Finite Group Databasebeta

← #11873288

Subgroups — #11873288

Order 1152.

790 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5625C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic
3#10592749C211yesmaximal, characteristic
4C3×#5045C211yesmaximal, characteristic
5#10591575C211yesmaximal, characteristic, complemented
6#10591575C211yesmaximal, characteristic, complemented
7#10591541C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10591190C211yesmaximal, characteristic
10#10591102C211yesmaximal, characteristic
11#10591056C211yesmaximal, characteristic
12#10590492C211yesmaximal, characteristic, complemented
13#10590490C211yesmaximal, characteristic, complemented
14#10590481C211yesmaximal, characteristic, complemented
15#10590480C211yesmaximal, characteristic, complemented
16#83451—31nomaximal
17#81499—31nomaximal
18C22×#634C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C3×#926C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#890—21no—
28C3×#890C2211yescharacteristic
29C3×#889—21no—
30C3×#887C2211yescharacteristic
31C3×#879—21no—
32C3×#879—21no—
33#63957—21no—
34#63957—21no—
35#63844—21no—
36#63844—21no—
37#63844C2211yescharacteristic
38#63844C2211yescharacteristic
39#63844C2211yescharacteristic
40#63844C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43#63657C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63576C2211yescharacteristic
52#63574C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#541—31no—
62#5625D311yescharacteristic
63#5516—31no—
64#5516—31no—
65C3×#485—31no—
66#5090—31no—
67#5090—31no—
68#5063—31no—
69#5063—31no—
70#5050—31no—
71#5050—31no—
72#5050—31no—
73#5050—61no—
74#5045—31no—
75#5045D311yescharacteristic
76#5030—31no—
77#5030—31no—
78C4×#216—31no—
79C4×#216—31no—
80#5000—31no—
81#4996—31no—
82#4877—31no—
83#4873—31no—
84#4857—31no—
85#4853—31no—
86#4795—31no—
87#4795—31no—
88#4790—31no—
89#4789—31no—
90#4739—31no—
91#4720—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—21no—
96C2×#634—22no—
97C2×#634—22no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C22⋊C4—21no—
104#3756—22no—
105#3756—22no—
106C2×C3⋊(C3⋊C8)C2311yescharacteristic
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C3×#217—21no—
109C3×#217—21no—
110C3×#217D411yescharacteristic
111C3×#217D411yescharacteristic
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3D411yescharacteristic
115C3×C4⋊Dic3D411yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133#3724—21no—
134#3724—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3719—22no—
140#3719—22no—
141#3127—91noSylow
142C22×Dic6—31no—
143C22×Dic6—31no—
144C22×Dic6—61no—
145C3×C4⋊Q8—31no—
146C3×#126—61no—
147C3×#126—61no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125—61no—
151C3×C22⋊Q8—21no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8C2×D311yescharacteristic
154C3×C22⋊Q8C2×D311yescharacteristic
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×#117—31no—
158C3×#117—31no—
159Q8×Dic3C2×D311yescharacteristic
160#944C2×D311yescharacteristic
161C2×#216—31no—
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—61no—
168C2×#216—61no—
169#926C2×D311yescharacteristic
170#926C2×D311yescharacteristic
171#924C2×D311yescharacteristic
172C2×Dic12—31no—
173C2×Dic12—31no—
174#890—21no—
175#890C2×D311yescharacteristic
176#889—21no—
177#887—31no—
178#887—31no—
179#887—31no—
180#887—31no—
181#887—61no—
182#887—61no—
183#887C2×D311yescharacteristic
184#879—21no—
185#879—21no—
186#877—61no—
187#877—61no—
188#877—61no—
189#877—61no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C4×Dic6—61no—
196C3×#107—31no—
197C3×#106—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×C22⋊C8—31no—
201#835—31no—
202#835—31no—
203#835C2×D311yescharacteristic
204#835C2×D311yescharacteristic
205#830—31no—
206#830—31no—
207#830—61no—
