Finite Group Databasebeta

← #11872686

Subgroups — #11872686

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594357C211yesmaximal, characteristic, complemented
2#10594343C211yesmaximal, characteristic
3#10592588C211yesmaximal, characteristic, complemented
4C3×#4888C211yesmaximal, characteristic, complemented
5C3×#4875C211yesmaximal, characteristic, complemented
6#10590951C211yesmaximal, characteristic
7#10590813C211yesmaximal, characteristic, complemented
8#10590791C211yesmaximal, characteristic, complemented
9#10590699C211yesmaximal, characteristic, complemented
10#10590604C211yesmaximal, characteristic, complemented
11#10590536C211yesmaximal, characteristic, complemented
12#10590487C211yesmaximal, characteristic, complemented
13#10590483C211yesmaximal, characteristic, complemented
14#10590482C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic
16#81497—31nomaximal
17#81096—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C2×#3744C2211yescharacteristic
20#64102C2211yescharacteristic
21#64096C2211yescharacteristic
22C3×#897C2211yescharacteristic
23C3×#892C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C4×#627—21no—
27#63909C2211yescharacteristic
28#63907—21no—
29#63878—21no—
30#63877—21no—
31#63871—21no—
32#63864C2211yescharacteristic
33#63855C2211yescharacteristic
34#63853—21no—
35#63848—21no—
36#63844C2211yescharacteristic
37#63843C2211yescharacteristic
38#63843C2211yescharacteristic
39#63837—21no—
40C2×#3719C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C32×#107C2211yescharacteristic
44#63642C2211yescharacteristic
45#63637C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63574C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61#5733—31no—
62#5643—31no—
63#5572—31no—
64#5516—31no—
65C3×#485—31no—
66C3×#477—31no—
67#5094—31no—
68#5050—31no—
69#5028—31no—
70#5003—31no—
71#4889—31no—
72#4889—31no—
73#4889—61no—
74#4888D311yescharacteristic, complemented
75#4885—31no—
76#4875D311yescharacteristic, complemented
77#4873—31no—
78#4854—31no—
79#4852—31no—
80#4845—31no—
81#4840—31no—
82#4809—31no—
83#4806—31no—
84#4798—31no—
85#4798—31no—
86#4790—31no—
87#4789—31no—
88#4789—31no—
89#4788—31no—
90#4738—31no—
91#4720—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#626—21no—
101C2×D3×Dic3—21no—
102D3×Dic6—22no—
103D3×Dic6—22no—
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3752—21no—
108#3750—21no—
109C4×C3⋊Dic3—21no—
110C4×C3⋊Dic3C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112#3744—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130#3722—21no—
131#3722—21no—
132#3722—21no—
133(C2×D3)⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3D411yescharacteristic
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138#3719—22no—
139#3718—22no—
140#3717—22no—
141#3121—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C3×C4⋊Q8—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×#117—31no—
148#947—31no—
149#947—61no—
150#946—61no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153C2×#216—31no—
154C2×#216—31no—
155C2×#216—31no—
156C2×#215—31no—
157#930—31no—
158#926—31no—
159C2×Dic12—31no—
160C2×#204—31no—
161C2×#204—31no—
162C2×#204—31no—
163C2×#204—61no—
164#898—61no—
165#898—61no—
166#897—61no—
167#897C2×D311yescharacteristic
168#895—31no—
169#894—61no—
170#893—31no—
171#893—31no—
172#893—61no—
173#892—61no—
174#892C2×D311yescharacteristic
175#888C2×D311yescharacteristic
176#887—31no—
177#887—31no—
178#887—31no—
179#887—31no—
180#887—31no—
181#887—61no—
182#887—61no—
183#887C2×D311yescharacteristic
184#885—61no—
185#883—61no—
186#877—61no—
187#877—61no—
188#875—31no—
189#872—31no—
190#872—61no—
191C4×Dic6—31no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C4×Dic6—61no—
195C3×#107—21no—
196C3×#107—31no—
197C3×#107C2×D311yescharacteristic
198C3×#107C2×D311yescharacteristic
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×C22⋊C8—31no—
206#830—31no—
207#821—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8C2×D311yescharacteristic
210#816—31no—
211#816C2×D311yescharacteristic
212#816C2×D311yescharacteristic
213#815—31no—
214#815—31no—
215#815—61no—
