Finite Group Databasebeta

← C2×#23750225 #34058046

Subgroups — C2×#23750225 #34058046

Order 19072.

1260 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750225C2116yesmaximal, direct product factor
2C2×#18011907C211yesmaximal, characteristic, complemented
3C2×#18011901C211yesmaximal, characteristic, complemented
4C2×#18011896C211yesmaximal, characteristic, complemented
5C2×#18011894C211yesmaximal, characteristic, complemented
6C2×#18011893C211yesmaximal, characteristic, complemented
7C2×#18011892C211yesmaximal, characteristic, complemented
8C2×#18011884C211yesmaximal, characteristic, complemented
9C2×#18011883C211yesmaximal, characteristic, complemented
10C2×#18011883C211yesmaximal, characteristic, complemented
11C2×#18011883C211yesmaximal, characteristic, complemented
12C2×#18011882C211yesmaximal, characteristic, complemented
13C2×C4×C22⋊D149C211yesmaximal, characteristic, complemented
14C2×#18011871C211yesmaximal, characteristic, complemented
15C2×#18011867C211yesmaximal, characteristic, complemented
16C2×#121×C149C211yesmaximal, characteristic, complemented
17C22×D596C2211yescharacteristic
18C22×C22⋊D149C2211yescharacteristic
19C22×C22⋊D149C2211yescharacteristic
20C22×C22⋊D149C2211yescharacteristic
21C22×C22⋊D149C2211yescharacteristic
22C22×C22⋊D149C2211yescharacteristic
23C22×C22⋊D149C2211yescharacteristic
24C23×Dic149C2211yescharacteristic
25C23×Dic149C2211yescharacteristic
26C22×C4×D149C2211yescharacteristic
27C22×C4×D149C2211yescharacteristic
28#18011907C2218yescomplemented
29#18011901C2218yescomplemented
30#18011896C2218yescomplemented
31#18011894C2218yescomplemented
32#18011893C2218yescomplemented
33#18011892C2218yescomplemented
34#18011884C2218yescomplemented
35#18011883C2218yescomplemented
36#18011883C2218yescomplemented
37#18011883C2218yescomplemented
38#18011882C2218yescomplemented
39C4×C22⋊D149C2218yescomplemented
40#18011871C2218yescomplemented
41#18011867C2218yescomplemented
42C2×C4⋊Dic149C2211yescharacteristic
43C2×#14558715C2211yescharacteristic
44C2×#14558715C2211yescharacteristic
45C2×#14558715C2211yescharacteristic
46C2×#14558715C2211yescharacteristic
47C2×#14558715C2211yescharacteristic
48C2×#14558715C2211yescharacteristic
49C2×C22⋊Dic149C2211yescharacteristic
50C2×C22⋊Dic149C2211yescharacteristic
51C2×C22⋊Dic149C2211yescharacteristic
52C2×C22⋊Dic149C2211yescharacteristic
53C2×#14558713C2211yescharacteristic
54C2×#14558713C2211yescharacteristic
55C2×#14558713C2211yescharacteristic
56C2×#14558713C2211yescharacteristic
57C2×C4×Dic149C2211yescharacteristic
58C2×C4×Dic149C2211yescharacteristic
59C22×D4×C149C2211yescharacteristic
60C22×D4×C149C2211yescharacteristic
61C22×D4×C149C2211yescharacteristic
62C23×C4×C149C2211yescharacteristic
63#121×C149C2218yescomplemented
64C2×C4⋊C4×C149C2211yescharacteristic
65C2×C22⋊C4×C149C2211yescharacteristic
66C2×C22⋊C4×C149C2211yescharacteristic
67C23×D149C2311yescharacteristic
68C23×D149C2311yescharacteristic
69C2×D596—42no—
70C2×D596C2314yes—
71C2×C22⋊D149—24no—
72C2×C22⋊D149—24no—
73C2×C22⋊D149—42no—
74C2×C22⋊D149—42no—
75C2×C22⋊D149—42no—
