Finite Group Databasebeta

← #15676089

Subgroups — #15676089

Order 2944.

668 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625055C211yesmaximal, characteristic
2C2×C4×C22⋊D23C211yesmaximal, characteristic, complemented
3C2×#10625063C211yesmaximal, characteristic, complemented
4#13092318C211yesmaximal, characteristic, complemented
5#13092317C211yesmaximal, characteristic, complemented
6#13092317C211yesmaximal, characteristic, complemented
7#13092312C211yesmaximal, characteristic, complemented
8#13092310C211yesmaximal, characteristic, complemented
9#13092309C211yesmaximal, characteristic, complemented
10#13092296C211yesmaximal, characteristic, complemented
11#13092295C211yesmaximal, characteristic, complemented
12#13092288C211yesmaximal, characteristic, complemented
13#13092276C211yesmaximal, characteristic, complemented
14#13092268C211yesmaximal, characteristic, complemented
15C23×#385C211yesmaximal, characteristic, complemented
16C23×C4×C23C2211yescharacteristic
17C22×C22⋊D23C2211yescharacteristic
18C22×C22⋊D23C2211yescharacteristic
19C22×D92C2211yescharacteristic
20C22×C4×D23C2211yescharacteristic
21C22×C4×D23C2211yescharacteristic
22C2×C4⋊C4×C23C2211yescharacteristic
23C2×C4⋊C4×C23C2211yescharacteristic
24C2×C22⋊C4×C23C2211yescharacteristic
25C2×C22⋊C4×C23C2211yescharacteristic
26C2×C22⋊Dic23C2211yescharacteristic
27C2×C22⋊Dic23C2211yescharacteristic
28C4×C22⋊D23—24no—
29C2×(C2×D23)⋊C4C2211yescharacteristic
30C2×(C2×D23)⋊C4C2211yescharacteristic
31C2×(C2×D23)⋊C4C2211yescharacteristic
32C2×(C2×D23)⋊C4C2211yescharacteristic
33C2×(C2×D23)⋊C4C2211yescharacteristic
34C2×(C2×D23)⋊C4C2211yescharacteristic
35C2×(C2×D23)⋊C4C2211yescharacteristic
36C2×(C2×D23)⋊C4C2211yescharacteristic
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#10625063—24no—
47#10625055C418yescomplemented
48C23×#95C2211yescharacteristic
49C23×#95C2211yescharacteristic
50C23⋊#95C2211yescharacteristic
51C23⋊#95C2211yescharacteristic
52C23⋊#95C2211yescharacteristic
53C23⋊#95C2211yescharacteristic
54C24×C23C2311yescharacteristic
55C23×D23C2311yescharacteristic
56C23×D23C2311yescharacteristic
57C22×C4×C23—22no—
58C22×C4×C23—41no—
59C22×C4×C23—41no—
60C22×C4×C23C2311yescharacteristic
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—41no—
69C2×C22⋊D23—41no—
70C2×C22⋊D23C2×C414yes—
71C2×C22⋊D23C2×C414yescomplemented
72C22×Dic23C2311yescharacteristic
73C22×Dic23C2311yescharacteristic
74C22×Dic23C2311yescharacteristic
75C22×Dic23C2311yescharacteristic
76C22×Dic23C2311yescharacteristic
77C22×Dic23C2311yescharacteristic
78C2×D92—41no—
79C2×D92—41no—
80C2×D92C2×C414yescomplemented
81C2×C4×D23—22no—
82C2×C4×D23—22no—
83C2×C4×D23—22no—
84C2×C4×D23—41no—
85C2×C4×D23—41no—
86C2×C4×D23C2×C414yescomplemented
87C4⋊C4×C23—22no—
88C4⋊C4×C23—41no—
89C22⋊C4×C23—41no—
90C22⋊C4×C23C2×C414yescomplemented
91C22⋊Dic23—22no—
92C22⋊Dic23—41no—
93(C2×D23)⋊C4—22no—
94(C2×D23)⋊C4—22no—
95(C2×D23)⋊C4—22no—
96(C2×D23)⋊C4—41no—
97(C2×D23)⋊C4—41no—
98(C2×D23)⋊C4—41no—
99(C2×D23)⋊C4—41no—
100(C2×D23)⋊C4C2×C414yescomplemented
101C4⋊Dic23—22no—
102Dic23⋊C4—22no—
103Dic23⋊C4—22no—
104Dic23⋊C4—41no—
105Dic23⋊C4C2×C414yescomplemented
106C4×Dic23—22no—
107C4×Dic23—41no—
108C4×Dic23—41no—
109C4×Dic23D414yescomplemented
110C23×C23—21no—
