Finite Group Databasebeta

← #11883914

Subgroups — #11883914

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
1C9×#548C211yesmaximal, characteristic, complemented
2C2×#63512C211yesmaximal, characteristic, complemented
3C22×#3675C211yesmaximal, characteristic, complemented
4D4×D36C211yesmaximal, characteristic, complemented
5#10588919C211yesmaximal, characteristic, complemented
6#10588908C211yesmaximal, characteristic, complemented
7#10588739C211yesmaximal, characteristic, complemented
8#10588738C211yesmaximal, characteristic, complemented
9#10588732C211yesmaximal, characteristic, complemented
10#10588729C211yesmaximal, characteristic, complemented
11#10588721C211yesmaximal, characteristic, complemented
12#10588719C211yesmaximal, characteristic, complemented
13#10588710C211yesmaximal, characteristic, complemented
14#10588709C211yesmaximal, characteristic, complemented
15#10588688C211yesmaximal, characteristic, complemented
16#83542—31nomaximal
17C2×C9×#41C2211yescharacteristic, complemented
18C22×Q8×C9C2211yescharacteristic, complemented
19C2×D4×D9—21no—
20C22×D36C2211yescharacteristic
21C22×D36C2211yescharacteristic
22C9×#124—21no—
23C9×#124C2211yescharacteristic, complemented
24C9×C22⋊Q8—21no—
25C9×C22⋊Q8C2211yescharacteristic, complemented
26C9×#121—21no—
27C9×#121C2211yescharacteristic, complemented
28C4×Q8×C9C2211yescharacteristic, complemented
29C4×D4×C9—21no—
30C4×D4×C9C2211yescharacteristic
31#63512—24no—
32C2×#3675—24no—
33C2×#3675C2211yescharacteristic
34C2×#3675C2211yescharacteristic
35C2×#3675C2211yescharacteristic, complemented
36C2×#3675C2211yescharacteristic, complemented
37C2×#3675C2211yescharacteristic, complemented
38C2×#3675C2211yescharacteristic, complemented
39C2×#3673C2211yescharacteristic
40C2×#3673C2211yescharacteristic, complemented
41C2×#3673C2211yescharacteristic, complemented
42#63492C2211yescharacteristic
43#63492C2211yescharacteristic
44C2×#3667C2211yescharacteristic, complemented
45C22×C9⋊C8C2211yescharacteristic, complemented
46#63457—21no—
47#63444—21no—
48#63444—21no—
49#63436C2211yescharacteristic
50C4×D36C2211yescharacteristic
51#63395C2211yescharacteristic, complemented
52#63395C2211yescharacteristic, complemented
53#63392C2211yescharacteristic, complemented
54#63389C2211yescharacteristic, complemented
55#63389C2211yescharacteristic, complemented
56#63369C2211yescharacteristic
57#63369C2211yescharacteristic, complemented
58#63369C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60C4⋊(C9⋊C8)C2211yescharacteristic, complemented
61#63362C2211yescharacteristic, complemented
62C3×#548D311yescharacteristic
63C2×#949—31no—
64C22×#215—31no—
65D4×D12—31no—
66#5238—31no—
67#5227—31no—
68#5058—31no—
69#5057—31no—
70#5049—31no—
71#5046—31no—
72#5038—31no—
73#5036—31no—
74#5027—31no—
75#5026—31no—
76#5011—31no—
77C23×D9—21no—
78C23×D9—21no—
79C9×#41—22no—
80C9×#41—41no—
81C2×Q8×C9—21no—
82C2×Q8×C9—22no—
83C2×Q8×C9—41no—
84C2×Q8×C9C2311yescharacteristic
85C2×Q8×C9C2311yescharacteristic
86C2×D4×C9—21no—
87C2×D4×C9—21no—
88C2×D4×C9D411yescharacteristic
89C2×D4×C9C2311yescharacteristic
90C22×C4×C9—21no—
91C22×C4×C9—21no—
92C22×C4×C9C2311yescharacteristic
93C22×C4×C9C2311yescharacteristic
94C2×#611—21no—
95C2×#611—21no—
96D4×D9—44no—
97C2×D36—22no—
98C2×D36—22no—
99C2×D36—21no—
100C2×D36—21no—
101C2×D36—21no—
102C2×D36—21no—
103C2×D36—41no—
104C2×D36—41no—
105C2×D36C2311yescharacteristic
106C2×D36C2311yescharacteristic
107C2×D36C2311yescharacteristic
