Finite Group Databasebeta

← #11883899

Subgroups — #11883899

Order 1152.

819 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D42×C9C211yesmaximal, characteristic, complemented
2C2×#63495C211yesmaximal, characteristic, complemented
3C22×#3672C211yesmaximal, characteristic, complemented
4#10589654C211yesmaximal, characteristic, complemented
5#10588898C211yesmaximal, characteristic, complemented
6#10588897C211yesmaximal, characteristic, complemented
7#10588756C211yesmaximal, characteristic, complemented
8#10588752C211yesmaximal, characteristic, complemented
9#10588721C211yesmaximal, characteristic, complemented
10#10588720C211yesmaximal, characteristic, complemented
11#10588718C211yesmaximal, characteristic, complemented
12#10588716C211yesmaximal, characteristic, complemented
13#10588699C211yesmaximal, characteristic, complemented
14#10588694C211yesmaximal, characteristic, complemented
15#10588688C211yesmaximal, characteristic, complemented
16#83491—31nomaximal
17C22×D4×C9—21no—
18C22×D4×C9C2211yescharacteristic
19C22×D4×C9C2211yescharacteristic
20C2×#3697C2211yescharacteristic, complemented
21C22×Dic18C2211yescharacteristic, complemented
22C9×#127C2211yescharacteristic
23C9×#121—21no—
24C9×#121C2211yescharacteristic
25C9×#121C2211yescharacteristic
26C9×#120—21no—
27C9×#120—21no—
28C4×D4×C9C2211yescharacteristic
29C4×D4×C9C2211yescharacteristic
30#63501—21no—
31#63495—24no—
32C2×#3673C2211yescharacteristic
33C2×#3673C2211yescharacteristic, complemented
34C2×#3673C2211yescharacteristic, complemented
35C2×#3672—24no—
36C2×#3672C2211yescharacteristic
37C2×#3672C2211yescharacteristic
38C2×#3672C2211yescharacteristic, complemented
39C2×#3672C2211yescharacteristic, complemented
40C2×#3672C2211yescharacteristic, complemented
41C2×#3672C2211yescharacteristic, complemented
42#63492C2211yescharacteristic, complemented
43#63486C2211yescharacteristic, complemented
44C2×#3667C2211yescharacteristic, complemented
45C22×C9⋊C8C2211yescharacteristic, complemented
46#63458—21no—
47#63447—21no—
48#611⋊C4—21no—
49#63437C2211yescharacteristic, complemented
50C4×Dic18C2211yescharacteristic, complemented
51#63392C2211yescharacteristic
52#63392C2211yescharacteristic, complemented
53#63392C2211yescharacteristic, complemented
54#63389C2211yescharacteristic, complemented
55#63389C2211yescharacteristic, complemented
56#63369C2211yescharacteristic, complemented
57#63368C2211yescharacteristic, complemented
58#63368C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60C4⋊(C9⋊C8)C2211yescharacteristic, complemented
61#63362C2211yescharacteristic, complemented
62C3×D42D311yescharacteristic
63C22×#214—31no—
64C2×#932—31no—
65#5552—31no—
66#5218—31no—
67#5217—31no—
68#5075—31no—
69#5074—31no—
70#5042—31no—
71#5040—31no—
72#5038—31no—
73#5037—31no—
74#5018—31no—
75#5016—31no—
76#5011—31no—
77C24×C9—21no—
78C24×C9—21no—
79C2×D4×C9—22no—
80C2×D4×C9—22no—
81C2×D4×C9—21no—
82C2×D4×C9—21no—
83C2×D4×C9—21no—
