Finite Group Databasebeta

← #11811915

Subgroups — #11811915

Order 1152.

1837 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C2×#64084C211yesmaximal, characteristic, complemented
3C2×#63866C211yesmaximal, characteristic, complemented
4C2×#63857C211yesmaximal, characteristic, complemented
5C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×#4929C211yesmaximal, characteristic, complemented
7#10591375C214yesmaximal, complemented
8#10591320C211yesmaximal, characteristic, complemented
9#10591312C214yesmaximal, complemented
10#76498—31nomaximal
11#73489—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626C2212yes—
17C22×#624C2212yes—
18C2×#3799—24no—
19C2×#3799—24no—
20C2×#3799—24no—
21C2×C32×C42C2211yescharacteristic
22C2×#3752C2214yes—
23#64084—24no—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2214yes—
29C2×#3722C2214yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31#63866—24no—
32#63857—24no—
33C3×C3⋊#95C2214yes—
34C3×C3⋊#95C2212yes—
35C22×#239—31no—
36C22×#235—31no—
37C2×#944—31no—
38C2×#924—31no—
39C2×#897—31no—
40C2×#875—31no—
41C2×#875—31no—
42C2×#875—61no—
43C2×#869—31no—
44C3×#391—31no—
45C3×C4×C22⋊C4—31no—
46#4988—31no—
47#4961—34no—
48#4939—31no—
49C4×(C2×D3)⋊C4D311yescharacteristic, complemented
50#4929D311yescharacteristic, complemented
51#4672—34no—
52#4668—34no—
53#4668—34no—
54C23×C3⋊D3C2312yes—
55C23×C3×D3C2311yescharacteristic
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)D414yes—
62C2×#634—22no—
63C2×#634—22no—
64C2×#634—22no—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2311yescharacteristic
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3D414yes—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6D414yes—
75C2×#626—24no—
76C2×#626—24no—
77C2×#626—24no—
78C2×#624—24no—
79C2×#624—24no—
80C2×#624—24no—
81#3799—232no—
82C32×C42—22no—
83#3752—28no—
84C3×(C2×D3)⋊C4—24no—
85C3×C4⋊Dic3—22no—
86C3×C4×Dic3—22no—
87Dic3⋊Dic3—24no—
88Dic3⋊Dic3—28no—
89#3722—28no—
90(C2×D3)⋊Dic3—24no—
91#2432—91noSylow
92C22×C3×Q8—31no—
93C23×C3×C4—31no—
94C22×#67—32no—
95C2×#239—64no—
96C2×#239—64no—
97C2×#239—64no—
98C2×#235—64no—
99C2×#235—64no—
100C2×#235—64no—
101C22×D12—31no—
102C22×D12—31no—
103C22×D12—32no—
104C22×D12—61no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3C2×D311yescharacteristic
108C22×Dic6—31no—
109C22×Dic6—31no—
110C22×Dic6—61no—
111C22×Dic6C2×D311yescharacteristic
112C2×C3×C4⋊C4—31no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C42—21no—
115C2×C3×C42—31no—
116C2×C3×C42C2×D311yescharacteristic
117C2×C3×C42C2×D311yescharacteristic
118C2×#217—32no—
119#944—64no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4—34no—
123C2×(C2×D3)⋊C4—34no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—64no—
126C2×(C2×D3)⋊C4C2×D312yes—
127C2×C4⋊Dic3—32no—
128C2×C4⋊Dic3—34no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130#924—64no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—34no—
133C2×C4×Dic3C2×D311yescharacteristic
134#897—64no—
135#875—64no—
136#875—64no—
137#875—68no—
138#869—64no—
139C3×#95—32no—
140C3×#95—34no—
141C3⋊#95C2×D312yes—
142C3⋊#95C2×D314yes—
143C23×C32C2411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—24no—
147C22×C3⋊D3—24no—
148C22×C3⋊D3C2×D414yes—
149C22×C3×D3—21no—
150C22×C3×D3—21no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3C2×D412yes—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C4⋊(C3⋊D3)—28no—
164#634—44no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—24no—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D414yes—
175C2×C3×Dic3#4114yescomplemented
176C3×C4×D3—28no—
177C3×Dic6—28no—
178#626—216no—
179#624—216no—
180C22×#41—91no—
181C2×C4⋊Q8—91no—
182C2×#124—91no—
183C2×C22⋊Q8—91no—
184#394—94no—
185#391—31no—
186#390—91no—
187#385—94no—
188C4×C22⋊C4—31no—
189C24×C3—31no—
190C23×D3—32no—
191C23×D3—32no—
192C23×D3—62no—
193C23×D3C22×D311yescharacteristic
194C2×C3×Q8—34no—
