Finite Group Databasebeta

← #11811917

Subgroups — #11811917

Order 1152.

1801 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×#63873C211yesmaximal, characteristic, complemented
4C2×#63864C211yesmaximal, characteristic, complemented
5#10592687C211yesmaximal, characteristic, complemented
6C3×#4973C211yesmaximal, characteristic, complemented
7#10591378C214yesmaximal, complemented
8#10591292C214yesmaximal, complemented
9C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
10#82759—31nomaximal
11#76498—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626C2212yes—
17C22×#624C2212yes—
18C2×#3799—24no—
19C2×#3799—24no—
20C2×#3799—24no—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×#3752C2214yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#897—24no—
28C2×#3724C2214yes—
29C2×#3722C2214yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31#63873—24no—
32#63864—24no—
33C3×C3⋊#95C2214yes—
34#63579C2212yes—
35C22×#239—31no—
36C22×#235—31no—
37C2×C3×C22⋊Q8—31no—
38C2×#947—31no—
39C2×#944—31no—
40C2×#944—31no—
41C2×#897D311yescharacteristic, complemented
42C2×#875—31no—
43C3×#391—31no—
44C4×#217—31no—
45#4989—34no—
46#4988—31no—
47#4988—31no—
48#4988—61no—
49#4973D311yescharacteristic, complemented
50#4959—34no—
51C4×(C2×D3)⋊C4—31no—
52#4672—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—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2311yescharacteristic
65C22×C3×Dic3C2312yes—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3D414yes—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—22no—
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×C4⋊C4—22no—
83#3752—28no—
84C4×C3⋊Dic3—22no—
85C3×(C2×D3)⋊C4—24no—
86C3×C4⋊Dic3—24no—
87C3×C4×Dic3—22no—
88#3724—28no—
89#3722—28no—
90(C2×D3)⋊Dic3—24no—
91#2432—91noSylow
92C22×C3×Q8—31no—
93C22×C3×Q8—31no—
94C23×C3×C4—31no—
95C22×#67—32no—
96C2×#239—64no—
97C2×#239—64no—
98C2×#239—64no—
99C2×#235—64no—
100C2×#235—64no—
101C2×#235—64no—
102C22×D12—31no—
103C22×D12—31no—
104C22×D12—32no—
105C22×D12—61no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3C2×D311yescharacteristic
109C22×Dic6C2×D311yescharacteristic
110C22×Dic6C2×D311yescharacteristic
111C3×C22⋊Q8—64no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C22⋊C4—32no—
117C2×C3×C42—31no—
118C2×#217—32no—
119#947—64no—
120#944—64no—
121#944—64no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—34no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—34no—
126C2×(C2×D3)⋊C4—34no—
127C2×(C2×D3)⋊C4—64no—
128C2×(C2×D3)⋊C4C2×D312yes—
129C2×C4⋊Dic3C2×D312yes—
130C2×Dic3⋊C4—34no—
131C2×Dic3⋊C4—34no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—61no—
135C2×C4×Dic3C2×D311yescharacteristic
136#897—24no—
137#875—64no—
138C3×#95—34no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95C2×D314yes—
142C23×C32C2411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—24no—
146C22×C3⋊D3—24no—
147C22×C3⋊D3C2×D414yes—
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3C2×D412yes—
153C2×C32×C4—22no—
154C2×C32×C4—24no—
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3#4114yescomplemented
161C4⋊(C3⋊D3)—28no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C2×D414yes—
173C2×C3×Dic3C2×D412yes—
174C3×C4×D3—28no—
175C3×Dic6—28no—
176C3×Dic6—44no—
177#626—216no—
178#624—216no—
179C22×#41—91no—
180C2×C4⋊Q8—91no—
181C2×#124—91no—
182C2×C22⋊Q8—31no—
183#394—94no—
184#391—31no—
185#390—91no—
186#385—94no—
187C4×C22⋊C4—91no—
188C24×C3—31no—
189C23×D3—32no—
190C23×D3—32no—
191C23×D3—62no—
192C23×D3C22×D311yescharacteristic
193C2×C3×Q8—34no—
194C2×C3×Q8—62no—
195C2×C3×Q8—62no—
196C2×C3×Q8—62no—
197C2×C3×Q8—62no—
198C2×C3×Q8—62no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—31no—
