Finite Group Databasebeta

← #15676640

Subgroups — #15676640

Order 2944.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic23C211yesmaximal, characteristic, complemented
2C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic, complemented
3C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic, complemented
4C2×#10625048C211yesmaximal, characteristic, complemented
5#13092351C211yesmaximal, characteristic, complemented
6#13092345C211yesmaximal, characteristic, complemented
7#13092340C211yesmaximal, characteristic, complemented
8#13092339C211yesmaximal, characteristic, complemented
9#13092333C211yesmaximal, characteristic, complemented
10#13092332C211yesmaximal, characteristic, complemented
11#13092325C211yesmaximal, characteristic
12C4⋊C4×Dic23C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic23C211yesmaximal, characteristic, complemented
14#13092264C211yesmaximal, characteristic, complemented
15C23×#394C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C22×C22⋊D23C2211yescharacteristic
18C22×C22⋊D23C2211yescharacteristic
19C23×Dic23C2211yescharacteristic
20C23×Dic23C2211yescharacteristic
21C22×C4×D23C2211yescharacteristic
22C2×C4⋊C4×C23C2211yescharacteristic
23C2×C22⋊C4×C23C2211yescharacteristic
24C2×C22⋊C4×C23C2211yescharacteristic
25C2×C22⋊C4×C23C2211yescharacteristic
26C2×C22⋊C4×C23C2211yescharacteristic
27C2×C22⋊Dic23C2211yescharacteristic
28C2×C22⋊Dic23C2211yescharacteristic
29C2×C22⋊Dic23C2211yescharacteristic
30C2×C22⋊Dic23C2211yescharacteristic
31D4×Dic23—24no—
32C2×(C2×D23)⋊C4C2211yescharacteristic
33C2×(C2×D23)⋊C4C2211yescharacteristic
34C2×(C2×D23)⋊C4C2211yescharacteristic
35C2×(C2×D23)⋊C4C2211yescharacteristic
36C2×C4⋊Dic23C2211yescharacteristic
37C2×C4⋊Dic23C2211yescharacteristic
38C2×Dic23⋊C4C2211yescharacteristic
39C2×Dic23⋊C4C2211yescharacteristic
40C2×Dic23⋊C4C2211yescharacteristic
41C2×Dic23⋊C4C2211yescharacteristic
42C2×C4×Dic23C2211yescharacteristic
43C2×C4×Dic23C2211yescharacteristic
44C2×C4×Dic23C2211yescharacteristic
45C2×C4×Dic23C2211yescharacteristic
46(C22⋊D23)⋊C4—24no—
47(C22⋊D23)⋊C4—24no—
48#10625048—24no—
49C23×#95C2211yescharacteristic
50C23⋊#95C2211yescharacteristic
51C23⋊#95C2211yescharacteristic
52C23⋊#95C2211yescharacteristic
53C23⋊#95C2211yescharacteristic
54C23⋊#95C2211yescharacteristic
55C24×C23C2311yescharacteristic
56C24×C23C2311yescharacteristic
57C23×D23C2311yescharacteristic
58C2×D4×C23—22no—
59C2×D4×C23—22no—
60C2×D4×C23—22no—
61C22×C4×C23C2311yescharacteristic
62C22×C4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C2×C22⋊D23—22no—
67C2×C22⋊D23—22no—
68C2×C22⋊D23—22no—
69C2×C22⋊D23—22no—
70C2×C22⋊D23—22no—
71C2×C22⋊D23—22no—
72C22×Dic23—22no—
73C22×Dic23—22no—
74C22×Dic23—22no—
75C22×Dic23—22no—
76C22×Dic23—22no—
77C22×Dic23D414yescomplemented
78C22×Dic23C2311yescharacteristic
79C22×Dic23C2311yescharacteristic
80C22×Dic23C2311yescharacteristic
81C22×Dic23C2311yescharacteristic
82C22×Dic23C2311yescharacteristic
83C22×Dic23C2311yescharacteristic
84C22×Dic23C2311yescharacteristic
85C2×C4×D23—22no—
86C2×C4×D23—22no—
87C2×C4×D23—22no—
88C4⋊C4×C23—22no—
89C22⋊C4×C23—22no—
90C22⋊C4×C23—22no—
91C22⋊C4×C23—22no—
92C22⋊C4×C23—22no—
93C22⋊Dic23—22no—
94C22⋊Dic23—22no—
95C22⋊Dic23—22no—
96C22⋊Dic23—22no—
97(C2×D23)⋊C4—22no—
98(C2×D23)⋊C4—22no—
99(C2×D23)⋊C4—22no—
100(C2×D23)⋊C4—22no—
101C4⋊Dic23—22no—
102C4⋊Dic23—22no—
103Dic23⋊C4—22no—
