Finite Group Databasebeta

← #11873297

Subgroups — #11873297

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×#5812C211yesmaximal, characteristic
2#10594824C211yesmaximal, characteristic
3#10592927C211yesmaximal, characteristic
4C3×#5228C211yesmaximal, characteristic
5#10591625C211yesmaximal, characteristic, complemented
6#10591625C211yesmaximal, characteristic, complemented
7#10591576C211yesmaximal, characteristic, complemented
8Dic3×#216C211yesmaximal, characteristic, complemented
9#10591547C211yesmaximal, characteristic, complemented
10#10591545C211yesmaximal, characteristic, complemented
11#10591541C211yesmaximal, characteristic, complemented
12#10591537C211yesmaximal, characteristic, complemented
13#10591134C211yesmaximal, characteristic
14#10591102C211yesmaximal, characteristic
15#10591056C211yesmaximal, characteristic
16#82555—31nomaximal
17#80177—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×Q8×Dic3—21no—
23C3×Q8×Dic3—21no—
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C3×#926—21no—
31C3×#926—21no—
32C3×#926C2211yescharacteristic
33C3×#926C2211yescharacteristic
34C3×#924C2211yescharacteristic
35#63956—21no—
36#63956—21no—
37#63869C2211yescharacteristic
38#63866C2211yescharacteristic
39#63847—21no—
40#63846—21no—
41#63844C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic
43#63662C2211yescharacteristic
44#63662C2211yescharacteristic
45#63657C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63576C2211yescharacteristic
50#63575C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#519—31no—
62#5812D311yescharacteristic
63#5625—31no—
64#5518—31no—
65C3×#451—31no—
66#5228—31no—
67#5228—31no—
68#5228—61no—
69#5228D311yescharacteristic
70#5184—31no—
71#5182—31no—
72#5182—31no—
73Dic3×Q16—31no—
74#5045—31no—
75#5031—31no—
76#5031—31no—
77#5030—31no—
78#5030—31no—
79C4×#216—31no—
80C4×#216—31no—
81#5022—31no—
82#5022—31no—
83#5000—31no—
84#4996—31no—
85#4996—31no—
86#4799—31no—
87#4796—31no—
88#4790—31no—
89#4789—31no—
90#4723—31no—
91#4720—31no—
92C2×C32×Q8—22no—
93C2×C32×Q8—22no—
94C2×C32×Q8—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101#3757—21no—
102#3756—22no—
103#3756—22no—
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105#3750—21no—
106C2×C3⋊(C3⋊C8)C2311yescharacteristic
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C3×#217—21no—
109C3×#217—21no—
110C3×#217D411yescharacteristic
111C3×#217D411yescharacteristic
112C3×#216—22no—
113C3×#216—22no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3D411yescharacteristic
119C3×C4⋊Dic3D411yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3127—91noSylow
142C22×C3×Q8—21no—
143C22×C3×Q8C2×D311yescharacteristic
144C22×C3×Q8C2×D311yescharacteristic
145C2×C3×Q16—31no—
146C2×C3×Q16—31no—
147C3×C22⋊Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—31no—
152C3×C4×Q8—61no—
153C3×C4×Q8—61no—
154C3×#117—31no—
155C3×#117—31no—
156C3×#117—61no—
157C3×#117—61no—
158Q8×Dic3—21no—
159Q8×Dic3—21no—
160Q8×Dic3—31no—
161Q8×Dic3C2×D311yescharacteristic
162Q8×Dic3C2×D311yescharacteristic
163Q8×Dic3C2×D311yescharacteristic
164Q8×Dic3C2×D311yescharacteristic
165#944—31no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—61no—
171C2×#216—61no—
172C2×#216C2×D311yescharacteristic
173C2×#216C2×D311yescharacteristic
174#926—21no—
175#926—21no—
176#926C2×D311yescharacteristic
177#926C2×D311yescharacteristic
178#924—31no—
179#924—31no—
180#924—61no—
181#924C2×D311yescharacteristic
182#890—31no—
183#890—61no—
184#889—61no—
185#889—61no—
186#889—61no—
187#887—31no—
188#879—61no—
189#879—61no—
190#879—61no—
191#879—61no—
192#870—31no—
193#869—31no—
194C4×Dic6—31no—
195C4×Dic6—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×C22⋊C8—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#835C2×D311yescharacteristic
208#835C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211#830—61no—
212#830C2×D311yescharacteristic
213#818—31no—
214#817—31no—
215#816—31no—
216#816—31no—
217#815—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C32×Q8—24no—
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8#4112yes—
240C32×Q8#4112yes—
241C2×C32×C4—24no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250#634—21no—
251#634—21no—
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—91no—
267#519—31no—
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—22no—
282C2×C3×Q8—22no—
283C2×C3×Q8—22no—
284C2×C3×Q8—22no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8—31no—
290C2×C3×Q8—41no—
291C2×C3×Q8—42no—
292C2×C3×Q8—42no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—41no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×Dic6—31no—
304C2×Dic6—31no—
305C2×Dic6—61no—
306C2×Dic6C22×D311yescharacteristic
307C3×Q16—62no—
308C3×Q16—62no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C22⋊C4—31no—
322C3×C22⋊C4—31no—
323C3×C22⋊C4—61no—
324C3×C22⋊C4—61no—
325C3×C42—31no—
326C3×C42—31no—
327C3×C42—61no—
328C3×C42—61no—
329C3×C42—61no—
330C3×C42—61no—
331C3×C42—61no—
332#217—21no—
333#217—21no—
334#217—61no—
335#217—61no—
336#217—121no—
337#217#6711yescharacteristic