84C2×D4×C9—21no—
85C2×D4×C9—21no—
86C2×D4×C9—21no—
87C2×D4×C9—41no—
88C2×D4×C9—41no—
89C2×D4×C9—44no—
90C2×D4×C9D411yescharacteristic
91C2×D4×C9C2311yescharacteristic
92C2×D4×C9C2311yescharacteristic
93C2×D4×C9C2311yescharacteristic
94C22×C4×C9—21no—
95C22×C4×C9C2311yescharacteristic
96C22×C4×C9C2311yescharacteristic
97C2×#611—21no—
98C2×#611—21no—
99C22×Dic9—21no—
100#3697—22no—
101#3697—41no—
102C2×D36C2311yescharacteristic
103C2×C4×D9—21no—
104C2×Dic18—22no—
105C2×Dic18—21no—
106C2×Dic18—41no—
107C2×Dic18C2311yescharacteristic
108C2×Dic18C2311yescharacteristic
109C9×C4⋊C4D411yescharacteristic
110C9×C4⋊C4C2311yescharacteristic
111C9×C22⋊C4—21no—
112C9×C22⋊C4—21no—
113C9×C22⋊C4—21no—
114C9×C22⋊C4D411yescharacteristic
115C9×C22⋊C4D411yescharacteristic
116C42×C9C2311yescharacteristic
117#3676—21no—
118#3673—22no—
119#3673—22no—
120#3673—41no—
121#3672—22no—
122#3672—22no—
123#3672—22no—
124#3672—22no—
125#3672—41no—
126#3672D414yescomplemented
127(C2×D9)⋊C4—21no—
128(C2×D9)⋊C4—21no—
129(C2×D9)⋊C4—21no—
130C4⋊Dic9C2311yescharacteristic
131Dic9⋊C4—21no—
132Dic9⋊C4—21no—
133C4×Dic9—21no—
134#3667—22no—
135C2×C9⋊C8—22no—
136C2×C9⋊C8C2311yescharacteristic
137C2×C9⋊C8C2311yescharacteristic
138C2×C9⋊C8C2311yescharacteristic
139C2×C9⋊C8C2311yescharacteristic
140#3265—91noSylow
141C22×C3×D4—21no—
142C22×C3×D4C2×D311yescharacteristic
143C22×C3×D4C2×D311yescharacteristic
144C2×#235—31no—
145C22×Dic6—31no—
146C3×#127C2×D311yescharacteristic
147C3×#121—21no—
148C3×#121C2×D311yescharacteristic
149C3×#121C2×D311yescharacteristic
150C3×#120—21no—
151C3×#120—21no—
152C3×C4×D4C2×D311yescharacteristic
153C3×C4×D4C2×D311yescharacteristic
154#939—61no—
155C2×#214—31no—
156C2×#214—31no—
157C2×#214—31no—
158C2×#214—31no—
159C2×#214—31no—
160C2×#214—31no—
161C2×#214—64no—
162#932—64no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166#930—31no—
167#924—31no—
168C2×#208—31no—
169C22×C3⋊C8—31no—
170#896—61no—
171#885—61no—
172#67⋊C4—61no—
173#875—31no—
174C4×Dic6—31no—
175#832—31no—
176#832—31no—
177#832—31no—
178#830—31no—
179#830—31no—
180#810—31no—
181#810—31no—
182#809—31no—
183#807—31no—
184C4⋊(C3⋊C8)—31no—
185#803—31no—
186C23×C9—21no—
187C23×C9—21no—
188C23×C9—21no—
189C23×C9—42no—
190C23×C9—42no—
191C23×C9—42no—
192C23×C9—42no—
193C23×C9—81no—
194C23×C9—81no—
195C23×C9C2×D411yescharacteristic
196C23×C9C2×D411yescharacteristic
197C22×D9—21no—
198D4×C9—22no—
199D4×C9—21no—
200D4×C9—21no—
201D4×C9—21no—
202D4×C9—21no—
203D4×C9—21no—
204D4×C9—42no—
205D4×C9—42no—
206D4×C9—42no—
207D4×C9—42no—
208D4×C9—42no—
209D4×C9—81no—
210D4×C9C2×D412yes—
211C2×C4×C9—21no—
212C2×C4×C9—21no—
213C2×C4×C9—21no—
214C2×C4×C9—21no—
215C2×C4×C9—21no—
216C2×C4×C9—42no—
217C2×C4×C9C2×D411yescharacteristic
218C2×C4×C9C2×D411yescharacteristic
219C2×C4×C9C2×D411yescharacteristic
220C2×C4×C9C2×D411yescharacteristic
221C2×C4×C9C2411yescharacteristic
222#611—42no—
223#611—42no—
224C2×Dic9—21no—
225C2×Dic9—21no—
