Finite Group Databasebeta

← #34047831

Subgroups — #34047831

Order 19072.

688 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011881C211yesmaximal, characteristic
2#23749527C211yesmaximal, characteristic, complemented
3#23749526C211yesmaximal, characteristic, complemented
4#23749525C211yesmaximal, characteristic, complemented
5#23749518C211yesmaximal, characteristic, complemented
6#23749517C211yesmaximal, characteristic, complemented
7#23749516C211yesmaximal, characteristic, complemented
8#23749515C211yesmaximal, characteristic, complemented
9#23749514C211yesmaximal, characteristic, complemented
10#23749503C211yesmaximal, characteristic, complemented
11#23749503C211yesmaximal, characteristic, complemented
12#23749501C211yesmaximal, characteristic, complemented
13#23749480C211yesmaximal, characteristic, complemented
14#23749480C211yesmaximal, characteristic, complemented
15#388×C149C211yesmaximal, characteristic, complemented
16C24×D149C2211yescharacteristic
17C22×D596C2211yescharacteristic
18C22×D596C2211yescharacteristic
19C22×C22⋊D149C2211yescharacteristic
20C22×C4×D149C2211yescharacteristic, complemented
21#18011881C418yescomplemented
22C2×C4⋊Dic149C2211yescharacteristic, complemented
23C2×#14558715C2211yescharacteristic, complemented
24C2×C22⋊Dic149C2211yescharacteristic
25C2×C22⋊Dic149C2211yescharacteristic
26C2×#14558713C2211yescharacteristic
27C2×#14558713C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×#14558713C2211yescharacteristic, complemented
37C2×#14558713C2211yescharacteristic, complemented
38C2×#14558713C2211yescharacteristic, complemented
39C2×C4×Dic149C2211yescharacteristic, complemented
40C2×C4×Dic149C2211yescharacteristic, complemented
41#18011818C2211yescharacteristic, complemented
42#18011818C2211yescharacteristic, complemented
43#18011818C2211yescharacteristic, complemented
44#18011818C2211yescharacteristic, complemented
45C2×C4⋊C4×C149C2211yescharacteristic, complemented
46C2×C22⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C42×C149C2211yescharacteristic, complemented
50#95×C149C2211yescharacteristic, complemented
51#95×C149C2211yescharacteristic, complemented
52C23×D149—41no—
53C23×D149—41no—
54C23×D149—41no—
55C23×D149—41no—
56C23×D149—41no—
57C23×D149—41no—
58C23×D149C2×C414yescomplemented
59C23×D149C2311yescharacteristic
60C23×D149C2311yescharacteristic
61C23×D149C2311yescharacteristic
62C2×D596—41no—
63C2×D596—41no—
64C2×D596—41no—
65C2×D596—41no—
66C2×D596C2×C414yes—
67C2×D596C2×C414yes—
68C2×C22⋊D149—41no—
69C2×C22⋊D149—41no—
70C2×C22⋊D149C2×C414yes—
71C22×Dic149C2311yescharacteristic
72C22×Dic149C2311yescharacteristic
73C22×Dic149C2311yescharacteristic
74C22×Dic149C2311yescharacteristic
75C22×Dic149C2311yescharacteristic
76C2×C4×D149—41no—
77C2×C4×D149—41no—
78C2×C4×D149—41no—
79C4⋊Dic149—41no—
80#14558715—41no—
81C22⋊Dic149—41no—
82C22⋊Dic149—41no—
83#14558713—41no—
84#14558713—41no—
85#14558713—41no—
86#14558713—41no—
87#14558713—41no—
88#14558713—41no—
89#14558713—41no—
90#14558713—41no—
91#14558713—41no—
92#14558713—41no—
93#14558713—41no—
94#14558713C2×C414yescomplemented
95#14558713C2×C414yescomplemented
96C4×Dic149—41no—
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—41no—
106C22⋊C4×C149—41no—
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—21no—
119C22×D149—21no—
120C22×D149—21no—
121C22×D149—21no—
122C22×D149—21no—
123C22×D149—21no—
124C22×D149—21no—
125C22×D149—21no—
126C22×D149—21no—
127C22×D149—21no—
128C22×D149—44no—
129C22×D149—44no—
130C22×D149—44no—
131C22×D149—44no—
132C22×D149—44no—
133C22×D149—44no—
134C22×D149—44no—
135C22×D149C22×C412yes—
136C22×D149C22×C412yes—
137C22×D149C22×C412yes—
138D596—44no—
139D596—44no—
140C22⋊D149—44no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149—21no—