76C2×C22⋊D149—42no—
77C2×C22⋊D149C2314yes—
78C2×C22⋊D149C2314yes—
79C2×C22⋊D149C2314yes—
80C2×C22⋊D149C2314yes—
81C2×C22⋊D149C2314yes—
82C2×C22⋊D149C2314yes—
83C22×Dic149—24no—
84C22×Dic149—42no—
85C22×Dic149C2311yescharacteristic
86C22×Dic149C2311yescharacteristic
87C22×Dic149C2311yescharacteristic
88C22×Dic149C2311yescharacteristic
89C22×Dic149C2314yes—
90C22×Dic149C2311yescharacteristic
91C22×Dic149C2314yes—
92C22×Dic149C2311yescharacteristic
93C2×C4×D149—42no—
94C2×C4×D149—42no—
95C2×C4×D149C2314yes—
96C2×C4×D149C2314yes—
97C4⋊Dic149C2314yes—
98#14558715C2314yes—
99#14558715C2314yes—
100#14558715C2314yes—
101#14558715C2314yes—
102#14558715C2314yes—
103#14558715C2314yes—
104C22⋊Dic149C2314yes—
105C22⋊Dic149C2314yes—
106C22⋊Dic149C2314yes—
107C22⋊Dic149C2314yes—
108#14558713C2314yes—
109#14558713C2314yes—
110#14558713C2314yes—
111#14558713C2314yes—
112C4×Dic149C2314yes—
113C4×Dic149C2314yes—
114C24×C149C2311yescharacteristic
115C24×C149C2311yescharacteristic
116C24×C149C2311yescharacteristic
117C2×D4×C149—42no—
118C2×D4×C149—42no—
119C2×D4×C149—42no—
120C2×D4×C149C2314yes—
121C2×D4×C149C2314yes—
122C2×D4×C149C2314yes—
123C22×C4×C149—42no—
124C22×C4×C149C2311yescharacteristic
125C22×C4×C149C2311yescharacteristic
126C22×C4×C149C2311yescharacteristic
127C22×C4×C149C2311yescharacteristic
128C22×C4×C149C2314yes—
129C4⋊C4×C149C2314yes—
130C22⋊C4×C149C2314yes—
131C22⋊C4×C149C2314yes—
132C22×D149—22no—
133C22×D149—22no—
134C22×D149—22no—
135C22×D149—22no—
136C22×D149—22no—
137C22×D149—22no—
138C22×D149C2412yes—
139C22×D149C2412yes—
140D596—44no—
141C22⋊D149—28no—
142C22⋊D149—28no—
143C22⋊D149—44no—
144C22⋊D149—44no—
145C22⋊D149—44no—
146C22⋊D149—44no—
147C2×Dic149—22no—
148C2×Dic149—22no—
149C2×Dic149—22no—
150C2×Dic149—22no—
151C2×Dic149—22no—
152C2×Dic149—28no—
153C2×Dic149—44no—
154C2×Dic149#4114yes—
155C2×Dic149C2412yes—
156C2×Dic149C2412yes—
157C2×Dic149C2412yes—
158C2×Dic149C2412yes—
159C2×Dic149C2412yes—
160C2×Dic149C2412yes—
161C4×D149—44no—
162C4×D149—44no—
163C23×C149—22no—
164C23×C149—22no—
165C23×C149—22no—
166C23×C149—22no—
167C23×C149—22no—
168C23×C149—22no—
169C23×C149—22no—
170C23×C149—22no—
171C23×C149—22no—
172C23×C149C2412yes—
173C23×C149C2412yes—
174C23×C149C2412yes—
175C23×C149C2411yescharacteristic
176D4×C149—44no—
177D4×C149—44no—
178D4×C149—44no—
179C2×C4×C149—22no—
180C2×C4×C149—22no—
181C2×C4×C149—22no—
182C2×C4×C149—22no—
183C2×C4×C149—44no—
184C2×C4×C149C2412yes—
185C2×C4×C149C2412yes—
186C2×C4×C149C2412yes—
187C2×C4×C149C2412yes—
188C22×C149—22no—
189C22×C149—22no—
190C22×C149—22no—
191C22×C149—22no—
192C22×C149—22no—
193C22×C149—22no—
194C22×C149—22no—
195C22×C149—22no—
196C22×C149—22no—
197C22×C149—44no—
198C22×C149—44no—
199C22×C149—44no—
200C22×C149C2×#4112yes—
201C22×C149H(5,𝔽2)12yes—
202C22×C149H(5,𝔽2)12yes—
203C22×C149C2511yescharacteristic
204C2×D149—22no—
205C2×D149—22no—
206C2×D149—22no—
207C2×D149—22no—
208C2×D149—22no—
209C2×D149—22no—
210C2×D149—44no—
211C2×D149—44no—
212C4×C149—22no—
213C4×C149—22no—
214C4×C149—22no—
215C4×C149—22no—
216Dic149—22no—
