Finite Group Databasebeta

← C2×#23750273 #34058145

Subgroups — C2×#23750273 #34058145

Order 19072.

1632 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
1C22×#14558736C211yesmaximal, characteristic, complemented
2C22×#14558735C211yesmaximal, characteristic, complemented
3#23750273C2116yesmaximal, direct product factor
4C2×#18011910C211yesmaximal, characteristic, complemented
5C2×#18011896C211yesmaximal, characteristic, complemented
6C2×#18011895C211yesmaximal, characteristic, complemented
7C2×#18011893C211yesmaximal, characteristic, complemented
8C2×#18011889C211yesmaximal, characteristic, complemented
9C2×#18011888C211yesmaximal, characteristic, complemented
10C2×#18011884C211yesmaximal, characteristic, complemented
11C2×#18011883C211yesmaximal, characteristic, complemented
12C2×#18011871C211yesmaximal, characteristic, complemented
13C2×#18011871C211yesmaximal, characteristic, complemented
14C22×#14558715C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×D149C211yesmaximal, characteristic, complemented
16C2×#123×C149C211yesmaximal, characteristic, complemented
17C2×#14558736—28no—
18C2×#14558736C2218yescomplemented
19C2×#14558735—28no—
20C2×#14558735C2218yescomplemented
21C22×Dic298C2211yescharacteristic
22C22×Dic298C2211yescharacteristic
23C22×D596C2211yescharacteristic
24C22×C22⋊D149C2211yescharacteristic
25C22×C22⋊D149C2211yescharacteristic
26C22×C22⋊D149C2211yescharacteristic
27C22×C22⋊D149C2211yescharacteristic
28C23×Dic149C2211yescharacteristic
29C23×Dic149C2211yescharacteristic
30C23×Dic149C2211yescharacteristic
31C22×C4×D149C2211yescharacteristic
32C22×C4×D149C2211yescharacteristic
33C22×C4×D149C2211yescharacteristic
34C22×C4×D149C2211yescharacteristic
35#18011910C2218yescomplemented
36#18011896C2218yescomplemented
37#18011895C2218yescomplemented
38#18011893C2218yescomplemented
39#18011889C2218yescomplemented
40#18011888C2218yescomplemented
41#18011884C2218yescomplemented
42#18011883C2218yescomplemented
43#18011871C2218yescomplemented
44#18011871C2218yescomplemented
45C2×C4⋊Dic149C2211yescharacteristic
46C2×C4⋊Dic149C2211yescharacteristic
47C2×#14558715C2211yescharacteristic
48C2×#14558715C2211yescharacteristic
49C2×#14558715C2211yescharacteristic
50C2×#14558715C2211yescharacteristic
51C2×#14558715C2211yescharacteristic
52C2×#14558715C2211yescharacteristic
53C2×#14558715C2218yescomplemented
54C4⋊C4×D149C2218yescomplemented
55C2×C22⋊Dic149C2211yescharacteristic
56C2×#14558713C2211yescharacteristic
57C2×#14558713C2211yescharacteristic
58C2×#14558713C2211yescharacteristic
59C2×#14558713C2211yescharacteristic
60C2×C4×Dic149C2211yescharacteristic
61C22×D4×C149C2211yescharacteristic
62C23×C4×C149C2211yescharacteristic
63#123×C149C2218yescomplemented
64C2×C4⋊C4×C149C2211yescharacteristic
65C2×C4⋊C4×C149C2211yescharacteristic
66C2×C22⋊C4×C149C2211yescharacteristic
67C2×C22⋊C4×C149C2211yescharacteristic
68C2×C22⋊C4×C149C2211yescharacteristic
69C23×D149C2311yescharacteristic
70C23×D149C2311yescharacteristic
71#14558736—232no—
72#14558735—232no—
73C2×Dic298—24no—
74C2×Dic298—24no—
75C2×Dic298C2314yes—
76C2×Dic298C2314yes—
77C2×D596—24no—
78C2×D596C2314yes—
