Finite Group Databasebeta

← C4×#10625055 #15675908

Subgroups — C4×#10625055 #15675908

Order 2944.

824 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625055C211yesmaximal, characteristic
2C2×C4×D92C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D23C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D23C211yesmaximal, characteristic, complemented
5C2×C42×D23C211yesmaximal, characteristic, complemented
6#13092317C211yesmaximal, characteristic, complemented
7#13092314C211yesmaximal, characteristic, complemented
8#13092310C211yesmaximal, characteristic, complemented
9#13092306C211yesmaximal, characteristic, complemented
10#13092295C211yesmaximal, characteristic, complemented
11#13092293C211yesmaximal, characteristic, complemented
12#13092276C211yesmaximal, characteristic, complemented
13C4×Dic23⋊C4C211yesmaximal, characteristic, complemented
14C4×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
16C23×C4×C23C2211yescharacteristic
17C22×C22⋊D23C2211yescharacteristic
18C22×C22⋊D23C2211yescharacteristic
19C22×D92C2211yescharacteristic
20C22×C4×D23C2211yescharacteristic
21C22×C4×D23C2211yescharacteristic
22C22×C4×D23C2211yescharacteristic
23C22×C4×D23C2211yescharacteristic
24C2×C22⋊C4×C23C2211yescharacteristic
25C2×C22⋊C4×C23C2211yescharacteristic
26C2×C42×C23C2211yescharacteristic
27C2×C42×C23C2211yescharacteristic
28C2×C22⋊Dic23C2211yescharacteristic
29C2×C22⋊Dic23C2211yescharacteristic
30C4×C22⋊D23—24no—
31C4×C22⋊D23—24no—
32C2×(C2×D23)⋊C4C2211yescharacteristic
33C2×(C2×D23)⋊C4C2211yescharacteristic
34C2×(C2×D23)⋊C4C2211yescharacteristic
35C2×(C2×D23)⋊C4C2211yescharacteristic
36C2×(C2×D23)⋊C4C2211yescharacteristic
37C2×(C2×D23)⋊C4C2211yescharacteristic
38C2×C4⋊Dic23C2211yescharacteristic
39C2×Dic23⋊C4C2211yescharacteristic
40C2×Dic23⋊C4C2211yescharacteristic
41C2×Dic23⋊C4C2211yescharacteristic
42C2×Dic23⋊C4C2211yescharacteristic
43C2×C4×Dic23C2211yescharacteristic
44C2×C4×Dic23C2211yescharacteristic
45C2×C4×Dic23C2211yescharacteristic
46C2×C4×Dic23C2211yescharacteristic
47#10625055C418yesdirect product factor
48C4×D92—24no—
49C42×D23—24no—
50C23×#95C2211yescharacteristic
51C23×#95C2211yescharacteristic
52C23⋊#95C2211yescharacteristic
53C23⋊#95C2211yescharacteristic
54C23⋊#95C2211yescharacteristic
55C23⋊#95C2211yescharacteristic
56C24×C23C2311yescharacteristic
57C23×D23C2311yescharacteristic
58C23×D23C2311yescharacteristic
59C22×C4×C23—22no—
60C22×C4×C23—22no—
61C22×C4×C23—22no—
62C22×C4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C22×C4×C23C2311yescharacteristic
67C22×C4×C23C2311yescharacteristic
68C2×C22⋊D23—22no—
69C2×C22⋊D23—22no—
70C2×C22⋊D23—22no—
71C2×C22⋊D23—22no—
72C2×C22⋊D23C2×C414yescomplemented
73C2×C22⋊D23C2×C414yescomplemented
74C22×Dic23C2311yescharacteristic
75C22×Dic23C2311yescharacteristic
76C22×Dic23C2311yescharacteristic
77C22×Dic23C2311yescharacteristic
