Finite Group Databasebeta

← #15682716

Subgroups — #15682716

Order 2944.

712 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625161C211yesmaximal, characteristic, complemented
2C2×#10625089C211yesmaximal, characteristic, complemented
3C2×#10625087C211yesmaximal, characteristic, complemented
4#13092997C211yesmaximal, characteristic, complemented
5#13092576C211yesmaximal, characteristic, complemented
6#13092572C211yesmaximal, characteristic, complemented
7#13092571C211yesmaximal, characteristic, complemented
8#13092563C211yesmaximal, characteristic, complemented
9#13092562C211yesmaximal, characteristic, complemented
10#13092558C211yesmaximal, characteristic, complemented
11#13092557C211yesmaximal, characteristic, complemented
12#13092415C211yesmaximal, characteristic, complemented
13#103×D23C211yesmaximal, characteristic, complemented
14#13092382C211yesmaximal, characteristic, complemented
15C23×#452C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17#10625161—24no—
18#10625161—24no—
19C2×#67292C2211yescharacteristic
20C2×Q8×D23C2211yescharacteristic
21C2×Q8×D23C2211yescharacteristic
22C2×#67290—21no—
23C2×#67290—21no—
24C2×#67290C2211yescharacteristic
25C2×#67290C2211yescharacteristic
26C2×#67288—21no—
27C2×#67288C2211yescharacteristic
28C22×Dic46—21no—
29C22×Dic46C2211yescharacteristic
30C2×Q16×C23C2211yescharacteristic
31C2×SD16×C23C2211yescharacteristic
32C23×C22⋊Q8C2211yescharacteristic
33#10625117C2211yescharacteristic
34C2×#67275C2211yescharacteristic
35C2×#67275C2211yescharacteristic
36C2×#67274C2211yescharacteristic
37C2×#67272C2211yescharacteristic
38#10625101C2211yescharacteristic
39#10625089—24no—
40#10625087—24no—
41C2×#67263C2211yescharacteristic
42C2×#67263C2211yescharacteristic
43C2×#67262C2211yescharacteristic
44C2×C8×D23C2211yescharacteristic
45#10625067—21no—
46#10625066—21no—
47#10625066C2211yescharacteristic
48C4⋊C4×D23C2211yescharacteristic
49#10625055—21no—
50#10625055—21no—
51C23×#103C2211yescharacteristic
52C23×#102C2211yescharacteristic
53C23×C22⋊C8C2211yescharacteristic
54#10625017C2211yescharacteristic
55#10625014C2211yescharacteristic
56C22⋊(C23⋊C8)C2211yescharacteristic
57(C2×D23)⋊C8C2211yescharacteristic
58(C2×D23)⋊C8C2211yescharacteristic
59#10624998C2211yescharacteristic
60#10624998C2211yescharacteristic
61#10624992C2211yescharacteristic
62#10624992C2211yescharacteristic
63#41×C23—22no—
64#41×C23—22no—
65C2×Q8×C23C2311yescharacteristic
66C2×Q8×C23C2311yescharacteristic
67C2×D4×C23—21no—
68C2×D4×C23C2311yescharacteristic
69C22×C4×C23—21no—
70C22×C4×C23C2311yescharacteristic
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23D411yescharacteristic
75C2×C22⋊D23D411yescharacteristic
76C22×Dic23—21no—
77C22×Dic23—21no—
78C22×Dic23—21no—
79#67292—22no—
80#67292—22no—
81Q8×D23—22no—
82Q8×D23—22no—
83Q8×D23—22no—
84Q8×D23D414yescomplemented
85#67290—28no—
86#67290—28no—
87#67290—22no—
88#67290—22no—
89#67290—22no—
90#67290D414yescomplemented
91#67288—28no—
92#67288—22no—
93#67288—22no—
94C2×D92—21no—
95C2×D92—21no—
96C2×D92D411yescharacteristic
97C2×D92C2311yescharacteristic
98C2×C4×D23—21no—
99C2×C4×D23—21no—
100C2×C4×D23—21no—
101C2×C4×D23—21no—
102C2×C4×D23C2311yescharacteristic
103C2×C4×D23C2311yescharacteristic
104C2×Dic46—28no—
105C2×Dic46—21no—
106C2×Dic46—21no—
107C2×Dic46—21no—
108C2×Dic46—22no—
109C2×Dic46—22no—
110C2×Dic46D411yescharacteristic
111C2×Dic46C2311yescharacteristic
112C2×Dic46C2311yescharacteristic
113Q16×C23—22no—
114SD16×C23—22no—
115C2×C8×C23C2311yescharacteristic
116C2×C8×C23C2311yescharacteristic