208#830C2×D311yescharacteristic
209#816—31no—
210#816—31no—
211#815—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214C8×Dic3—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—61no—
224#810—61no—
225#808—31no—
226#808—31no—
227#808C2×D311yescharacteristic
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic
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—24no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247#634—24no—
248#634—21no—
249#634—21no—
250#634#4112yes—
251#634#4112yes—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3⋊(C3⋊C8)—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—31no—
267#519—91no—
268#485—31no—
269#485—91no—
270#479—91no—
271#479—91no—
272#462—91no—
273#462—91no—
274#451—91no—
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×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C22×C3×C4—21no—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×Dic3—61no—
289C22×Dic3—61no—
290C22×Dic3—121no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—31no—
294C2×Dic6—31no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—62no—
298C2×Dic6—62no—
299C2×Dic6—62no—
300C2×Dic6—62no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—122no—
304C2×Dic6—122no—
305C2×Dic6—121no—
306C2×Dic6C22×D311yescharacteristic
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—41no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C22⋊C4—21no—
328C3×C22⋊C4—21no—
329C3×C22⋊C4—31no—
330C3×C22⋊C4—31no—
331C3×C22⋊C4—41no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C42—31no—
335C3×C42—31no—
336C3×C42—61no—
337C3×C42—61no—
338C3×C42—61no—
339#217—21no—
340#217—21no—
341#217#6711yescharacteristic
342#217#6711yescharacteristic
343#216—62no—
344#216—62no—
345#216—62no—
346#216—62no—
347#216—62no—
348#216—62no—
349#216—122no—
350#216—122no—
351C4⋊Dic3—21no—
352C4⋊Dic3—21no—
353C4⋊Dic3#6711yescharacteristic
354C4⋊Dic3#6711yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356C4⋊Dic3C22×D311yescharacteristic
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—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371C4×Dic3—21no—
372C4×Dic3—21no—
373C4×Dic3—21no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3C22×D311yescharacteristic
383C4×Dic3C22×D311yescharacteristic
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392Dic12—62no—
393Dic12—62no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32C22×D411yescharacteristic
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4C2×#4111yescharacteristic
402C32×C4C2×#4111yescharacteristic
403C3⋊Dic3—22no—
404C3⋊Dic3—22no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—21no—
408C3×Dic3—21no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C22×Q8—91no—
414C2×Q16—91no—
415C2×Q16—91no—
416C2×Q16—91no—
417C2×Q16—91no—
418C4⋊Q8—31no—
419#126—61no—
420#126—61no—
421#125—31no—
422#125—61no—
423#125—61no—
424C22⋊Q8—31no—
425C22⋊Q8D3211yescharacteristic
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×Q8—181no—
433C4×Q8—181no—
434#117—31no—
435#117—31no—
436#117—181no—
437#117—181no—
438#107—31no—
439#107—91no—
440#106—31no—
441#106—91no—
442C4⋊C8—91no—
443C4⋊C8—91no—
444#103—31no—
445#103—31no—
446#103—91no—
447#103—91no—
448#103—91no—
449#103—91no—
450#103—91no—
451#103—91no—
452C22⋊C8—31no—
453C22⋊C8—91no—
454#97—91no—
455C4×C8—91no—
456C23×C3—21no—
457C23×C3D3×D411yescharacteristic
458C23×C3C2×#6711yescharacteristic
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—41no—
464C3×Q8—41no—
465C3×Q8—61no—
466C3×Q8—61no—
467C2×C3×C4—21no—
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—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4D3×D411yescharacteristic
490C2×C3×C4C2×#6711yescharacteristic
491C2×C3×C4C23×D311yescharacteristic
492C2×C3×C4C23×D311yescharacteristic
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—64no—