79C2×C22⋊D149—24no—
80C2×C22⋊D149—24no—
81C2×C22⋊D149—24no—
82C2×C22⋊D149D418yescomplemented
83C2×C22⋊D149C2314yes—
84C2×C22⋊D149C2314yes—
85C2×C22⋊D149C2314yes—
86C2×C22⋊D149C2314yes—
87C22×Dic149—24no—
88C22×Dic149—24no—
89C22×Dic149—24no—
90C22×Dic149C2311yescharacteristic
91C22×Dic149C2311yescharacteristic
92C22×Dic149C2311yescharacteristic
93C22×Dic149C2314yes—
94C22×Dic149C2314yes—
95C22×Dic149C2311yescharacteristic
96C22×Dic149C2314yes—
97C22×Dic149C2311yescharacteristic
98C22×Dic149C2311yescharacteristic
99C2×C4×D149—24no—
100C2×C4×D149—24no—
101C2×C4×D149—24no—
102C2×C4×D149—24no—
103C2×C4×D149C2314yes—
104C2×C4×D149C2314yes—
105C2×C4×D149C2314yes—
106C2×C4×D149C2314yes—
107C4⋊Dic149C2314yes—
108C4⋊Dic149C2314yes—
109#14558715C2314yes—
110#14558715C2314yes—
111#14558715C2314yes—
112#14558715C2314yes—
113#14558715C2314yes—
114#14558715C2314yes—
115C22⋊Dic149C2314yes—
116#14558713C2314yes—
117#14558713C2314yes—
118#14558713C2314yes—
119#14558713C2314yes—
120C4×Dic149C2314yes—
121C24×C149C2311yescharacteristic
122C24×C149C2311yescharacteristic
123C2×D4×C149—24no—
124C2×D4×C149C2314yes—
125C22×C4×C149—24no—
126C22×C4×C149C2311yescharacteristic
127C22×C4×C149C2311yescharacteristic
128C22×C4×C149C2311yescharacteristic
129C22×C4×C149C2311yescharacteristic
130C22×C4×C149C2314yes—
131C22×C4×C149C2311yescharacteristic
132C4⋊C4×C149C2314yes—
133C4⋊C4×C149C2314yes—
134C22⋊C4×C149C2314yes—
135C22⋊C4×C149C2314yes—
136C22⋊C4×C149C2314yes—
137C22×D149—22no—
138C22×D149—22no—
139C22×D149—22no—
140C22×D149—22no—
141C22×D149—22no—
142C22×D149C2×D414yes—
143C22×D149C2412yes—
144C22×D149C2412yes—
145Dic298—28no—
146Dic298—28no—
147D596—28no—
148C22⋊D149—28no—
149C22⋊D149—28no—
150C22⋊D149—28no—
151C22⋊D149C2×D4116yescomplemented
152C2×Dic149—22no—
153C2×Dic149—22no—
154C2×Dic149—22no—
155C2×Dic149—28no—
156C2×Dic149—22no—
157C2×Dic149—28no—
158C2×Dic149—28no—
159C2×Dic149C2×D414yes—
160C2×Dic149#4114yescomplemented
161C2×Dic149C2412yes—
162C2×Dic149C2412yes—
163C2×Dic149C2412yes—
164C2×Dic149C2412yes—
165C2×Dic149C2412yes—
166C2×Dic149C2412yes—
167C4×D149—28no—
168C4×D149—28no—
169C4×D149—28no—
170C4×D149—28no—
171C23×C149—22no—
172C23×C149—22no—
173C23×C149—22no—
174C23×C149—22no—
175C23×C149—22no—
176C23×C149C2×D414yes—
177C23×C149C2412yes—
178C23×C149C2412yes—
179C23×C149C2411yescharacteristic
180D4×C149—28no—
181C2×C4×C149—22no—
182C2×C4×C149—22no—
183C2×C4×C149—22no—
184C2×C4×C149—28no—
185C2×C4×C149—22no—
186C2×C4×C149—22no—
187C2×C4×C149C2412yes—
188C2×C4×C149C2412yes—
189C2×C4×C149C2412yes—
190C2×C4×C149C2412yes—
191C2×C4×C149C2412yes—
192C22×C149—28no—
193C22×C149—22no—
194C22×C149—22no—
195C22×C149—22no—
196C22×C149—22no—
197C22×C149—22no—
198C22×C149—44no—
199C22×C149C22×D414yes—
200C22×C149C22×D412yes—
201C22×C149C2×#4112yes—
202C22×C1492−1+412yes—
203C22×C149C2511yescharacteristic
204C2×D149—28no—
205C2×D149—22no—
206C2×D149—22no—
207C2×D149—22no—
208C2×D149—22no—
209C2×D149—22no—
210C2×D149—44no—
211C2×D149C22×D414yes—
212C4×C149—22no—
213C4×C149—22no—
214C4×C149—22no—
215C4×C149—22no—
216C4×C149—22no—
217Dic149—22no—
218Dic149—22no—
219Dic149—22no—
