Finite Group Databasebeta

← #11867801

Subgroups — #11867801

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596287C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3#10595043C211yesmaximal, characteristic
4C2×#63817C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591601C212yesmaximal, complemented
7#10591600C212yesmaximal, complemented
8#10591591C212yesmaximal, complemented
9#10591590C212yesmaximal, complemented
10#10591130C211yesmaximal, characteristic, complemented
11#10591084C211yesmaximal, characteristic, complemented
12#83986—31nomaximal
13#78800—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17#64156—21no—
18#64155C2212yes—
19#64155C2212yes—
20#64153—21no—
21#64138—22no—
22#64135C2211yescharacteristic
23C2×C3×#216C2212yes—
24C3×#942—24no—
25C2×C3×#215C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29#63978—22no—
30#63916C2212yes—
31#63909—21no—
32#63871C2212yes—
33#63857—21no—
34C2×#3712C2212yes—
35#63817—24no—
36C2×#3710C2212yes—
37C3×#835C2212yes—
38C3×#835C2212yes—
39#63575C2212yes—
40#63573C2212yes—
41#63566C2211yescharacteristic
42#63566C2211yescharacteristic
43#63563C2211yescharacteristic
44#63563C2211yescharacteristic
45C2×C3×#137—31no—
46#5833—31no—
47#5816—31no—
48#5816—31no—
49#5816—61no—
50C2×#942D311yescharacteristic, complemented
51C2×#907—31no—
52C2×#901—31no—
53#5510—31no—
54C2×C3×#103—31no—
55#5233—31no—
56C2×#835D311yescharacteristic, complemented
57#5189—32no—
58#5188—32no—
59#5174—32no—
60#5171—32no—
61#5121—31no—
62#5113—31no—
63#4964—31no—
64#4816—32no—
65#4813—32no—
66#4812—32no—
67#4807—32no—
68C2×C32×Q8—21no—
69C2×C32×Q8—22no—
70C2×C32×Q8—22no—
71C2×C32×Q8C2312yes—
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×#638D412yes—
75#3828—22no—
76#3828—22no—
77C2×C4⋊(C3⋊D3)D411yescharacteristic
78C2×C4×C3⋊D3C2312yes—
79C2×#634D411yescharacteristic
80C2×C3×#67—21no—
81C22×C3×Dic3—21no—
82C3×#235—22no—
83C3×#235—22no—
84C2×C3×D12C2311yescharacteristic
85C2×C3×C4×D3—21no—
86C2×C3×Dic6C2311yescharacteristic
87C2×#626—22no—
88#3757—21no—
89#3752—22no—
90#3752—22no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93#3750—22no—
94#3750—22no—
95C4×C3⋊Dic3—21no—
96C3×#216—24no—
97C3×#215—24no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2312yes—
100C3×#208D414yescomplemented
101C2×C3×C3⋊C8—22no—
102C2×C3×C3⋊C8C2311yescharacteristic
103C2×C3×C3⋊C8C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105Dic3⋊Dic3—22no—
106#3722—22no—
107(C2×D3)⋊Dic3—22no—
108#3712—24no—
109#3710—24no—
110#3063—91noSylow
111C2×C3×#41—31no—
112C22×C3×Q8—21no—
113C22×C3×Q8C2×D311yescharacteristic
114C22×C3×Q8C2×D311yescharacteristic
115C2×#235—31no—
116C2×#235—31no—
117C2×#235—61no—
118C2×#235C2×D311yescharacteristic
119C3×#137—64no—
120C2×C3×Q16—32no—
121C2×C3×SD16—32no—
122C2×C3×M16—31no—
123C22×C3×C8—31no—
124C2×C3×C4⋊C4—31no—
125#947—61no—
126#947—61no—
127#947—62no—
128#946—32no—
129#946—32no—
130#946—32no—
131#946—32no—
132#946—32no—
133#946—62no—
134#946—62no—
135#944—61no—
136#944—61no—
137#944—62no—
138C2×#216C2×D312yes—
139#942—24no—
140C2×#215C2×D312yes—
141#939—62no—
142#938—32no—
143#930—61no—
144#930—62no—
