Finite Group Databasebeta

← #11864522

Subgroups — #11864522

Order 1152.

1479 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic, complemented
3C22×#3718C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592933C211yesmaximal, characteristic, complemented
6#10591185C214yesmaximal, complemented
7#10591170C214yesmaximal, complemented
8#10591099C211yesmaximal, characteristic, complemented
9#10591083C211yesmaximal, characteristic, complemented
10#84117—31nomaximal
11#83411—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1010—24no—
14C3×#1010—24no—
15C2×C3×D3×Q8—21no—
16C2×C3×#237—22no—
17C2×C3×#237—21no—
18C2×C3×#235C2212yes—
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2212yes—
22C22×C3×Dic6C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#944—21no—
26C3×#936—21no—
27C3×#935—22no—
28C3×#926C2211yescharacteristic
29C3×#924C2214yes—
30C2×#3718—24no—
31C2×#3718C2214yes—
32C2×#3718C2212yes—
33#63827—24no—
34C2×#3715C2212yes—
35#63657C2214yes—
36#63565C2212yes—
37#63565C2214yes—
38#63562C2212yes—
39C2×C3×2−1+4—31no—
40C2×#1010D311yescharacteristic
41C3×#536—31no—
42#5825D311yescharacteristic, complemented
43C2×#951—31no—
44C22×#216—31no—
45C22×#216—31no—
46C2×#942—31no—
47#5239—34no—
48#5234—31no—
49#5234—31no—
50#5234—61no—
51#5233—31no—
52#5228—34no—
53#5225—31no—
54#5050—34no—
55#5047—34no—
56#5004—31no—
57#5002—31no—
58C32×#41—22no—
59C32×#41—22no—
60C2×C32×Q8D411yescharacteristic
61C2×C32×D4D412yes—
62C2×C32×D4D411yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—22no—
66C2×C3×#67—21no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3—21no—
70C3×D3×Q8—28no—
71C3×#237—216no—
72C3×#237—28no—
73C3×#235—22no—
74C3×#235—24no—
75C3×#235—24no—
76C3×#235D414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6—21no—
82C2×C3×Dic6—22no—
83C2×C3×Dic6—24no—
84C2×C3×Dic6—24no—
85C2×C3×Dic6—22no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—21no—
88C2×C3×Dic6D414yes—
89C2×C3×Dic6C2312yes—
90C2×C3×Dic6C2311yescharacteristic
91C2×C3×Dic6C2312yes—
92#3748—22no—
93C2×C3⋊(C3⋊C8)—22no—
94C2×C3⋊(C3⋊C8)C2312yes—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—24no—
97C3×#217—21no—
98C3×C4⋊Dic3C2312yes—
99C3×Dic3⋊C4—24no—
100C3×C4×Dic3—21no—
101#3718—24no—
102#3718—28no—
103#3715—24no—
104#3011—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C2×D311yescharacteristic
114C22×C3×Q8—31no—
115C22×C3×Q8—32no—
116C22×C3×Q8—31no—
117C22×C3×Q8—61no—
118#1010—24no—
119#1010—24no—
120C2×D3×Q8—21no—
121C2×#237—22no—
122C2×#237—21no—
123C2×#235C2×D312yes—
124C2×#235C2×D311yescharacteristic
125C22×Dic6C2×D312yes—
126C22×Dic6C2×D311yescharacteristic
127C22×Dic6C2×D311yescharacteristic
128C3×C4⋊Q8—61no—
129C3×#124—61no—
130C3×#123—62no—
131C3×C22⋊Q8—34no—
132C3×#117—31no—
133#951—64no—
134#944—21no—
135C2×#216—32no—
136C2×#216—34no—
137C2×#216—32no—
138C2×#216—34no—
139C2×#216—64no—
140C2×#216—64no—
141#942—64no—
142C2×#215—32no—
143#936—21no—
144#935—22no—
145C2×#214—32no—
