Finite Group Databasebeta

← #15676730

Subgroups — #15676730

Order 2944.

864 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67288C211yesmaximal, characteristic
2C2×#10625065C211yesmaximal, characteristic, complemented
3C2×#10625054C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D23C211yesmaximal, characteristic, complemented
5#13092338C211yesmaximal, characteristic, complemented
6#13092337C211yesmaximal, characteristic, complemented
7#13092333C211yesmaximal, characteristic, complemented
8#13092332C211yesmaximal, characteristic, complemented
9#13092295C211yesmaximal, characteristic, complemented
10#13092293C211yesmaximal, characteristic, complemented
11#13092291C211yesmaximal, characteristic, complemented
12#13092290C211yesmaximal, characteristic, complemented
13#13092288C211yesmaximal, characteristic, complemented
14#13092279C211yesmaximal, characteristic, complemented
15C23×#385C211yesmaximal, characteristic, complemented
16C23×C4×C23C2211yescharacteristic
17C22×C22⋊D23C2211yescharacteristic
18C22×C22⋊D23C2211yescharacteristic
19C2×#67288—24no—
20C2×#67288—24no—
21C2×#67288—24no—
22C22×D92C2211yescharacteristic
23C22×C4×D23C2211yescharacteristic
24C22×C4×D23C2211yescharacteristic
25C22×C4×D23C2211yescharacteristic
26C22×C4×D23C2211yescharacteristic
27C22×Dic46C2211yescharacteristic
28C2×C4⋊C4×C23C2211yescharacteristic
29C2×C4⋊C4×C23C2211yescharacteristic
30C2×C22⋊C4×C23C2211yescharacteristic
31C2×C22⋊C4×C23C2211yescharacteristic
32C2×C22⋊Dic23C2211yescharacteristic
33C2×C22⋊Dic23C2211yescharacteristic
34C2×(C2×D23)⋊C4C2211yescharacteristic
35C2×(C2×D23)⋊C4C2211yescharacteristic
36C2×(C2×D23)⋊C4C2211yescharacteristic
37C2×(C2×D23)⋊C4C2211yescharacteristic
38C2×(C2×D23)⋊C4C2211yescharacteristic
39C2×(C2×D23)⋊C4C2211yescharacteristic
40C2×C4⋊Dic23C2211yescharacteristic
41C2×C4⋊Dic23C2211yescharacteristic
42C2×Dic23⋊C4C2211yescharacteristic
43C2×Dic23⋊C4C2211yescharacteristic
44C2×Dic23⋊C4C2211yescharacteristic
45C2×Dic23⋊C4C2211yescharacteristic
46#10625065—24no—
47C4⋊C4×D23—24no—
48#10625054—24no—
49C23×#95C2211yescharacteristic
50C23×#95C2211yescharacteristic
51C23⋊#95C2211yescharacteristic
52C23⋊#95C2211yescharacteristic
53C23⋊#95C2211yescharacteristic
54C23⋊#95C2211yescharacteristic
55C23⋊#95C2211yescharacteristic
56C23⋊#95C2211yescharacteristic
57C24×C23C2311yescharacteristic
58C23×D23C2311yescharacteristic
59C23×D23C2311yescharacteristic
60C22×C4×C23—22no—
61C22×C4×C23—22no—
62C22×C4×C23—22no—
63C22×C4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C22×C4×C23C2311yescharacteristic
67C22×C4×C23C2311yescharacteristic
68C22×C4×C23C2311yescharacteristic
69C2×C22⋊D23—22no—
70C2×C22⋊D23—22no—
71C2×C22⋊D23—22no—
72C2×C22⋊D23—22no—
73C2×C22⋊D23—22no—
74C2×C22⋊D23D414yes—
75C22×Dic23C2311yescharacteristic
76C22×Dic23C2311yescharacteristic
77C22×Dic23C2311yescharacteristic
78C22×Dic23C2311yescharacteristic
79C22×Dic23C2311yescharacteristic
80C22×Dic23C2311yescharacteristic
81#67288—232no—
82C2×D92—22no—
83C2×D92—22no—
84C2×D92D414yes—
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×D23—22no—
94C2×C4×D23—22no—
95C2×C4×D23—22no—
96C2×C4×D23D414yes—
97C2×Dic46—22no—
98C2×Dic46—22no—
99C2×Dic46—22no—
100C4⋊C4×C23—22no—
101C4⋊C4×C23—22no—
102C22⋊C4×C23—22no—
103C22⋊C4×C23—22no—
104C22⋊Dic23—22no—
105C22⋊Dic23—22no—
106(C2×D23)⋊C4—22no—
107(C2×D23)⋊C4—22no—
108(C2×D23)⋊C4—22no—
109(C2×D23)⋊C4—22no—
110(C2×D23)⋊C4—22no—
111(C2×D23)⋊C4—22no—
112C4⋊Dic23—22no—
113C4⋊Dic23—22no—
114Dic23⋊C4—22no—
115Dic23⋊C4—22no—
116Dic23⋊C4—22no—