226C2×Dic9—21no—
227C2×Dic9—42no—
228D36—21no—
229D36—21no—
230C4×D9—42no—
231Dic18—21no—
232Dic18—21no—
233Dic18—21no—
234Dic18—42no—
235Dic18C2×D412yescomplemented
236C9⋊C8—21no—
237C9⋊C8—21no—
238C9⋊C8—21no—
239C9⋊C8C2×D412yescomplemented
240C2×AGL(1,ℤ/8)—91no—
241C22×SD16—91no—
242#548—91no—
243D42D911yescharacteristic, complemented
244#496—91no—
245#468—91no—
246#466—91no—
247#463—91no—
248#460—91no—
249#450—91no—
250#449—91no—
251#448—91no—
252#447—91no—
253#440—91no—
254#435—91no—
255C24×C3—21no—
256C24×C3—21no—
257C2×C3×D4—22no—
258C2×C3×D4—22no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—41no—
266C2×C3×D4—41no—
267C2×C3×D4—44no—
268C2×C3×D4#6711yescharacteristic
269C2×C3×D4C22×D311yescharacteristic
270C2×C3×D4C22×D311yescharacteristic
271C2×C3×D4C22×D311yescharacteristic
272C22×C3×C4—21no—
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C22×D311yescharacteristic
275C2×#67—61no—
276C2×#67—61no—
277C22×Dic3—61no—
278#235—62no—
279#235—121no—
280C2×D12—31no—
281C2×C4×D3—61no—
282C2×Dic6—31no—
283C2×Dic6—31no—
284C2×Dic6—62no—
285C2×Dic6—61no—
286C2×Dic6—121no—
287C3×C4⋊C4#6711yescharacteristic
288C3×C4⋊C4C22×D311yescharacteristic
289C3×C22⋊C4—21no—
290C3×C22⋊C4—21no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4#6711yescharacteristic
293C3×C22⋊C4#6711yescharacteristic
294C3×C42C22×D311yescharacteristic
295#217—61no—
296#214—34no—
297#214—62no—
298#214—62no—
299#214—62no—
300#214—62no—
301#214—121no—
302#213—62no—
303#213—62no—
304#213—121no—
305(C2×D3)⋊C4—61no—
306(C2×D3)⋊C4—61no—
307(C2×D3)⋊C4—61no—
308C4⋊Dic3—31no—
309Dic3⋊C4—61no—
310Dic3⋊C4—61no—
311C4×Dic3—61no—
312#208—62no—
313C2×C3⋊C8—31no—
314C2×C3⋊C8—31no—
315C2×C3⋊C8—31no—
316C2×C3⋊C8—31no—
317C2×C3⋊C8—62no—
318C22×C9—21no—
319C22×C9—21no—
320C22×C9—21no—
321C22×C9—22no—
322C22×C9—21no—
323C22×C9—21no—
324C22×C9—41no—
325C22×C9—41no—
326C22×C9—41no—
327C22×C9—41no—
328C22×C9—41no—
329C22×C9—41no—
330C22×C9—41no—
331C22×C9—41no—
332C22×C9—84no—
333C22×C9—84no—
334C22×C9AGL(1,ℤ/8)12yescomplemented
335C22×C9C22×D411yescharacteristic
336C2×D9—41no—
337C2×D9—41no—
338C2×D9—41no—
339C4×C9—21no—
340C4×C9—21no—
341C4×C9—21no—
342C4×C9—21no—
343C4×C9—41no—
344C4×C9C22×D411yescharacteristic
345C4×C9H(5,𝔽2)11yescharacteristic
346Dic9—22no—
347Dic9—41no—
348Dic9—41no—
349C2×#41—91no—
350C22×Q8—91no—
351C22×D4—21no—
352C22×D4C2×D911yescharacteristic
353C22×D4C2×D911yescharacteristic
354AGL(1,ℤ/8)—184no—
355C2×SD16—91no—
356C2×SD16—91no—
357C2×SD16—91no—
358C2×SD16—91no—
359C2×SD16—91no—
360C2×SD16—91no—
361C2×SD16—184no—
362C2×D8—91no—
363C2×D8—91no—
364C2×D8—91no—
365C2×M16—91no—
366C22×C8—91no—
367#127C2×D911yescharacteristic
368#124—91no—
369#124—181no—
370C22⋊Q8—91no—
371C22⋊Q8—181no—
372#121—21no—
373#121—91no—
374#121—181no—
375#121C2×D911yescharacteristic
376#121C2×D911yescharacteristic
377#120—21no—
378#120—21no—
379C4×Q8—91no—
380C4×D4—181no—
381C4×D4C2×D911yescharacteristic