498C2×Dic3—64no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3—124no—
506C2×Dic3C2×#6711yescharacteristic
507C2×Dic3C2×#6711yescharacteristic
508C2×Dic3C2×#6711yescharacteristic
509C2×Dic3C2×#6711yescharacteristic
510Dic6—21no—
511Dic6—21no—
512Dic6—32no—
513Dic6—32no—
514Dic6—32no—
515Dic6—32no—
516Dic6—62no—
517Dic6—62no—
518Dic6—64no—
519Dic6—64no—
520Dic6—61no—
521Dic6—61no—
522Dic6—61no—
523Dic6—61no—
524Dic6—121no—
525Dic6—121no—
526Dic6—124no—
527C3×C8—61no—
528C3×C8—61no—
529C3⋊C8—21no—
530C3⋊C8—21no—
531C3⋊C8—61no—
532C3⋊C8—61no—
533C3⋊C8—61no—
534C3⋊C8—61no—
535C3⋊C8—121no—
536C3⋊C8—121no—
537C2×C32—41no—
538C2×C32#52511yescharacteristic
539C2×C32#57811yescharacteristic
540C2×C32#57811yescharacteristic
541C2×Q8—31no—
542C2×Q8—91no—
543C2×Q8—91no—
544C2×Q8—182no—
545C2×Q8—182no—
546C2×Q8—181no—
547C2×Q8C2×D3211yescharacteristic
548C22×C4—181no—
549C22×C4C2×D3211yescharacteristic
550Q16—182no—
551Q16—182no—
552Q16—182no—
553Q16—182no—
554C2×C8—31no—
555C2×C8—31no—
556C2×C8—91no—
557C2×C8—91no—
558C4⋊C4—21no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—31no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4C2×D3211yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—31no—
578C22⋊C4—31no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C42—31no—
582C42—31no—
583C42—61no—
584C42—61no—
585C42—61no—
586C42—181no—
587C42—181no—
588C42—181no—
589C42—181no—
590C22×C3—22no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C22×#6711yescharacteristic
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—81no—
616C3×C4—81no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4—121no—
621C3×C4D3×#4111yescharacteristic
622C3×C4D3×#4111yescharacteristic
623C3×C4D3×#4111yescharacteristic
624C3×C4D3×#4111yescharacteristic
625Dic3—21no—
626Dic3—21no—
627Dic3—21no—
628Dic3—21no—
629Dic3—41no—
630Dic3—41no—
631Dic3—41no—
632Dic3—41no—
633Dic3—62no—
634Dic3—62no—
635Dic3—62no—
636Dic3—62no—
637Dic3—122no—
638Dic3—122no—
639C32#312711yescharacteristic, complemented, Sylow
640C23D3×#6711yescharacteristic
641Q8—21no—
642Q8—21no—
643Q8—61no—
644Q8—61no—
645Q8—92no—
646Q8—92no—
647Q8—184no—
648Q8—181no—
649Q8—181no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—184no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4D3×#6711yescharacteristic
666C2×C4C22×D3211yescharacteristic
667C8—61no—
668C8—61no—
669C8—181no—
670C8—181no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—42no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3#565611yescharacteristic
678C2×C3#577111yescharacteristic
679C2×C3#577911yescharacteristic
680C2×C3#582811yescharacteristic
681C2×C3#583811yescharacteristic
682C2×C3#583811yescharacteristic
683C22—21no—
684C22—21no—
685C22—21no—
686C22C2×D3×#6711yescharacteristic
687C4—21no—
688C4—41no—
689C4—41no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—61no—
694C4—121no—
695C4—121no—
696C4—121no—
697C4—121no—
698C4—182no—
699C4—182no—
700C4#6431211yescharacteristic
701C4#6431211yescharacteristic
702C3—21no—
703C3#8149911yescharacteristic, complemented
704C3#8345111yescharacteristic, complemented
705C2—41no—
706C2#1059515911yescharacteristic
707C2#1059532811yescharacteristic
708C2#1059546711yescharacteristic
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. #10591575C2semidirect
6. #10591575C2semidirect
7. #10591541C2semidirect
8. #10591537C2semidirect
12. #10590492C2semidirect
13. #10590490C2semidirect
14. #10590481C2semidirect
15. #10590480C2semidirect
639. C32#3127semidirect
703. C3#81499semidirect
704. C3#83451semidirect

Maximal subgroups

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

subgroupindex
C3×#56252
#105948282
#105927492
C3×#50452
#105915752
#105915412
#105915372
#105911902
#105911022
#105910562
#105904922
#105904902
#105904812
#105904802
#834513
#814993