78C22×Dic23C2311yescharacteristic
79C22×Dic23C2311yescharacteristic
80C2×D92—22no—
81C2×D92—22no—
82C2×D92C2×C414yescomplemented
83C2×C4×D23—22no—
84C2×C4×D23—22no—
85C2×C4×D23—22no—
86C2×C4×D23—22no—
87C2×C4×D23—22no—
88C2×C4×D23—22no—
89C2×C4×D23—22no—
90C2×C4×D23—22no—
91C2×C4×D23—22no—
92C2×C4×D23—22no—
93C2×C4×D23C2×C414yescomplemented
94C2×C4×D23D414yescomplemented
95C22⋊C4×C23—22no—
96C22⋊C4×C23C2×C414yescomplemented
97C42×C23—22no—
98C42×C23—22no—
99C22⋊Dic23—22no—
100C22⋊Dic23—22no—
101(C2×D23)⋊C4—22no—
102(C2×D23)⋊C4—22no—
103(C2×D23)⋊C4—22no—
104(C2×D23)⋊C4—22no—
105(C2×D23)⋊C4—22no—
106(C2×D23)⋊C4C2×C414yescomplemented
107C4⋊Dic23—22no—
108Dic23⋊C4—22no—
109Dic23⋊C4—22no—
110Dic23⋊C4—22no—
111Dic23⋊C4C2×C414yescomplemented
112C4×Dic23—22no—
113C4×Dic23—22no—
114C4×Dic23—22no—
115C4×Dic23D414yescomplemented
116C23×C23—21no—
117C23×C23—21no—
118C23×C23—21no—
119C23×C23—21no—
120C23×C23—21no—
121C23×C23—21no—
122C23×C23C22×C412yes—
123C23×C23C2411yescharacteristic
124C22×D23—21no—
125C22×D23—21no—
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—21no—
130C22×D23—21no—
131C22×D23—21no—
132C22×D23—21no—
133C22×D23—21no—
134C22×D23C22×C412yes—
135C22×D23C22×C412yes—
136C22×D23C2×D412yes—
137C22×D23#4112yes—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—21no—
147C2×C4×C23—21no—
148C2×C4×C23—21no—
149C2×C4×C23—21no—
150C2×C4×C23—44no—
151C2×C4×C23C22×C412yes—
152C2×C4×C23C22×C412yes—
153C2×C4×C23C2×D412yes—
154C2×C4×C23C2×D412yes—
155C2×C4×C23#4112yes—
156C2×C4×C23#4112yes—
157C22⋊D23—28no—
158C22⋊D23—28no—
159C2×Dic23—21no—
160C2×Dic23—21no—
161C2×Dic23—21no—
162C2×Dic23—21no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—21no—
166C2×Dic23—21no—
167C2×Dic23—21no—
168C2×Dic23—21no—
169C2×Dic23—21no—
170C2×Dic23—21no—
171C2×Dic23C22×C412yes—
172C2×Dic23C22×C412yes—
173C2×Dic23C2×D412yes—
174C2×Dic23C2×D412yes—
175C2×Dic23C2×D412yes—
176C2×Dic23#4112yes—
177D92—28no—
178C4×D23—28no—
179C4×D23—28no—
180C4×D23—28no—
181C4×D23—44no—
182C4×#121—231nomaximal, Sylow
183C22×C23—22no—
184C22×C23—22no—
185C22×C23—22no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—41no—
189C22×C23—41no—
190C22×C23C23×C411yescharacteristic
191C22×C23C22×D411yescharacteristic
192C22×C23C22×D411yescharacteristic
193C22×C23C2×#4111yescharacteristic
194C22×C23C2×#4111yescharacteristic
195C22×C23C2×#4111yescharacteristic
196C22×C23C2×#4111yescharacteristic
197C2×D23—22no—
198C2×D23—22no—
199C2×D23—22no—
200C2×D23—22no—
201C2×D23—22no—
202C2×D23—22no—
203C2×D23—22no—
204C2×D23—22no—
205C2×D23—22no—
206C2×D23—41no—
207C2×D23—41no—
208C2×D23—41no—
209C2×D23—41no—
210C2×D23C4×D414yescomplemented
211C4×C23—22no—
212C4×C23—22no—
213C4×C23—22no—
214C4×C23—41no—
215C4×C23—41no—
216C4×C23#12114yescomplemented
217Dic23—22no—
218Dic23—22no—
219Dic23—22no—
220Dic23—41no—
221Dic23—41no—
222Dic23C4×D414yescomplemented