220Dic149—22no—
221Dic149C22×D414yes—
222Dic149C2×#4114yescomplemented
223C2×C149—24no—
224C2×C149—42no—
225C2×C149#54714yescomplemented
226C2×C149C23×D411yescharacteristic
227C2×C149C22×#4111yescharacteristic
228C2×C149C2×2−1+411yescharacteristic
229D149—24no—
230D149—42no—
231C149C2×#54711yescharacteristic, complemented, Sylow
232C2×#547—1491nomaximal, Sylow
233C22×#41—1491no—
234C22×#41—1491no—
235#547—14916no—
236C2×C4⋊Q8—1491no—
237C2×#123—1491no—
238C2×#123—1491no—
239C2×#123—1491no—
240C2×#123D14911yescharacteristic, complemented
241C2×C22⋊Q8—1491no—
242C2×C22⋊Q8—1491no—
243C2×#121—1491no—
244C2×#121—1491no—
245C2×C4×D4—1491no—
246C2×C4×D4—1491no—
247C22×C4⋊C4—1491no—
248C22×C4⋊C4—1491no—
249C2×#41—2988no—
250C2×#41—2988no—
251C2×#41—1498no—
252C2×#41—1498no—
253C22×Q8—1491no—
254C22×Q8—1491no—
255C22×D4—1491no—
256C22×D4—1491no—
257C22×D4—1491no—
258C22×D4—1491no—
259C22×D4—1491no—
260C22×D4C2×D14911yescharacteristic
261C23×C4—1491no—
262C23×C4—1491no—
263C23×C4—1491no—
264C23×C4—1491no—
265C23×C4—1491no—
266C23×C4—1491no—
267C23×C4—1491no—
268C23×C4C2×D14911yescharacteristic
269C4⋊Q8—1498no—
270#123—1498no—
271#123—1498no—
272#123—1498no—
273#123C2×D14918yescomplemented
274C22⋊Q8—1498no—
275C22⋊Q8—1498no—
276#121—1498no—
277#121—1498no—
278C4×D4—1498no—
279C4×D4—1498no—
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⋊C4—1498no—
287C2×C4⋊C4—1491no—
288C2×C4⋊C4—1491no—
289C2×C4⋊C4—1498no—
290C2×C4⋊C4C2×D14911yescharacteristic
291C2×C4⋊C4C2×D14911yescharacteristic
292C2×C22⋊C4—1491no—
293C2×C22⋊C4—1491no—
294C2×C22⋊C4—1491no—
295C2×C22⋊C4—1491no—
296C2×C22⋊C4—1491no—
297C2×C22⋊C4C2×D14911yescharacteristic
298C2×C22⋊C4C2×D14911yescharacteristic
299C2×C22⋊C4C2×D14911yescharacteristic
300C2×C42—1491no—
301C24—1491no—
302C24—1491no—
303C24C22×D14911yescharacteristic
304C24C22×D14911yescharacteristic
305#41—29832no—
306#41—29832no—
307C2×Q8—2984no—
308C2×Q8—2984no—
309C2×Q8—1494no—
310C2×Q8—1494no—
311C2×D4—24no—
312C2×D4—2984no—
313C2×D4—2984no—
314C2×D4—2984no—
315C2×D4—2984no—
316C2×D4—1494no—
317C2×D4—1494no—
318C2×D4—1494no—
319C2×D4—1498no—
320C2×D4—1494no—
321C2×D4—1494no—
322C2×D4C22×D14914yes—
323C22×C4—24no—
324C22×C4—2984no—
325C22×C4—2984no—
326C22×C4—2984no—
327C22×C4—2984no—
328C22×C4—2984no—
329C22×C4—2984no—
330C22×C4—2984no—
331C22×C4—1494no—
332C22×C4—1494no—
333C22×C4—1494no—
334C22×C4—1491no—
335C22×C4—1491no—
336C22×C4—1491no—
337C22×C4—1491no—
338C22×C4—1494no—
339C22×C4—1494no—
340C22×C4—1494no—
341C22×C4—1494no—
342C22×C4—1491no—
343C22×C4—1491no—
344C22×C4C22×D14914yes—
345C22×C4C22×D14911yescharacteristic
346C22×C4C22×D14911yescharacteristic
347C22×C4C22×D14911yescharacteristic
348C22×C4C22×D14911yescharacteristic
349C22×C4C22×D14911yescharacteristic
350C4⋊C4—1494no—
351C4⋊C4—1494no—
352C4⋊C4—1494no—
353C4⋊C4—1494no—
354C4⋊C4—1494no—
355C4⋊C4—1494no—
356C4⋊C4—1494no—
357C4⋊C4—1494no—
358C4⋊C4C22×D14914yes—
359C4⋊C4C22×D14914yes—
360C22⋊C4—1494no—
361C22⋊C4—1494no—
362C22⋊C4—1494no—
363C22⋊C4—1494no—
364C22⋊C4—1494no—
365C22⋊C4C22×D14914yes—
366C22⋊C4C22×D14914yes—
367C22⋊C4C22×D14914yes—
368C42—1494no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—2982no—