382C4×D4C2×D911yescharacteristic
383#107—91no—
384C4⋊C8—91no—
385#103—91no—
386#103—91no—
387#102—91no—
388#102—91no—
389#102—91no—
390#102—91no—
391C22⋊C8—91no—
392C22⋊C8—91no—
393#97—91no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—81no—
402C23×C3—81no—
403C23×C3C2×#6711yescharacteristic
404C23×C3C2×#6711yescharacteristic
405C22×D3—61no—
406C3×D4—22no—
407C3×D4—21no—
408C3×D4—21no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—21no—
412C3×D4—42no—
413C3×D4—42no—
414C3×D4—42no—
415C3×D4—42no—
416C3×D4—42no—
417C3×D4—81no—
418C3×D4D3×D412yes—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—42no—
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C2×#6711yescharacteristic
427C2×C3×C4C2×#6711yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430#67—122no—
431#67—122no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—122no—
436D12—61no—
437D12—61no—
438C4×D3—122no—
439Dic6—32no—
440Dic6—61no—
441Dic6—61no—
442Dic6—61no—
443Dic6—122no—
444C3⋊C8—32no—
445C3⋊C8—61no—
446C3⋊C8—61no—
447C3⋊C8—61no—
448C2×C9—22no—
449C2×C9—41no—
450C2×C9—42no—
451C2×C9—81no—
452C2×C9—81no—
453C2×C9D4211yescharacteristic
454C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
455C2×C9#57711yescharacteristic
456D9—81no—
457C24—21no—
458C24—21no—
459#41—182no—
460#41—361no—
461C2×Q8—91no—
462C2×Q8—91no—
463C2×Q8—182no—
464C2×Q8—181no—
465C2×Q8—361no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—44no—
477C2×D4—91no—
478C2×D4—181no—
479C2×D4—181no—
480C2×D4#61111yescharacteristic
481C2×D4C22×D911yescharacteristic
482C2×D4C22×D911yescharacteristic
483C2×D4C22×D911yescharacteristic
484C22×C4—21no—
485C22×C4—181no—
486C22×C4—181no—
487C22×C4C22×D911yescharacteristic
488C22×C4C22×D911yescharacteristic
489SD16—94no—
490SD16—182no—
491SD16—182no—
492SD16—182no—
493SD16—182no—
494SD16—361no—
495D8—182no—
496D8—182no—
497D8—361no—
498M16—182no—
499C2×C8—91no—
500C2×C8—91no—
501C2×C8—91no—
502C2×C8—91no—
503C2×C8—182no—
504C4⋊C4—91no—
505C4⋊C4—181no—
506C4⋊C4—181no—
507C4⋊C4#61111yescharacteristic
508C4⋊C4C22×D911yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—181no—
513C22⋊C4—181no—
514C22⋊C4—181no—
515C22⋊C4—181no—
516C22⋊C4#61111yescharacteristic
517C22⋊C4#61111yescharacteristic
518C42—181no—
519C42C22×D911yescharacteristic
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—84no—
535C22×C3—84no—
536C22×C3#93212yes—
537C22×C3C22×#6711yescharacteristic
538C2×D3—121no—
539C2×D3—121no—
540C2×D3—121no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—41no—
546C3×C4C2×D3×D411yescharacteristic
547C3×C4#100411yescharacteristic
548Dic3—62no—
549Dic3—121no—
550Dic3—121no—
551C9#326511yescharacteristic, complemented, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—81no—
560C23—81no—
561C23—181no—
562C23C2×#61111yescharacteristic
563C23C2×#61111yescharacteristic
564Q8—92no—
565Q8—181no—
566Q8—181no—
567Q8—181no—
568Q8—362no—
569D4—22no—
570D4—21no—
571D4—21no—