195C2×C3×Q8—62no—
196C2×C3×Q8—62no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—31no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4—34no—
203C22×C3×C4—32no—
204C22×C3×C4—62no—
205C22×C3×C4—62no—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—64no—
211C2×#67—64no—
212C2×#67—64no—
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—62no—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D311yescharacteristic
219C22×Dic3C22×D312yes—
220#239—632no—
221#235—632no—
222C2×D12—34no—
223C2×D12—34no—
224C2×D12—64no—
225C2×D12—64no—
226C2×D12—64no—
227C2×D12—64no—
228C2×D12—62no—
229C2×D12—62no—
230C2×D12—62no—
231C2×D12—62no—
232C2×D12—122no—
233C2×D12—122no—
234C2×C4×D3—22no—
235C2×C4×D3—22no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3D1214yes—
243C2×Dic6—22no—
244C2×Dic6—22no—
245C2×Dic6—64no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—62no—
251C2×Dic6—62no—
252C2×Dic6—122no—
253C2×Dic6—122no—
254C2×Dic6D1214yes—
255C3×C4⋊C4—62no—
256C3×C22⋊C4—64no—
257C3×C42—24no—
258C3×C42—22no—
259C3×C42—22no—
260C3×C42—62no—
261#217—64no—
262(C2×D3)⋊C4—24no—
263(C2×D3)⋊C4—68no—
264(C2×D3)⋊C4—68no—
265(C2×D3)⋊C4—68no—
266(C2×D3)⋊C4—616no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—68no—
269C4⋊Dic3—22no—
270C4⋊Dic3—68no—
271C4⋊Dic3—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—68no—
274C4×Dic3—22no—
275C22×C32C22×D411yescharacteristic
276C22×C32C22×D411yescharacteristic
277C22×C32C22×D411yescharacteristic
278C22×C32C2×#4112yes—
279C22×C322−1+412yes—
280C2×C3⋊D3—24no—
281C2×C3⋊D3—28no—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—44no—
285C2×C3×D3—22no—
286C2×C3×D3—22no—
287C2×C3×D3—22no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C32×C4—42no—
291C32×C4#12014yes—
292C3⋊Dic3—42no—
293C3×Dic3—22no—
294C3×Dic3—24no—
295C3×Dic3—24no—
296C3×Dic3—42no—
297C2×#41—184no—
298C2×#41—184no—
299C2×#41—184no—
300C22×Q8—31no—
301C22×Q8—91no—
302C22×D4—92no—
303C22×D4—91no—
304C23×C4—31no—
305C23×C4—92no—
306C4⋊Q8—184no—
307#124—184no—
308C22⋊Q8—184no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—92no—
311C2×C4⋊C4—94no—
312C2×C22⋊C4—32no—
313C2×C22⋊C4—94no—
314C2×C22⋊C4—92no—
315C2×C22⋊C4—94no—
316C2×C42—31no—
317C2×C42D3211yescharacteristic
318#95—32no—
319#95—34no—
320C23×C3—21no—
321C23×C3—32no—
322C23×C3—61no—
323C23×C3—61no—
324C23×C3—62no—
325C23×C3—62no—
326C23×C3C23×D311yescharacteristic
327C23×C3C23×D311yescharacteristic
328C22×D3—22no—
329C22×D3—21no—
330C22×D3—21no—
331C22×D3—22no—
332C22×D3—34no—
333C22×D3—34no—
334C22×D3—64no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—64no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—64no—
341C22×D3—64no—
342C22×D3—64no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—124no—
346C22×D3—124no—
347C22×D3C2×D1212yes—
348C3×Q8—68no—
349C2×C3×C4—24no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—32no—
360C2×C3×C4—34no—
361C2×C3×C4—34no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—62no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—68no—
371C2×C3×C4—62no—
372C2×C3×C4—64no—
373C2×C3×C4C2×D1212yes—
374C2×C3×C4C2×D1212yes—
375C2×C3×C4D3×D412yes—
376C2×C3×C4D3×D412yes—
377C2×C3×C4D3×D412yes—
378C2×C3×C4D3×D412yes—
379#67—616no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—24no—
388C2×Dic3—64no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3C2×D1214yes—
398C2×Dic3C2×D1212yes—
399C2×Dic3#23514yescomplemented
400D12—616no—
401D12—68no—
402D12—68no—
403D12—128no—
404C4×D3—28no—
405C4×D3—616no—
406C4×D3—616no—
407Dic6—28no—
408Dic6—128no—
409Dic6—124no—
410Dic6—124no—
411C2×C32C2×#12011yescharacteristic
412C2×C32#53211yescharacteristic
413C2×C32#53611yescharacteristic
414C2×C32#54712yes—
415C2×C32#54812yes—
416C3⋊D3—44no—
417C3×D3—42no—
418C24—31no—
419C24—92no—
420#41—1832no—
421C2×Q8—34no—
422C2×Q8—62no—
423C2×Q8—62no—
424C2×Q8—182no—
425C2×Q8—182no—
426C2×Q8—182no—
427C2×D4—94no—
