#2375009811yescharacteristic
511C2D4×C22⋊D14911yescharacteristic
512C2#2375026511yescharacteristic
513C2#2375026911yescharacteristic
514C2#2375030111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC22×C22⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011880C2
hypercenterC22×C22⋊C4D149
hypocenterC149#2358
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D149C2semidirect
3. C2×#18011871C2semidirect
4. C22×C22⋊Dic149C2semidirect
5. #23749525C2semidirect
6. #23749519C2semidirect
7. #23749513C2semidirect
8. #23749504C2semidirect
9. #23749502C2semidirect
10. #23749501C2semidirect
11. #23749498C2semidirect
12. #23749497C2semidirect
13. C22⋊C4×Dic149C2semidirect
14. C4×C22⋊Dic149C2semidirect
15. C22×C22⋊C4×C149C2semidirect
21. C22×C4×D149C22semidirect
22. #18011880C4semidirect
25. C2×#14558715C22semidirect
26. C2×#14558715C22semidirect
27. C2×#14558715C22semidirect
36. C2×#14558713C22semidirect
37. C2×#14558713C22semidirect
38. C2×#14558713C22semidirect
39. C2×C4×Dic149C22semidirect
40. C2×C4×Dic149C22semidirect
41. C2×C4×Dic149C22semidirect
42. #18011818C22semidirect
43. #18011818C22semidirect
44. #18011818C22semidirect
45. #18011818C22semidirect
46. #18011818C22semidirect
47. #18011818C22semidirect
63. C2×C22⋊D149C2×C4semidirect
64. C2×C22⋊D149C2×C4semidirect
65. C2×C22⋊D149C2×C4semidirect
88. C22⋊Dic149C2×C4semidirect
89. C22⋊Dic149C2×C4semidirect
90. C22⋊Dic149C2×C4semidirect
91. C22⋊Dic149D4semidirect
104. C24×C149C2×C4semidirect
121. C22⋊C4×C149D4semidirect
219. C22×C149C4×D4semidirect
220. C22×C149C4×D4semidirect
257. C149#2358semidirect
263. C22×C22⋊C4D149semidirect
321. C24C4×D149semidirect
376. C22⋊C4C22⋊D149semidirect
484. C22#18011871semidirect
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×#180118802
C2×C4×C22⋊D1492
C2×#180118712
C22×C22⋊Dic1492
#237495252
#237495192
#237495132
#237495042
#237495022
#237495012
#237494982
#237494972
C22⋊C4×Dic1492
C4×C22⋊Dic1492
C22×C22⋊C4×C1492
#2358149