Finite Group Databasebeta

← #11865114

Subgroups — #11865114

Order 1152.

1531 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2#10596287C211yesmaximal, characteristic, complemented
3#10594795C212yesmaximal, complemented
4C2×C3×#836C211yesmaximal, characteristic, complemented
5#10591649C214yesmaximal, complemented
6#10591646C214yesmaximal, complemented
7#10591110C212yesmaximal, complemented
8#84116—31nomaximal
9#78709—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C3×#1007—22no—
13C3×#1007—24no—
14C3×#1007C2214yes—
15C2×C3×#239—22no—
16C2×C3×D3×Q8—22no—
17C2×C3×#235—22no—
18C2×C3×#235C2212yes—
19#64156C2212yescomplemented
20#64155—22no—
21#64153C2212yescomplemented
22#64138—22no—
23#64135C2211yescharacteristic
24C2×C3×#208C2212yes—
25#63833—22no—
26#63831C2214yescomplemented
27#63830—22no—
28#63829—24no—
29#63825C2214yescomplemented
30C3×#836C2214yescomplemented
31#63568C2218yescomplemented
32C2×C3×2−1+4—31no—
33C2×#1007D311yescharacteristic, complemented
34#5822—32no—
35#5816—31no—
36#5816—31no—
37#5816—61no—
38#5748—32no—
39C2×C3×#101—31no—
40#5246—34no—
41#5245—34no—
42#5236—32no—
43C2×#836D311yescharacteristic, complemented
44#5139—32no—
45#4753—34no—
46#4752—34no—
47C2×C32×Q8—22no—
48C2×C32×Q8—22no—
49C2×C32×Q8D412yes—
50C2×C32×Q8C2312yes—
51C22×C32×C4D412yes—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—22no—
55#3828—22no—
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×#634C2311yescharacteristic
59C2×C3×#67—22no—
60C3×#239—28no—
61C3×#239—28no—
62C3×D3×Q8—28no—
63C3×D3×Q8—28no—
64C3×#235—28no—
65C3×#235—28no—
66C3×#235—22no—
67C3×#235—22no—
68C3×#235D414yes—
69C3×#235C2314yes—
70C2×C3×D12—22no—
71C2×C3×D12D412yes—
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6D412yes—
76#3757—21no—
77#3752—24no—
78C4⋊(C3⋊Dic3)—21no—
79#3750—24no—
80C4×C3⋊Dic3C2312yes—
81C3×#208—22no—
82C3×#208C2314yes—
83C2×C3×C3⋊C8—22no—
84#3719—24no—
85#3717—24no—
86#3716—24no—
87#3714—24no—
88#3020—91noSylow
89C3×2−1+4—34no—
90C3×2−1+4—64no—
91C3×2−1+4—62no—
92C2×C3×#41—32no—
93C2×C3×#41—62no—
94C2×C3×#41—62no—
95C22×C3×Q8—21no—
96C22×C3×Q8—62no—
97C22×C3×Q8C2×D311yescharacteristic
98C22×C3×Q8C2×D311yescharacteristic
99#1007—22no—
100#1007—24no—
101#1007C2×D314yes—
102C2×#239—22no—
103C2×D3×Q8—22no—
104C2×#235—22no—
105C2×#235—31no—
106C2×#235—31no—
107C2×#235—61no—
108C2×#235C2×D312yes—
109C2×C3×M16—32no—
110#951—34no—
111#950—64no—
112#949—34no—
113#947—32no—
114#947—32no—
115#947—62no—
116#946—64no—
117#946—62no—
118#946—62no—
119#944—32no—
120#944—32no—
121#944—62no—
122#942—62no—
123#932—62no—
124#929—64no—
125#929—62no—
126#929—62no—
127#926—31no—
128#926—31no—
129#926—61no—
130C2×#208C2×D312yes—
131#909—34no—
132#909—62no—
133#908—34no—
134#908—62no—
135#904—64no—
136C3×#101—34no—
137#837—38no—
138#836C2×D314yescomplemented
139#825—38no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—21no—
142C22×C3×D3—22no—
143C32×Q8—24no—
144C32×Q8—24no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D414yes—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2411yescharacteristic
152#638—41no—
153#638—41no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—21no—
156C4⋊(C3⋊D3)—22no—
157C4×C3⋊D3—42no—
158#634—22no—
159C3×#67—24no—
160C3×#67—24no—
161C2×C3×Dic3—22no—
162C3×D12—28no—
163C3×D12—22no—
164C3×D12C2×D414yes—
165C3×C4×D3—216no—
166C3×C4×D3—24no—
167C3×C4×D3—24no—
168C3×Dic6—28no—
169C3×Dic6—22no—
170C3×Dic6C2×D414yes—
171C3×C3⋊C8—24no—
172C2×2−1+4—31no—
173#575—92no—
174#536—91no—
175#456—94no—
176#454—94no—
177#421—92no—
178C2×#101—31no—
179C3×#41—34no—
180C3×#41—34no—
181C3×#41—68no—