217Dic149—22no—
218Dic149—22no—
219Dic149—22no—
220Dic149—22no—
221Dic149C2×#4114yes—
222C2×C149—42no—
223C2×C149—42no—
224C2×C149—42no—
225C2×C149#54014yescomplemented
226C2×C149C22×#4111yescharacteristic
227C2×C149C2×H(5,𝔽2)11yescharacteristic
228C2×C149C2×H(5,𝔽2)11yescharacteristic
229D149—42no—
230D149—42no—
231C149C2×#54011yescharacteristic, complemented, Sylow
232C2×#540—1491nomaximal, Sylow
233#540—14916no—
234C2×#127—1491no—
235C2×#125—1491no—
236C2×#123—1491no—
237C2×#123—1491no—
238C2×#123—1491no—
239C2×#123—1491no—
240C2×#121—1491no—
241C2×#121—1491no—
242C2×#121—1491no—
243C2×#121—1491no—
244C2×#121—1491no—
245C2×#121D14911yescharacteristic, complemented
246C2×C4×D4—1491no—
247C2×C4×D4—1491no—
248C2×#117—1491no—
249C22×D4—1491no—
250C22×D4—1491no—
251C22×D4—1491no—
252C22×D4—1491no—
253C22×D4—1491no—
254C22×D4—1491no—
255C22×D4—1491no—
256C22×D4C2×D14911yescharacteristic
257C22×D4C2×D14911yescharacteristic
258C22×D4C2×D14911yescharacteristic
259C23×C4—1491no—
260C23×C4—1491no—
261C23×C4—1491no—
262C23×C4—1491no—
263C23×C4C2×D14911yescharacteristic
264#127—1498no—
265#125—1498no—
266#123—1498no—
267#123—1498no—
268#123—1498no—
269#123—1498no—
270#121—1498no—
271#121—1498no—
272#121—1498no—
273#121—1498no—
274#121—1498no—
275#121C2×D14918yescomplemented
276C4×D4—1498no—
277C4×D4—1498no—
278#117—1498no—
279C2×C4⋊C4—1491no—
280C2×C4⋊C4—1491no—
281C2×C4⋊C4—1491no—
282C2×C4⋊C4—1491no—
283C2×C4⋊C4—1491no—
284C2×C4⋊C4—1491no—
285C2×C4⋊C4—1491no—
286C2×C4⋊C4C2×D14911yescharacteristic
287C2×C22⋊C4—1491no—
288C2×C22⋊C4—1491no—
289C2×C22⋊C4—1491no—
290C2×C22⋊C4—1491no—
291C2×C22⋊C4—1491no—
292C2×C22⋊C4—1491no—
293C2×C22⋊C4—1491no—
294C2×C22⋊C4—1491no—
295C2×C22⋊C4C2×D14911yescharacteristic
296C2×C22⋊C4C2×D14911yescharacteristic
297C2×C42—1491no—
298C2×C42—1491no—
299C24—1491no—
300C24—1491no—
301C24C22×D14911yescharacteristic
302C24C22×D14911yescharacteristic
303C24C22×D14911yescharacteristic
304C2×D4—42no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—2984no—
308C2×D4—2984no—
309C2×D4—5962no—
310C2×D4—5962no—
311C2×D4—5962no—
312C2×D4—5962no—
313C2×D4—5962no—
314C2×D4—1494no—
315C2×D4—1494no—
316C2×D4—1494no—
317C2×D4—1494no—
318C2×D4—1494no—
319C2×D4—1494no—
320C2×D4—1494no—
321C2×D4C22×D14914yes—
322C2×D4C22×D14914yes—
323C2×D4C22×D14914yes—
324C22×C4—42no—
325C22×C4—2984no—
326C22×C4—5962no—
327C22×C4—5962no—
328C22×C4—5962no—
329C22×C4—1494no—
330C22×C4—1491no—
331C22×C4—1491no—
332C22×C4—1491no—
333C22×C4—1491no—
334C22×C4—1491no—
335C22×C4—1494no—
336C22×C4—1494no—
337C22×C4—1494no—
338C22×C4—1491no—
339C22×C4C22×D14911yescharacteristic
340C22×C4C22×D14911yescharacteristic
341C22×C4C22×D14911yescharacteristic
342C22×C4C22×D14911yescharacteristic
343C22×C4C22×D14914yes—
344C4⋊C4—1494no—
345C4⋊C4—1494no—
346C4⋊C4—1494no—
347C4⋊C4—1494no—
348C4⋊C4—1494no—
349C4⋊C4—1494no—
350C4⋊C4—1494no—
351C4⋊C4C22×D14914yes—
352C22⋊C4—1494no—
353C22⋊C4—1494no—
354C22⋊C4—1494no—
355C22⋊C4—1494no—
356C22⋊C4—1494no—
357C22⋊C4—1494no—
358C22⋊C4—1494no—
359C22⋊C4—1494no—
360C22⋊C4C22×D14914yes—
