Finite Group Databasebeta

← #121×C22⋊C9 #11919695

Subgroups — #121×C22⋊C9 #11919695

Order 1152.

1062 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊C9C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊C9C212yesmaximal, complemented
3C22×C4×C22⋊C9C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊C9C211yesmaximal, characteristic, complemented
5C22⋊C4×C22⋊C9C212yesmaximal, complemented
6C22×C3×#121C311yesmaximal, characteristic
7C23×C22⋊C9C2212yes—
8C23×C22⋊C9C2211yescharacteristic
9D4×C22⋊C9—24no—
10D4×C22⋊C9—22no—
11C2×C4×C22⋊C9—22no—
12C2×C4×C22⋊C9C2211yescharacteristic
13C2×C4×C22⋊C9C2212yes—
14C2×C4×C22⋊C9C2211yescharacteristic
15C9×#121—41nomaximal
16C23×C3×D4C2×C311yescharacteristic
17C23×C3×D4C2×C312yes—
18C24×C3×C4C2×C311yescharacteristic
19C2×C3×#121—31no—
20C2×C3×#121—32no—
21C2×C3×#121—31no—
22C2×C3×#121—31no—
23C2×C3×#121—32no—
24C2×C3×#121—31no—
25C22×C3×C4⋊C4C2×C311yescharacteristic
26C22×C3×C22⋊C4C2×C312yes—
27C22×C22⋊C9—21no—
28C22×C22⋊C9—21no—
29C22×C22⋊C9—22no—
30C22×C22⋊C9—22no—
31C22×C22⋊C9—22no—
32C22×C22⋊C9D412yescomplemented
33C22×C22⋊C9C2311yescharacteristic
34C2×D4×C9—41no—
35C2×D4×C9—42no—
36C22×C4×C9—41no—
37C4×C22⋊C9—21no—
38C4×C22⋊C9—22no—
39C4×C22⋊C9D412yescomplemented
40C9×C4⋊C4—41no—
41C9×C22⋊C4—42no—
42C22×#121C911yescharacteristic, complemented, Sylow
43C25×C3C22×C312yes—
44C25×C3C22×C311yescharacteristic
45C22×C3×D4—24no—
46C22×C3×D4—22no—
47C22×C3×D4—31no—
48C22×C3×D4—32no—
49C22×C3×D4—31no—
50C22×C3×D4—32no—
51C22×C3×D4—32no—
52C22×C3×D4—32no—
53C22×C3×D4—32no—
54C22×C3×D4—62no—
55C22×C3×D4—64no—
56C23×C3×C4—22no—
57C23×C3×C4—31no—
58C23×C3×C4—31no—
59C23×C3×C4—31no—
60C23×C3×C4—31no—
61C23×C3×C4—62no—
62C23×C3×C4C22×C311yescharacteristic
63C23×C3×C4C22×C312yes—
64C23×C3×C4C22×C311yescharacteristic
65C3×#121—32no—
66C3×#121—32no—
67C3×#121—34no—
68C3×#121—34no—
69C3×#121—32no—
70C3×#121—31no—
71C3×#121—32no—
72C3×#121—31no—
73C3×#121—31no—
74C3×#121—32no—
75C3×#121A411yescharacteristic
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C22⋊C4—32no—
80C2×C3×C22⋊C4—32no—
81C2×C3×C22⋊C4—32no—
82C2×C3×C22⋊C4—32no—
83C23×C9—41no—
84C23×C9—42no—
85C2×C22⋊C9—22no—
86C2×C22⋊C9—42no—
87C2×C22⋊C9C2×D411yescharacteristic
88C2×C22⋊C9C2×D411yescharacteristic
89C2×C22⋊C9#4111yescharacteristic
90D4×C9—82no—
91D4×C9—84no—
92C2×C4×C9—41no—
93C2×C4×C9—41no—
94C2×C4×C9—42no—
95C2×C4×C9—82no—
96C23×D4C2×C912yescomplemented
97C23×D4C2×C911yescharacteristic, complemented
98C24×C4C2×C911yescharacteristic, complemented
99C2×#121—31no—
100C2×#121—32no—
101C2×#121—31no—
102C2×#121—31no—
103C2×#121—32no—
104C2×#121—31no—
105C22×C4⋊C4C2×C911yescharacteristic, complemented
106C22×C22⋊C4C2×C912yescomplemented
107C24×C3—21no—
108C24×C3—21no—
109C24×C3—22no—
110C24×C3—22no—
111C24×C3—22no—
112C24×C3—31no—
113C24×C3—32no—
114C24×C3—31no—
115C24×C3—32no—
116C24×C3—32no—
117C24×C3—61no—
118C24×C3—61no—
119C24×C3—62no—
120C24×C3—62no—
121C24×C3—62no—
122C24×C3C3×D412yes—
123C24×C3C23×C311yescharacteristic
124C2×C3×D4—32no—
125C2×C3×D4—34no—
126C2×C3×D4—32no—
127C2×C3×D4—32no—
128C2×C3×D4—32no—
129C2×C3×D4—32no—
130C2×C3×D4—31no—
131C2×C3×D4—62no—
132C2×C3×D4—62no—
133C2×C3×D4—64no—
134C2×C3×D4—62no—
135C2×C3×D4—64no—
136C2×C3×D4—62no—
137C2×C3×D4—64no—
138C2×C3×D4—64no—
139C2×C3×D4—64no—
140C2×C3×D4—64no—
141C2×C3×D4—64no—
142C2×C3×D4—64no—
143C2×C3×D4—64no—
144C2×C3×D4—64no—
145C2×C3×D4C2×A412yes—
146C2×C3×D4C2×A411yescharacteristic
147C22×C3×C4—21no—
148C22×C3×C4—22no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—32no—
152C22×C3×C4—32no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—32no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—32no—
160C22×C3×C4—62no—
161C22×C3×C4—62no—
162C22×C3×C4—62no—
163C22×C3×C4—62no—