108C2×C4×D9—21no—
109C9×C4⋊C4—21no—
110C9×C4⋊C4—21no—
111C9×C4⋊C4D411yescharacteristic
112C9×C4⋊C4C2311yescharacteristic
113C9×C22⋊C4—21no—
114C9×C22⋊C4—21no—
115C9×C22⋊C4—21no—
116C9×C22⋊C4—21no—
117C9×C22⋊C4D411yescharacteristic
118C9×C22⋊C4D411yescharacteristic
119C42×C9—21no—
120C42×C9C2311yescharacteristic
121#3675—22no—
122#3675—22no—
123#3675—22no—
124#3675—22no—
125#3675—41no—
126#3675D414yescomplemented
127#3673—22no—
128#3673—22no—
129#3673—41no—
130(C2×D9)⋊C4—21no—
131(C2×D9)⋊C4—21no—
132(C2×D9)⋊C4—21no—
133C4⋊Dic9C2311yescharacteristic
134#3667—22no—
135C2×C9⋊C8—22no—
136C2×C9⋊C8C2311yescharacteristic
137C2×C9⋊C8C2311yescharacteristic
138C2×C9⋊C8C2311yescharacteristic
139C2×C9⋊C8C2311yescharacteristic
140#3265—91noSylow
141C2×C3×#41C2×D311yescharacteristic
142C22×C3×Q8C2×D311yescharacteristic
143C2×D3×D4—61no—
144C22×D12—31no—
145C22×D12—31no—
146C3×#124—21no—
147C3×#124C2×D311yescharacteristic
148C3×C22⋊Q8—21no—
149C3×C22⋊Q8C2×D311yescharacteristic
150C3×#121—21no—
151C3×#121C2×D311yescharacteristic
152C3×C4×Q8C2×D311yescharacteristic
153C3×C4×D4—21no—
154C3×C4×D4C2×D311yescharacteristic
155#949—64no—
156C2×#215—31no—
157C2×#215—31no—
158C2×#215—31no—
159C2×#215—31no—
160C2×#215—31no—
161C2×#215—31no—
162C2×#215—64no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166#930—31no—
167#930—31no—
168C2×#208—31no—
169C22×C3⋊C8—31no—
170#895—61no—
171#882—61no—
172#882—61no—
173#874—31no—
174C4×D12—31no—
175#835—31no—
176#835—31no—
177#832—31no—
178#830—31no—
179#830—31no—
180#809—31no—
181#809—31no—
182#809—31no—
183#807—31no—
184C4⋊(C3⋊C8)—31no—
185#803—31no—
186C23×C9—21no—
187C23×C9C2×D411yescharacteristic
188C23×C9C2×D411yescharacteristic
189C22×D9—21no—
190C22×D9—21no—
191C22×D9—21no—
192C22×D9—42no—
193C22×D9—42no—
194C22×D9—42no—
195C22×D9—42no—
196C22×D9—81no—
197C22×D9—81no—
198Q8×C9—21no—
199Q8×C9—21no—
200Q8×C9—21no—
201Q8×C9—42no—
202Q8×C9C2×D412yescomplemented
203D4×C9—22no—
204D4×C9—21no—
205D4×C9—21no—
206D4×C9—42no—
207D4×C9—42no—
208C2×C4×C9—21no—
209C2×C4×C9—21no—
210C2×C4×C9—21no—
211C2×C4×C9—21no—
212C2×C4×C9—21no—
213C2×C4×C9—21no—
214C2×C4×C9—21no—
215C2×C4×C9—42no—
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—
225D36—21no—
226D36—21no—
227D36—21no—
228D36—21no—
229D36—21no—
230D36—42no—
231D36—42no—
232D36—42no—
233D36—81no—
234D36C2×D412yes—
235C4×D9—42no—
236C9⋊C8—21no—
237C9⋊C8—21no—
238C9⋊C8—21no—
239C9⋊C8C2×D412yescomplemented
240C2×AGL(1,ℤ/8)—91no—
241C22×SD16—91no—
242#548D911yescharacteristic, complemented
243D42—91no—
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—
255C23×D3—61no—
256C23×D3—61no—
257C3×#41—22no—
258C3×#41—41no—
259C2×C3×Q8—21no—
260C2×C3×Q8—22no—
261C2×C3×Q8—41no—
262C2×C3×Q8C22×D311yescharacteristic
263C2×C3×Q8C22×D311yescharacteristic
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4#6711yescharacteristic
267C2×C3×D4C22×D311yescharacteristic
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C2×#67—61no—
273C2×#67—61no—
274D3×D4—124no—
275C2×D12—31no—
276C2×D12—31no—
277C2×D12—31no—
278C2×D12—62no—
279C2×D12—62no—
280C2×D12—61no—
281C2×D12—61no—
282C2×D12—61no—
283C2×D12—61no—
284C2×D12—121no—
285C2×D12—121no—
286C2×C4×D3—61no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4#6711yescharacteristic
290C3×C4⋊C4C22×D311yescharacteristic
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—21no—
294C3×C22⋊C4—21no—
295C3×C22⋊C4#6711yescharacteristic
296C3×C22⋊C4#6711yescharacteristic
297C3×C42—21no—