428C2×D4—184no—
429C2×D4—184no—
430C2×D4—184no—
431C2×D4—182no—
432C2×D4—182no—
433C22×C4—31no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—34no—
437C22×C4—32no—
438C22×C4—62no—
439C22×C4—62no—
440C22×C4—92no—
441C22×C4—184no—
442C22×C4—184no—
443C22×C4—184no—
444C22×C4C2×D3212yes—
445C22×C4C2×D3211yescharacteristic
446C4⋊C4—62no—
447C4⋊C4—184no—
448C4⋊C4—188no—
449C22⋊C4—64no—
450C22⋊C4—188no—
451C22⋊C4—188no—
452C22⋊C4—184no—
453C42—22no—
454C42—62no—
455C22×C3—22no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—22no—
459C22×C3—21no—
460C22×C3—62no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—122no—
464C22×C3—122no—
465C22×C3C22×D1211yescharacteristic
466C22×C3C22×D1211yescharacteristic
467C22×C3C2×#23512yes—
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C2×D3×D411yescharacteristic
470C22×C3C2×D3×D411yescharacteristic
471C22×C3C2×D3×D411yescharacteristic
472C22×C3#100712yes—
473C22×C3D3×#4112yes—
474C22×C3#101012yes—
475C2×D3—22no—
476C2×D3—22no—
477C2×D3—22no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—64no—
481C2×D3—64no—
482C2×D3—68no—
483C2×D3—68no—
484C2×D3—124no—
485C2×D3—128no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—124no—
491C2×D3—124no—
492C2×D3—242no—
493C2×D3—244no—
494C2×D3—242no—
495C3×C4—24no—
496C3×C4—44no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—62no—
500C3×C4—64no—
501C3×C4—64no—
502C3×C4—122no—
503C3×C4#88214yes—
504C3×C4#88214yes—
505Dic3—24no—
506Dic3—22no—
507Dic3—24no—
508Dic3—42no—
509Dic3—124no—
510Dic3—122no—
511Dic3—122no—
512C32#243211yescharacteristic, complemented, Sylow
513C23—32no—
514C23—62no—
515C23—61no—
516C23—62no—
517C23—61no—
518C23—94no—
519C23—184no—
520C23—182no—
521C23—182no—
522C23—184no—
523C23C22×D3211yescharacteristic
524Q8—68no—
525Q8—364no—
526D4—1816no—
527D4—188no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—32no—
532C2×C4—34no—
533C2×C4—34no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—61no—
539C2×C4—62no—
540C2×C4—68no—
541C2×C4—62no—
542C2×C4—64no—
543C2×C4—1816no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—182no—
547C2×C4D3×D1212yes—
548C2×C4D3×D1212yes—
549C2×C4#381112yes—
550C2×C3—22no—
551C2×C3—21no—
552C2×C3—22no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—122no—
556C2×C3#547711yescharacteristic
557C2×C3C2×#88211yescharacteristic
558C2×C3C2×#88211yescharacteristic
559C2×C3#552611yescharacteristic
560C2×C3#555112yes—
561C2×C3#555212yes—
562C2×C3#557612yes—
563C2×C3#563112yes—
564C2×C3#566811yescharacteristic
565C2×C3#572411yescharacteristic
566D3—42no—
567D3—124no—
568D3—124no—
569D3—244no—
570C22—62no—
571C22—62no—
572C22—62no—
573C22—122no—
574C22—122no—
575C22—188no—
576C22—184no—
577C22—362no—
578C22—364no—
579C22—362no—
580C22#6429712yes—
581C22C2×D3×D1211yescharacteristic
582C22C2×D3×D1211yescharacteristic
583C22D3×#23512yes—
584C22C2×#381111yescharacteristic
585C4—42no—
586C4—64no—
587C4—62no—
588C4—64no—
589C4—122no—
590C4—362no—
591C4#6392314yes—
592C3—21no—
593C3#7348911yescharacteristic, complemented
594C3#7649811yescharacteristic, complemented
595C2—122no—
596C2—364no—
597C2#1059389311yescharacteristic
598C2#1059389912yes—
599C2#1059396911yescharacteristic
600C2#1059483412yes—
601C2C2×#6392311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC22×#3799C2
hypercenterC2×C42D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#64084C2semidirect
3. C2×#63866C2semidirect
4. C2×#63857C2semidirect
5. C3×C4×(C2×D3)⋊C4C2semidirect
6. C3×#4929C2semidirect
7. #10591375C2semidirect
8. #10591320C2semidirect
9. #10591312C2semidirect
49. C4×(C2×D3)⋊C4D3semidirect
50. #4929D3semidirect
175. C2×C3×Dic3#41semidirect
399. C2×Dic3#235semidirect
512. C32#2432semidirect
593. C3#73489semidirect
594. C3#76498semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
C2×#640842
C2×#638662
C2×#638572
C3×C4×(C2×D3)⋊C42
C3×#49292
#105913752
#105913202
#105913122
#764983
#734893