145#929—62no—
146#929—62no—
147#929—64no—
148#926—31no—
149#926—31no—
150#926—61no—
151C2×C4⋊Dic3C2×D311yescharacteristic
152#924—61no—
153C2×#208C2×D311yescharacteristic
154C22×C3⋊C8C2×D311yescharacteristic
155#907—64no—
156#901—64no—
157C2×ΓL(1,𝔽25)—32no—
158C2×ΓL(1,𝔽25)—32no—
159C2×D3×C8—32no—
160C2×D3×C8—32no—
161#897—32no—
162#897—61no—
163#895—32no—
164#895—61no—
165C3×#103—32no—
166C3×#103—32no—
167#835—31no—
168#835—31no—
169#835C2×D312yes—
170#835C2×D312yes—
171#832—31no—
172#832—31no—
173#821—31no—
174#821—31no—
175#818—32no—
176#817—32no—
177#816—31no—
178#816—31no—
179#808—32no—
180#807—32no—
181C23×C32C2×D411yescharacteristic
182C22×C3⋊D3C2×D412yes—
183C22×C3×D3—21no—
184C32×Q8—22no—
185C32×Q8—22no—
186C32×Q8—42no—
187C2×C32×C4—22no—
188C2×C32×C4—42no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D412yes—
191C2×C32×C4#4112yes—
192C2×C32×C4C2411yescharacteristic
193#638—24no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3C2×D412yes—
197C4⋊(C3⋊D3)—22no—
198C4×C3⋊D3—22no—
199C4×C3⋊D3—22no—
200#634—22no—
201C3×#67—42no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—81no—
205C3×D12—21no—
206C3×D12—21no—
207C3×C4×D3—42no—
208C3×Dic6—21no—
209C3×Dic6—21no—
210#626—82no—
211C3×C3⋊C8—21no—
212C3×C3⋊C8—21no—
213C3×C3⋊C8C2×D414yes—
214C2×#137—31no—
215C2×#131—91no—
216#537—91no—
217#536—91no—
218#470—92no—
219#468—92no—
220#467—92no—
221#465—92no—
222#428—91no—
223#416—91no—
224C2×#103—31no—
225C3×#41—62no—
226C3×#41—62no—
227C2×C3×Q8—22no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—22no—
231C2×C3×Q8—22no—
232C2×C3×Q8—22no—
233C2×C3×Q8—22no—
234C2×C3×Q8—22no—
235C2×C3×Q8—31no—
236C2×C3×Q8—42no—
237C2×C3×Q8—42no—
238C2×C3×Q8C22×D312yes—
239C2×C3×Q8C22×D312yes—
240C2×C3×D4—31no—
241C2×C3×D4—61no—
242C22×C3×C4—22no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—61no—
247C22×C3×C4—61no—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—21no—
251C2×#67—32no—
252C2×#67—32no—
253C2×#67—62no—
254C2×#67—62no—
255C22×Dic3—21no—
256#235—22no—
257#235—22no—
258#235—62no—
259#235—62no—
260#235—62no—
261#235—62no—
262#235—122no—
263#235—122no—
264C2×D12—31no—
265C2×D12—31no—
266C2×D12—61no—
267C2×D12—62no—
268C2×D12C22×D311yescharacteristic
269C2×C4×D3—21no—
270C2×C4×D3—32no—
271C2×C4×D3—32no—
272C2×C4×D3—62no—
273C2×Dic6—31no—
274C2×Dic6—31no—
275C2×Dic6—61no—
276C2×Dic6C22×D311yescharacteristic
277C3×Q16—64no—
278C3×SD16—64no—
279C3×M16—34no—
280C2×C3×C8—32no—
281C2×C3×C8—31no—
282C2×C3×C8—31no—
283C2×C3×C8—62no—
284C3×C4⋊C4—32no—
285C3×C4⋊C4—61no—
286#217—62no—
287#217—62no—
288#217—61no—
289#217—61no—
290#216—24no—
291#215—24no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—64no—
300(C2×D3)⋊C4—64no—
301C4⋊Dic3—21no—
302C4⋊Dic3—31no—
303C4⋊Dic3—31no—
304C4⋊Dic3—31no—
305C4⋊Dic3—31no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3—62no—
309C4⋊Dic3C22×D312yes—
310Dic3⋊C4—62no—
311Dic3⋊C4—62no—
312Dic3⋊C4—62no—
313Dic3⋊C4—62no—
314Dic3⋊C4—62no—
315Dic3⋊C4—64no—
316Dic3⋊C4—64no—
317C4×Dic3—62no—
318C4×Dic3—61no—
319C4×Dic3—61no—
320#208#6714yescomplemented
321C2×C3⋊C8—22no—
322C2×C3⋊C8C22×D311yescharacteristic
