Finite Group Databasebeta

← #11873290

Subgroups — #11873290

Order 1152.

764 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5625C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic
3#10592744C211yesmaximal, characteristic
4C3×#5050C211yesmaximal, characteristic
5#10591576C211yesmaximal, characteristic, complemented
6#10591574C211yesmaximal, characteristic, complemented
7#10591574C211yesmaximal, characteristic, complemented
8Dic3×#216C211yesmaximal, characteristic, complemented
9#10591185C211yesmaximal, characteristic
10#10591127C211yesmaximal, characteristic
11#10591056C211yesmaximal, characteristic
12#10590493C211yesmaximal, characteristic, complemented
13#10590491C211yesmaximal, characteristic, complemented
14#10590477C211yesmaximal, characteristic, complemented
15#10590476C211yesmaximal, characteristic, complemented
16#83451—31nomaximal
17#80177—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20#64135C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#890—21no—
28C3×#890C2211yescharacteristic
29C3×#889—21no—
30C3×#887C2211yescharacteristic
31C3×#879—21no—
32C3×#879—21no—
33#63955—21no—
34#63955—21no—
35#63843—21no—
36#63843—21no—
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43#63662C2211yescharacteristic
44#63662C2211yescharacteristic
45#63657C2211yescharacteristic
46#63635C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#541—31no—
62#5812—31no—
63#5625D311yescharacteristic
64#5516—31no—
65C3×#451—31no—
66#5228—31no—
67#5184—31no—
68#5182—31no—
69#5182—31no—
70Dic3×Q16—31no—
71#5090—31no—
72#5090—31no—
73#5063—31no—
74#5063—31no—
75#5050—31no—
76#5050D311yescharacteristic
77#5045—31no—
78#5045—31no—
79#5045—31no—
80#5045—61no—
81#5030—31no—
82#5030—31no—
83C4×#216—31no—
84C4×#216—31no—
85#5000—31no—
86#4799—31no—
87#4796—31no—
88#4790—31no—
89#4789—31no—
90#4723—31no—
91#4720—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3×Dic3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—22no—
97C2×C3×Dic6—22no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C22⋊C4—21no—
104#3757—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4×C3⋊Dic3—21no—
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×#217—21no—
111C3×#217D411yescharacteristic
112C3×#217D411yescharacteristic
113C3×#216—22no—
114C3×#216—22no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3D411yescharacteristic
118C3×C4⋊Dic3D411yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3718—22no—
140#3718—22no—
141#3127—91noSylow
142C22×C3×Q8—31no—
143C22×Dic6C2×D311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C3×C4⋊Q8—31no—
147C3×#126—61no—
148C3×#126—61no—
149C3×#125—31no—
150C3×#125—61no—
151C3×#125—61no—
152C3×C22⋊Q8—21no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8C2×D311yescharacteristic
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×#117—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—61no—
164Q8×Dic3—61no—
165Q8×Dic3C2×D311yescharacteristic
166#944C2×D311yescharacteristic
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216C2×D311yescharacteristic
172C2×#216C2×D311yescharacteristic
173#926—31no—
174#926—31no—
175#926—61no—
176#926—61no—
177#926—61no—
178#926C2×D311yescharacteristic
179#924C2×D311yescharacteristic
180#890—21no—
181#890C2×D311yescharacteristic
182#889—21no—
183#887—61no—
184#887—61no—
185#887C2×D311yescharacteristic
186#879—21no—
187#879—21no—
188#877—61no—
189#877—61no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×C22⋊C8—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—61no—
206#835—61no—
207#830—31no—
208#830—31no—
209#830—61no—
210#830C2×D311yescharacteristic
211#818—31no—
212#817—31no—
213#816—31no—
214#816—31no—
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218C8×Dic3—31no—
219#810—31no—
220#810—31no—
221#810C2×D311yescharacteristic
222#810C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—61no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3×Dic3—24no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×Dic6—24no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6#4112yes—
261C3×Dic6#4112yes—
262C3⋊(C3⋊C8)—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—31no—
267#519—91no—
268#485—91no—
269#485—91no—
270#479—91no—
271#479—91no—
272#462—91no—
273#462—91no—
274#451—31no—
275#451—91no—
276#441—91no—
277#441—91no—
278C4×Q16—91no—
279C4×Q16—91no—
280#433—91no—
281C2×C3×Q8—21no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—62no—
286C2×C3×Q8—62no—
287C2×C3×Q8—61no—
288C2×C3×Q8C22×D311yescharacteristic
289C2×C3×Q8C22×D311yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4—61no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×Dic3—21no—
295C2×Dic6—21no—
296C2×Dic6—22no—
297C2×Dic6—22no—
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C3×Q16—62no—
302C3×Q16—62no—
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—41no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C4⋊C4C22×D311yescharacteristic
321C3×C22⋊C4—21no—
322C3×C22⋊C4—21no—
323C3×C22⋊C4—31no—
324C3×C22⋊C4—31no—
325C3×C22⋊C4—41no—
326C3×C22⋊C4—61no—
327C3×C42—31no—
328C3×C42—31no—
329C3×C42—61no—
330C3×C42—61no—
331#217—21no—
332#217—61no—
333#217—61no—