111C23×C23—21no—
112C23×C23—21no—
113C23×C23—21no—
114C23×C23—21no—
115C23×C23—21no—
116C23×C23C22×C412yes—
117C23×C23C2411yescharacteristic
118C22×D23—21no—
119C22×D23—21no—
120C22×D23—21no—
121C22×D23—21no—
122C22×D23—21no—
123C22×D23—21no—
124C22×D23—21no—
125C22×D23—21no—
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—21no—
130C22×D23C22×C412yes—
131C22×D23C22×C412yes—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
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×C23—44no—
148C2×C4×C23C22×C412yes—
149C2×C4×C23C22×C412yes—
150C2×C4×C23C2×D412yes—
151C22⋊D23—28no—
152C22⋊D23—44no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—21no—
157C2×Dic23—21no—
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×Dic23C22×C412yes—
167C2×Dic23C22×C412yes—
168C2×Dic23C2×D412yes—
169C2×Dic23C2×D412yes—
170C2×Dic23#4112yes—
171D92—44no—
172C4×D23—28no—
173C4×D23—44no—
174#2324—231nomaximal, Sylow
175C22×C23—22no—
176C22×C23—22no—
177C22×C23—22no—
178C22×C23—41no—
179C22×C23—41no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23C23×C411yescharacteristic
183C22×C23C22×D411yescharacteristic
184C22×C23C2×#4111yescharacteristic
185C22×C23H(5,𝔽2)11yescharacteristic
186C22×C23H(5,𝔽2)11yescharacteristic
187C22×C23H(5,𝔽2)11yescharacteristic
188C22×C232−1+411yescharacteristic
189C2×D23—22no—
190C2×D23—22no—
191C2×D23—22no—
192C2×D23—22no—
193C2×D23—22no—
194C2×D23—22no—
195C2×D23—41no—
196C2×D23—41no—
197C2×D23—41no—
198C2×D23—41no—
199C2×D23—41no—
200C2×D23—41no—
201C2×D23—41no—
202C2×D23—41no—
203C4×C23—22no—
204C4×C23—22no—
205C4×C23—22no—
206C4×C23—41no—
207C4×C23—41no—
208C4×C23—41no—
209Dic23—22no—
210Dic23—22no—
211Dic23—41no—
212Dic23—41no—
213Dic23—41no—
214Dic23C4×D414yes—
215C2×#121—231no—
216C2×C4×D4—231no—
217C2×#117—231no—
218#390—231no—
219#390—231no—
220#390—231no—
221#389—231no—
222#388—231no—
223#388—231no—
224#386—231no—
225#386—231no—
226#385—231no—
227#385D2311yescharacteristic, complemented
228#380—231no—
229C4×C4⋊C4—231no—
230C2×C23—42no—
231C2×C23C2×C4×D411yescharacteristic
232C2×C23#51811yescharacteristic
233C2×C23#52011yescharacteristic
234C2×C23#53511yescharacteristic
235C2×C23#53711yescharacteristic
236C2×C23#54011yescharacteristic
237C2×C23#54211yescharacteristic
238D23—42no—
239D23—42no—
240C22×D4—231no—
241C22×D4—231no—
242C22×D4—231no—
243C23×C4—231no—
244C23×C4—231no—
245C23×C4C2×D2311yescharacteristic
246#121—238no—
247C4×D4—464no—
248#117—464no—
249C2×C4⋊C4—231no—
250C2×C4⋊C4—231no—
251C2×C4⋊C4—231no—
252C2×C4⋊C4—231no—
253C2×C4⋊C4—231no—
254C2×C4⋊C4C2×D2311yescharacteristic
255C2×C4⋊C4C2×D2311yescharacteristic
256C2×C22⋊C4—231no—
257C2×C22⋊C4—231no—
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×C42—231no—
269C2×C42—231no—
270C2×C42—231no—
271C2×C42—231no—
272#95—231no—
273#95—231no—
274#95—231no—
275#95—231no—
276#95C2×D2311yescharacteristic
277#95C2×D2311yescharacteristic
278C23#232411yescharacteristic, complemented, Sylow
279C24—231no—
280C24—231no—
281C24C22×D2311yescharacteristic
282C2×D4—234no—
283C2×D4—234no—
284C2×D4—234no—
285C2×D4—462no—
286C2×D4—462no—
287C2×D4—921no—
288C2×D4—921no—
289C2×D4—921no—
290C2×D4—921no—
291C22×C4—22no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—231no—
295C22×C4—231no—
