Finite Group Databasebeta

← #11787688

Subgroups — #11787688

Order 1152.

815 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4#10591220C211yesmaximal, characteristic, complemented
5#10591100C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#72100—31nomaximal
9#70365—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12Q8×C3⋊Dic3—21no—
13D4×C3⋊Dic3—21no—
14D4×C3⋊Dic3—22no—
15#64135—21no—
16#64135C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×#951—22no—
20C3×#951C414yescomplemented
21C2×C3×#216—21no—
22C2×C3×#214—21no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C3×#837—22no—
27#63579—22no—
28#63566—21no—
29#63566—21no—
30C2×C3×#137—31no—
31#5827—31no—
32#5827—31no—
33#5827—61no—
34C2×#951D311yescharacteristic
35C2×C3×#104—31no—
36C2×#837D311yescharacteristic
37#5229—31no—
38#5225—31no—
39#5120—31no—
40#4929—31no—
41#4555—31no—
42#4554—31no—
43#4554—31no—
44#4523—31no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41C2×C412yes—
48C32×#41D412yes—
49C2×C32×Q8D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3D412yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6C2×C412yescomplemented
64#3757—22no—
65#3757—21no—
66C4⋊(C3⋊Dic3)—22no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)D411yescharacteristic
70C4⋊(C3⋊Dic3)D411yescharacteristic
71C4×C3⋊Dic3—22no—
72C4×C3⋊Dic3—21no—
73C3×#216—24no—
74C3×#214—24no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208C2×C412yescomplemented
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83#1882—91noSylow
84C2×C3×#41—21no—
85C2×C3×#41C2×D311yescharacteristic
86C2×C3×#41C2×D311yescharacteristic
87C22×C3×Q8—31no—
88C22×Dic6C2×D311yescharacteristic
89C3×#137—34no—
90C3×#137—62no—
91C2×C3×Q16—61no—
92C2×C3×SD16—61no—
93C2×C3×M16—31no—
94C2×C3×M16—31no—
95C2×C3×C42—31no—
96#951—22no—
97#951Dic314yescomplemented
98Q8×Dic3—62no—
99Q8×Dic3—61no—
100Q8×Dic3—61no—
101C2×#216—21no—
102D4×Dic3—62no—
103D4×Dic3—62no—
104D4×Dic3—64no—
105D4×Dic3—62no—
106D4×Dic3—61no—
107D4×Dic3—61no—
108C2×#214—21no—
109#926—31no—
110#926—31no—
111#926—61no—
112#926—61no—
113#926—61no—
114#926—62no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—61no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3—62no—
121C2×C4×Dic3C2×D311yescharacteristic
122C2×#208C2×D311yescharacteristic
123C2×#208C2×D311yescharacteristic
124C3×#104—62no—
125#837—22no—
126#835—61no—
127#835—61no—
128C3⋊#95—62no—
129C3⋊#95—62no—
130#816—61no—
131#816—61no—
132C23×C32—21no—
133C23×C32C2×D411yescharacteristic
134C32×Q8—21no—
135C32×Q8C22⋊C412yes—
136C32×D4—22no—
137C32×D4—22no—
138C32×D4—21no—
139C32×D4C22⋊C412yes—
140C2×C32×C4—21no—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—42no—
153C2×C3⋊Dic3—82no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—41no—
163C3×Dic6—41no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—41no—
166C2×#137—31no—
167#520—91no—
168C2×#104—31no—
169#419—91no—
170#391—91no—
171#343—91no—
172#339—91no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—22no—
180C3×#41—22no—
181C3×#41C4×D312yes—
182C3×#41C2×Dic312yes—
183C3×#41#6712yes—
184C3×#41#6712yes—
185C2×C3×Q8—21no—
186C2×C3×Q8—32no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×Q8D1211yescharacteristic
193C2×C3×Q8#6711yescharacteristic
194C2×C3×D4—22no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4D1211yescharacteristic
199C2×C3×D4#6711yescharacteristic
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—62no—
213C22×Dic3—64no—
214C22×Dic3—62no—
215C22×Dic3—62no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6C2×Dic312yescomplemented
222C3×Q16—64no—
223C3×SD16—64no—
224C3×M16—32no—
225C3×M16—61no—
226C3×M16—61no—
227C3×M16—61no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C3×C42—61no—
231C3×C42—61no—
232#217—64no—
233#217—62no—
234#217—62no—
235#217—62no—
236#217—61no—
237#217—61no—
238#216—24no—
239#214—24no—
240C4⋊Dic3—31no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—62no—
247C4⋊Dic3—64no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4×Dic3—21no—
256C4×Dic3—21no—
257C4×Dic3—64no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263#208—21no—
264#208—21no—
265#208—21no—
266#208C2×Dic312yescomplemented
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
269C22×C32—22no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32C4×D411yescharacteristic
275C22×C32#12011yescharacteristic
276C22×C32#12111yescharacteristic
277C32×C4—22no—
278C32×C4C2×C22⋊C411yescharacteristic
279C32×C4C4×D411yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4#12311yescharacteristic
282C3⋊Dic3—42no—
283C3⋊Dic3—41no—
284C3⋊Dic3—41no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C2×#41D3211yescharacteristic
288C22×Q8—31no—
289#137—34no—
290#137—62no—
291C2×Q16—61no—
292C2×SD16—61no—
293C2×M16—31no—
294C2×M16—31no—
295C4×Q8—181no—
296C4×D4—182no—
297C4×D4—181no—
298#117—91no—
299#117—181no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—181no—