334#217—121no—
335#217#6711yescharacteristic
336#217#6711yescharacteristic
337#216—22no—
338#216—22no—
339#216—62no—
340#216—62no—
341#216—62no—
342#216—62no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3#6711yescharacteristic
356C4⋊Dic3#6711yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—21no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367C4×Dic3—21no—
368C4×Dic3—21no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—121no—
380C4×Dic3C22×D311yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32C22×D411yescharacteristic
394C32×C4—21no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C4C2×#4111yescharacteristic
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—31no—
410C2×Q16—31no—
411C2×Q16—31no—
412C2×Q16—91no—
413C2×Q16—91no—
414C4⋊Q8—31no—
415#126—61no—
416#126—61no—
417#125—31no—
418#125—61no—
419#125—61no—
420C22⋊Q8—31no—
421C22⋊Q8D3211yescharacteristic
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—181no—
429C4×Q8—181no—
430#117—31no—
431#117—91no—
432#117—181no—
433#117—181no—
434#107—91no—
435#107—91no—
436#106—91no—
437#106—91no—
438C4⋊C8—91no—
439C4⋊C8—91no—
440#103—31no—
441#103—31no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448C22⋊C8—31no—
449C22⋊C8—91no—
450#97—91no—
451C4×C8—91no—
452C23×C3—21no—
453C23×C3D3×D411yescharacteristic
454C23×C3C2×#6711yescharacteristic
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—32no—
460C3×Q8—32no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—64no—
464C3×Q8—61no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—61no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—64no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4D3×D411yescharacteristic
492C2×C3×C4C2×#6711yescharacteristic
493C2×C3×C4C23×D311yescharacteristic
494C2×C3×C4C23×D311yescharacteristic
495C2×Dic3—24no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3C2×#6711yescharacteristic
507C2×Dic3C2×#6711yescharacteristic
508C2×Dic3C2×#6711yescharacteristic
509C2×Dic3C2×#6711yescharacteristic
510Dic6—24no—
511Dic6—21no—
512Dic6—21no—
513Dic6—21no—
514Dic6—21no—
515Dic6#23712yes—
516Dic6#23712yes—
517C3×C8—61no—
518C3×C8—61no—
519C3⋊C8—21no—
520C3⋊C8—21no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—121no—
526C3⋊C8—121no—
527C2×C32—41no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—62no—
535C2×Q8—62no—
536C2×Q8—61no—
537C2×Q8C2×D3211yescharacteristic
538C22×C4—61no—
539C22×C4C2×D3211yescharacteristic
540Q16—62no—
541Q16—62no—
542Q16—182no—
543Q16—182no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8—91no—
547C2×C8—91no—
548C4⋊C4—21no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—61no—
570C22⋊C4—181no—
571C42—31no—
572C42—31no—
573C42—61no—
574C42—61no—
575C42—181no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3C2×D3×D411yescharacteristic
591C22×C3C22×#6711yescharacteristic
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—62no—
606C3×C4—62no—
607C3×C4—81no—
608C3×C4—81no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4C2×#23711yescharacteristic
612C3×C4C2×#23711yescharacteristic
613C3×C4D3×#4111yescharacteristic
614C3×C4D3×#4111yescharacteristic
615Dic3—21no—
616Dic3—21no—
617Dic3—21no—
618Dic3—21no—
619Dic3—22no—
620Dic3—22no—
621Dic3—41no—
622Dic3—41no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628Dic3—241no—
629C32#312711yescharacteristic, complemented, Sylow
630C23D3×#6711yescharacteristic
631Q8—21no—
632Q8—21no—
633Q8—32no—
634Q8—32no—
635Q8—64no—
636Q8—61no—
637Q8—61no—
638Q8—61no—
639Q8—61no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—64no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4D3×#6711yescharacteristic
656C2×C4C22×D3211yescharacteristic
657C8—61no—
658C8—61no—
659C8—181no—
660C8—181no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—41no—
665C2×C3—41no—
666C2×C3—81no—
667C2×C3#558611yescharacteristic
668C2×C3#576611yescharacteristic
669C2×C3#577911yescharacteristic
670C2×C3#582811yescharacteristic
671C2×C3#583811yescharacteristic
672C2×C3#583811yescharacteristic
673C22—21no—
674C22—21no—
675C22—21no—
676C22C2×D3×#6711yescharacteristic
677C4—21no—
678C4—41no—
679C4—41no—
680C4—62no—
681C4—62no—
682C4—61no—
683C4—61no—
684C4—61no—
685C4—61no—
686C4—121no—
687C4—121no—
688C4—361no—
689C4—361no—
690C4D3×#23711yescharacteristic
691C4D3×#23711yescharacteristic
692C3—21no—
693C3#8017711yescharacteristic, complemented
694C3#8345111yescharacteristic, complemented
695C2—41no—
696C2#1059515411yescharacteristic
697C2#1059532711yescharacteristic
698C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#3127
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
5. #10591576C2semidirect
6. #10591574C2semidirect
7. #10591574C2semidirect
8. Dic3×#216C2semidirect
12. #10590493C2semidirect
13. #10590491C2semidirect
14. #10590477C2semidirect
15. #10590476C2semidirect
629. C32#3127semidirect
693. C3#80177semidirect
694. C3#83451semidirect

Maximal subgroups

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

subgroupindex
C3×#56252
#105948182
#105927442
C3×#50502
#105915762
#105915742
Dic3×#2162
#105911852
#105911272
#105910562
#105904932
#105904912
#105904772
#105904762
#834513
#801773