144C2×Dic149—21no—
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×Dic149C22×C412yes—
156C4×D149—44no—
157C23×C149—21no—
158C23×C149—21no—
159C23×C149—21no—
160C23×C149—21no—
161C23×C149—21no—
162C23×C149—21no—
163C23×C149C22×C412yes—
164C23×C149C2411yescharacteristic
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×C149—21no—
177C2×C4×C149—21no—
178C2×C4×C149—21no—
179C2×C4×C149—21no—
180C2×C4×C149—21no—
181C2×C4×C149C22×C412yes—
182C2×C4×C149C22×C412yes—
183C22×C149—22no—
184C22×C149—22no—
185C22×C149—22no—
186C22×C149—41no—
187C22×C149—41no—
188C22×C149—41no—
189C22×C149—41no—
190C22×C149C23×C411yescharacteristic
191C22×C149H(5,𝔽2)11yescharacteristic
192C22×C149H(5,𝔽2)11yescharacteristic
193C22×C149H(5,𝔽2)11yescharacteristic
194C22×C149H(5,𝔽2)11yescharacteristic
195C22×C149H(5,𝔽2)11yescharacteristic
196C22×C149H(5,𝔽2)11yescharacteristic
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—22no—
206C2×D149—416no—
207C2×D149—41no—
208C2×D149—41no—
209C2×D149—41no—
210C2×D149—41no—
211C2×D149—41no—
212C2×D149—41no—
213C2×D149—41no—
214C2×D149—41no—
215C2×D149—41no—
216C2×D149—41no—
217C2×D149—41no—
218C2×D149—41no—
219C4×C149—22no—
220C4×C149—22no—
221C4×C149—41no—
222C4×C149—41no—
223C4×C149—41no—
224C4×C149—41no—
225Dic149—22no—
226Dic149—41no—
227Dic149—41no—
228Dic149—41no—
229Dic149—41no—
230C2×C149—42no—
231C2×C149#51811yescharacteristic
232C2×C149#51811yescharacteristic
233C2×C149#51811yescharacteristic
234C2×C149#56011yescharacteristic
235C2×C149#56011yescharacteristic
236C2×C149#56011yescharacteristic
237C2×C149H(3,𝔽4)11yescharacteristic
238D149—42no—
239D149—42no—
240D149—42no—
241C149#237511yescharacteristic, complemented, Sylow
242#2375—1491nomaximal, Sylow
243C2×#120—1491no—
244#390—1491no—
245#390—1491no—
246#390—1491no—
247#388—1491no—
248#388—1491no—
249#388—1491no—
250#388—1491no—
251#388—1491no—
252#388D14911yescharacteristic, complemented
253#386—1491no—
254#386—1491no—
255#386—1491no—
256#379—1491no—
257#379—1491no—
258C25—1491no—
259C22×D4—1491no—
260C22×D4—1491no—
261C22×D4—1491no—
262C23×C4—1491no—
263#120—1498no—
264C2×C4⋊C4—1491no—
265C2×C4⋊C4—1491no—
266C2×C4⋊C4C2×D14911yescharacteristic, complemented
267C2×C22⋊C4—1491no—
268C2×C22⋊C4—1491no—
269C2×C22⋊C4—1491no—
270C2×C22⋊C4—1491no—
271C2×C22⋊C4—1491no—
272C2×C22⋊C4—1491no—
273C2×C22⋊C4—1491no—
274C2×C22⋊C4—1491no—
275C2×C22⋊C4—1491no—
276C2×C22⋊C4—1491no—
277C2×C22⋊C4—1491no—
278C2×C22⋊C4—1491no—
279C2×C22⋊C4—1491no—
280C2×C22⋊C4—1491no—
281C2×C22⋊C4—1491no—
282C2×C22⋊C4C2×D14911yescharacteristic
283C2×C22⋊C4C2×D14911yescharacteristic
284C2×C22⋊C4C2×D14911yescharacteristic
285C2×C42—1491no—
286C2×C42—1491no—
287C2×C42C2×D14911yescharacteristic, complemented
288#95—1491no—
289#95—1491no—
290#95—1491no—
291#95—1491no—
292#95C2×D14911yescharacteristic, complemented
293#95C2×D14911yescharacteristic, complemented
294C24—5961no—
295C24—5961no—
296C24—5961no—
297C24—5961no—
298C24—5961no—
299C24—5961no—
300C24—1491no—
301C24—1491no—
302C24—1491no—
303C24—1494no—
304C24C22×D14911yescharacteristic
305C2×D4—5961no—
306C2×D4—5961no—
307C2×D4—5961no—
308C2×D4—5961no—
309C2×D4—5961no—
310C2×D4—5961no—
311C2×D4—1494no—
312C2×D4—1494no—
313C2×D4—1494no—
314C22×C4—5961no—
315C22×C4—5961no—
316C22×C4—5961no—
317C22×C4—1491no—
318C22×C4—1491no—
319C22×C4—1491no—
320C22×C4—1491no—
321C22×C4—1491no—
322C22×C4C22×D14911yescharacteristic
323C22×C4C22×D14911yescharacteristic
324C22×C4C22×D14911yescharacteristic
325C22×C4C22×D14911yescharacteristic
326C22×C4C22×D14911yescharacteristic
327C22×C4C22×D14911yescharacteristic
328C4⋊C4—41no—
329C4⋊C4—5961no—
330C4⋊C4—5961no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—5961no—
334C22⋊C4—5961no—
335C22⋊C4—5961no—
336C22⋊C4—5961no—
337C22⋊C4—5961no—