104Dic23⋊C4—22no—
105Dic23⋊C4—22no—
106Dic23⋊C4—22no—
107C4×Dic23—22no—
108C4×Dic23—22no—
109C4×Dic23—22no—
110C4×Dic23D414yescomplemented
111C23×C23—21no—
112C23×C23—21no—
113C23×C23—21no—
114C23×C23—21no—
115C23×C23—21no—
116C23×C23—21no—
117C23×C23—21no—
118C23×C23—21no—
119C23×C23—21no—
120C23×C23—21no—
121C23×C23—21no—
122C23×C23—21no—
123C23×C23C2×D412yes—
124C23×C23#4112yes—
125C23×C23C2411yescharacteristic
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—21no—
130C22×D23—21no—
131C22×D23—21no—
132C22×D23#4112yes—
133D4×C23—28no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
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×C23C2×D412yes—
148C2×C4×C23#4112yes—
149C22⋊D23—28no—
150C22⋊D23—28no—
151C2×Dic23—21no—
152C2×Dic23—21no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—21no—
157C2×Dic23—28no—
158C2×Dic23—21no—
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—44no—
168C2×Dic23C2×D412yes—
169C2×Dic23C2×D412yes—
170C2×Dic23C2×D412yes—
171C2×Dic23C2×D412yes—
172C2×Dic23#4112yes—
173C2×Dic23#4112yes—
174C4×D23—44no—
175#2392—231nomaximal, Sylow
176C22×C23—22no—
177C22×C23—22no—
178C22×C23—22no—
179C22×C23—22no—
180C22×C23—22no—
181C22×C23—22no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—41no—
189C22×C23—41no—
190C22×C23C22×D411yescharacteristic
191C22×C23C22×D411yescharacteristic
192C22×C23C2×#4111yescharacteristic
193C22×C23C2×#4111yescharacteristic
194C22×C23C2×#4111yescharacteristic
195C22×C23C2×#4111yescharacteristic
196C22×C23C2×#4111yescharacteristic
197C2×D23—22no—
198C2×D23—22no—
199C2×D23—22no—
200C2×D23—41no—
201C2×D23—41no—
202C2×D23—41no—
203C2×D23—41no—
204C4×C23—22no—
205C4×C23—22no—
206C4×C23—41no—
207C4×C23—41no—
208C4×C23—41no—
209Dic23—22no—
210Dic23—22no—
211Dic23—22no—
212Dic23—41no—
213Dic23—41no—
214Dic23—41no—
215Dic23#12114yes—
216C2×C4×D4—231no—
217C2×C4×D4—231no—
218C2×C4×D4—231no—
219C2×#117—231no—
220#398—231no—
221#397—231no—
222#396—231no—
223#396—231no—
224#394—231no—
225#394—231no—
226#394D2311yescharacteristic, complemented
227#392—231no—
228C4×C4⋊C4—231no—
229C4×C22⋊C4—231no—
230C4×C22⋊C4—231no—
231C2×C23—42no—
232C2×C23—42no—
233C2×C23C2×#12111yescharacteristic
234C2×C23#52511yescharacteristic
235C2×C23#52511yescharacteristic
236C2×C23#52511yescharacteristic
237C2×C23#52911yescharacteristic
238C2×C23#52911yescharacteristic
239C2×C23#53211yescharacteristic
240D23—42no—
241C22×D4—231no—
242C22×D4—231no—
243C22×D4C2×D2311yescharacteristic
244C23×C4—231no—
245C23×C4—231no—
246C23×C4—231no—
247C4×D4—464no—
248C4×D4—464no—
249C4×D4—464no—
250#117—464no—
251C2×C4⋊C4—231no—
252C2×C4⋊C4—231no—
253C2×C4⋊C4—231no—
254C2×C4⋊C4—231no—
255C2×C4⋊C4—231no—
256C2×C4⋊C4—231no—
257C2×C4⋊C4C2×D2311yescharacteristic
258C2×C22⋊C4—231no—
259C2×C22⋊C4—231no—
260C2×C22⋊C4—231no—
261C2×C22⋊C4—231no—
262C2×C22⋊C4—231no—
263C2×C22⋊C4—231no—
264C2×C22⋊C4—231no—
265C2×C22⋊C4—231no—
266C2×C22⋊C4C2×D2311yescharacteristic
267C2×C22⋊C4C2×D2311yescharacteristic
268C2×C22⋊C4C2×D2311yescharacteristic
269C2×C22⋊C4C2×D2311yescharacteristic
270C2×C42—231no—
271C2×C42—231no—
272C2×C42—231no—
273C2×C42—231no—
274#95—231no—
275#95—231no—
276#95—231no—
277#95—231no—
278#95—231no—
279#95C2×D2311yescharacteristic
280C23#239211yescharacteristic, complemented, Sylow
281C24—231no—
282C24C22×D2311yescharacteristic
283C24C22×D2311yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—462no—