146#926C2×D311yescharacteristic
147#924C2×D314yes—
148C2×#208—31no—
149C2×#208—31no—
150C2×#208—61no—
151C22×C3⋊C8—31no—
152C22×C3⋊C8—31no—
153C22×C3⋊C8—61no—
154#835—34no—
155#835—32no—
156#832—32no—
157#830—34no—
158#830—34no—
159#830—64no—
160#810—32no—
161#810—34no—
162#809—32no—
163C23×C32C2×D412yes—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—21no—
166C32×Q8—22no—
167C32×D4—24no—
168C32×D4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×D412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C3×#67—28no—
177C3×#67—24no—
178C2×C3×Dic3—28no—
179C2×C3×Dic3—24no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—42no—
185C3×D12—21no—
186C3×D12C2×D412yes—
187C3×C4×D3—28no—
188C3×C4×D3—24no—
189C3×Dic6—28no—
190C3×Dic6—24no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6—22no—
194C3×Dic6—22no—
195C3×Dic6—42no—
196C3×Dic6C2×D412yes—
197C3×Dic6C2×D414yes—
198C3⋊(C3⋊C8)—22no—
199C3⋊(C3⋊C8)—22no—
200C2×2−1+4—31no—
201C2×#137—91no—
202C22×Q16—91no—
203#536—31no—
204#452—94no—
205#451—94no—
206#419—91no—
207#416—91no—
208#408—91no—
209C3×#41—22no—
210C3×#41—22no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—34no—
214C3×#41—42no—
215C3×#41—42no—
216C3×#41—64no—
217C3×#41—64no—
218C3×#41—616no—
219C3×#41—68no—
220C3×#41—62no—
221C2×C3×Q8—21no—
222C2×C3×Q8—34no—
223C2×C3×Q8—32no—
224C2×C3×Q8—31no—
225C2×C3×Q8—32no—
226C2×C3×Q8—64no—
227C2×C3×Q8—64no—
228C2×C3×Q8—68no—
229C2×C3×Q8—62no—
230C2×C3×Q8—62no—
231C2×C3×Q8—61no—
232C2×C3×Q8—61no—
233C2×C3×Q8—62no—
234C2×C3×Q8—62no—
235C2×C3×Q8#6711yescharacteristic
236C2×C3×Q8#6711yescharacteristic
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—31no—
240C2×C3×D4—62no—
241C2×C3×D4—61no—
242C2×C3×D4#6712yes—
243C2×C3×D4#6711yescharacteristic
244C2×C3×D4#6712yes—
245C2×C3×D4#6711yescharacteristic
246C22×C3×C4—21no—
247C22×C3×C4—22no—
248C22×C3×C4—62no—
249C22×C3×C4—61no—
250C22×C3×C4—62no—
251C22×C3×C4—61no—
252C22×C3×C4—61no—
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D312yes—
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D311yescharacteristic
257C2×#67—22no—
258C2×#67—21no—
259C22×Dic3—22no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262D3×Q8—28no—
263#237—216no—
264#237—28no—
265#235—22no—
266#235—24no—
267#235—24no—
268#235#6714yes—
269C2×D12C22×D311yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3—21no—
272C2×Dic6—22no—
273C2×Dic6—21no—
274C2×Dic6—22no—
275C2×Dic6—24no—
276C2×Dic6—24no—
277C2×Dic6—22no—
278C2×Dic6—22no—
279C2×Dic6—21no—
280C2×Dic6#6714yes—
281C2×Dic6C22×D312yes—
282C2×Dic6C22×D311yescharacteristic
283C2×Dic6C22×D312yes—
284C3×C4⋊C4—32no—
285C3×C4⋊C4—64no—
286C3×C22⋊C4—61no—
287C3×C22⋊C4—64no—
288C3×C42—61no—
289#217—24no—
290#217—21no—
291#216—68no—
292#216—64no—
293#216—64no—
294#216—68no—
295#215—64no—
296#214—64no—
297C4⋊Dic3C22×D312yes—
298Dic3⋊C4—24no—
299C4×Dic3—21no—
300#208—62no—
301#208—62no—
302#208—122no—
303C2×C3⋊C8—32no—
304C2×C3⋊C8—32no—
