Finite Group Databasebeta

← #11794059

Subgroups — #11794059

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591213C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70217—31nomaximal
9#69651—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×#3754—22no—
13C2×#3754—22no—
14C2×#3754—22no—
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#217—21no—
17C2×C3×#217—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#832—22no—
23#63579—21no—
24#63579—21no—
25Dic3⋊(C3⋊C8)—22no—
26#63567—22no—
27C22×#214—31no—
28C22×#214—31no—
29C22×#214—61no—
30C2×C3×#102—31no—
31C3×#390—31no—
32#5221D311yescharacteristic
33C2×#832D311yescharacteristic
34C2×#816—31no—
35C2×Dic3⋊C8—31no—
36#4973—31no—
37C2×#810—31no—
38#4929—31no—
39C2×C4⋊(C3⋊C8)—31no—
40#4529—31no—
41#4529—31no—
42C24×C32—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4D412yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634D412yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61#3754—28no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)D412yes—
65C3×#217—42no—
66C3×#217—42no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#2055—91noSylow
77C22×C3×D4—21no—
78C22×C3×D4C2×D311yescharacteristic
79C22×C3×D4C2×D311yescharacteristic
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C22⋊C4—61no—
87C2×C3×C22⋊C4—61no—
88C2×C3×C42—31no—
89C2×#217—21no—
90C2×#217—21no—
91C2×#214—62no—
92C2×#214—62no—
93C2×#214—62no—
94C2×#214—62no—
95C2×#214—64no—
96C2×#214—64no—
97C2×#214—64no—
98C2×#214—62no—
99C2×#214—62no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4×Dic3C2×D311yescharacteristic
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106C22×C3⋊C8C2×D311yescharacteristic
107C3×#102—62no—
108#832—22no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113#816—62no—
114Dic3⋊C8—62no—
115#810—62no—
116C4⋊(C3⋊C8)—62no—
117C23×C32—22no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32C2×D411yescharacteristic
125C32×D4—22no—
126C32×D4—22no—
127C32×D4—41no—
128C32×D4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138#634—22no—
139#634—22no—
140#634—41no—
141#634—41no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3SD1612yescomplemented
154C3⋊(C3⋊C8)—22no—
155C3×C3⋊C8—41no—
156C22×SD16—91no—
157C2×C4⋊C8—91no—
158C2×#103—91no—
159C2×#102—31no—
160#391—91no—
161#390—31no—
162#340—91no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—41no—
166C2×C3×D4—22no—
167C2×C3×D4—22no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—22no—
179C2×C3×D4—41no—
180C2×C3×D4—41no—
181C2×C3×D4—41no—
182C2×C3×D4D1212yes—
183C2×C3×D4#6712yes—
184C22×C3×C4—21no—
185C22×C3×C4—31no—
186C22×C3×C4—31no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—121no—
196C22×Dic3#6711yescharacteristic
197C22×Dic3#6711yescharacteristic
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C2×Dic6—62no—
202C2×Dic6—62no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—121no—
214C2×Dic6—121no—
215C2×Dic6—121no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C2×C3×C8—61no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C22⋊C4—122no—
224C3×C22⋊C4—122no—
225C3×C42—61no—
226C3×C42—61no—
227#217—42no—
228#217—42no—
229#214—616no—
230#214—68no—
231#214—68no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—21no—
236C4×Dic3—21no—
237C4×Dic3—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C22×C32—42no—
251C22×C32—42no—
252C22×C32—42no—
253C22×C32—81no—
254C22×C32—81no—
255C22×C32—81no—
256C22×C32—81no—
257C22×C32#12111yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32#12111yescharacteristic
260C22×C32C2×SD1611yescharacteristic
261C22×C32#13511yescharacteristic
262C22×C32AGL(1,ℤ/8)11yescharacteristic
263C22×C32#13711yescharacteristic
264C32×C4#12011yescharacteristic
265C32×C4#12311yescharacteristic
266C32×C4#12311yescharacteristic
267C32×C4#12411yescharacteristic
268C3⋊Dic3—42no—
269C3×Dic3—22no—
270C3×Dic3—41no—
271C3×Dic3—81no—
272C3×Dic3—81no—
273C22×Q8—91no—
274C22×D4D3211yescharacteristic
275C2×SD16—182no—
276C2×SD16—182no—
277C2×SD16—182no—
278C22×C8—31no—
279C22×C8—91no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C22⋊C4—61no—
283C2×C22⋊C4—61no—
284C2×C42—31no—
285C4⋊C8—182no—
286#103—182no—
287#102—62no—
288#95—181no—
289#95—181no—
290C23×C3—22no—
291C23×C3—22no—
292C23×C3—21no—
293C23×C3—42no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—81no—
309C23×C3—81no—
310C23×C3—81no—
311C23×C3—81no—
312C23×C3D3×D411yescharacteristic
313C23×C3C2×#6711yescharacteristic
314C3×D4—24no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—42no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—32no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4#23511yescharacteristic