323C2×C3⋊C8C22×D311yescharacteristic
324C2×C3⋊C8C22×D312yes—
325ΓL(1,𝔽25)—64no—
326ΓL(1,𝔽25)—64no—
327D3×C8—64no—
328D3×C8—64no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32#12112yes—
332C22×C32C22×D411yescharacteristic
333C2×C3⋊D3—22no—
334C2×C3⋊D3—22no—
335C2×C3⋊D3—22no—
336C2×C3×D3—41no—
337C2×C3×D3—41no—
338C2×C3×D3—41no—
339C32×C4—42no—
340C32×C4#12112yes—
341C32×C4C22×D411yescharacteristic
342C32×C4C2×#4111yescharacteristic
343C3⋊Dic3—22no—
344C3⋊Dic3—41no—
345C3⋊Dic3—41no—
346C3×Dic3—41no—
347C3×Dic3—42no—
348C2×#41—31no—
349C2×#41—91no—
350C22×Q8D3211yescharacteristic
351#137—64no—
352C2×Q16—32no—
353C2×SD16—32no—
354#131—184no—
355C2×M16—31no—
356C2×M16—92no—
357C22×C8—31no—
358C22×C8—92no—
359C4⋊Q8—181no—
360#124—181no—
361#123—182no—
362C22⋊Q8—92no—
363C22⋊Q8—92no—
364C22⋊Q8—92no—
365C22⋊Q8—181no—
366#121—92no—
367#121—181no—
368#121—182no—
369#117—91no—
370C2×C4⋊C4—31no—
371#107—92no—
372#106—92no—
373#103—32no—
374#103—32no—
375#103—91no—
376#103—91no—
377#102—91no—
378#102—91no—
379C23×C3—21no—
380C23×C3—61no—
381C23×C3D3×D411yescharacteristic
382C23×C3D3×D411yescharacteristic
383C22×D3—21no—
384C22×D3—32no—
385C22×D3—32no—
386C22×D3—62no—
387C3×Q8—22no—
388C3×Q8—22no—
389C3×Q8—22no—
390C3×Q8—22no—
391C3×Q8—42no—
392C3×Q8—42no—
393C3×Q8—44no—
394C3×Q8—42no—
395C3×Q8—42no—
396C3×Q8—61no—
397C3×Q8—61no—
398C3×D4—61no—
399C3×D4—61no—
400C3×D4—122no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—44no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—122no—
414C2×C3×C4—241no—
415C2×C3×C4#23512yes—
416C2×C3×C4D3×D412yes—
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4#23712yes—
420C2×C3×C4C2×#6712yes—
421C2×C3×C4C23×D311yescharacteristic
422C2×C3×C4C23×D311yescharacteristic
423#67—42no—
424#67—64no—
425#67—64no—
426#67—124no—
427#67—242no—
428C2×Dic3—22no—
429C2×Dic3—21no—
430C2×Dic3—32no—
431C2×Dic3—32no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—81no—
440D12—21no—
441D12—21no—
442D12—62no—
443D12—62no—
444D12—122no—
445D12—242no—
446C4×D3—42no—
447C4×D3—62no—
448C4×D3—62no—
449C4×D3—62no—
450C4×D3—62no—
451C4×D3—122no—
452C4×D3—122no—
453Dic6—21no—
454Dic6—21no—
455Dic6—62no—
456Dic6—62no—
457Dic6—122no—
458C3×C8—34no—
459C3×C8—61no—
460C3×C8—61no—
461C3⋊C8—21no—
462C3⋊C8—21no—
463C3⋊C8C2×#6714yes—
464C2×C32—22no—
465C2×C32C2×#12111yescharacteristic
466C2×C32#57711yescharacteristic
467C2×C32#57811yescharacteristic
468C3⋊D3—42no—
469C3×D3—81no—
470#41—62no—
471#41—62no—
472#41—182no—
473#41—182no—
474C2×Q8—21no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—31no—
478C2×Q8—91no—
479C2×Q8C2×D3212yes—
480C2×D4—31no—
481C2×D4—61no—
482C2×D4—92no—
483C2×D4—91no—
484C2×D4—182no—
485C22×C4—21no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—92no—
489C22×C4C2×D3211yescharacteristic
490Q16—64no—
491SD16—64no—
492M16—34no—
493M16—184no—
494C2×C8—32no—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—62no—
498C2×C8—184no—
499C4⋊C4—32no—
500C4⋊C4—61no—
501C4⋊C4—91no—
502C4⋊C4—91no—
503C4⋊C4—182no—
504C4⋊C4—182no—
505C4⋊C4—182no—
506C22⋊C4—182no—
507C22⋊C4—182no—
508C22⋊C4—182no—
509C22⋊C4—182no—
510C22⋊C4—181no—
