Finite Group Databasebeta

← #11868766

Subgroups — #11868766

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 691 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5688C211yesmaximal, characteristic
2C4×D3×Dic6C211yesmaximal, characteristic
3#10592762C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5#10590600C211yesmaximal, characteristic
6#10590600C211yesmaximal, characteristic
7#10590489C211yesmaximal, characteristic, complemented
8#10590488C211yesmaximal, characteristic, complemented
9#10590487C211yesmaximal, characteristic, complemented
10#10590486C211yesmaximal, characteristic, complemented
11#10590437C211yesmaximal, characteristic
12#10590436C211yesmaximal, characteristic
13#10590336C211yesmaximal, characteristic
14#10590292C211yesmaximal, characteristic, complemented
15#10590286C211yesmaximal, characteristic, complemented
16#83367—31nomaximal
17#81230—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C3×#896—21no—
22C3×#896—21no—
23C3×#892C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#888C2211yescharacteristic
26C3×#888C2211yescharacteristic
27C3×#887—21no—
28C3×#887—21no—
29C3×C42×D3C2211yescharacteristic
30C3×#870C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C4×#627—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34D3×Dic3⋊C4—21no—
35C4×D3×Dic3—21no—
36#63844C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63837—21no—
39C2×#3711C2211yescharacteristic
40C2×#3711C2211yescharacteristic
41#63637C2211yescharacteristic
42#63637C2211yescharacteristic
43#63635C2211yescharacteristic
44#63634C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C3×#810C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#808C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63576C2211yescharacteristic
52#63575C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61C3×#533—31no—
62#5688D311yescharacteristic
63C4×D3×Q8—31no—
64C2×C4×Dic6—31no—
65C3×#479—31no—
66#5094—31no—
67#5094—31no—
68#5091—31no—
69#5091—31no—
70#5063—31no—
71#5063—31no—
72#5063—31no—
73#5063—31no—
74#5063—61no—
75#5063D311yescharacteristic, complemented
76#5022—31no—
77#5004—31no—
78#5004—31no—
79#4995—31no—
80#4995—31no—
81#4924—31no—
82#4881—31no—
83#4875—31no—
84#4861—31no—
85#4854—31no—
86#4837—31no—
87#4829—31no—
88#4802—31no—
89#4802—31no—
90#4793—31no—
91#4791—31no—
92C2×#634C2311yescharacteristic
93C2×C3×C4×D3D411yescharacteristic
94C2×C3×C4×D3D411yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102D3×Dic6—22no—
103D3×Dic6Q814yescomplemented
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C42C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
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×Dic3D411yescharacteristic
128C3×C4×Dic3D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137#3711—22no—
138#3711—22no—
139#3078—91noSylow
140C2×D3×Q8—31no—
141C22×Dic6—31no—
142C3×C4⋊Q8—31no—
143C3×C4⋊Q8—31no—
144C3×#125—21no—
145C3×#125—31no—
146C3×#125C2×D311yescharacteristic
147C3×#125C2×D311yescharacteristic
148C3×C22⋊Q8—61no—
149C3×C22⋊Q8—61no—
150C3×C4×Q8—31no—
151C3×C4×Q8—61no—
152C3×C4×Q8—61no—
153C3×#117—31no—
154C3×#117—31no—
155C2×C3×C42—31no—
156Q8×Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×Dic3⋊C4—61no—
159C2×C4×Dic3—61no—
160C2×#208—31no—
161C2×#208—31no—
162C2×ΓL(1,𝔽25)—31no—
163C2×ΓL(1,𝔽25)—31no—
164#896—21no—
165#896—21no—
166#892C2×D311yescharacteristic
167#892C2×D311yescharacteristic
168D3×C4⋊C4—31no—
169D3×C4⋊C4—61no—
170#888C2×D311yescharacteristic
171#888C2×D311yescharacteristic
172#887—21no—
173#887—21no—
174#887—31no—
175#887—61no—
176C42×D3—61no—
177C42×D3C2×D311yescharacteristic
178#870C2×D311yescharacteristic
179C4×Dic6—31no—
180C4×Dic6—31no—
181C4×Dic6—31no—
182C4×Dic6—31no—
183C4×Dic6—61no—
184C4×Dic6—61no—
185C4×Dic6—61no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C3×#107—31no—
189C3×#106—31no—
190C3×C4⋊C8—31no—
191C3×#103—31no—
192C3×#103—31no—
193#835—31no—
194#835—31no—
195#818—31no—
196#817—31no—
197#816—31no—
198#816—31no—
199Dic3⋊C8—31no—
200Dic3⋊C8—31no—
201#810—31no—
202#810—31no—