298C3×C42C22×D311yescharacteristic
299#215—34no—
300#215—62no—
301#215—62no—
302#215—62no—
303#215—62no—
304#215—121no—
305#213—62no—
306#213—62no—
307#213—121no—
308(C2×D3)⋊C4—61no—
309(C2×D3)⋊C4—61no—
310(C2×D3)⋊C4—61no—
311C4⋊Dic3—31no—
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—21no—
322C22×C9—21no—
323C22×C9—41no—
324C22×C9—41no—
325C22×C9—41no—
326C22×C9AGL(1,ℤ/8)12yescomplemented
327C22×C9C22×D411yescharacteristic
328C2×D9—22no—
329C2×D9—41no—
330C2×D9—41no—
331C2×D9—41no—
332C2×D9—41no—
333C2×D9—41no—
334C2×D9—41no—
335C2×D9—41no—
336C2×D9—41no—
337C2×D9—84no—
338C2×D9—84no—
339C4×C9—21no—
340C4×C9—21no—
341C4×C9—22no—
342C4×C9—21no—
343C4×C9—21no—
344C4×C9—41no—
345C4×C9—41no—
346C4×C9C22×D411yescharacteristic
347C4×C9H(5,𝔽2)11yescharacteristic
348Dic9—41no—
349C2×#41C2×D911yescharacteristic, complemented
350C22×Q8C2×D911yescharacteristic, complemented
351C22×D4—91no—
352C22×D4—91no—
353C22×D4—181no—
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#127—91no—
368#124—21no—
369#124C2×D911yescharacteristic, complemented
370C22⋊Q8—21no—
371C22⋊Q8C2×D911yescharacteristic, complemented
372#121—21no—
373#121—91no—
374#121—91no—
375#121—181no—
376#121C2×D911yescharacteristic, complemented
377#120—181no—
378#120—181no—
379C4×Q8C2×D911yescharacteristic, complemented
380C4×D4—21no—
381C4×D4—91no—
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×C3C2×#6711yescharacteristic
396C23×C3C2×#6711yescharacteristic
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—61no—
400C22×D3—122no—
401C22×D3—122no—
402C22×D3—122no—
403C22×D3—122no—
404C22×D3—241no—
405C22×D3—241no—
406C3×Q8—21no—
407C3×Q8—21no—
408C3×Q8—21no—
409C3×Q8—42no—
410C3×Q8D3×D412yes—
411C3×D4—22no—
412C3×D4—21no—
413C3×D4—21no—
414C3×D4—42no—
415C3×D4—42no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—42no—
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—
433D12—32no—
434D12—61no—
435D12—61no—
436D12—61no—
437D12—61no—
438D12—61no—
439D12—122no—
440D12—122no—
441D12—122no—
442D12—241no—
443C4×D3—122no—
444C3⋊C8—32no—
445C3⋊C8—61no—
446C3⋊C8—61no—
447C3⋊C8—61no—
448C2×C9—22no—
449C2×C9—41no—
450C2×C9—81no—
451C2×C9D4211yescharacteristic
452C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
453C2×C9#57711yescharacteristic
454D9—42no—
455D9—81no—
456D9—81no—
457C24—181no—
458C24—181no—
459#41—22no—
460#41—41no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—41no—
464C2×Q8C22×D911yescharacteristic
465C2×Q8C22×D911yescharacteristic
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—91no—
469C2×D4—91no—
470C2×D4—91no—
471C2×D4—182no—
472C2×D4—182no—
473C2×D4—181no—
474C2×D4—181no—
475C2×D4—181no—
476C2×D4—181no—
477C2×D4—181no—
478C2×D4—181no—
479C2×D4—361no—
480C2×D4—361no—
481C2×D4—364no—
482C2×D4#61111yescharacteristic
483C2×D4C22×D911yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
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—21no—
505C4⋊C4—21no—
506C4⋊C4—91no—
507C4⋊C4#61111yescharacteristic
508C4⋊C4C22×D911yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—181no—
514C22⋊C4—181no—
515C22⋊C4—181no—
516C22⋊C4#61111yescharacteristic
517C22⋊C4#61111yescharacteristic
518C42—21no—
519C42C22×D911yescharacteristic
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3#94912yes—
529C22×C3C22×#6711yescharacteristic
530C2×D3—62no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—121no—
534C2×D3—121no—
535C2×D3—121no—
536C2×D3—121no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—244no—
