Finite Group Databasebeta

← #11792365

Subgroups — #11792365

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#951C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic
3#10594855C211yesmaximal, characteristic, complemented
4#10592939C211yesmaximal, characteristic, complemented
5#10591110C211yesmaximal, characteristic, complemented
6#10591100C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#72120—31nomaximal
9#72111—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13#64135C2211yescharacteristic
14#64135C2211yescharacteristic
15C3×#951—21no—
16C3×#951—22no—
17C3×#951—22no—
18C3×#950—22no—
19C3×#949—21no—
20C2×C3×#216—21no—
21C3×#942—21no—
22C2×C3×#214—21no—
23C3×#932—21no—
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26#63961—22no—
27#63873—21no—
28#63863—21no—
29#63856—22no—
30#63661—22no—
31#63568—22no—
32#63566—22no—
33C3×#575—31no—
34C2×C3×#137—31no—
35#5825—31no—
36C2×#951D311yescharacteristic, complemented
37#5822D311yescharacteristic
38#5816—31no—
39#5240—31no—
40#5240—31no—
41#5240—61no—
42#5236—31no—
43#5225—31no—
44#5139—31no—
45#5120—31no—
46#4559—31no—
47#4556—31no—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8D411yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4D411yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—21no—
58C22×C3×Dic3—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C3×#235—21no—
63C2×C3×D12D411yescharacteristic
64C2×C3×C4×D3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D412yes—
71C2×C3×Dic6D411yescharacteristic
72#3757—21no—
73#3757D412yes—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)—21no—
76C4×C3⋊Dic3—21no—
77C4×C3⋊Dic3—21no—
78C3×#216—22no—
79C3×#216—24no—
80C3×#215—22no—
81C3×#214—22no—
82C3×#214—24no—
83C3×#213—22no—
84C3×#208—21no—
85C3×#208—21no—
86C3×#208—21no—
87C3×#208D412yes—
88C2×C3×C3⋊C8—21no—
89C2×C3×C3⋊C8D412yes—
90#3724—24no—
91(C2×D3)⋊Dic3—24no—
92#2009—91noSylow
93C2×C3×#41—21no—
94C2×C3×#41—31no—
95C2×C3×#41C2×D311yescharacteristic
96C2×C3×#41C2×D311yescharacteristic
97C22×C3×Q8—31no—
98C2×#235C2×D311yescharacteristic
99C22×Dic6C2×D311yescharacteristic
100C3×#137—62no—
101C3×#137—62no—
102C3×#137—61no—
103C3×#137—61no—
104C3×AGL(1,ℤ/8)—61no—
105C3×AGL(1,ℤ/8)—61no—
106C3×#135—62no—
107C2×C3×Q16—61no—
108C2×C3×SD16—61no—
109C2×C3×M16—31no—
110C2×C3×M16—31no—
111#951—21no—
112#951—22no—
113#951—22no—
114#950—22no—
115#949—21no—
116#947—61no—
117#946—62no—
118#944—61no—
119#944—61no—
120C2×#216—21no—
121#942—21no—
122#936—61no—
123#935—62no—
124C2×#214—21no—
125#932—21no—
126#929—62no—
127#926—31no—
128#926—31no—
129#926—31no—
130#926—31no—
131#926—61no—
132#926—61no—
133#924—62no—
134C2×#208C2×D311yescharacteristic
135C2×#208C2×D311yescharacteristic
136#837—62no—
137#835—62no—
138#834—62no—
139#834—62no—
140#834—64no—
141#825—62no—
142#816—62no—
143C23×C32—21no—
144C23×C32C2×D411yescharacteristic
145C22×C3×D3—21no—
146C32×Q8—21no—
147C32×Q8—21no—
148C32×D4—21no—
149C32×D4—21no—
150C32×D4—41no—
151C32×D4—41no—
152C2×C32×C4—21no—
153C2×C32×C4—41no—
154C2×C32×C4—41no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4#4111yescharacteristic
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—41no—
163C3×#67—41no—
164C3×#67—41no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—41no—
168C2×C3×Dic3—41no—
169C3×D12—21no—
170C3×D12—21no—
171C3×C4×D3—41no—
172C3×C4×D3—41no—
173C3×Dic6—22no—
174C3×Dic6—21no—
175C3×Dic6—22no—
176C3×Dic6—21no—
177C3×Dic6—41no—
178C3×Dic6—41no—
179C3×C3⋊C8—22no—
180C3×C3⋊C8—22no—
181#575—31no—
182C2×#137—31no—
183#536—91no—
184#421—91no—
185#419—91no—
186#410—91no—
187#344—91no—
188C3×#41—21no—
189C3×#41—21no—
190C3×#41—21no—
191C3×#41—21no—
192C3×#41—21no—
193C3×#41—21no—
194C3×#41—21no—