203#810—31no—
204#810—31no—
205#810—31no—
206#810—31no—
207#810—31no—
208#810—31no—
209#810—61no—
210#810—61no—
211#810C2×D311yescharacteristic
212#810C2×D311yescharacteristic
213#808—31no—
214#808—31no—
215#808—31no—
216#808—31no—
217#808—31no—
218#808—61no—
219#808C2×D311yescharacteristic
220#807—31no—
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—61no—
226#807C2×D311yescharacteristic
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233C22×C3×D3C2×D411yescharacteristic
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241#634—21no—
242#634C2×Q812yes—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×C4×D3—22no—
251C3×C4×D3—41no—
252C3×C4×D3C2×Q812yes—
253C3×C4×D3#4112yes—
254C3×Dic6—21no—
255C3×Dic6—42no—
256C3×Dic6—42no—
257C3×Dic6C2×Q812yes—
258#627—24no—
259D3×Dic3—24no—
260D3×Dic3—42no—
261C3⋊(C3⋊C8)—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#533—31no—
266C2×C4×Q8—91no—
267#479—31no—
268#479—91no—
269#479—91no—
270#479—91no—
271#477—91no—
272#477—91no—
273#475—91no—
274#475—91no—
275#428—91no—
276#428—91no—
277#423—91no—
278#419—91no—
279#419—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×Q8—61no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288D3×Q8—34no—
289D3×Q8—62no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3#6711yescharacteristic
293C2×C4×D3#6711yescharacteristic
294C2×C4×D3C22×D311yescharacteristic
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—34no—
300C2×Dic6—61no—
301C2×Dic6—62no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6C22×D311yescharacteristic
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—41no—
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⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C22⋊C4—61no—
328C3×C22⋊C4—61no—
329C3×C42—21no—
330C3×C42—31no—
331C3×C42—31no—
332C3×C42—31no—
333C3×C42—61no—
334C3×C42—61no—
335C3×C42—61no—
336C3×C42C22×D311yescharacteristic
337C3×C42C22×D311yescharacteristic
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—21no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—121no—
360C4×Dic3—21no—
361C4×Dic3—21no—
362C4×Dic3—21no—
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—121no—
370C4×Dic3#6711yescharacteristic
371C4×Dic3#6711yescharacteristic
372C4×Dic3C22×D311yescharacteristic
373#208—62no—
374#208—62no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383ΓL(1,𝔽25)—62no—
384ΓL(1,𝔽25)—62no—
385C22×C32C22×D411yescharacteristic
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3C22⋊Q812yes—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—41no—
392C32×C4—41no—
393C32×C4C22×Q811yescharacteristic
394C32×C4C2×#4111yescharacteristic
395C3⋊Dic3—22no—
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3C22⋊Q812yes—
403C3×Dic3#13712yes—
404C22×Q8—91no—
405C2×M16—91no—
406C2×M16—91no—
407C4⋊Q8—31no—
408C4⋊Q8—31no—
409#125—31no—
410#125D3211yescharacteristic
411C22⋊Q8—61no—
412C22⋊Q8—61no—
413C4×Q8—31no—
414C4×Q8—61no—
415C4×Q8—61no—
416C4×Q8—91no—
417C4×Q8—91no—
418C4×Q8—91no—
419C4×Q8—181no—
420C4×Q8—181no—
421#117—31no—
422#117—31no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—181no—
425C2×C42—31no—
426C2×C42—181no—
427#107—31no—
428#107—91no—
429#107—91no—
430#107—91no—
431#106—31no—
432#106—91no—
433#106—91no—
434#106—91no—
435C4⋊C8—31no—
436C4⋊C8—91no—
437C4⋊C8—91no—
438C4⋊C8—91no—
439#103—31no—
440#103—31no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447C23×C3—31no—
448C22×D3C2×#6711yescharacteristic
449C3×Q8—32no—
450C3×Q8—61no—
451C3×Q8—122no—
452C3×Q8—122no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—32no—
463C2×C3×C4—32no—
464C2×C3×C4—31no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—62no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—121no—
473C2×C3×C4D3×D411yescharacteristic
474C2×C3×C4D3×D411yescharacteristic
475C2×C3×C4C2×#6711yescharacteristic
476C2×C3×C4C2×#6711yescharacteristic
477C2×C3×C4C23×D311yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—64no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—121no—
489C2×Dic3—121no—