223C2×#121—231no—
224C2×C4×D4—231no—
225C2×C4×D4—231no—
226C2×C4×D4—231no—
227C22×C42—231no—
228#390—231no—
229#389—231no—
230#388—231no—
231#388—231no—
232#386—231no—
233#386—231no—
234#380—231no—
235C4×C4⋊C4—231no—
236C4×C22⋊C4—231no—
237C4×C22⋊C4D2311yescharacteristic, complemented
238C2×C23—42no—
239C2×C23C2×C4×D411yescharacteristic
240C2×C23C2×C4×D411yescharacteristic
241C2×C23C4×#4111yescharacteristic
242C2×C23C2×#12111yescharacteristic
243C2×C23#52511yescharacteristic
244C2×C23#52911yescharacteristic
245C2×C23#53211yescharacteristic
246D23—24no—
247D23—42no—
248C22×D4—231no—
249C22×D4—231no—
250C22×D4—231no—
251C23×C4—231no—
252C23×C4—231no—
253C23×C4—231no—
254C23×C4—231no—
255C23×C4C2×D2311yescharacteristic
256#121—238no—
257C4×D4—464no—
258C4×D4—464no—
259C4×D4—464no—
260C2×C4⋊C4—231no—
261C2×C4⋊C4—231no—
262C2×C4⋊C4—231no—
263C2×C4⋊C4—231no—
264C2×C4⋊C4—231no—
265C2×C22⋊C4—231no—
266C2×C22⋊C4—231no—
267C2×C22⋊C4—231no—
268C2×C22⋊C4—231no—
269C2×C22⋊C4—231no—
270C2×C22⋊C4—231no—
271C2×C22⋊C4—231no—
272C2×C22⋊C4—231no—
273C2×C22⋊C4C2×D2311yescharacteristic
274C2×C22⋊C4C2×D2311yescharacteristic
275C2×C42—231no—
276C2×C42—231no—
277C2×C42—231no—
278C2×C42—231no—
279C2×C42—464no—
280C2×C42C2×D2311yescharacteristic
281C2×C42C2×D2311yescharacteristic
282#95—231no—
283#95—231no—
284#95—231no—
285#95—231no—
286#95C2×D2311yescharacteristic
287#95C2×D2311yescharacteristic
288C23C4×#12111yescharacteristic, complemented, Sylow
289C24—231no—
290C24—231no—
291C24C22×D2311yescharacteristic
292C2×D4—234no—
293C2×D4—234no—
294C2×D4—234no—
295C2×D4—462no—
296C2×D4—462no—
297C2×D4—462no—
298C2×D4—462no—
299C2×D4—462no—
300C2×D4—462no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—231no—
305C22×C4—231no—
306C22×C4—231no—
307C22×C4—231no—
308C22×C4—234no—
309C22×C4—234no—
310C22×C4—231no—
311C22×C4—231no—
312C22×C4—462no—
313C22×C4—462no—
314C22×C4—462no—
315C22×C4—462no—
316C22×C4—462no—
317C22×C4—462no—
318C22×C4—462no—
319C22×C4—462no—
320C22×C4—462no—
321C22×C4—462no—
322C22×C4C22×D2311yescharacteristic
323C22×C4C22×D2311yescharacteristic
324C22×C4C22×D2311yescharacteristic
325C22×C4C22×D2311yescharacteristic
326C22×C4C22×D2311yescharacteristic
327C22×C4C22×D2311yescharacteristic
328C4⋊C4—234no—
329C4⋊C4—462no—
330C4⋊C4—462no—
331C4⋊C4—462no—
332C4⋊C4—462no—
333C22⋊C4—22no—
334C22⋊C4—234no—
335C22⋊C4—462no—
336C22⋊C4—462no—
337C22⋊C4—462no—
338C22⋊C4—462no—
339C22⋊C4—462no—
340C22⋊C4—462no—
341C22⋊C4—462no—
342C22⋊C4C4×D2314yescomplemented
343C42—22no—
344C42—22no—
345C42—234no—
346C42—462no—
347C42—462no—
348C42—462no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—232no—
356C23—232no—
357C23—232no—
358C23—232no—
359C23—461no—
360C23—461no—
361C23—461no—
362C23—461no—
363C23—461no—
364C23—461no—
365C23—461no—
366C23—461no—
367C23—461no—
368C23—461no—
369C23C2×C4×D2312yes—
370C23C23×D2311yescharacteristic