195C3×#41—21no—
196C3×#41—41no—
197C3×#41—41no—
198C3×#41—41no—
199C3×#41—41no—
200C3×#41—61no—
201C3×#41—61no—
202C3×#41—61no—
203C3×#41—61no—
204C2×C3×Q8—21no—
205C2×C3×Q8—31no—
206C2×C3×Q8—32no—
207C2×C3×Q8—61no—
208C2×C3×Q8—61no—
209C2×C3×Q8—61no—
210C2×C3×Q8—61no—
211C2×C3×Q8—61no—
212C2×C3×Q8#6711yescharacteristic
213C2×C3×Q8#6711yescharacteristic
214C2×C3×D4—22no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—31no—
219C2×C3×D4—61no—
220C2×C3×D4#6711yescharacteristic
221C2×C3×D4#6711yescharacteristic
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—21no—
231C22×Dic3—21no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236C2×D12#6711yescharacteristic
237C2×C4×D3—21no—
238C2×Dic6—21no—
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6—21no—
242C2×Dic6—21no—
243C2×Dic6#6712yes—
244C2×Dic6#6711yescharacteristic
245C3×Q16—64no—
246C3×Q16—62no—
247C3×SD16—64no—
248C3×SD16—62no—
249C3×SD16—62no—
250C3×D8—62no—
251C3×M16—32no—
252C3×M16—61no—
253C3×M16—61no—
254C3×M16—61no—
255C2×C3×C8—32no—
256C2×C3×C8—61no—
257#217—32no—
258#217—32no—
259#217—62no—
260#217—64no—
261#217—62no—
262#217—61no—
263#217—61no—
264#216—22no—
265#216—24no—
266#215—22no—
267#214—22no—
268#214—24no—
269#213—22no—
270(C2×D3)⋊C4—64no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3—121no—
276C4⋊Dic3—121no—
277Dic3⋊C4—64no—
278Dic3⋊C4—64no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C4×Dic3—121no—
284C4×Dic3—121no—
285#208—21no—
286#208—21no—
287#208—21no—
288#208#6712yes—
289C2×C3⋊C8—21no—
290C2×C3⋊C8#6712yes—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32—81no—
294C22×C32#12011yescharacteristic
295C22×C32#12111yescharacteristic
296C22×C32#12711yescharacteristic
297C2×C3×D3—42no—
298C2×C3×D3—41no—
299C32×C4—41no—
300C32×C4#12011yescharacteristic
301C32×C4#12011yescharacteristic
302C32×C4#12111yescharacteristic
303C32×C4#12111yescharacteristic
304C3⋊Dic3—42no—
305C3⋊Dic3—81no—
306C3×Dic3—42no—
307C3×Dic3—41no—
308C2×#41—31no—
309C2×#41D3211yescharacteristic
310C22×Q8—31no—
311#137—62no—
312#137—62no—
313#137—61no—
314#137—61no—
315AGL(1,ℤ/8)—61no—
316AGL(1,ℤ/8)—61no—
317#135—62no—
318C2×Q16—61no—
319C2×SD16—61no—
320C2×M16—31no—
321C2×M16—31no—
322C4⋊Q8—181no—
323#124—181no—
324#123—182no—
325C22⋊Q8—182no—
326#117—91no—
327#117—91no—
328#104—182no—
329#103—182no—
330#99—182no—
331C23×C3—22no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—61no—
336C23×C3D3×D411yescharacteristic
337C23×C3D3×D411yescharacteristic
338C22×D3—21no—
339C3×Q8—21no—
340C3×Q8—21no—
341C3×Q8—21no—
342C3×Q8—21no—
343C3×Q8—41no—
344C3×Q8—41no—
345C3×Q8—62no—
346C3×Q8—61no—
347C3×Q8—62no—
348C3×Q8—61no—
349C3×Q8—121no—
350C3×Q8—121no—
351C3×D4—21no—
352C3×D4—21no—
353C3×D4—21no—
354C3×D4—21no—
355C3×D4—41no—
356C3×D4—41no—
357C3×D4—42no—
358C3×D4—42no—
359C3×D4—41no—
360C3×D4—41no—
361C3×D4—41no—
362C3×D4—41no—
363C3×D4—61no—
364C3×D4—61no—
365C3×D4—121no—
366C3×D4—121no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—61no—
383C2×C3×C4—62no—
384C2×C3×C4—121no—
385C2×C3×C4—121no—
386C2×C3×C4—121no—
387C2×C3×C4—121no—
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4#23711yescharacteristic
393C2×C3×C4#23711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C2×#6711yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400#67—41no—
401#67—41no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—122no—
409C2×Dic3—122no—
410C2×Dic3—121no—
411C2×Dic3—121no—
412D12—21no—
413D12—21no—
414C4×D3—41no—
415C4×D3—41no—
416Dic6—22no—
417Dic6—21no—
418Dic6—22no—
419Dic6—21no—
420Dic6—41no—
421Dic6—41no—
422C3×C8—62no—
423C3×C8—62no—
424C3⋊C8—22no—
425C3⋊C8—22no—
426C2×C32—21no—
427C2×C32—21no—
428C2×C32—21no—
429C2×C32—81no—
430C2×C32#39211yescharacteristic