216Dic3⋊C8—31no—
217Dic3⋊C8C2×D311yescharacteristic
218C8×Dic3—31no—
219C8×Dic3—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—61no—
224#810C2×D311yescharacteristic
225#810C2×D311yescharacteristic
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#808—31no—
231#808—31no—
232#808C2×D311yescharacteristic
233#807C2×D311yescharacteristic
234C4⋊(C3⋊C8)—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—21no—
245C4×C3⋊D3—81no—
246#634—21no—
247#634#4112yes—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—81no—
261C3×Dic6#4112yes—
262#627—24no—
263#626—81no—
264D3×Dic3—24no—
265C32×C8—21no—
266C3⋊(C3⋊C8)—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#542—91no—
270#519—91no—
271#485—31no—
272#482—91no—
273#477—31no—
274#475—91no—
275#464—91no—
276#464—91no—
277#451—91no—
278#448—91no—
279#441—91no—
280#440—91no—
281C4×Q16—91no—
282C4×SD16—91no—
283#433—91no—
284C2×C3×Q8—31no—
285C2×C3×Q8—31no—
286C2×C3×Q8—61no—
287C22×C3×C4—31no—
288C2×#67—61no—
289C22×Dic3—61no—
290D3×Q8—62no—
291D3×Q8—62no—
292C2×D12—31no—
293C2×D12—31no—
294C2×D12—61no—
295C2×D12—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×C4×D3—121no—
300C2×C4×D3C22×D311yescharacteristic
301C2×Dic6—21no—
302C2×Dic6—31no—
303C2×Dic6—31no—
304C2×Dic6—61no—
305C2×Dic6—62no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—62no—
309C2×Dic6C22×D311yescharacteristic
310C2×Dic6C22×D311yescharacteristic
311C2×C3×C8—21no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
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—31no—
330C3×C42—61no—
331C3×C42—61no—
332#217—31no—
333#217—31no—
334#216—62no—
335#216—62no—
336#216—62no—
337#215—62no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—31no—
341(C2×D3)⋊C4—31no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—121no—
351C4⋊Dic3—21no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D311yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—121no—
369C4×Dic3—21no—
370C4×Dic3—21no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—61no—
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×Dic3—121no—
383C4×Dic3C22×D311yescharacteristic
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389Dic12—62no—
390#204—62no—
391#204—62no—
392#204—64no—
393#204—62no—
394C22×C32C22×D411yescharacteristic
395C2×C3⋊D3—41no—
396C2×C3⋊D3—41no—
397C2×C3⋊D3—41no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C32×C4—41no—
402C32×C4—41no—
403C32×C4C2×#4111yescharacteristic
404C32×C4C2×#4111yescharacteristic
405C3⋊Dic3—22no—
406C3⋊Dic3—21no—
407C3⋊Dic3—21no—
408C3×Dic3—22no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C22×Q8—91no—
416C2×Q16—91no—
417C2×Q16—91no—
418C2×SD16—91no—
419C2×SD16—91no—
420C4⋊Q8—31no—
421#126—181no—
422#124—91no—
423#124—181no—
424#123—181no—
425C22⋊Q8—31no—
426C22⋊Q8—181no—
427#121—91no—
428C4×Q8—31no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×Q8—91no—
433C4×Q8—181no—
434C4×Q8—181no—
435C4×D4—91no—
436#117—31no—
437#117—91no—
438#117—181no—
439#117—181no—
440#107—31no—
441#107D3211yescharacteristic
442#106—31no—
443#106—91no—
444C4⋊C8—31no—
445C4⋊C8—91no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103—31no—
450#103—91no—
451#103—91no—
452#102—91no—
453#102—91no—
454C22⋊C8—31no—
455C22⋊C8—91no—
456#97—91no—
457C4×C8—91no—
458C23×C3—31no—
459C22×D3—61no—
460C22×D3—61no—
461C22×D3—121no—
462C22×D3D3×D411yescharacteristic
463C3×Q8—32no—
464C3×Q8—61no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—241no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4C23×D311yescharacteristic
485C2×C3×C4C23×D311yescharacteristic
486#67—241no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—64no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—121no—
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503C2×Dic3D3×D411yescharacteristic
504D12—62no—
505D12—61no—
506D12—61no—
507D12—61no—
508D12—61no—
509D12—121no—
510D12—241no—
511C4×D3—21no—
512C4×D3—21no—
513C4×D3—64no—
514C4×D3—241no—
515C4×D3—241no—
516C4×D3—242no—
517Dic6—21no—
518Dic6—21no—
519Dic6—21no—
520Dic6—32no—
521Dic6—32no—
522Dic6—62no—
523Dic6—64no—
524Dic6—64no—
525Dic6—61no—