338C22⋊C4—5961no—
339C22⋊C4—5961no—
340C22⋊C4—5961no—
341C22⋊C4—5961no—
342C22⋊C4—5961no—
343C22⋊C4—5961no—
344C22⋊C4—5961no—
345C22⋊C4—5961no—
346C22⋊C4—1494no—
347C22⋊C4—1494no—
348C22⋊C4C4×D14914yescomplemented
349C42—41no—
350C42—5961no—
351C42—5961no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—2981no—
359C23—2981no—
360C23—2981no—
361C23—2981no—
362C23—2981no—
363C23—2981no—
364C23—2981no—
365C23—2981no—
366C23—2981no—
367C23—2981no—
368C23—2981no—
369C23—2981no—
370C23—2981no—
371C23—2981no—
372C23—2981no—
373C23—2981no—
374C23—2981no—
375C23—2981no—
376C23—5964no—
377C23—5964no—
378C23—5964no—
379C23—5964no—
380C23—5964no—
381C23—5964no—
382C23—5964no—
383C23—1492no—
384C23—1492no—
385C23—1492no—
386C23C2×C4×D14912yes—
387C23C23×D14911yescharacteristic
388D4—5964no—
389D4—5964no—
390D4—5964no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—2981no—
408C2×C4—2981no—
409C2×C4—2981no—
410C2×C4—2981no—
411C2×C4—2981no—
412C2×C4—2981no—
413C2×C4—2981no—
414C2×C4—2981no—
415C2×C4—2981no—
416C2×C4—2981no—
417C2×C4—2981no—
418C2×C4—2981no—
419C2×C4—2981no—
420C2×C4—2981no—
421C2×C4—5964no—
422C2×C4—1492no—
423C2×C4C2×C4×D14912yes—
424C2×C4C2×C4×D14912yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—2982no—
433C22—2982no—
434C22—2982no—
435C22—2982no—
436C22—2982no—
437C22—2982no—
438C22—2982no—
439C22—2982no—
440C22—2982no—
441C22—59616no—
442C22—5961no—
443C22—5961no—
444C22—5961no—
445C22—5961no—
446C22—5961no—
447C22—5961no—
448C22—5961no—
449C22—5961no—
450C22—5961no—
451C22—5961no—
452C22—5961no—
453C22—5961no—
454C22C22×C4×D14911yescharacteristic
455C22#1801195611yescharacteristic
456C22#1801195611yescharacteristic
457C22#1801195711yescharacteristic
458C22#1801195711yescharacteristic
459C22#1801195711yescharacteristic
460C22#1801195711yescharacteristic
461C4—22no—
462C4—22no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—2982no—
468C4—5961no—
469C4—5961no—
470C4—5961no—
471C4—5961no—
472C2—42no—
473C2—5962no—
474C2—5962no—
475C2—5962no—
476C2#2375009711yescharacteristic
477C2#2375009711yescharacteristic
478C2#2375009911yescharacteristic
479C2#2375036311yescharacteristic
480C2#2375036511yescharacteristic
481C2#2375036611yescharacteristic
482C2#2375036711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#388×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011881C2
hypercenter#388D149
hypocenterC149#2375
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #23749527C2semidirect
3. #23749526C2semidirect
4. #23749525C2semidirect
5. #23749518C2semidirect
6. #23749517C2semidirect
7. #23749516C2semidirect
8. #23749515C2semidirect
9. #23749514C2semidirect
10. #23749503C2semidirect
11. #23749503C2semidirect
12. #23749501C2semidirect
13. #23749480C2semidirect
14. #23749480C2semidirect
15. #388×C149C2semidirect
20. C22×C4×D149C22semidirect
21. #18011881C4semidirect
22. C2×C4⋊Dic149C22semidirect
23. C2×#14558715C22semidirect
36. C2×#14558713C22semidirect
37. C2×#14558713C22semidirect
38. C2×#14558713C22semidirect
39. C2×C4×Dic149C22semidirect
40. C2×C4×Dic149C22semidirect
41. #18011818C22semidirect
42. #18011818C22semidirect
43. #18011818C22semidirect
44. #18011818C22semidirect
45. C2×C4⋊C4×C149C22semidirect
49. C2×C42×C149C22semidirect
50. #95×C149C22semidirect
51. #95×C149C22semidirect
58. C23×D149C2×C4semidirect
94. #14558713C2×C4semidirect
95. #14558713C2×C4semidirect
108. C22⋊C4×C149C2×C4semidirect
241. C149#2375semidirect
252. #388D149semidirect
266. C2×C4⋊C4C2×D149semidirect
287. C2×C42C2×D149semidirect
292. #95C2×D149semidirect
293. #95C2×D149semidirect
348. 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
#237495272
#237495262
#237495252
#237495182
#237495172
#237495162
#237495152
#237495142
#237495032
#237495012
#237494802
#388×C1492
#2375149