182C3×#41—68no—
183C3×#41—68no—
184C3×#41—62no—
185C3×#41—68no—
186C3×#41—62no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C2×C3×Q8—22no—
190C2×C3×Q8—22no—
191C2×C3×Q8—22no—
192C2×C3×Q8—22no—
193C2×C3×Q8—32no—
194C2×C3×Q8—42no—
195C2×C3×Q8—42no—
196C2×C3×Q8—62no—
197C2×C3×Q8—68no—
198C2×C3×Q8—68no—
199C2×C3×Q8D1212yes—
200C2×C3×Q8#6712yes—
201C2×C3×Q8C22×D312yes—
202C2×C3×Q8C22×D312yes—
203C2×C3×D4—32no—
204C2×C3×D4—62no—
205C2×C3×D4—62no—
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—64no—
209C22×C3×C4—62no—
210C22×C3×C4D1212yes—
211C22×C3×C4#6712yes—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—22no—
215C2×#67—62no—
216C2×#67—61no—
217C2×#67—61no—
218#239—28no—
219#239—28no—
220D3×Q8—28no—
221D3×Q8—28no—
222#235—28no—
223#235—28no—
224#235—22no—
225#235—22no—
226#235—62no—
227#235—62no—
228#235—62no—
229#235—62no—
230#235—122no—
231#235—122no—
232#235#6714yes—
233#235C22×D314yes—
234C2×D12—22no—
235C2×D12—31no—
236C2×D12—31no—
237C2×D12—61no—
238C2×D12#6712yes—
239C2×C4×D3—24no—
240C2×C4×D3—22no—
241C2×C4×D3—62no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×Dic6—22no—
245C2×Dic6—31no—
246C2×Dic6—31no—
247C2×Dic6—61no—
248C2×Dic6#6712yes—
249C3×M16—34no—
250C3×M16—62no—
251C2×C3×C8—62no—
252#217—62no—
253#217—61no—
254#217—61no—
255#216—64no—
256#215—64no—
257#214—64no—
258#213—64no—
259(C2×D3)⋊C4—68no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262C4⋊Dic3—62no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265Dic3⋊C4—68no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—62no—
271#208—22no—
272#208C22×D314yes—
273C2×C3⋊C8—22no—
274Dic12—64no—
275D24—64no—
276#204—64no—
277#204—64no—
278C22×C32—41no—
279C22×C32#12011yescharacteristic
280C22×C32#12011yescharacteristic
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—42no—
283C2×C3⋊D3—41no—
284C2×C3×D3—24no—
285C2×C3×D3—44no—
286C32×C4—24no—
287C32×C4#12012yes—
288C32×C4C22×D412yes—
289C3⋊Dic3—42no—
290C3⋊Dic3—41no—
291C3×Dic3—24no—
2922−1+4—34no—
2932−1+4—64no—
2942−1+4—62no—
295C2×#41—32no—
296C2×#41—62no—
297C2×#41—62no—
298C2×#41—91no—
299C22×Q8—62no—
300C22×Q8D3211yescharacteristic
301#137—94no—
302#137—182no—
303AGL(1,ℤ/8)—94no—
304AGL(1,ℤ/8)—182no—
305#135—184no—
306C2×M16—32no—
307C4⋊Q8—92no—
308#124—92no—
309#123—182no—
310C22⋊Q8—182no—
311#117—91no—
312#104—98no—
313#101—34no—
314C23×C3—21no—
315C23×C3—62no—
316C23×C3C2×D1211yescharacteristic
317C23×C3C2×#6711yescharacteristic
318C22×D3—22no—
319C22×D3—62no—
320C22×D3—61no—
321C22×D3—61no—
322C3×Q8—24no—
323C3×Q8—24no—
324C3×Q8—24no—
325C3×Q8—24no—
326C3×Q8—34no—
327C3×Q8—44no—
328C3×Q8—44no—
329C3×Q8—68no—
330C3×Q8—62no—
331C3×D4—34no—
332C3×D4—68no—
333C3×D4—64no—
334C3×D4—64no—
335C3×D4—62no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—24no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—616no—
348C2×C3×C4—62no—
349C2×C3×C4—64no—
350C2×C3×C4—64no—
351C2×C3×C4C2×D1214yes—
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4D3×D412yes—
354C2×C3×C4D3×D412yes—
355C2×C3×C4C2×#6714yes—
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6712yes—
358C2×C3×C4C2×#6712yes—
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—24no—
362#67—24no—
363#67—122no—
364#67—122no—
365#67—121no—
366#67—121no—
367#67—121no—
368#67—121no—
369C2×Dic3—22no—
370C2×Dic3—64no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—61no—
374C2×Dic3—62no—
375C2×Dic3—61no—
376D12—28no—
377D12—22no—
378D12—62no—
379D12—62no—
380D12—122no—
381D12C2×#6714yes—
382C4×D3—216no—
383C4×D3—24no—
384C4×D3—24no—
385C4×D3—124no—
386C4×D3—122no—
387C4×D3—122no—
388Dic6—28no—