431C3×D3—81no—
432#41—21no—
433#41—21no—
434#41—21no—
435#41—21no—
436#41—61no—
437#41—61no—
438#41—61no—
439#41—61no—
440C2×Q8—32no—
441C2×Q8—31no—
442C2×Q8—61no—
443C2×Q8—61no—
444C2×Q8—61no—
445C2×Q8—61no—
446C2×Q8—61no—
447C2×Q8#62511yescharacteristic
448C2×D4—21no—
449C2×D4—31no—
450C2×D4—61no—
451C2×D4#62511yescharacteristic
452C22×C4—21no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4C2×D3211yescharacteristic
456Q16—64no—
457Q16—62no—
458SD16—64no—
459SD16—62no—
460SD16—62no—
461D8—62no—
462M16—32no—
463M16—61no—
464M16—61no—
465M16—61no—
466C2×C8—32no—
467C2×C8—61no—
468C4⋊C4—184no—
469C4⋊C4—181no—
470C4⋊C4—181no—
471C22⋊C4—92no—
472C22⋊C4—184no—
473C22⋊C4—181no—
474C42—181no—
475C42—181no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—42no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—81no—
485C22×C3—81no—
486C22×C3—81no—
487C22×C3—82no—
488C22×C3—122no—
489C22×C3—121no—
490C22×C3#93711yescharacteristic
491C22×C3#93711yescharacteristic
492C22×C3#93911yescharacteristic
493C22×C3#93911yescharacteristic
494C22×C3#94011yescharacteristic
495C22×C3#94011yescharacteristic
496C2×D3—42no—
497C2×D3—41no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—42no—
503C3×C4—41no—
504C3×C4—41no—
505C3×C4—121no—
506C3×C4—122no—
507C3×C4#93711yescharacteristic
508C3×C4#93711yescharacteristic
509C3×C4#93811yescharacteristic
510C3×C4#93811yescharacteristic
511C3×C4#93911yescharacteristic
512C3×C4#93911yescharacteristic
513C3×C4#95311yescharacteristic
514C3×C4#95311yescharacteristic
515Dic3—42no—
516Dic3—41no—
517Dic3—122no—
518Dic3—122no—
519Dic3—242no—
520Dic3—241no—
521Dic3—241no—
522Dic3—242no—
523C32#200911yescharacteristic, complemented, Sylow
524C23—21no—
525C23—61no—
526C23#381111yescharacteristic
527Q8—21no—
528Q8—21no—
529Q8—62no—
530Q8—61no—
531Q8—62no—
532Q8—61no—
533Q8—121no—
534Q8—121no—
535D4—21no—
536D4—21no—
537D4—41no—
538D4—41no—
539D4—61no—
540D4—61no—
541D4—121no—
542D4—121no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—62no—
547C2×C4—61no—
548C2×C4—121no—
549C2×C4—121no—
550C2×C4—121no—
551C2×C4—121no—
552C2×C4—182no—
553C2×C4—361no—
554C2×C4#380511yescharacteristic
555C2×C4C2×#62511yescharacteristic
556C2×C4D3×#6711yescharacteristic
557C2×C4D3×#6711yescharacteristic
558C2×C4D3×#6711yescharacteristic
559C2×C4D3×#6711yescharacteristic
560C8—62no—
561C8—62no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—41no—
570C2×C3—41no—
571C2×C3—41no—
572C2×C3—82no—
573C2×C3—81no—
574C2×C3—81no—
575C2×C3—241no—
576C2×C3#522311yescharacteristic
577C2×C3#522311yescharacteristic
578D3—81no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—122no—
583C22—121no—
584C22#6397911yescharacteristic
585C22#6398011yescharacteristic
586C22#6398311yescharacteristic
587C4—41no—
588C4—121no—
589C4—122no—
590C4—362no—
591C4—721no—
592C4#6397011yescharacteristic
593C4#6397011yescharacteristic
594C4#6397611yescharacteristic
595C4#6397611yescharacteristic
596C3—21no—
597C3#7211111yescharacteristic, complemented
598C3#7212011yescharacteristic, complemented
599C2—21no—
600C2—21no—
601C2—21no—
602C2—81no—
603C2—241no—
604C2#1059172311yescharacteristic
subgroupG/H
centerC2#10591723
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#392
prime radicalC3×#5822C2
hypercenterC2×#41D32
hypocenterC32#2009
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#951C2semidirect
3. #10594855C2semidirect
4. #10592939C2semidirect
5. #10591110C2semidirect
6. #10591100C2semidirect
7. #10589171C2semidirect
36. C2×#951D3semidirect
523. C32#2009semidirect
597. C3#72111semidirect
598. C3#72120semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9512
C3×#58222
#105948552
#105929392
#105911102
#105911002
#105891712
#721203
#721113