371D4—468no—
372D4—468no—
373D4—468no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—44no—
387C2×C4—232no—
388C2×C4—232no—
389C2×C4—232no—
390C2×C4—232no—
391C2×C4—232no—
392C2×C4—232no—
393C2×C4—468no—
394C2×C4—468no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—461no—
398C2×C4—461no—
399C2×C4—461no—
400C2×C4—461no—
401C2×C4—468no—
402C2×C4—461no—
403C2×C4—461no—
404C2×C4—461no—
405C2×C4—461no—
406C2×C4—461no—
407C2×C4—461no—
408C2×C4—924no—
409C2×C4C2×C4×D2312yes—
410C2×C4C2×C4×D2312yes—
411C2×C4#6728812yes—
412C2×C4#6728812yes—
413C2×C4D4×D2312yes—
414C2×C4D4×D2312yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—234no—
423C22—462no—
424C22—462no—
425C22—462no—
426C22—462no—
427C22—462no—
428C22—462no—
429C22—462no—
430C22—462no—
431C22—462no—
432C22—921no—
433C22—921no—
434C22—921no—
435C22—921no—
436C22C22×C4×D2311yescharacteristic
437C22C2×#6728811yescharacteristic
438C22C2×#6728811yescharacteristic
439C22C2×D4×D2311yescharacteristic
440C22C2×D4×D2311yescharacteristic
441C22#41×D2311yescharacteristic
442C22#41×D2311yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—41no—
447C4—41no—
448C4—234no—
449C4—462no—
450C4—462no—
451C4—462no—
452C4—921no—
453C4—921no—
454C4#1062505514yesdirect product factor
455C2—42no—
456C2—464no—
457C2—922no—
458C2C4×D4×D2311yescharacteristic
459C2C4×D4×D2311yescharacteristic
460C2C4×#6728811yescharacteristic
461C2C2×#1062505511yescharacteristic
462C2#1309292611yescharacteristic
463C2#1309294511yescharacteristic
464C2#1309296411yescharacteristic
subgroupG/H
centerC22×C4C22×D23
commutatorC22×C23C23×C4
FrattiniC23C23×D23
FittingC4×C22⋊C4×C23C2
socle, cosocleC23×C23C24
prime radicalC2×#10625055C2
hypercenterC4×C22⋊C4D23
hypocenterC23C4×#121
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D92C2semidirect
3. C2×C4×C22⋊D23C2semidirect
4. C2×C4×C22⋊D23C2semidirect
5. C2×C42×D23C2semidirect
6. #13092317C2semidirect
7. #13092314C2semidirect
8. #13092310C2semidirect
9. #13092306C2semidirect
10. #13092295C2semidirect
11. #13092293C2semidirect
12. #13092276C2semidirect
13. C4×Dic23⋊C4C2semidirect
14. C4×(C2×D23)⋊C4C2semidirect
15. C4×C22⋊C4×C23C2semidirect
47. #10625055C4direct (N × H)
72. C2×C22⋊D23C2×C4semidirect
73. C2×C22⋊D23C2×C4semidirect
82. C2×D92C2×C4semidirect
93. C2×C4×D23C2×C4semidirect
94. C2×C4×D23D4semidirect
96. C22⋊C4×C23C2×C4semidirect
106. (C2×D23)⋊C4C2×C4semidirect
111. Dic23⋊C4C2×C4semidirect
115. C4×Dic23D4semidirect
210. C2×D23C4×D4semidirect
216. C4×C23#121semidirect
222. Dic23C4×D4semidirect
237. C4×C22⋊C4D23semidirect
288. C23C4×#121semidirect
342. C22⋊C4C4×D23semidirect
454. C4#10625055direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106250552
C2×C4×D922
C2×C4×C22⋊D232
C2×C42×D232
#130923172
#130923142
#130923102
#130923062
#130922952
#130922932
#130922762
C4×Dic23⋊C42
C4×(C2×D23)⋊C42
C4×C22⋊C4×C232
C4×#12123