346C2×C3×C4#23511yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4#23711yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—41no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—41no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3#21412yescomplemented
377Dic6—64no—
378Dic6—62no—
379Dic6—62no—
380Dic6—62no—
381Dic6—62no—
382Dic6—122no—
383Dic6—122no—
384Dic6—122no—
385Dic6—121no—
386Dic6—121no—
387Dic6—121no—
388Dic6—121no—
389C3×C8—121no—
390C3⋊C8—41no—
391C3⋊C8—64no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C2×C32—82no—
395C2×C32#39411yescharacteristic
396C2×C32#46011yescharacteristic
397C2×C32#46111yescharacteristic
398C2×C32#46311yescharacteristic
399C2×C32#46411yescharacteristic
400C2×C32#46511yescharacteristic
401C2×C32#46811yescharacteristic
402C24—21no—
403C2×Q8—92no—
404C2×Q8—181no—
405C2×Q8—181no—
406C2×Q8—181no—
407C2×Q8—181no—
408C2×Q8—181no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4#62612yes—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—181no—
420C22×C4C2×D3211yescharacteristic
421SD16—188no—
422C2×C8—61no—
423C2×C8—61no—
424C2×C8—61no—
425C2×C8—92no—
426C2×C8—181no—
427C2×C8—181no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4—61no—
432C22⋊C4—122no—
433C22⋊C4—122no—
434C42—61no—
435C42—61no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—44no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—82no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—82no—
454C22×C3—82no—
455C22×C3—82no—
456C22×C3—81no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3—81no—
464C22×C3#88411yescharacteristic
465C22×C3#88411yescharacteristic
466C22×C3#91111yescharacteristic
467C22×C3#91211yescharacteristic
468C22×C3D3×SD1611yescharacteristic
469C22×C3#91511yescharacteristic
470C22×C3#93011yescharacteristic
471C22×C3#93211yescharacteristic
472C22×C3C2×#21411yescharacteristic
473C22×C3#93811yescharacteristic
474C22×C3#93911yescharacteristic
475C22×C3#93911yescharacteristic
476C22×C3#95011yescharacteristic
477C22×C3#95111yescharacteristic
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—62no—
483C3×C4—121no—
484C3×C4—241no—
485C3×C4—241no—
486C3×C4#88211yescharacteristic
487C3×C4#88311yescharacteristic
488C3×C4#88311yescharacteristic
489C3×C4#88511yescharacteristic
490C3×C4#88511yescharacteristic
491C3×C4#88611yescharacteristic
492C3×C4#92911yescharacteristic
493C3×C4#93711yescharacteristic
494Dic3—22no—
495Dic3—41no—
496Dic3—81no—
497Dic3—81no—
498Dic3—124no—
499Dic3—122no—
500Dic3—122no—
501C32#205511yescharacteristic, complemented, Sylow
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23D3×#6711yescharacteristic
510Q8—182no—
511Q8—182no—
512Q8—361no—
513Q8—361no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—32no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—182no—
531C2×C4—361no—
532C2×C4—361no—
533C2×C4#380411yescharacteristic
534C2×C4#380411yescharacteristic
535C2×C4#380411yescharacteristic
536C2×C4C2×#62611yescharacteristic
537C2×C4#381111yescharacteristic
538C2×C4#381111yescharacteristic
539C8—121no—
540C8—182no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—84no—
549C2×C3—82no—
550C2×C3—82no—
551C2×C3#476211yescharacteristic
552C2×C3#476711yescharacteristic
553C2×C3#477811yescharacteristic
554C2×C3#478011yescharacteristic
555C2×C3#495911yescharacteristic
556C2×C3#496111yescharacteristic
557C2×C3#501611yescharacteristic
558C2×C3#501911yescharacteristic
559C2×C3#504111yescharacteristic
560C2×C3#504211yescharacteristic
561C2×C3#505411yescharacteristic
562C2×C3#507511yescharacteristic
563C2×C3#515311yescharacteristic
564C2×C3#516211yescharacteristic
565C22—42no—
566C22—42no—
567C22—42no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22D3×#21411yescharacteristic
573C22#6392911yescharacteristic
574C22#6393211yescharacteristic
575C22#6393311yescharacteristic
576C22#6395811yescharacteristic
577C22#6397111yescharacteristic
578C22#6397811yescharacteristic
579C4—62no—
580C4—121no—
581C4—241no—
582C4—241no—
583C4—362no—
584C4#6395311yescharacteristic
585C4#6396611yescharacteristic
586C4#6397511yescharacteristic
587C4#6398111yescharacteristic
588C3—21no—
589C3#6965111yescharacteristic, complemented
590C3#7021711yescharacteristic, complemented
591C2—82no—
592C2#1059143911yescharacteristic
593C2#1059144111yescharacteristic
594C2#1059146011yescharacteristic
595C2#1059146211yescharacteristic
596C2#1059146811yescharacteristic
597C2#1059148911yescharacteristic
598C2#1059171211yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591213C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63567C2semidirect
7. #10589163C2semidirect
153. C2×C3×Dic3SD16semidirect
376. C2×Dic3#214semidirect
501. C32#2055semidirect
589. C3#69651semidirect
590. C3#70217semidirect

Maximal subgroups

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

subgroupindex
C22×#37542
C3×#52212
C2×C3×#8322
#105912132
C2×Dic3⋊(C3⋊C8)2
C2×#635672
#105891632
#702173
#696513