117C4⋊C4×C23—21no—
118C4⋊C4×C23C2311yescharacteristic
119C22⋊C4×C23—21no—
120#67275—22no—
121#67275—22no—
122#67274—22no—
123#67272—22no—
124(C2×D23)⋊C4—21no—
125(C2×D23)⋊C4—21no—
126(C2×D23)⋊C4—21no—
127C4⋊Dic23C2311yescharacteristic
128Dic23⋊C4—21no—
129Dic23⋊C4—21no—
130C2×C23⋊C8C2311yescharacteristic
131C2×C23⋊C8C2311yescharacteristic
132#67263—22no—
133#67263—22no—
134#67262—22no—
135C8×D23—22no—
136C23×C23—21no—
137C23×C23C2×D411yescharacteristic
138C22×D23—21no—
139C22×D23C2×D411yescharacteristic
140C22×D23C2×D411yescharacteristic
141Q8×C23—21no—
142Q8×C23—21no—
143Q8×C23—21no—
144Q8×C23C2×D412yes—
145D4×C23—24no—
146D4×C23—21no—
147D4×C23C2×D412yes—
148C2×C4×C23—24no—
149C2×C4×C23—21no—
150C2×C4×C23—21no—
151C2×C4×C23—21no—
152C2×C4×C23—21no—
153C2×C4×C23—21no—
154C2×C4×C23C2×D411yescharacteristic
155C2×C4×C23C2411yescharacteristic
156C22⋊D23—24no—
157C22⋊D23—22no—
158C22⋊D23—24no—
159C22⋊D23—22no—
160C22⋊D23—81no—
161C2×Dic23—24no—
162C2×Dic23—24no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—24no—
166C2×Dic23—21no—
167C2×Dic23C2×D411yescharacteristic
168C2×Dic23C2×D411yescharacteristic
169D92—22no—
170D92—21no—
171D92—21no—
172D92—42no—
173D92—81no—
174C4×D23—24no—
175C4×D23—24no—
176C4×D23—21no—
177C4×D23—21no—
178C4×D23—42no—
179C4×D23—81no—
180C4×D23C2×D412yes—
181C4×D23C2×D412yes—
182Dic46—24no—
183Dic46—24no—
184Dic46—21no—
185Dic46—21no—
186Dic46—22no—
187Dic46—24no—
188Dic46C2×D412yes—
189Dic46C2×D412yes—
190C8×C23—21no—
191C8×C23—21no—
192C23⋊C8—21no—
193C23⋊C8—21no—
194#3013—231nomaximal, Sylow
195C22×C23—21no—
196C22×C23—22no—
197C22×C23—21no—
198C22×C23—21no—
199C22×C23—41no—
200C22×C23—41no—
201C22×C23C22×D411yescharacteristic
202C2×D23—21no—
203C2×D23—21no—
204C2×D23—21no—
205C2×D23—21no—
206C2×D23—21no—
207C2×D23—41no—
208C2×D23—41no—
209C2×D23—41no—
210C2×D23#12012yes—
211C4×C23—21no—
212C4×C23—22no—
213C4×C23—41no—
214C4×C23—41no—
215C4×C23C22×D411yescharacteristic
216C4×C23C22×D411yescharacteristic
217Dic23—21no—
218Dic23—22no—
219Dic23—22no—
220Dic23—41no—
221Dic23#12012yes—
222C2×2−1+4—231no—
223C2×#137—231no—
224C2×#135—231no—
225#537—231no—
226#452—231no—
227#452D2311yescharacteristic, complemented
228#451—231no—
229#451—231no—
230#449—231no—
231#449—231no—
232#448—231no—
233#448—231no—
234#417—231no—
235C2×#103—231no—
236#408—231no—
237C2×C23—41no—
238C2×C23—42no—
239C2×C23C2×#12011yescharacteristic
240C2×C23#57711yescharacteristic
241C2×C23#57811yescharacteristic
242D23—22no—
243D23—41no—
244D23—81no—
2452−1+4—464no—
2462−1+4—464no—
247C2×#41—231no—
248C2×#41—231no—
249C2×#41—231no—
250C2×#41—231no—
251C2×#41—461no—
252C2×#41—461no—
253C2×#41—461no—
254C2×#41C2×D2311yescharacteristic
255C22×Q8—231no—
256C22×Q8—231no—
257C22×Q8—231no—
258C22×Q8—461no—
259#137—464no—
260#135—464no—
261C2×Q16—231no—
262C2×Q16—231no—
263C2×Q16C2×D2311yescharacteristic
264C2×SD16—231no—
265C2×SD16—231no—
266C2×SD16—231no—
267C2×SD16C2×D2311yescharacteristic
268C2×D8—231no—
269C2×M16—231no—
270C22×C8—231no—
271C22⋊Q8—231no—
272C22⋊Q8—461no—
273C22⋊Q8C2×D2311yescharacteristic
274#121—231no—
275#121—231no—
276#121—461no—
277#121—461no—
278#121—461no—
279C2×C4⋊C4—231no—
280#103—231no—
281#103—231no—
282#103—231no—
283#103—231no—
284#103—231no—
285#103C2×D2311yescharacteristic
286#102—231no—
287#102C2×D2311yescharacteristic
288C22⋊C8—231no—
289C22⋊C8—231no—
290C22⋊C8—231no—
291C22⋊C8C2×D2311yescharacteristic
292C23#301311yescharacteristic, complemented, Sylow
293#41—22no—
294#41—22no—
295#41—234no—
296#41—462no—
297#41—462no—
298#41—468no—
299#41—462no—