288C2×D4—462no—
289C2×D4—462no—
290C2×D4—462no—
291C2×D4—462no—
292C2×D4—462no—
293C22×C4—231no—
294C22×C4—234no—
295C22×C4—231no—
296C22×C4—231no—
297C22×C4—231no—
298C22×C4—231no—
299C22×C4—231no—
300C22×C4—231no—
301C22×C4—462no—
302C22×C4—462no—
303C22×C4—462no—
304C22×C4—462no—
305C22×C4—462no—
306C22×C4—462no—
307C22×C4—462no—
308C22×C4—462no—
309C22×C4C22×D2311yescharacteristic
310C22×C4C22×D2311yescharacteristic
311C22×C4C22×D2311yescharacteristic
312C22×C4C22×D2311yescharacteristic
313C22×C4C22×D2311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—462no—
316C4⋊C4—462no—
317C4⋊C4—462no—
318C4⋊C4—462no—
319C4⋊C4—462no—
320C4⋊C4—462no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—462no—
326C22⋊C4—462no—
327C22⋊C4—462no—
328C22⋊C4—462no—
329C22⋊C4—462no—
330C22⋊C4—462no—
331C22⋊C4—462no—
332C22⋊C4—462no—
333C42—234no—
334C42—462no—
335C42—462no—
336C42—462no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—232no—
350C23—461no—
351C23—461no—
352C23—461no—
353C23—461no—
354C23—461no—
355C23—461no—
356C23D4×D2312yes—
357C23#6729012yes—
358C23C23×D2311yescharacteristic
359D4—28no—
360D4—468no—
361D4—468no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—232no—
376C2×C4—232no—
377C2×C4—232no—
378C2×C4—232no—
379C2×C4—232no—
380C2×C4—232no—
381C2×C4—468no—
382C2×C4—461no—
383C2×C4—461no—
384C2×C4—461no—
385C2×C4—461no—
386C2×C4—461no—
387C2×C4—461no—
388C2×C4—461no—
389C2×C4—461no—
390C2×C4—461no—
391C2×C4—461no—
392C2×C4—461no—
393C2×C4—461no—
394C2×C4—461no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—924no—
398C2×C4—924no—
399C2×C4D4×D2312yes—
400C2×C4#6729012yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—462no—
416C22—462no—
417C22—462no—
418C22—921no—
419C22—921no—
420C22—921no—
421C22—921no—
422C22C2×D4×D2311yescharacteristic
423C22C2×D4×D2311yescharacteristic
424C22C2×#6729011yescharacteristic
425C22C2×#6729011yescharacteristic
426C22#41×D2311yescharacteristic
427C22#41×D2311yescharacteristic
428C22#41×D2311yescharacteristic
429C4—22no—
430C4—22no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—234no—
435C4—462no—
436C4—462no—
437C4—462no—
438C4—921no—
439C4—921no—
440C4—921no—
441C2—42no—
442C2—42no—
443C2—922no—
444C2#121×D2311yescharacteristic
445C2#1309292311yescharacteristic
446C2#1309292511yescharacteristic
447C2#1309292711yescharacteristic
448C2#1309294411yescharacteristic
449C2#1309294611yescharacteristic
450C2#1309296211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutator, socle, cosocleC23×C23C24
FittingC23×#394C2
prime radical#13092325C2
hypercenter#394D23
hypocenterC23#2392
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic23C2semidirect
2. C2×(C22⋊D23)⋊C4C2semidirect
3. C2×(C22⋊D23)⋊C4C2semidirect
4. C2×#10625048C2semidirect
5. #13092351C2semidirect
6. #13092345C2semidirect
7. #13092340C2semidirect
8. #13092339C2semidirect
9. #13092333C2semidirect
10. #13092332C2semidirect
12. C4⋊C4×Dic23C2semidirect
13. C22⋊C4×Dic23C2semidirect
14. #13092264C2semidirect
15. C23×#394C2semidirect
77. C22×Dic23D4semidirect
110. C4×Dic23D4semidirect
226. #394D23semidirect
280. C23#2392semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic232
C2×(C22⋊D23)⋊C42
C2×#106250482
#130923512
#130923452
#130923402
#130923392
#130923332
#130923322
#130923252
C4⋊C4×Dic232
C22⋊C4×Dic232
#130922642
C23×#3942
#239223