389Dic6—22no—
390Dic6—62no—
391Dic6—62no—
392Dic6—122no—
393Dic6C2×#6714yes—
394C3×C8—64no—
395C3⋊C8—24no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32—21no—
399C2×C32C2×#12011yescharacteristic
400C3⋊D3—81no—
401C3×D3—44no—
402#41—34no—
403#41—34no—
404#41—68no—
405#41—68no—
406#41—68no—
407#41—62no—
408#41—68no—
409#41—62no—
410#41—182no—
411#41—182no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—32no—
415C2×Q8—62no—
416C2×Q8—68no—
417C2×Q8—68no—
418C2×Q8—91no—
419C2×Q8#62612yes—
420C2×Q8C2×D3212yes—
421C2×D4—32no—
422C2×D4—62no—
423C2×D4—62no—
424C2×D4—91no—
425C2×D4—181no—
426C22×C4—64no—
427C22×C4—62no—
428C22×C4—181no—
429C22×C4#62612yes—
430C22×C4C2×D3211yescharacteristic
431Q16—184no—
432SD16—184no—
433SD16—184no—
434D8—184no—
435M16—34no—
436M16—62no—
437C2×C8—62no—
438C4⋊C4—181no—
439C4⋊C4—184no—
440C22⋊C4—181no—
441C22⋊C4—184no—
442C42—92no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—42no—
449C22×C3—64no—
450C22×C3—124no—
451C22×C3#88211yescharacteristic
452C22×C3#88211yescharacteristic
453C22×C3#95311yescharacteristic
454C22×C3#95311yescharacteristic
455C22×C3C22×D1211yescharacteristic
456C22×C3C22×#6711yescharacteristic
457C2×D3—24no—
458C2×D3—44no—
459C2×D3—122no—
460C2×D3—124no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—121no—
464C2×D3—121no—
465C3×C4—24no—
466C3×C4—24no—
467C3×C4—22no—
468C3×C4—22no—
469C3×C4—44no—
470C3×C4—64no—
471C3×C4#88212yes—
472C3×C4#95312yes—
473C3×C4C2×D3×D412yes—
474C3×C4C22×#6712yes—
475Dic3—24no—
476Dic3—122no—
477Dic3—124no—
478Dic3—122no—
479Dic3—122no—
480Dic3—121no—
481Dic3—121no—
482C32#302011yescharacteristic, complemented, Sylow
483C23—62no—
484C23—181no—
485C23C2×#62611yescharacteristic
486Q8—24no—
487Q8—24no—
488Q8—34no—
489Q8—68no—
490Q8—62no—
491Q8—182no—
492D4—34no—
493D4—68no—
494D4—64no—
495D4—64no—
496D4—62no—
497D4—182no—
498D4—361no—
499D4—361no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—616no—
503C2×C4—62no—
504C2×C4—64no—
505C2×C4—64no—
506C2×C4—182no—
507C2×C4—181no—
508C2×C4—362no—
509C2×C4C2×#62614yes—
510C2×C4C2×#62611yescharacteristic
511C2×C4D3×#6712yes—
512C2×C4D3×#6712yes—
513C2×C4C22×D3211yescharacteristic
514C8—64no—
515C2×C3—22no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—124no—
526C2×C3C2×#88211yescharacteristic
527C2×C3C2×#95311yescharacteristic
528D3—44no—
529D3—242no—
530D3—241no—
531D3—241no—
532C22—41no—
533C22—64no—
534C22—124no—
535C22—362no—
536C22—361no—
537C22#6397711yescharacteristic
538C22#6397711yescharacteristic
539C22C22×#62611yescharacteristic
540C4—24no—
541C4—64no—
542C4—362no—
543C4—361no—
544C4#6397712yes—
545C4C2×D3×#6712yes—
546C3—21no—
547C3#7870911yescharacteristic, complemented
548C3#8411611yescharacteristic, complemented
549C2—21no—
550C2—21no—
551C2—21no—
552C2—124no—
553C2—721no—
554C2C2×#6397711yescharacteristic
subgroupG/H
centerC2C2×#63977
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC2×C32C2×#120
hypercenterC22×Q8D32
hypocenterC32#3020
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. #10596287C2semidirect
3. #10594795C2semidirect
4. C2×C3×#836C2semidirect
5. #10591649C2semidirect
6. #10591646C2semidirect
7. #10591110C2semidirect
19. #64156C22semidirect
21. #64153C22semidirect
26. #63831C22semidirect
29. #63825C22semidirect
30. C3×#836C22semidirect
31. #63568C22semidirect
33. C2×#1007D3semidirect
43. C2×#836D3semidirect
138. #836C2×D3semidirect
482. C32#3020semidirect
547. C3#78709semidirect
548. C3#84116semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
#105962872
#105947952
C2×C3×#8362
#105916492
#105916462
#105911102
#841163
#787093