202C22×C3×C4—32no—
203C22×C3×C4—34no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—64no—
213C2×#67—64no—
214C2×#67—64no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—62no—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D311yescharacteristic
222#239—632no—
223#235—632no—
224C2×D12—34no—
225C2×D12—34no—
226C2×D12—64no—
227C2×D12—64no—
228C2×D12—64no—
229C2×D12—64no—
230C2×D12—62no—
231C2×D12—62no—
232C2×D12—62no—
233C2×D12—62no—
234C2×D12—122no—
235C2×D12—122no—
236C2×C4×D3—22no—
237C2×C4×D3—22no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×C4×D3#6714yes—
245C2×Dic6—22no—
246C2×Dic6—22no—
247C2×Dic6—22no—
248C2×Dic6—22no—
249C2×Dic6—22no—
250C2×Dic6D1214yes—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—22no—
253C3×C4⋊C4—42no—
254C3×C4⋊C4—64no—
255C3×C22⋊C4—64no—
256C3×C42—62no—
257#217—64no—
258(C2×D3)⋊C4—24no—
259(C2×D3)⋊C4—68no—
260(C2×D3)⋊C4—68no—
261(C2×D3)⋊C4—68no—
262(C2×D3)⋊C4—68no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—128no—
265C4⋊Dic3—24no—
266Dic3⋊C4—68no—
267Dic3⋊C4—68no—
268C4×Dic3—22no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C4×Dic3—122no—
272C22×C32C22×D411yescharacteristic
273C22×C32C22×D411yescharacteristic
274C22×C32C22×D411yescharacteristic
275C22×C32C2×#4112yes—
276C22×C322−1+412yes—
277C2×C3⋊D3—24no—
278C2×C3⋊D3—28no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C2×C3⋊D3—44no—
282C2×C3×D3—22no—
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C32×C4—42no—
288C32×C4#12014yes—
289C3⋊Dic3—24no—
290C3×Dic3—22no—
291C3×Dic3—24no—
292C3×Dic3—42no—
293C3×Dic3—42no—
294C2×#41—184no—
295C2×#41—184no—
296C2×#41—184no—
297C22×Q8—31no—
298C22×Q8—31no—
299C22×D4—92no—
300C22×D4—91no—
301C23×C4—31no—
302C23×C4—92no—
303C4⋊Q8—184no—
304#124—184no—
305C22⋊Q8—64no—
306C2×C4⋊C4—32no—
307C2×C4⋊C4—94no—
308C2×C4⋊C4D3211yescharacteristic
309C2×C22⋊C4—32no—
310C2×C22⋊C4—94no—
311C2×C22⋊C4—92no—
312C2×C22⋊C4—94no—
313C2×C42—31no—
314C2×C42—91no—
315#95—34no—
316#95—92no—
317C23×C3—21no—
318C23×C3—32no—
319C23×C3—61no—
320C23×C3—61no—
321C23×C3—62no—
322C23×C3—62no—
323C23×C3C23×D311yescharacteristic
324C23×C3C23×D311yescharacteristic
325C22×D3—21no—
326C22×D3—21no—
327C22×D3—22no—
328C22×D3—22no—
329C22×D3—34no—
330C22×D3—34no—
331C22×D3—64no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—64no—
336C22×D3—64no—
337C22×D3—64no—
338C22×D3—64no—
339C22×D3—62no—
340C22×D3—124no—
341C22×D3—122no—
342C22×D3—122no—
343C22×D3—124no—
344C22×D3C2×#6712yes—
345C3×Q8—68no—
346C3×Q8—124no—
347C2×C3×C4—22no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—34no—
355C2×C3×C4—32no—
356C2×C3×C4—44no—
357C2×C3×C4—42no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—68no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4C2×D1212yes—
370C2×C3×C4D3×D412yes—
371C2×C3×C4D3×D412yes—
372C2×C3×C4D3×D412yes—
373C2×C3×C4D3×D412yes—
374C2×C3×C4C2×#6712yes—
375#67—616no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—34no—
387C2×Dic3—34no—
388C2×Dic3—64no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—122no—
394C2×Dic3—122no—
395C2×Dic3C2×D1214yes—
396C2×Dic3C2×#6712yes—
397D12—616no—
398D12—68no—
399D12—68no—
400D12—128no—
401C4×D3—28no—
402C4×D3—616no—
403C4×D3—616no—
404Dic6—28no—
405Dic6—44no—
406C2×C32C2×#12011yescharacteristic
407C2×C32#53211yescharacteristic
408C2×C32#53611yescharacteristic
409C2×C32#54712yes—
410C2×C32#54812yes—
411C3⋊D3—44no—
412C3×D3—42no—
413C24—31no—
414C24—92no—
415#41—1832no—
416C2×Q8—34no—
417C2×Q8—62no—
418C2×Q8—62no—
419C2×Q8—62no—
420C2×Q8—62no—
421C2×Q8—62no—
422C2×D4—94no—
423C2×D4—184no—
424C2×D4—184no—
425C2×D4—184no—
426C2×D4—182no—