302C2×C42—31no—
303#104—62no—
304#103—181no—
305#103—181no—
306#95—182no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3D3×D411yescharacteristic
312C23×C3D3×D411yescharacteristic
313C3×Q8—22no—
314C3×Q8—21no—
315C3×Q8—21no—
316C3×Q8—22no—
317C3×Q8—62no—
318C3×Q8—62no—
319C3×Q8—121no—
320C3×Q8—121no—
321C3×Q8(C2×D3)⋊C412yes—
322C3×Q8#21712yes—
323C3×D4—24no—
324C3×D4—24no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—22no—
333C3×D4(C2×D3)⋊C412yes—
334C3×D4#21712yes—
335C2×C3×C4—22no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4C2×C4×D311yescharacteristic
357C2×C3×C4C2×D1211yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4C22×Dic311yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—64no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—62no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—242no—
386C2×Dic3—244no—
387C2×Dic3—242no—
388C2×Dic3—242no—
389Dic6—22no—
390Dic6—22no—
391Dic6—41no—
392Dic6—41no—
393C3×C8—62no—
394C3×C8—121no—
395C3⋊C8—22no—
396C3⋊C8—41no—
397C2×C32—21no—
398C2×C32—21no—
399C2×C32—42no—
400C2×C32#38611yescharacteristic
401C2×C32#45511yescharacteristic
402C2×C32#45611yescharacteristic
403#41—21no—
404#41—21no—
405#41D3×Dic312yes—
406#41#62512yes—
407C2×Q8—32no—
408C2×Q8—61no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8#62611yescharacteristic
414C2×D4—21no—
415C2×D4#62611yescharacteristic
416C22×C4—21no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—92no—
420C22×C4—182no—
421C22×C4C2×D3211yescharacteristic
422Q16—64no—
423SD16—64no—
424M16—32no—
425M16—61no—
426M16—61no—
427M16—61no—
428C2×C8—61no—
429C2×C8—61no—
430C4⋊C4—91no—
431C4⋊C4—91no—
432C4⋊C4—182no—
433C4⋊C4—181no—
434C4⋊C4—181no—
435C22⋊C4—182no—
436C22⋊C4—181no—
437C42—61no—
438C42—61no—
439C42—182no—
440C42—181no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—24no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3#67⋊C411yescharacteristic
460C22×C3#88211yescharacteristic
461C22×C3D4×Dic311yescharacteristic
462C22×C3#93711yescharacteristic
463C22×C3#93911yescharacteristic
464C22×C3#93911yescharacteristic
465C3×C4—24no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—122no—
473C3×C4—122no—
474C3×C4#67⋊C411yescharacteristic
475C3×C4#88611yescharacteristic
476C3×C4C2×(C2×D3)⋊C411yescharacteristic
477C3×C4D4×Dic311yescharacteristic
478C3×C4#93511yescharacteristic
479C3×C4#93911yescharacteristic
480C3×C4#93911yescharacteristic
481C3×C4C2×#21711yescharacteristic
482Dic3—42no—
483Dic3—42no—
484Dic3—124no—
485Dic3—122no—
486Dic3—122no—
487Dic3—122no—
488Dic3—121no—
489Dic3—121no—
490Dic3—122no—
491Dic3—121no—
492Dic3—121no—
493C32#188211yescharacteristic, complemented, Sylow
494C23—21no—
495C23#381111yescharacteristic
496Q8—21no—
497Q8—62no—
498Q8—62no—
499Q8—121no—
500Q8—121no—
501Q8(C2×D3)⋊Dic312yes—
502D4—22no—
503D4—22no—
504D4—21no—
505D4(C2×D3)⋊Dic312yes—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—121no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—182no—
518C2×C4—362no—
519C2×C4—722no—
520C2×C4C2×D3×Dic311yescharacteristic
521C2×C4#380511yescharacteristic
522C2×C4#380511yescharacteristic
523C2×C4C2×#62511yescharacteristic
524C2×C4C2×#62611yescharacteristic
525C2×C4#381111yescharacteristic
526C8—62no—
527C8—121no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—41no—
536C2×C3—41no—
537C2×C3—44no—
538C2×C3—42no—
539C2×C3—42no—
540C2×C3#482511yescharacteristic
541C2×C3#482611yescharacteristic
542C2×C3#495811yescharacteristic
543C2×C3#520211yescharacteristic
544C2×C3#520511yescharacteristic
545C2×C3#522011yescharacteristic
546C22—21no—
547C22—21no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22#67⋊Dic311yescharacteristic
552C22#6398011yescharacteristic
553C22#6398111yescharacteristic
554C4—22no—
555C4—122no—
556C4—122no—
557C4—361no—
558C4—362no—
559C4—361no—
560C4C2×(C2×D3)⋊Dic311yescharacteristic
561C4#6396211yescharacteristic
562C4#67⋊Dic311yescharacteristic
563C4#6398011yescharacteristic
564C3—21no—
565C3#7036511yescharacteristic, complemented
566C3#7210011yescharacteristic, complemented
567C2—21no—
568C2—21no—
569C2—42no—
570C2#1059166811yescharacteristic
571C2#1059169011yescharacteristic
572C2#1059171311yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#120
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1882
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591220C2semidirect
5. #10591100C2semidirect
6. #10589168C2semidirect
7. #10589162C2semidirect
20. C3×#951C4semidirect
63. C2×C3×Dic6C2×C4semidirect
80. C3×#208C2×C4semidirect
97. #951Dic3semidirect
221. C2×Dic6C2×Dic3semidirect
266. #208C2×Dic3semidirect
493. C32#1882semidirect
565. C3#70365semidirect
566. C3#72100semidirect

Maximal subgroups

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

subgroupindex
#105962982
C2×C3×#9512
C2×C3×#8372
#105912202
#105911002
#105891682
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