375C23—2982no—
376C23—2982no—
377C23—2982no—
378C23—2982no—
379C23—1492no—
380C23—1494no—
381C23—1492no—
382C23D4×D14914yes—
383C23C23×D14912yes—
384C23C23×D14912yes—
385C23C23×D14911yescharacteristic
386Q8—2988no—
387Q8—2988no—
388D4—28no—
389D4—2988no—
390D4—2988no—
391D4—2988no—
392D4—2988no—
393D4—14916no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—28no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—2988no—
401C2×C4—2988no—
402C2×C4—2988no—
403C2×C4—2988no—
404C2×C4—2982no—
405C2×C4—2982no—
406C2×C4—2982no—
407C2×C4—2988no—
408C2×C4—2982no—
409C2×C4—2988no—
410C2×C4—2988no—
411C2×C4—1492no—
412C2×C4—1492no—
413C2×C4—1492no—
414C2×C4—1492no—
415C2×C4—1494no—
416C2×C4—1494no—
417C2×C4—1492no—
418C2×C4—1492no—
419C2×C4C23×D14912yes—
420C2×C4C23×D14912yes—
421C2×C4C23×D14912yes—
422C2×C4C23×D14912yes—
423C2×C4C23×D14912yes—
424C22—22no—
425C22—22no—
426C22—28no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—44no—
431C22—2982no—
432C22—2982no—
433C22—2988no—
434C22—2982no—
435C22—2982no—
436C22—2982no—
437C22—5964no—
438C22—1494no—
439C22C2×D4×D14914yes—
440C22C2×D4×D14912yes—
441C22#41×D14912yes—
442C22#1801195812yes—
443C22C24×D14911yescharacteristic
444C4—22no—
445C4—22no—
446C4—22no—
447C4—22no—
448C4—22no—
449C4—2982no—
450C4—2982no—
451C4—2982no—
452C4—2982no—
453C4—1494no—
454C4—1494no—
455C2—24no—
456C2—42no—
457C2—2984no—
458C2—5962no—
459C2#2375027314yesdirect product factor
460C2C22×D4×D14911yescharacteristic
461C2C2×#41×D14911yescharacteristic
462C2C2×#1801195811yescharacteristic
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#123×C149C2
socleC23×C149C24
hypercenterC2×#123D149
hypocenterC149C2×#547
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×#14558736C2semidirect
2. C22×#14558735C2semidirect
3. #23750273C2direct (N × H)
4. C2×#18011910C2semidirect
5. C2×#18011896C2semidirect
6. C2×#18011895C2semidirect
7. C2×#18011893C2semidirect
8. C2×#18011889C2semidirect
9. C2×#18011888C2semidirect
10. C2×#18011884C2semidirect
11. C2×#18011883C2semidirect
12. C2×#18011871C2semidirect
13. C2×#18011871C2semidirect
14. C22×#14558715C2semidirect
15. C2×C4⋊C4×D149C2semidirect
16. C2×#123×C149C2semidirect
18. C2×#14558736C22semidirect
20. C2×#14558735C22semidirect
35. #18011910C22semidirect
36. #18011896C22semidirect
37. #18011895C22semidirect
38. #18011893C22semidirect
39. #18011889C22semidirect
40. #18011888C22semidirect
41. #18011884C22semidirect
42. #18011883C22semidirect
43. #18011871C22semidirect
44. #18011871C22semidirect
53. C2×#14558715C22semidirect
54. C4⋊C4×D149C22semidirect
63. #123×C149C22semidirect
82. C2×C22⋊D149D4semidirect
151. C22⋊D149C2×D4semidirect
160. C2×Dic149#41semidirect
222. Dic149C2×#41semidirect
225. C2×C149#547semidirect
231. C149C2×#547semidirect
240. C2×#123D149semidirect
273. #123C2×D149semidirect
459. C2#23750273direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145587362
C22×#145587352
#237502732
C2×#180119102
C2×#180118962
C2×#180118952
C2×#180118932
C2×#180118892
C2×#180118882
C2×#180118842
C2×#180118832
C2×#180118712
C22×#145587152
C2×C4⋊C4×D1492
C2×#123×C1492
C2×#547149