164C22×C3×C4—62no—
165C22×C3×C4—62no—
166C22×C3×C4—62no—
167C22×C3×C4—62no—
168C22×C3×C4—61no—
169C22×C3×C4—62no—
170C22×C3×C4C3×D412yes—
171C22×C3×C4C2×A411yescharacteristic
172C3×C4⋊C4—32no—
173C3×C4⋊C4—32no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4C2×A411yescharacteristic
176C3×C22⋊C4—34no—
177C3×C22⋊C4—32no—
178C3×C22⋊C4—32no—
179C3×C22⋊C4—32no—
180C3×C22⋊C4C2×A412yes—
181C22×C9—42no—
182C22×C9—41no—
183C22×C9—81no—
184C22×C9—81no—
185C22×C9—82no—
186C22×C9—82no—
187C22×C9—82no—
188C22⋊C9#12111yescharacteristic, direct product factor
189C4×C9—42no—
190C4×C9—81no—
191C4×C9—82no—
192C25C22×C912yes—
193C25C22×C911yescharacteristic
194C22×D4—24no—
195C22×D4—22no—
196C22×D4—31no—
197C22×D4—32no—
198C22×D4—31no—
199C22×D4—32no—
200C22×D4—32no—
201C22×D4—32no—
202C22×D4—32no—
203C22×D4—62no—
204C22×D4—64no—
205C23×C4—22no—
206C23×C4—31no—
207C23×C4—31no—
208C23×C4—31no—
209C23×C4—31no—
210C23×C4—62no—
211C23×C4C22×C911yescharacteristic
212C23×C4C22×C912yes—
213C23×C4C22×C911yescharacteristic
214#121—32no—
215#121—32no—
216#121—34no—
217#121—34no—
218#121—32no—
219#121—31no—
220#121—32no—
221#121—31no—
222#121—31no—
223#121—32no—
224#121C22⋊C911yescharacteristic, direct product factor
225C2×C4⋊C4—31no—
226C2×C4⋊C4—31no—
227C2×C4⋊C4—32no—
228C2×C22⋊C4—32no—
229C2×C22⋊C4—32no—
230C2×C22⋊C4—32no—
231C2×C22⋊C4—32no—
232C23×C3—22no—
233C23×C3—31no—
234C23×C3—31no—
235C23×C3—31no—
236C23×C3—31no—
237C23×C3—32no—
238C23×C3—32no—
239C23×C3—32no—
240C23×C3—32no—
241C23×C3—31no—
242C23×C3—32no—
243C23×C3—42no—
244C23×C3—61no—
245C23×C3—61no—
246C23×C3—61no—
247C23×C3—61no—
248C23×C3—62no—
249C23×C3—62no—
250C23×C3—62no—
251C23×C3—62no—
252C23×C3—62no—
253C23×C3—62no—
254C23×C3—62no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—62no—
258C23×C3—62no—
259C23×C3—61no—
260C23×C3—61no—
261C23×C3—64no—
262C23×C3—62no—
263C23×C3—62no—
264C23×C3—62no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3—62no—
268C23×C3—122no—
269C23×C3—122no—
270C23×C3—122no—
271C23×C3—124no—
272C23×C3C2×C3×D411yescharacteristic
273C23×C3C2×C3×D411yescharacteristic
274C23×C3C3×#4111yescharacteristic
275C23×C3C22×A412yes—
276C23×C3C22×A411yescharacteristic
277C3×D4—24no—
278C3×D4—22no—
279C3×D4—64no—
280C3×D4—64no—
281C3×D4—64no—
282C3×D4—64no—
283C3×D4—68no—
284C3×D4—64no—
285C3×D4—62no—
286C2×C3×C4—22no—
287C2×C3×C4—32no—
288C2×C3×C4—31no—
289C2×C3×C4—32no—
290C2×C3×C4—32no—
291C2×C3×C4—32no—
292C2×C3×C4—31no—
293C2×C3×C4—32no—
294C2×C3×C4—62no—
295C2×C3×C4—61no—
296C2×C3×C4—62no—
297C2×C3×C4—61no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—64no—
301C2×C3×C4—62no—
302C2×C3×C4—61no—
303C2×C3×C4—62no—
304C2×C3×C4—61no—
305C2×C3×C4—62no—
306C2×C3×C4C22×A411yescharacteristic
307C2×C3×C4C22×A412yes—
308C2×C3×C4C22×A411yescharacteristic
309C2×C9—41no—
310C2×C9—41no—
311C2×C9—41no—
312C2×C9—82no—
313C2×C9—162no—
314C24—21no—
315C24—21no—
316C24—22no—
317C24—22no—
318C24—22no—
319C24—31no—
320C24—32no—
321C24—31no—
322C24—32no—
323C24—32no—
324C24—61no—
325C24—61no—
326C24—62no—
327C24—62no—
328C24—62no—
329C24D4×C912yescomplemented
330C24C23×C911yescharacteristic
331C2×D4—32no—
332C2×D4—34no—
333C2×D4—32no—
334C2×D4—32no—
335C2×D4—32no—
336C2×D4—32no—
337C2×D4—31no—
338C2×D4—62no—
339C2×D4—62no—
340C2×D4—64no—
341C2×D4—62no—
342C2×D4—64no—
343C2×D4—62no—
344C2×D4—64no—
345C2×D4—64no—
346C2×D4—64no—
347C2×D4—64no—
348C2×D4—64no—
349C2×D4—64no—
350C2×D4—64no—
351C2×D4—64no—
352C2×D4C2×C22⋊C912yescomplemented
353C2×D4C2×C22⋊C911yescharacteristic, complemented
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—32no—
359C22×C4—32no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—32no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—32no—
367C22×C4—62no—
368C22×C4—62no—