117Dic23⋊C4—22no—
118C23×C23—21no—
119C23×C23—21no—
120C23×C23—21no—
121C23×C23—21no—
122C23×C23—21no—
123C23×C23—21no—
124C23×C23C2×D412yes—
125C23×C23C2411yescharacteristic
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×D23—21no—
135C22×D23—21no—
136C22×D23C2×D412yes—
137C22×D23C2×D412yes—
138C22×D23C2×D412yes—
139C22×D23C2×D412yes—
140C2×C4×C23—28no—
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—21no—
151C2×C4×C23—21no—
152C2×C4×C23—21no—
153C2×C4×C23—21no—
154C2×C4×C23—21no—
155C2×C4×C23—21no—
156C2×C4×C23C2×D412yes—
157C2×C4×C23C2×D412yes—
158C2×C4×C23#4112yescomplemented
159C22⋊D23—28no—
160C22⋊D23—28no—
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×Dic23—21no—
172C2×Dic23—21no—
173C2×Dic23—21no—
174C2×Dic23—21no—
175C2×Dic23—21no—
176C2×Dic23C2×D412yes—
177C2×Dic23C2×D412yes—
178C2×Dic23#4112yescomplemented
179D92—28no—
180C4×D23—28no—
181C4×D23—28no—
182C4×D23—28no—
183C4×D23—44no—
184Dic46—28no—
185#2406—231nomaximal, Sylow
186C22×C23—22no—
187C22×C23—22no—
188C22×C23—22no—
189C22×C23—41no—
190C22×C23—41no—
191C22×C23—41no—
192C22×C23—41no—
193C22×C23C22×D411yescharacteristic
194C22×C23C22×D411yescharacteristic
195C22×C23C22×D411yescharacteristic
196C22×C23C2×#4111yescharacteristic
197C22×C23C2×#4111yescharacteristic
198C22×C232−1+411yescharacteristic
199C22×C232−1+411yescharacteristic
200C2×D23—22no—
201C2×D23—22no—
202C2×D23—22no—
203C2×D23—22no—
204C2×D23—22no—
205C2×D23—22no—
206C2×D23—22no—
207C2×D23—22no—
208C2×D23—22no—
209C2×D23—41no—
210C2×D23—41no—
211C2×D23—41no—
212C2×D23—41no—
213C2×D23#12014yes—
214C4×C23—22no—
215C4×C23—22no—
216C4×C23—22no—
217C4×C23—41no—
218C4×C23—41no—
219C4×C23—41no—
220Dic23—22no—
221Dic23—22no—
222Dic23—22no—
223Dic23—41no—
224Dic23—41no—
225Dic23—41no—
226C22×#41—231no—
227C2×#123—231no—
228C2×#123—231no—
229C22×C4⋊C4—231no—
230#395—231no—
231#395—231no—
232#394—231no—
233#394—231no—
234#386—231no—
235#386—231no—
236#385—231no—
237#385—231no—
238#385—231no—
239#385D2311yescharacteristic, complemented
240#381—231no—
241C2×C23—42no—
242C2×C23C2×#12011yescharacteristic
243C2×C23#52511yescharacteristic
244C2×C23#53611yescharacteristic
245C2×C23#54711yescharacteristic
246C2×C23#54711yescharacteristic
247C2×C23#54711yescharacteristic
248C2×C23#54711yescharacteristic
249D23—24no—
250D23—42no—
251C2×#41—464no—
252C2×#41—464no—
253C2×#41—464no—
254C22×Q8—231no—
255C22×D4—231no—
256C22×D4—231no—
257C22×D4—231no—
258C23×C4—231no—
259C23×C4—231no—
260C23×C4—231no—
261C23×C4—231no—
262C23×C4C2×D2311yescharacteristic
263#123—464no—
264#123—464no—
265C2×C4⋊C4—231no—
266C2×C4⋊C4—231no—
267C2×C4⋊C4—231no—
268C2×C4⋊C4—231no—
269C2×C4⋊C4—231no—
270C2×C4⋊C4—231no—
271C2×C4⋊C4—464no—
272C2×C4⋊C4C2×D2311yescharacteristic
273C2×C4⋊C4C2×D2311yescharacteristic
274C2×C22⋊C4—231no—
275C2×C22⋊C4—231no—
276C2×C22⋊C4—231no—
277C2×C22⋊C4—231no—
278C2×C22⋊C4—231no—
279C2×C22⋊C4—231no—
280C2×C22⋊C4—231no—
281C2×C22⋊C4—231no—
282C2×C22⋊C4C2×D2311yescharacteristic
283C2×C22⋊C4C2×D2311yescharacteristic
284#95—231no—
285#95—231no—
286#95—231no—
287#95—231no—
288#95—231no—
289#95—231no—
290#95C2×D2311yescharacteristic
291#95C2×D2311yescharacteristic
292C23#240611yescharacteristic, complemented, Sylow
293C24—231no—
294C24—231no—
295C24C22×D2311yescharacteristic
296#41—4632no—
297C2×Q8—462no—
298C2×Q8—462no—
299C2×Q8—462no—
300C2×D4—234no—
301C2×D4—234no—
302C2×D4—462no—
303C2×D4—462no—
304C2×D4—462no—
305C2×D4—462no—
306C2×D4—462no—
307C2×D4—462no—
308C2×D4—462no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—231no—