511C42—181no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—22no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—121no—
521C22×C3—121no—
522C22×C3—121no—
523C22×C3#88412yes—
524C22×C3#93812yes—
525C22×C3C2×D3×D411yescharacteristic
526C22×C3C2×D3×D411yescharacteristic
527C2×D3—41no—
528C2×D3—41no—
529C2×D3—41no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—62no—
534C2×D3—62no—
535C2×D3—62no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—22no—
542C3×C4—44no—
543C3×C4—42no—
544C3×C4—42no—
545C3×C4—121no—
546C3×C4—122no—
547C3×C4#88412yes—
548C3×C4#93812yes—
549C3×C4C2×#23511yescharacteristic
550C3×C4C2×D3×D411yescharacteristic
551C3×C4C2×#23711yescharacteristic
552C3×C4C22×#6711yescharacteristic
553Dic3—42no—
554Dic3—41no—
555Dic3—62no—
556Dic3—62no—
557Dic3—122no—
558Dic3—122no—
559Dic3—122no—
560Dic3—121no—
561Dic3—121no—
562Dic3—121no—
563Dic3—121no—
564C32#306311yescharacteristic, complemented, Sylow
565C23—61no—
566C23—92no—
567C23#381111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—42no—
571Q8—61no—
572Q8—61no—
573Q8—182no—
574D4—61no—
575D4—61no—
576D4—122no—
577D4—184no—
578D4—182no—
579D4—722no—
580C2×C4—22no—
581C2×C4—42no—
582C2×C4—62no—
583C2×C4—61no—
584C2×C4—92no—
585C2×C4—122no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—241no—
591C2×C4#380412yes—
592C2×C4D3×#6712yes—
593C2×C4#381111yescharacteristic
594C2×C4C22×D3211yescharacteristic
595C8—34no—
596C8—61no—
597C8—61no—
598C2×C3—22no—
599C2×C3—22no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—42no—
604C2×C3—241no—
605C2×C3C2×#88411yescharacteristic
606C2×C3#576211yescharacteristic
607C2×C3#576611yescharacteristic
608C2×C3#577811yescharacteristic
609C2×C3#577911yescharacteristic
610C2×C3C2×#93811yescharacteristic
611D3—81no—
612D3—122no—
613D3—122no—
614D3—242no—
615C22—21no—
616C22—21no—
617C22—121no—
618C22—121no—
619C22—121no—
620C22—182no—
621C22—182no—
622C22—182no—
623C22#6395812yes—
624C22C2×#381111yescharacteristic
625C4—42no—
626C4—121no—
627C4—122no—
628C4—182no—
629C4—361no—
630C4—361no—
631C4#6395812yes—
632C4C2×#380411yescharacteristic
633C4C2×D3×#6711yescharacteristic
634C3—21no—
635C3#7880011yescharacteristic, complemented
636C3#8398611yescharacteristic, complemented
637C2—22no—
638C2—241no—
639C2—362no—
640C2#1059532411yescharacteristic
641C2#1059533711yescharacteristic
642C2C2×#6395811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenterC22×Q8D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #10596287C2semidirect
2. C2×C3×#942C2semidirect
4. C2×#63817C2semidirect
5. C2×C3×#835C2semidirect
6. #10591601C2semidirect
7. #10591600C2semidirect
8. #10591591C2semidirect
9. #10591590C2semidirect
10. #10591130C2semidirect
11. #10591084C2semidirect
50. C2×#942D3semidirect
56. C2×#835D3semidirect
100. C3×#208D4semidirect
320. #208#67semidirect
564. C32#3063semidirect
635. C3#78800semidirect
636. C3#83986semidirect

Maximal subgroups

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

subgroupindex
#105962872
C2×C3×#9422
#105950432
C2×#638172
C2×C3×#8352
#105916012
#105916002
#105915912
#105915902
#105911302
#105910842
#839863
#788003