305C2×C3⋊C8—32no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—62no—
308C2×C3⋊C8—62no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8—122no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—24no—
315C22×C32#12012yes—
316C22×C32C22×D411yescharacteristic
317C2×C3×D3—22no—
318C2×C3×D3—42no—
319C32×C4—22no—
320C32×C4#12012yes—
321C32×C4C22×D411yescharacteristic
322C32×C4C22×D411yescharacteristic
323C3×Dic3—22no—
324C3×Dic3—24no—
325C3×Dic3—42no—
326C3×Dic3—42no—
3272−1+4—64no—
3282−1+4—64no—
329C2×#41—31no—
330C2×#41—32no—
331C2×#41—62no—
332C2×#41—61no—
333C2×#41D3211yescharacteristic
334C22×Q8—31no—
335C22×Q8—31no—
336C22×Q8—32no—
337C22×Q8—61no—
338#137—184no—
339C2×Q16—94no—
340C2×Q16—92no—
341C2×Q16—184no—
342C2×SD16—92no—
343C2×M16—91no—
344C22×C8—91no—
345C4⋊Q8—61no—
346#124—61no—
347#123—62no—
348C22⋊Q8—34no—
349#117—31no—
350#103—92no—
351#103—94no—
352#102—92no—
353C22⋊C8—94no—
354C23×C3—21no—
355C23×C3—22no—
356C23×C3—61no—
357C23×C3C2×#6712yes—
358C23×C3C2×#6712yes—
359C23×C3C2×#6711yescharacteristic
360C23×C3C2×#6711yescharacteristic
361C22×D3—21no—
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—34no—
365C3×Q8—32no—
366C3×Q8—42no—
367C3×Q8—68no—
368C3×Q8—64no—
369C3×Q8—62no—
370C3×Q8—61no—
371C3×Q8—62no—
372C3×Q8—62no—
373C3×Q8—122no—
374C3×D4—24no—
375C3×D4—24no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—32no—
379C3×D4—42no—
380C3×D4—44no—
381C3×D4—68no—
382C3×D4—64no—
383C3×D4—61no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—68no—
396C2×C3×C4—68no—
397C2×C3×C4—64no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—64no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—122no—
404C2×C3×C4D3×D412yes—
405C2×C3×C4D3×D412yes—
406C2×C3×C4C2×#6712yes—
407C2×C3×C4C2×#6712yes—
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C2×#6711yescharacteristic
410C2×C3×C4C2×#6712yes—
411C2×C3×C4C2×#6712yes—
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414#67—28no—
415#67—24no—
416C2×Dic3—28no—
417C2×Dic3—24no—
418C2×Dic3—21no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—42no—
423D12—21no—
424D12C2×#6712yes—
425C4×D3—28no—
426C4×D3—24no—
427Dic6—28no—
428Dic6—24no—
429Dic6—22no—
430Dic6—21no—
431Dic6—22no—
432Dic6—22no—
433Dic6—42no—
434Dic6C2×#6712yes—
435Dic6C2×#6714yes—
436C3⋊C8—62no—
437C3⋊C8—62no—
438C3⋊C8—62no—
439C3⋊C8—62no—
440C3⋊C8—122no—
441C3⋊C8—122no—
442C2×C32—22no—
443C2×C32—42no—
444C2×C32C2×#12011yescharacteristic
445C2×C32#57812yes—
446C3×D3—42no—
447#41—22no—
448#41—22no—
449#41—34no—
450#41—64no—
451#41—64no—
452#41—616no—
453#41—68no—
454#41—62no—
455C2×Q8—32no—
456C2×Q8—31no—
457C2×Q8—32no—
458C2×Q8—34no—
459C2×Q8—64no—
460C2×Q8—64no—
461C2×Q8—68no—
462C2×Q8—62no—
463C2×Q8—61no—
464C2×Q8—61no—
465C2×Q8—62no—
466C2×Q8—62no—
467C2×Q8—62no—
468C2×Q8#62511yescharacteristic
469C2×D4—31no—
470C2×D4—62no—
471C2×D4—61no—
472C2×D4#62512yes—
473C2×D4#62511yescharacteristic
474C22×C4—62no—
475C22×C4—61no—