338#217#6711yescharacteristic
339#216—22no—
340#216—22no—
341#216—62no—
342#216—62no—
343#216—62no—
344#216—62no—
345#216—122no—
346#216—122no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3#6711yescharacteristic
359C4⋊Dic3#6711yescharacteristic
360C4⋊Dic3C22×D311yescharacteristic
361C4⋊Dic3C22×D311yescharacteristic
362C4⋊Dic3C22×D311yescharacteristic
363Dic3⋊C4—21no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—121no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C4×Dic3—21no—
378C4×Dic3—21no—
379C4×Dic3—21no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3C22×D311yescharacteristic
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—61no—
391C2×C3⋊C8—61no—
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32C22×D411yescharacteristic
398C32×C4—22no—
399C32×C4—22no—
400C32×C4—21no—
401C32×C4C2×#4111yescharacteristic
402C32×C4C2×#4111yescharacteristic
403C3⋊Dic3—41no—
404C3⋊Dic3—41no—
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×Q8D3211yescharacteristic
414C2×Q16—31no—
415C2×Q16—31no—
416C2×Q16—91no—
417C2×Q16—91no—
418C4⋊Q8—91no—
419#126—181no—
420#126—181no—
421#125—91no—
422#125—181no—
423#125—181no—
424C22⋊Q8—31no—
425C22⋊Q8—91no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×Q8—61no—
431C4×Q8—61no—
432C4×Q8—91no—
433C4×Q8—91no—
434#117—31no—
435#117—31no—
436#117—61no—
437#117—61no—
438#107—91no—
439#107—91no—
440#106—91no—
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—24no—
460C3×Q8—24no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—22no—
466C3×Q8—22no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×Q8—44no—
470C3×Q8—61no—
471C3×Q8—61no—
472C3×Q8#23512yes—
473C3×Q8#23512yes—
474C3×Q8#23712yes—
475C3×Q8#23712yes—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—44no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4C2×#6711yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—121no—
514C2×Dic3—121no—
515C2×Dic3C2×#6711yescharacteristic
516C2×Dic3C2×#6711yescharacteristic
517C2×Dic3C2×#6711yescharacteristic
518C2×Dic3C2×#6711yescharacteristic
519Dic6—21no—
520Dic6—21no—
521Dic6—61no—
522Dic6—61no—
523Dic6—61no—
524Dic6—61no—
525Dic6—121no—
526Dic6—121no—
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—22no—
542C2×Q8—22no—
543C2×Q8—21no—
544C2×Q8—31no—
545C2×Q8—91no—
546C2×Q8C2×D3211yescharacteristic
547C2×Q8C2×D3211yescharacteristic
548C22×C4—21no—
549C22×C4C2×D3211yescharacteristic
550Q16—62no—
551Q16—62no—
552Q16—182no—
553Q16—182no—
554C2×C8—31no—
555C2×C8—31no—
556C2×C8—91no—
557C2×C8—91no—
558C4⋊C4—31no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—91no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C22⋊C4—31no—
577C22⋊C4—31no—
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22⋊C4—181no—
581C42—31no—
582C42—31no—
583C42—61no—
584C42—61no—
585C42—61no—
586C42—61no—
587C42—61no—
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—22no—
603C3×C4—22no—
604C3×C4—21no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—41no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—61no—
616C3×C4—61no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4—121no—
621C3×C4C2×#23511yescharacteristic
622C3×C4C2×#23511yescharacteristic
623C3×C4C2×#23711yescharacteristic
624C3×C4C2×#23711yescharacteristic
625Dic3—21no—
626Dic3—21no—
627Dic3—21no—
628Dic3—21no—
629Dic3—41no—
630Dic3—41no—
631Dic3—41no—
632Dic3—41no—
633Dic3—121no—
634Dic3—121no—
635Dic3—121no—
636Dic3—121no—
637Dic3—241no—
638Dic3—241no—
639C32#312711yescharacteristic, complemented, Sylow
640C23D3×#6711yescharacteristic
641Q8—24no—
642Q8—21no—
643Q8—21no—
644Q8—61no—
645Q8—61no—
646Q8—181no—
647Q8—181no—
648Q8#380412yes—
649Q8#380412yes—
650C2×C4—24no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
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#558611yescharacteristic
678C2×C3#576611yescharacteristic
679C2×C3#577911yescharacteristic
680C2×C3#579111yescharacteristic
681C2×C3#583811yescharacteristic
682C2×C3#583811yescharacteristic
683C22—21no—
684C22—21no—
685C22—21no—
686C22C2×D3×#6711yescharacteristic
687C4—22no—
688C4—22no—
689C4—21no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—61no—
694C4—121no—
695C4—121no—
696C4—121no—
697C4—121no—
698C4—361no—
699C4—361no—
700C4C2×#380411yescharacteristic
701C4C2×#380411yescharacteristic
702C3—21no—
703C3#8017711yescharacteristic, complemented
704C3#8255511yescharacteristic, complemented
705C2—41no—
706C2#1059532711yescharacteristic
707C2#1059532811yescharacteristic
708C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×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. #10591625C2semidirect
6. #10591625C2semidirect
7. #10591576C2semidirect
8. Dic3×#216C2semidirect
9. #10591547C2semidirect
10. #10591545C2semidirect
11. #10591541C2semidirect
12. #10591537C2semidirect
639. C32#3127semidirect
703. C3#80177semidirect
704. C3#82555semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
#105948242
#105929272
C3×#52282
#105916252
#105915762
Dic3×#2162
#105915472
#105915452
#105915412
#105915372
#105911342
#105911022
#105910562
#825553
#801773