540C2×D3—244no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—22no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—41no—
547C3×C4—41no—
548C3×C4C2×D3×D411yescharacteristic
549C3×C4#100411yescharacteristic
550Dic3—121no—
551C9#326511yescharacteristic, complemented, Sylow
552C23—21no—
553C23—181no—
554C23—181no—
555C23—181no—
556C23—362no—
557C23—362no—
558C23—362no—
559C23—362no—
560C23—721no—
561C23—721no—
562C23C2×#61111yescharacteristic
563C23C2×#61111yescharacteristic
564Q8—21no—
565Q8—21no—
566Q8—21no—
567Q8—42no—
568Q8D4×D912yescomplemented
569D4—22no—
570D4—21no—
571D4—21no—
572D4—42no—
573D4—42no—
574D4—92no—
575D4—181no—
576D4—181no—
577D4—181no—
578D4—181no—
579D4—181no—
580D4—362no—
581D4—362no—
582D4—362no—
583D4—362no—
584D4—362no—
585D4—721no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—181no—
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—81no—
609C2×C3D4×#6711yescharacteristic
610C2×C3C2×#94911yescharacteristic
611C2×C3#583711yescharacteristic
612D3—122no—
613D3—241no—
614D3—241no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—182no—
624C22—361no—
625C22—361no—
626C22—361no—
627C22—361no—
628C22—361no—
629C22—361no—
630C22—361no—
631C22—361no—
632C22—724no—
633C22—724no—
634C22#6351212yescomplemented
635C22C22×#61111yescharacteristic
636C4—21no—
637C4—21no—
638C4—22no—
639C4—21no—
640C4—21no—
641C4—41no—
642C4—41no—
643C4—361no—
644C4C2×D4×D911yescharacteristic
645C4#6371011yescharacteristic
646C3#8354211yescharacteristic
647C2—22no—
648C2—41no—
649C2—81no—
650C2—362no—
651C2—721no—
652C2—721no—
653C2D4×#61111yescharacteristic
654C2C2×#6351211yescharacteristic
655C2#1058993911yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#548C2
socleC22×C3C22×#67
hypercenter#548D9
hypocenterC9#3265
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C9×#548C2semidirect
2. C2×#63512C2semidirect
3. C22×#3675C2semidirect
4. D4×D36C2semidirect
5. #10588919C2semidirect
6. #10588908C2semidirect
7. #10588739C2semidirect
8. #10588738C2semidirect
9. #10588732C2semidirect
10. #10588729C2semidirect
11. #10588721C2semidirect
12. #10588719C2semidirect
13. #10588710C2semidirect
14. #10588709C2semidirect
15. #10588688C2semidirect
17. C2×C9×#41C22semidirect
18. C22×Q8×C9C22semidirect
23. C9×#124C22semidirect
25. C9×C22⋊Q8C22semidirect
27. C9×#121C22semidirect
28. C4×Q8×C9C22semidirect
35. C2×#3675C22semidirect
36. C2×#3675C22semidirect
37. C2×#3675C22semidirect
38. C2×#3675C22semidirect
40. C2×#3673C22semidirect
41. C2×#3673C22semidirect
44. C2×#3667C22semidirect
45. C22×C9⋊C8C22semidirect
51. #63395C22semidirect
52. #63395C22semidirect
53. #63392C22semidirect
54. #63389C22semidirect
55. #63389C22semidirect
57. #63369C22semidirect
58. #63369C22semidirect
59. #63366C22semidirect
60. C4⋊(C9⋊C8)C22semidirect
61. #63362C22semidirect
126. #3675D4semidirect
202. Q8×C9C2×D4semidirect
239. C9⋊C8C2×D4semidirect
242. #548D9semidirect
326. C22×C9AGL(1,ℤ/8)semidirect
349. C2×#41C2×D9semidirect
350. C22×Q8C2×D9semidirect
369. #124C2×D9semidirect
371. C22⋊Q8C2×D9semidirect
376. #121C2×D9semidirect
379. C4×Q8C2×D9semidirect
551. C9#3265semidirect
568. Q8D4×D9semidirect
634. C22#63512semidirect

Maximal subgroups

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

subgroupindex
C9×#5482
C2×#635122
C22×#36752
D4×D362
#105889192
#105889082
#105887392
#105887382
#105887322
#105887292
#105887212
#105887192
#105887102
#105887092
#105886882
#835423