427C2×D4—182no—
428C22×C4—32no—
429C22×C4—31no—
430C22×C4—34no—
431C22×C4—32no—
432C22×C4—32no—
433C22×C4—62no—
434C22×C4—62no—
435C22×C4—92no—
436C22×C4—184no—
437C22×C4—184no—
438C22×C4—184no—
439C22×C4C2×D3212yes—
440C22×C4C2×D3211yescharacteristic
441C4⋊C4—22no—
442C4⋊C4—64no—
443C4⋊C4—188no—
444C22⋊C4—64no—
445C22⋊C4—188no—
446C22⋊C4—188no—
447C22⋊C4—184no—
448C42—62no—
449C42—182no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—21no—
455C22×C3—62no—
456C22×C3—62no—
457C22×C3—62no—
458C22×C3—122no—
459C22×C3—122no—
460C22×C3C22×D1211yescharacteristic
461C22×C3C2×D3×D411yescharacteristic
462C22×C3C2×D3×D411yescharacteristic
463C22×C3C2×D3×D411yescharacteristic
464C22×C3C2×D3×D411yescharacteristic
465C22×C3#100712yes—
466C22×C3#100712yes—
467C22×C3D3×#4112yes—
468C22×C3D3×#4112yes—
469C22×C3C22×#6711yescharacteristic
470C2×D3—22no—
471C2×D3—22no—
472C2×D3—22no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—68no—
478C2×D3—68no—
479C2×D3—124no—
480C2×D3—128no—
481C2×D3—124no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—124no—
486C2×D3—122no—
487C2×D3—242no—
488C2×D3—244no—
489C2×D3—242no—
490C3×C4—24no—
491C3×C4—42no—
492C3×C4—42no—
493C3×C4—62no—
494C3×C4—64no—
495C3×C4—82no—
496C3×C4—122no—
497C3×C4—122no—
498C3×C4#88214yes—
499C3×C4#93714yes—
500Dic3—24no—
501Dic3—22no—
502Dic3—42no—
503Dic3—42no—
504Dic3—64no—
505Dic3—64no—
506Dic3—124no—
507C32#243211yescharacteristic, complemented, Sylow
508C23—32no—
509C23—61no—
510C23—61no—
511C23—62no—
512C23—62no—
513C23—94no—
514C23—182no—
515C23—184no—
516C23—184no—
517C23—182no—
518C23C22×D3211yescharacteristic
519Q8—68no—
520Q8—124no—
521D4—1816no—
522D4—188no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—34no—
526C2×C4—32no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—68no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—94no—
539C2×C4—1816no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4D3×D1212yes—
543C2×C4#380212yes—
544C2×C4D3×#6712yes—
545C2×C3—21no—
546C2×C3—22no—
547C2×C3—21no—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—122no—
551C2×C3C2×#88211yescharacteristic
552C2×C3#557612yes—
553C2×C3#563112yes—
554C2×C3#563112yes—
555C2×C3#563312yes—
556C2×C3#566811yescharacteristic
557C2×C3#572411yescharacteristic
558C2×C3C2×#93711yescharacteristic
559C2×C3#581611yescharacteristic
560C2×C3#583211yescharacteristic
561D3—42no—
562D3—124no—
563D3—124no—
564D3—244no—
565C22—62no—
566C22—62no—
567C22—62no—
568C22—122no—
569C22—122no—
570C22—188no—
571C22—184no—
572C22—362no—
573C22—364no—
574C22—362no—
575C22C2×D3×D1211yescharacteristic
576C22C2×#380211yescharacteristic
577C22#6431212yes—
578C22#6431612yes—
579C22C2×D3×#6711yescharacteristic
580C4—42no—
581C4—62no—
582C4—64no—
583C4—122no—
584C4—122no—
585C4—184no—
586C4#6392214yes—
587C3—21no—
588C3#7649811yescharacteristic, complemented
589C3#8275911yescharacteristic, complemented
590C2—122no—
591C2—364no—
592C2#1059432912yes—
593C2#1059453012yes—
594C2C2×#6392211yescharacteristic
595C2#1059515311yescharacteristic
596C2#1059534011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#3799C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#897C2semidirect
3. C2×#63873C2semidirect
4. C2×#63864C2semidirect
5. #10592687C2semidirect
6. C3×#4973C2semidirect
7. #10591378C2semidirect
8. #10591292C2semidirect
9. C4×(C2×D3)⋊Dic3C2semidirect
41. C2×#897D3semidirect
49. #4973D3semidirect
160. C2×C3⋊Dic3#41semidirect
507. C32#2432semidirect
588. C3#76498semidirect
589. C3#82759semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
C2×C3×#8972
C2×#638732
C2×#638642
#105926872
C3×#49732
#105913782
#105912922
C4×(C2×D3)⋊Dic32
#827593
#764983