369C22×C4—62no—
370C22×C4—62no—
371C22×C4—62no—
372C22×C4—62no—
373C22×C4—62no—
374C22×C4—62no—
375C22×C4—61no—
376C22×C4—62no—
377C22×C4D4×C912yescomplemented
378C22×C4C2×C22⋊C911yescharacteristic, complemented
379C4⋊C4—32no—
380C4⋊C4—32no—
381C4⋊C4—31no—
382C4⋊C4C2×C22⋊C911yescharacteristic, complemented
383C22⋊C4—34no—
384C22⋊C4—32no—
385C22⋊C4—32no—
386C22⋊C4—32no—
387C22⋊C4C2×C22⋊C912yescomplemented
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—31no—
394C22×C3—31no—
395C22×C3—31no—
396C22×C3—32no—
397C22×C3—31no—
398C22×C3—31no—
399C22×C3—31no—
400C22×C3—31no—
401C22×C3—31no—
402C22×C3—31no—
403C22×C3—32no—
404C22×C3—62no—
405C22×C3—62no—
406C22×C3—62no—
407C22×C3—62no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—62no—
412C22×C3—61no—
413C22×C3—61no—
414C22×C3—62no—
415C22×C3—62no—
416C22×C3—62no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3C3×#12111yescharacteristic
426C22×C3D4×A412yes—
427C22×C3C23×A411yescharacteristic
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—32no—
431C3×C4—61no—
432C3×C4—62no—
433C3×C4D4×A412yes—
434C9—41noSylow
435C23—22no—
436C23—31no—
437C23—31no—
438C23—31no—
439C23—31no—
440C23—32no—
441C23—32no—
442C23—31no—
443C23—32no—
444C23—32no—
445C23—32no—
446C23—42no—
447C23—61no—
448C23—61no—
449C23—61no—
450C23—61no—
451C23—62no—
452C23—62no—
453C23—62no—
454C23—62no—
455C23—62no—
456C23—62no—
457C23—62no—
458C23—61no—
459C23—61no—
460C23—62no—
461C23—62no—
462C23—61no—
463C23—61no—
464C23—64no—
465C23—62no—
466C23—62no—
467C23—62no—
468C23—62no—
469C23—62no—
470C23—62no—
471C23—122no—
472C23—122no—
473C23—122no—
474C23—124no—
475C23C2×D4×C911yescharacteristic
476C23C2×D4×C911yescharacteristic
477C23C9×#4111yescharacteristic
478C23C22×C22⋊C912yes—
479C23C22×C22⋊C911yescharacteristic
480D4—24no—
481D4—22no—
482D4—64no—
483D4—64no—
484D4—64no—
485D4—64no—
486D4—68no—
487D4—64no—
488D4—62no—
489C2×C4—22no—
490C2×C4—32no—
491C2×C4—31no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—31no—
496C2×C4—32no—
497C2×C4—62no—
498C2×C4—61no—
499C2×C4—62no—
500C2×C4—61no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—64no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—62no—
507C2×C4—61no—
508C2×C4—62no—
509C2×C4C22×C22⋊C911yescharacteristic
510C2×C4C22×C22⋊C912yes—
511C2×C4C22×C22⋊C911yescharacteristic
512C2×C3—22no—
513C2×C3—31no—
514C2×C3—31no—
515C2×C3—31no—
516C2×C3—31no—
517C2×C3—42no—
518C2×C3—62no—
519C2×C3—122no—
520C2×C3C2×D4×A411yescharacteristic
521C2×C3C2×D4×A411yescharacteristic
522C2×C3A4×#4111yescharacteristic
523C22—21no—
524C22—21no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—31no—
529C22—31no—
530C22—31no—
531C22—32no—
532C22—31no—
533C22—31no—
534C22—31no—
535C22—31no—
536C22—31no—
537C22—31no—
538C22—32no—
539C22—62no—
540C22—62no—
541C22—62no—
542C22—62no—
543C22—62no—
544C22—62no—
545C22—62no—
546C22—62no—
547C22—61no—
548C22—61no—
549C22—62no—
550C22—62no—
551C22—62no—
552C22—122no—
553C22—122no—
554C22—122no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22—122no—
559C22—122no—
560C22C9×#12111yescharacteristic, complemented
561C22D4×C22⋊C912yescomplemented
562C22C23×C22⋊C911yescharacteristic
563C4—21no—
564C4—22no—
565C4—32no—
566C4—61no—
567C4—62no—
568C4D4×C22⋊C912yescomplemented
569C3A4×#12111yescharacteristic
570C2—22no—
571C2—31no—
572C2—31no—
573C2—31no—
574C2—31no—
575C2—42no—
576C2—62no—
577C2—122no—
578C2C2×D4×C22⋊C911yescharacteristic
579C2C2×D4×C22⋊C911yescharacteristic
580C2#41×C22⋊C911yescharacteristic
subgroupG/H
center, FrattiniC22×C3C23×A4
commutatorC24C23×C9
Fitting, prime radicalC22×C3×#121C3
socle, cosocleC24×C3C23×C3
hypercenterC3×#121A4
hypocenterC22C9×#121
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22×C3 ◁ C3×#121