526Dic6—61no—
527Dic6—81no—
528Dic6—121no—
529Dic6#23912yes—
530C3×C8—22no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—61no—
534C3×C8—61no—
535C3⋊C8—21no—
536C3⋊C8—21no—
537C3⋊C8—61no—
538C3⋊C8—61no—
539C3⋊C8—121no—
540C2×C32#52511yescharacteristic
541C2×C32#57711yescharacteristic
542C2×C32#57811yescharacteristic
543C3⋊D3—81no—
544C3×D3—41no—
545C2×Q8—31no—
546C2×Q8—31no—
547C2×Q8—61no—
548C2×Q8—91no—
549C2×Q8—181no—
550C2×Q8—182no—
551C2×Q8—182no—
552C2×D4—91no—
553C2×D4—181no—
554C22×C4—31no—
555C22×C4—181no—
556C22×C4—181no—
557Q16—182no—
558Q16—182no—
559SD16—182no—
560SD16—182no—
561C2×C8—31no—
562C2×C8—31no—
563C2×C8—91no—
564C2×C8C2×D3211yescharacteristic
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—91no—
571C4⋊C4—91no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C4⋊C4C2×D3211yescharacteristic
577C4⋊C4C2×D3211yescharacteristic
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22⋊C4—91no—
581C22⋊C4—91no—
582C22⋊C4—181no—
583C22⋊C4—181no—
584C22⋊C4—181no—
585C22⋊C4—181no—
586C42—31no—
587C42—61no—
588C42—61no—
589C42—91no—
590C42—181no—
591C42—181no—
592C42—181no—
593C42—181no—
594C22×C3—21no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3C2×D3×D411yescharacteristic
599C22×C3C2×D3×D411yescharacteristic
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—21no—
603C2×D3—122no—
604C2×D3—121no—
605C2×D3—121no—
606C2×D3—121no—
607C2×D3—121no—
608C2×D3—121no—
609C2×D3—121no—
610C2×D3—241no—
611C2×D3—241no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—62no—
619C3×C4—61no—
620C3×C4—61no—
621C3×C4—61no—
622C3×C4—81no—
623C3×C4—81no—
624C3×C4—121no—
625C3×C4—121no—
626C3×C4—121no—
627C3×C4C2×#23911yescharacteristic
628C3×C4D3×#4111yescharacteristic
629C3×C4D3×#4111yescharacteristic
630C3×C4D3×#4111yescharacteristic
631Dic3—21no—
632Dic3—21no—
633Dic3—21no—
634Dic3—22no—
635Dic3—41no—
636Dic3—41no—
637Dic3—41no—
638Dic3—62no—
639Dic3—61no—
640Dic3—61no—
641Dic3—61no—
642Dic3—61no—
643Dic3—62no—
644Dic3—122no—
645Dic3—121no—
646Dic3—121no—
647C32#312111yescharacteristic, complemented, Sylow
648C23—31no—
649C23—181no—
650Q8—32no—
651Q8—61no—
652Q8—61no—
653Q8—61no—
654Q8—92no—
655Q8—184no—
656Q8—181no—
657Q8—241no—
658D4—181no—
659D4—181no—
660D4—721no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—91no—
673C2×C4—91no—
674C2×C4—184no—
675C2×C4—181no—
676C2×C4—721no—
677C2×C4C22×D3211yescharacteristic
678C8—21no—
679C8—61no—
680C8—61no—
681C8—181no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—121no—
686C2×C3#562711yescharacteristic
687C2×C3#565611yescharacteristic
688C2×C3#576611yescharacteristic
689C2×C3#577011yescharacteristic
690C2×C3#577511yescharacteristic
691C2×C3#577911yescharacteristic
692D3—41no—
693D3—242no—
694D3—241no—
695D3—241no—
696C22—61no—
697C22—61no—
698C22—61no—
699C22—361no—
700C22—361no—
701C22—361no—
702C22D32×D411yescharacteristic
703C4—41no—
704C4—41no—
705C4—61no—
706C4—62no—
707C4—61no—
708C4—61no—
709C4—121no—
710C4—121no—
711C4—121no—
712C4—182no—
713C4—181no—
714C4—181no—
715C4#6430611yescharacteristic
716C4D3×#23911yescharacteristic
717C3—21no—
718C3#8109611yescharacteristic, complemented
719C3#8149711yescharacteristic, complemented
720C2—121no—
721C2—721no—
722C2#1059461511yescharacteristic
723C2#1059473611yescharacteristic
724C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#63909C22
hypercenter#107D32
hypocenterC32#3121
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594357C2semidirect
3. #10592588C2semidirect
4. C3×#4888C2semidirect
5. C3×#4875C2semidirect
7. #10590813C2semidirect
8. #10590791C2semidirect
9. #10590699C2semidirect
10. #10590604C2semidirect
11. #10590536C2semidirect
12. #10590487C2semidirect
13. #10590483C2semidirect
14. #10590482C2semidirect
74. #4888D3semidirect
76. #4875D3semidirect
647. C32#3121semidirect
718. C3#81096semidirect
719. C3#81497semidirect

Maximal subgroups

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

subgroupindex
#105943572
#105943432
#105925882
C3×#48882
C3×#48752
#105909512
#105908132
#105907912
#105906992
#105906042
#105905362
#105904872
#105904832
#105904822
#105904242
#814973
#810963