361C22⋊C4C22×D14914yes—
362C42—1494no—
363C42—1494no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—22no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—2982no—
374C23—2982no—
375C23—2982no—
376C23—2982no—
377C23—2982no—
378C23—2982no—
379C23—1492no—
380C23—1492no—
381C23C23×D14912yes—
382C23C23×D14912yes—
383C23C23×D14912yes—
384C23C23×D14911yescharacteristic
385D4—44no—
386D4—44no—
387D4—44no—
388D4—2988no—
389D4—2988no—
390D4—5964no—
391D4—5964no—
392D4—5964no—
393D4—5964no—
394D4—5964no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—44no—
400C2×C4—2982no—
401C2×C4—2982no—
402C2×C4—2982no—
403C2×C4—2982no—
404C2×C4—2982no—
405C2×C4—2988no—
406C2×C4—5964no—
407C2×C4—5964no—
408C2×C4—5964no—
409C2×C4—1492no—
410C2×C4—1492no—
411C2×C4—1492no—
412C2×C4—1492no—
413C2×C4—1492no—
414C2×C4—1494no—
415C2×C4—1492no—
416C2×C4C23×D14912yes—
417C2×C4C23×D14912yes—
418C2×C4C23×D14912yes—
419C2×C4C23×D14912yes—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—44no—
430C22—44no—
431C22—44no—
432C22—2982no—
433C22—2982no—
434C22—2982no—
435C22—2982no—
436C22—2982no—
437C22—2982no—
438C22—5964no—
439C22—5964no—
440C22#41×D14912yes—
441C22#1801195612yes—
442C22#1801195612yes—
443C22C24×D14911yescharacteristic
444C4—22no—
445C4—22no—
446C4—22no—
447C4—22no—
448C4—2982no—
449C4—2982no—
450C4—2982no—
451C4—2982no—
452C4—2982no—
453C4—1494no—
454C2—42no—
455C2—42no—
456C2—42no—
457C2—5962no—
458C2—5962no—
459C2#2375022514yesdirect product factor
460C2C2×#41×D14911yescharacteristic
461C2C2×#1801195611yescharacteristic
462C2C2×#1801195611yescharacteristic
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#121×C149C2
socleC23×C149C24
hypercenterC2×#121D149
hypocenterC149C2×#540
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #23750225C2direct (N × H)
2. C2×#18011907C2semidirect
3. C2×#18011901C2semidirect
4. C2×#18011896C2semidirect
5. C2×#18011894C2semidirect
6. C2×#18011893C2semidirect
7. C2×#18011892C2semidirect
8. C2×#18011884C2semidirect
9. C2×#18011883C2semidirect
10. C2×#18011883C2semidirect
11. C2×#18011883C2semidirect
12. C2×#18011882C2semidirect
13. C2×C4×C22⋊D149C2semidirect
14. C2×#18011871C2semidirect
15. C2×#18011867C2semidirect
16. C2×#121×C149C2semidirect
28. #18011907C22semidirect
29. #18011901C22semidirect
30. #18011896C22semidirect
31. #18011894C22semidirect
32. #18011893C22semidirect
33. #18011892C22semidirect
34. #18011884C22semidirect
35. #18011883C22semidirect
36. #18011883C22semidirect
37. #18011883C22semidirect
38. #18011882C22semidirect
39. C4×C22⋊D149C22semidirect
40. #18011871C22semidirect
41. #18011867C22semidirect
63. #121×C149C22semidirect
225. C2×C149#540semidirect
231. C149C2×#540semidirect
245. C2×#121D149semidirect
275. #121C2×D149semidirect
459. C2#23750225direct (N × H)

Maximal subgroups

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

subgroupindex
#237502252
C2×#180119072
C2×#180119012
C2×#180118962
C2×#180118942
C2×#180118932
C2×#180118922
C2×#180118842
C2×#180118832
C2×#180118822
C2×C4×C22⋊D1492
C2×#180118712
C2×#180118672
C2×#121×C1492
C2×#540149