300#41—462no—
301#41—462no—
302#41—462no—
303#41—468no—
304#41—468no—
305#41—462no—
306C2×Q8—231no—
307C2×Q8—234no—
308C2×Q8—231no—
309C2×Q8—231no—
310C2×Q8—461no—
311C2×Q8—461no—
312C2×Q8—462no—
313C2×Q8—462no—
314C2×Q8—468no—
315C2×Q8—462no—
316C2×Q8—462no—
317C2×Q8—462no—
318C2×Q8—461no—
319C2×Q8C22×D2311yescharacteristic
320C2×Q8C22×D2311yescharacteristic
321C2×D4—21no—
322C2×D4—231no—
323C2×D4—231no—
324C2×D4—231no—
325C2×D4—231no—
326C2×D4—461no—
327C2×D4—461no—
328C2×D4—461no—
329C2×D4—461no—
330C2×D4—461no—
331C2×D4C22×D2311yescharacteristic
332C22×C4—21no—
333C22×C4—231no—
334C22×C4—231no—
335C22×C4—461no—
336C22×C4—461no—
337C22×C4—461no—
338C22×C4—461no—
339C22×C4—461no—
340C22×C4—461no—
341C22×C4—461no—
342C22×C4C22×D2311yescharacteristic
343Q16—22no—
344Q16—462no—
345Q16—462no—
346SD16—22no—
347SD16—462no—
348SD16—462no—
349SD16—462no—
350D8—462no—
351M16—462no—
352C2×C8—231no—
353C2×C8—231no—
354C2×C8—462no—
355C2×C8C22×D2311yescharacteristic
356C2×C8C22×D2311yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—231no—
359C4⋊C4—461no—
360C4⋊C4—461no—
361C4⋊C4C22×D2311yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—461no—
364C22⋊C4—461no—
365C22⋊C4—461no—
366C23—21no—
367C23—231no—
368C23—231no—
369C23—461no—
370C23D4×D2311yescharacteristic
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—232no—
375Q8—232no—
376Q8—462no—
377Q8—464no—
378Q8—464no—
379Q8—464no—
380Q8—461no—
381Q8—461no—
382Q8D4×D2312yes—
383D4—24no—
384D4—21no—
385D4—462no—
386D4—462no—
387D4—462no—
388D4—464no—
389D4—464no—
390D4—461no—
391D4—461no—
392D4—922no—
393D4—1841no—
394D4—1841no—
395D4D4×D2312yes—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—231no—
403C2×C4—232no—
404C2×C4—232no—
405C2×C4—231no—
406C2×C4—464no—
407C2×C4—464no—
408C2×C4—464no—
409C2×C4—464no—
410C2×C4—464no—
411C2×C4—461no—
412C2×C4—461no—
413C2×C4—461no—
414C2×C4—461no—
415C2×C4—461no—
416C2×C4—922no—
417C2×C4—1841no—
418C2×C4D4×D2311yescharacteristic
419C2×C4C23×D2311yescharacteristic
420C8—21no—
421C8—21no—
422C8—461no—
423C8—461no—
424C22—21no—
425C22—22no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—41no—
430C22—232no—
431C22—461no—
432C22—461no—
433C22—461no—
434C22—461no—
435C22—461no—
436C22—921no—
437C22—921no—
438C22—921no—
439C22C2×D4×D2311yescharacteristic
440C4—21no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—232no—
445C4—461no—
446C4—462no—
447C4—462no—
448C4—921no—
449C4C2×D4×D2311yescharacteristic
450C4C2×D4×D2311yescharacteristic
451C2—41no—
452C2—42no—
453C2—462no—
454C2—921no—
455C2—1841no—
456C2#120×D2311yescharacteristic
457C2#1309322411yescharacteristic
458C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#452C2
socleC22×C23C22×D4
hypercenter#452D23
hypocenterC23#3013
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#10625161C2semidirect
2. C2×#10625089C2semidirect
3. C2×#10625087C2semidirect
4. #13092997C2semidirect
5. #13092576C2semidirect
6. #13092572C2semidirect
7. #13092571C2semidirect
8. #13092563C2semidirect
9. #13092562C2semidirect
10. #13092558C2semidirect
11. #13092557C2semidirect
12. #13092415C2semidirect
13. #103×D23C2semidirect
14. #13092382C2semidirect
15. C23×#452C2semidirect
84. Q8×D23D4semidirect
90. #67290D4semidirect
227. #452D23semidirect
292. C23#3013semidirect

Maximal subgroups

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

subgroupindex
C2×#106251612
C2×#106250892
C2×#106250872
#130929972
#130925762
#130925722
#130925712
#130925632
#130925622
#130925582
#130925572
#130924152
#103×D232
#130923822
C23×#4522
#301323