476C22×C4—62no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4C2×D3212yes—
480C22×C4C2×D3211yescharacteristic
481Q16—188no—
482Q16—184no—
483SD16—184no—
484M16—182no—
485C2×C8—92no—
486C2×C8—92no—
487C2×C8—182no—
488C4⋊C4—32no—
489C4⋊C4—64no—
490C22⋊C4—61no—
491C22⋊C4—64no—
492C42—61no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—24no—
497C22×C3—24no—
498C22×C3—22no—
499C22×C3—21no—
500C22×C3—22no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—44no—
504C22×C3—62no—
505C22×C3—122no—
506C22×C3#93712yes—
507C22×C3#95312yes—
508C22×C3C22×#6711yescharacteristic
509C22×C3C22×#6711yescharacteristic
510C2×D3—22no—
511C2×D3—42no—
512C3×C4—22no—
513C3×C4—22no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—22no—
517C3×C4—42no—
518C3×C4—64no—
519C3×C4—62no—
520C3×C4—122no—
521C3×C4—122no—
522C3×C4#93712yes—
523C3×C4#95312yes—
524C3×C4C2×D3×D411yescharacteristic
525C3×C4C2×D3×D411yescharacteristic
526C3×C4C22×#6711yescharacteristic
527C3×C4C22×#6711yescharacteristic
528Dic3—22no—
529Dic3—24no—
530Dic3—42no—
531Dic3—42no—
532C32#301111yescharacteristic, complemented, Sylow
533C23—61no—
534C23C2×#62512yes—
535C23C2×#62511yescharacteristic
536Q8—22no—
537Q8—34no—
538Q8—32no—
539Q8—68no—
540Q8—62no—
541Q8—61no—
542Q8—64no—
543Q8—62no—
544Q8—62no—
545Q8—122no—
546D4—24no—
547D4—22no—
548D4—32no—
549D4—68no—
550D4—64no—
551D4—61no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—68no—
555C2×C4—68no—
556C2×C4—62no—
557C2×C4—61no—
558C2×C4—64no—
559C2×C4—64no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—122no—
563C2×C4C2×#62512yes—
564C2×C4C2×#62511yescharacteristic
565C2×C4D3×#6712yes—
566C2×C4D3×#6712yes—
567C2×C4C22×D3211yescharacteristic
568C8—182no—
569C8—182no—
570C2×C3—22no—
571C2×C3—22no—
572C2×C3—22no—
573C2×C3—21no—
574C2×C3—42no—
575C2×C3—42no—
576C2×C3—42no—
577C2×C3—82no—
578C2×C3—122no—
579C2×C3C2×#93711yescharacteristic
580C2×C3#583812yes—
581C2×C3#583812yes—
582C2×C3C2×#95311yescharacteristic
583D3—42no—
584C22—22no—
585C22—24no—
586C22—22no—
587C22—62no—
588C22—122no—
589C22#6397612yes—
590C22C22×#62511yescharacteristic
591C4—22no—
592C4—64no—
593C4—62no—
594C4—122no—
595C4—122no—
596C4#6397612yes—
597C4C2×D3×#6711yescharacteristic
598C4C2×D3×#6711yescharacteristic
599C3—21no—
600C3#8341111yescharacteristic, complemented
601C3#8411711yescharacteristic, complemented
602C2—22no—
603C2—42no—
604C2—122no—
605C2#1059544512yes—
606C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
hypercenterC2×#41D32
hypocenterC32#3011
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5825C2semidirect
3. C22×#3718C2semidirect
4. C2×#63827C2semidirect
5. #10592933C2semidirect
6. #10591185C2semidirect
7. #10591170C2semidirect
8. #10591099C2semidirect
9. #10591083C2semidirect
42. #5825D3semidirect
532. C32#3011semidirect
600. C3#83411semidirect
601. C3#84117semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C3×#58252
C22×#37182
C2×#638272
#105929332
#105911852
#105911702
#105910992
#105910832
#841173
#834113