Complements

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

NH ≅ G/Ntype
1. C2×D4×C22⋊C9C2semidirect
2. C2×D4×C22⋊C9C2semidirect
3. C22×C4×C22⋊C9C2semidirect
4. C4⋊C4×C22⋊C9C2semidirect
5. C22⋊C4×C22⋊C9C2semidirect
32. C22×C22⋊C9D4semidirect
39. C4×C22⋊C9D4semidirect
42. C22×#121C9semidirect
96. C23×D4C2×C9semidirect
97. C23×D4C2×C9semidirect
98. C24×C4C2×C9semidirect
105. C22×C4⋊C4C2×C9semidirect
106. C22×C22⋊C4C2×C9semidirect
188. C22⋊C9#121direct (N × H)
224. #121C22⋊C9direct (N × H)
329. C24D4×C9semidirect
352. C2×D4C2×C22⋊C9semidirect
353. C2×D4C2×C22⋊C9semidirect
377. C22×C4D4×C9semidirect
378. C22×C4C2×C22⋊C9semidirect
382. C4⋊C4C2×C22⋊C9semidirect
387. C22⋊C4C2×C22⋊C9semidirect
560. C22C9×#121semidirect
561. C22D4×C22⋊C9semidirect
568. C4D4×C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊C92
C22×C4×C22⋊C92
C4⋊C4×C22⋊C92
C22⋊C4×C22⋊C92
C22×C3×#1213
C9×#1214