572D4—21no—
573D4—21no—
574D4—21no—
575D4—42no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—81no—
581D4—181no—
582D4—181no—
583D4—362no—
584D4—362no—
585D4D4×D912yes—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—42no—
592C2×C4—181no—
593C2×C4—181no—
594C2×C4—181no—
595C2×C4—362no—
596C2×C4—362no—
597C2×C4C2×#61111yescharacteristic
598C2×C4C2×#61111yescharacteristic
599C2×C4C2×#61111yescharacteristic
600C2×C4C2×#61111yescharacteristic
601C2×C4C23×D911yescharacteristic
602C8—92no—
603C8—181no—
604C8—181no—
605C8—181no—
606C2×C3—22no—
607C2×C3—41no—
608C2×C3—42no—
609C2×C3—81no—
610C2×C3—81no—
611C2×C3C2×#93211yescharacteristic
612C2×C3D4×#6711yescharacteristic
613C2×C3#583611yescharacteristic
614D3—241no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—22no—
620C22—21no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—84no—
630C22—84no—
631C22—361no—
632C22—361no—
633C22—361no—
634C22#6349512yescomplemented
635C22C22×#61111yescharacteristic
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—41no—
641C4—182no—
642C4—361no—
643C4—361no—
644C4C2×D4×D911yescharacteristic
645C4#6371011yescharacteristic
646C3#8349111yescharacteristic
647C2—22no—
648C2—41no—
649C2—42no—
650C2—81no—
651C2—81no—
652C2—721no—
653C2C2×#6349511yescharacteristic
654C2D4×#61111yescharacteristic
655C2#1058993811yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingD42×C9C2
socleC22×C3C22×#67
hypercenterD42D9
hypocenterC9#3265
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. D42×C9C2semidirect
2. C2×#63495C2semidirect
3. C22×#3672C2semidirect
4. #10589654C2semidirect
5. #10588898C2semidirect
6. #10588897C2semidirect
7. #10588756C2semidirect
8. #10588752C2semidirect
9. #10588721C2semidirect
10. #10588720C2semidirect
11. #10588718C2semidirect
12. #10588716C2semidirect
13. #10588699C2semidirect
14. #10588694C2semidirect
15. #10588688C2semidirect
20. C2×#3697C22semidirect
21. C22×Dic18C22semidirect
33. C2×#3673C22semidirect
34. C2×#3673C22semidirect
38. C2×#3672C22semidirect
39. C2×#3672C22semidirect
40. C2×#3672C22semidirect
41. C2×#3672C22semidirect
42. #63492C22semidirect
43. #63486C22semidirect
44. C2×#3667C22semidirect
45. C22×C9⋊C8C22semidirect
49. #63437C22semidirect
50. C4×Dic18C22semidirect
52. #63392C22semidirect
53. #63392C22semidirect
54. #63389C22semidirect
55. #63389C22semidirect
56. #63369C22semidirect
57. #63368C22semidirect
58. #63368C22semidirect
59. #63366C22semidirect
60. C4⋊(C9⋊C8)C22semidirect
61. #63362C22semidirect
126. #3672D4semidirect
235. Dic18C2×D4semidirect
239. C9⋊C8C2×D4semidirect
243. D42D9semidirect
334. C22×C9AGL(1,ℤ/8)semidirect
551. C9#3265semidirect
634. C22#63495semidirect

Maximal subgroups

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

subgroupindex
D42×C92
C2×#634952
C22×#36722
#105896542
#105888982
#105888972
#105887562
#105887522
#105887212
#105887202
#105887182
#105887162
#105886992
#105886942
#105886882
#834913