313C22×C4—231no—
314C22×C4—231no—
315C22×C4—234no—
316C22×C4—231no—
317C22×C4—231no—
318C22×C4—231no—
319C22×C4—462no—
320C22×C4—462no—
321C22×C4—462no—
322C22×C4—462no—
323C22×C4—462no—
324C22×C4—462no—
325C22×C4—462no—
326C22×C4—462no—
327C22×C4—462no—
328C22×C4—462no—
329C22×C4—462no—
330C22×C4C22×D2311yescharacteristic
331C22×C4C22×D2311yescharacteristic
332C22×C4C22×D2311yescharacteristic
333C22×C4C22×D2311yescharacteristic
334C22×C4C22×D2311yescharacteristic
335C22×C4C22×D2311yescharacteristic
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—462no—
339C4⋊C4—462no—
340C4⋊C4—462no—
341C4⋊C4—462no—
342C4⋊C4—462no—
343C4⋊C4—462no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—462no—
347C22⋊C4—462no—
348C22⋊C4—462no—
349C22⋊C4—462no—
350C22⋊C4—462no—
351C22⋊C4—462no—
352C22⋊C4—462no—
353C22⋊C4—462no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—232no—
361C23—232no—
362C23—232no—
363C23—232no—
364C23—461no—
365C23—461no—
366C23—461no—
367C23—461no—
368C23—461no—
369C23—461no—
370C23—461no—
371C23—461no—
372C23—461no—
373C23—461no—
374C23D4×D2312yes—
375C23C23×D2311yescharacteristic
376Q8—468no—
377D4—468no—
378D4—468no—
379D4—468no—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—232no—
397C2×C4—232no—
398C2×C4—232no—
399C2×C4—468no—
400C2×C4—468no—
401C2×C4—468no—
402C2×C4—461no—
403C2×C4—461no—
404C2×C4—461no—
405C2×C4—461no—
406C2×C4—461no—
407C2×C4—461no—
408C2×C4—461no—
409C2×C4—461no—
410C2×C4—461no—
411C2×C4—461no—
412C2×C4—461no—
413C2×C4—461no—
414C2×C4—461no—
415C2×C4—461no—
416C2×C4—461no—
417C2×C4—924no—
418C2×C4#6728812yescomplemented
419C2×C4D4×D2312yes—
420C2×C4D4×D2312yes—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—234no—
429C22—462no—
430C22—462no—
431C22—462no—
432C22—462no—
433C22—462no—
434C22—462no—
435C22—462no—
436C22—462no—
437C22—462no—
438C22—921no—
439C22—921no—
440C22—921no—
441C22—921no—
442C22C2×#6728811yescharacteristic
443C22C2×D4×D2311yescharacteristic
444C22C2×D4×D2311yescharacteristic
445C22C2×D4×D2311yescharacteristic
446C22#1062515811yescharacteristic
447C22#41×D2311yescharacteristic
448C22#1062516111yescharacteristic
449C4—22no—
450C4—22no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—462no—
456C4—462no—
457C4—462no—
458C4—921no—
459C4—921no—
460C4—921no—
461C2—42no—
462C2—464no—
463C2—922no—
464C2#120×D2311yescharacteristic
465C2#1309292611yescharacteristic
466C2#1309299011yescharacteristic
467C2#1309306511yescharacteristic
468C2#1309306811yescharacteristic
469C2#1309306911yescharacteristic
470C2#1309307211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutator, socle, cosocleC23×C23C24
FittingC23×#385C2
prime radicalC22×#67288C2
hypercenter#385D23
hypocenterC23#2406
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#10625065C2semidirect
3. C2×#10625054C2semidirect
4. C2×C4⋊C4×D23C2semidirect
5. #13092338C2semidirect
6. #13092337C2semidirect
7. #13092333C2semidirect
8. #13092332C2semidirect
9. #13092295C2semidirect
10. #13092293C2semidirect
11. #13092291C2semidirect
12. #13092290C2semidirect
13. #13092288C2semidirect
14. #13092279C2semidirect
15. C23×#385C2semidirect
158. C2×C4×C23#41semidirect
178. C2×Dic23#41semidirect
239. #385D23semidirect
292. C23#2406semidirect
418. C2×C4#67288semidirect

Maximal subgroups

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

subgroupindex
C22×#672882
C2×#106250652
C2×#106250542
C2×C4⋊C4×D232
#130923382
#130923372
#130923332
#130923322
#130922952
#130922932
#130922912
#130922902
#130922882
#130922792
C23×#3852
#240623