296C22×C4—231no—
297C22×C4—234no—
298C22×C4—231no—
299C22×C4—231no—
300C22×C4—231no—
301C22×C4—462no—
302C22×C4—462no—
303C22×C4—462no—
304C22×C4—921no—
305C22×C4—921no—
306C22×C4C22×D2311yescharacteristic
307C22×C4C22×D2311yescharacteristic
308C22×C4C22×D2311yescharacteristic
309C22×C4C22×D2311yescharacteristic
310C22×C4C22×D2311yescharacteristic
311C22×C4C22×D2311yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—234no—
315C4⋊C4—462no—
316C4⋊C4—462no—
317C4⋊C4—462no—
318C4⋊C4—921no—
319C22⋊C4—41no—
320C22⋊C4—234no—
321C22⋊C4—462no—
322C22⋊C4—462no—
323C22⋊C4—462no—
324C22⋊C4—462no—
325C22⋊C4—921no—
326C22⋊C4—921no—
327C22⋊C4—921no—
328C22⋊C4—921no—
329C22⋊C4—921no—
330C22⋊C4C4×D2314yescomplemented
331C42—234no—
332C42—462no—
333C42—921no—
334C42—921no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—232no—
342C23—232no—
343C23—461no—
344C23—461no—
345C23—461no—
346C23—461no—
347C23—461no—
348C23—461no—
349C23—461no—
350C23—461no—
351C23—461no—
352C23—461no—
353C23—461no—
354C23—461no—
355C23C2×C4×D2312yes—
356C23C23×D2311yescharacteristic
357D4—468no—
358D4—924no—
359D4—924no—
360C2×C4—21no—
361C2×C4—21no—
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—44no—
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—924no—
396C2×C4C2×C4×D2312yes—
397C2×C4C2×C4×D2312yes—
398C2×C4D4×D2312yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—462no—
407C22—462no—
408C22—462no—
409C22—462no—
410C22—462no—
411C22—462no—
412C22—921no—
413C22—921no—
414C22—921no—
415C22—921no—
416C22—921no—
417C22—921no—
418C22—921no—
419C22—921no—
420C22C22×C4×D2311yescharacteristic
421C22C2×D4×D2311yescharacteristic
422C22#1062515511yescharacteristic
423C22#1062515511yescharacteristic
424C22#1062515811yescharacteristic
425C22#41×D2311yescharacteristic
426C22#1062516011yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—234no—
434C4—462no—
435C4—462no—
436C4—921no—
437C4—921no—
438C4—921no—
439C2—42no—
440C2—922no—
441C2—922no—
442C2C4×D4×D2311yescharacteristic
443C2#1309288911yescharacteristic
444C2#1309289811yescharacteristic
445C2#1309298211yescharacteristic
446C2#1309299711yescharacteristic
447C2#1309301911yescharacteristic
448C2#1309303711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#385C2
socle, cosocleC23×C23C24
prime radicalC2×#10625055C2
hypercenter#385D23
hypocenterC23#2324
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D23C2semidirect
3. C2×#10625063C2semidirect
4. #13092318C2semidirect
5. #13092317C2semidirect
6. #13092317C2semidirect
7. #13092312C2semidirect
8. #13092310C2semidirect
9. #13092309C2semidirect
10. #13092296C2semidirect
11. #13092295C2semidirect
12. #13092288C2semidirect
13. #13092276C2semidirect
14. #13092268C2semidirect
15. C23×#385C2semidirect
47. #10625055C4semidirect
71. C2×C22⋊D23C2×C4semidirect
80. C2×D92C2×C4semidirect
86. C2×C4×D23C2×C4semidirect
90. C22⋊C4×C23C2×C4semidirect
100. (C2×D23)⋊C4C2×C4semidirect
105. Dic23⋊C4C2×C4semidirect
109. C4×Dic23D4semidirect
227. #385D23semidirect
278. C23#2324semidirect
330. C22⋊C4C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250552
C2×C4×C22⋊D232
C2×#106250632
#130923182
#130923172
#130923122
#130923102
#130923092
#130922962
#130922952
#130922882
#130922762
#130922682
C23×#3852
#232423