490C2×Dic3—122no—
491C2×Dic3C2×#6711yescharacteristic
492C2×Dic3C2×#6711yescharacteristic
493C2×Dic3C2×#6711yescharacteristic
494C4×D3—22no—
495C4×D3—41no—
496C4×D3—64no—
497C4×D3—122no—
498C4×D3D3×Q812yes—
499C4×D3#23912yes—
500Dic6—21no—
501Dic6—32no—
502Dic6—32no—
503Dic6—42no—
504Dic6—42no—
505Dic6—62no—
506Dic6—64no—
507Dic6—61no—
508Dic6—61no—
509Dic6—64no—
510Dic6—121no—
511Dic6D3×Q812yes—
512C3×C8—61no—
513C3×C8—61no—
514C3⋊C8—21no—
515C3⋊C8—21no—
516C3⋊C8—61no—
517C3⋊C8—61no—
518C3⋊C8—61no—
519C3⋊C8—61no—
520C3⋊C8—121no—
521C3⋊C8—121no—
522C2×C32C2×C22⋊Q811yescharacteristic
523C2×C32C2×#13711yescharacteristic
524C2×C32#57511yescharacteristic
525C3×D3—22no—
526C2×Q8—31no—
527C2×Q8—61no—
528C2×Q8—61no—
529C2×Q8—94no—
530C2×Q8—91no—
531C2×Q8—181no—
532C2×Q8—182no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—181no—
537C22×C4—181no—
538M16—182no—
539M16—182no—
540C2×C8—31no—
541C2×C8—31no—
542C2×C8—91no—
543C2×C8—91no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—91no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4C2×D3211yescharacteristic
560C4⋊C4C2×D3211yescharacteristic
561C22⋊C4—61no—
562C22⋊C4—61no—
563C42—31no—
564C42—31no—
565C42—31no—
566C42—61no—
567C42—61no—
568C42—61no—
569C42—181no—
570C42—181no—
571C42—181no—
572C42C2×D3211yescharacteristic
573C22×C3—21no—
574C22×C3—32no—
575C22×C3—61no—
576C22×C3—61no—
577C22×C3C2×D3×D411yescharacteristic
578C22×C3C22×#6711yescharacteristic
579C2×D3—21no—
580C2×D3—21no—
581C2×D3#94612yes—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—32no—
589C3×C4—32no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—61no—
597C3×C4—62no—
598C3×C4—81no—
599C3×C4—81no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4C2×D3×Q811yescharacteristic
604C3×C4C2×D3×Q811yescharacteristic
605C3×C4C2×#23911yescharacteristic
606C3×C4D3×#4111yescharacteristic
607Dic3—21no—
608Dic3—22no—
609Dic3—41no—
610Dic3—41no—
611Dic3—41no—
612Dic3—62no—
613Dic3—62no—
614Dic3—122no—
615Dic3—121no—
616Dic3—121no—
617Dic3—241no—
618Dic3#94612yes—
619Dic3#95112yes—
620C32#307811yescharacteristic, complemented, Sylow
621C23—31no—
622Q8—32no—
623Q8—61no—
624Q8—92no—
625Q8—122no—
626Q8—122no—
627Q8—184no—
628Q8—181no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—32no—
634C2×C4—32no—
635C2×C4—31no—
636C2×C4—62no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—121no—
642C2×C4—184no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—362no—
646C2×C4D3×#6711yescharacteristic
647C2×C4D3×#6711yescharacteristic
648C2×C4C22×D3211yescharacteristic
649C8—61no—
650C8—61no—
651C8—181no—
652C8—181no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—62no—
657C2×C3D3×C22⋊Q811yescharacteristic
658C2×C3#576811yescharacteristic
659C2×C3D3×#13711yescharacteristic
660C2×C3C2×#94611yescharacteristic
661C2×C3#582211yescharacteristic
662C2×C3C2×#95111yescharacteristic
663D3—22no—
664C22—32no—
665C22—61no—
666C22—61no—
667C22C2×D3×#6711yescharacteristic
668C4—21no—
669C4—21no—
670C4—32no—
671C4—32no—
672C4—41no—
673C4—41no—
674C4—62no—
675C4—61no—
676C4—121no—
677C4—121no—
678C4—121no—
679C4—182no—
680C4—361no—
681C4D32×Q811yescharacteristic
682C4D3×#23911yescharacteristic
683C3—21no—
684C3#8123011yescharacteristic, complemented
685C3#8336711yescharacteristic, complemented
686C2—62no—
687C2D3×#94611yescharacteristic
688C2#1059545311yescharacteristic
689C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#125D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #10592762C2semidirect
4. C3×#5063C2semidirect
7. #10590489C2semidirect
8. #10590488C2semidirect
9. #10590487C2semidirect
10. #10590486C2semidirect
14. #10590292C2semidirect
15. #10590286C2semidirect
75. #5063D3semidirect
103. D3×Dic6Q8semidirect
620. C32#3078semidirect
684. C3#81230semidirect
685. C3#83367semidirect

Maximal subgroups

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

subgroupindex
C3×#56882
C4×D3×Dic62
#105927622
C3×#50632
#105906002
#105904892
#105904882
#105904872
#105904862
#105904372
#105904362
#105903362
#105902922
#105902862
#833673
#812303