Finite Group Databasebeta

← #11802700

Subgroups — #11802700

Order 1152.

1320 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3697C211yesmaximal, characteristic
2C2×#63454C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
4C9×#380C211yesmaximal, characteristic, complemented
5#10588892C211yesmaximal, characteristic, complemented
6#10588667C211yesmaximal, characteristic, complemented
7#10588667C211yesmaximal, characteristic, complemented
8#10588637C212yesmaximal, complemented
9#10588636C212yesmaximal, complemented
10#10588345C212yesmaximal, complemented
11#10588326C212yesmaximal, complemented
12#74003—31nomaximal
13C23×C4×C9C2211yescharacteristic
14C22×#611C2211yescharacteristic
15C22×#611C2211yescharacteristic
16C2×#3697—24no—
17C2×#3697—24no—
18C2×#3697C418yescomplemented
19C22×D36C2211yescharacteristic
20C22×C4×D9C2211yescharacteristic
21C22×C4×D9C2212yes—
22C22×C4×D9C2211yescharacteristic
23C22×Dic18C2211yescharacteristic
24C2×C9×C4⋊C4C2211yescharacteristic
25C2×C9×C4⋊C4C2211yescharacteristic
26C2×C9×C22⋊C4C2212yes—
27C2×#3676C2212yes—
28C2×(C2×D9)⋊C4C2212yes—
29C2×(C2×D9)⋊C4C2212yes—
30C2×(C2×D9)⋊C4C2212yes—
31C2×C4⋊Dic9C2211yescharacteristic
32C2×C4⋊Dic9C2211yescharacteristic
33C2×Dic9⋊C4C2212yes—
34C2×C4×Dic9C2212yes—
35#63454—24no—
36C4⋊C4×D9—24no—
37C9×#95C2212yes—
38C9⋊#95C2212yes—
39C9⋊#95C2212yes—
40C9⋊#95C2212yes—
41C22×#235—31no—
42C2×#892—31no—
43C2×D3×C4⋊C4—31no—
44C3×#380D311yescharacteristic
45#5212—31no—
46#4987—31no—
47#4987—31no—
48#4957—32no—
49#4956—32no—
50#4665—32no—
51#4646—32no—
52C24×C9C2311yescharacteristic
53C23×D9C2311yescharacteristic
54C23×D9C2311yescharacteristic
55C22×C4×C9—22no—
56C22×C4×C9—22no—
57C22×C4×C9C2×C414yescomplemented
58C22×C4×C9C2312yes—
59C22×C4×C9C2312yes—
60C22×C4×C9C2311yescharacteristic
61C22×C4×C9C2311yescharacteristic
62C2×#611—22no—
63C2×#611—22no—
64C2×#611—22no—
65C2×#611—22no—
66C2×#611C2×C414yes—
67C2×#611C2×C414yescomplemented
68C22×Dic9C2312yes—
69C22×Dic9C2312yes—
70C22×Dic9C2311yescharacteristic
71C22×Dic9C2311yescharacteristic
72#3697—232no—
73C2×D36—22no—
74C2×D36—22no—
75C2×D36C2×C414yes—
76C2×C4×D9—22no—
77C2×C4×D9—22no—
78C2×C4×D9—24no—
79C2×C4×D9—42no—
80C2×C4×D9—42no—
81C2×C4×D9C2×C414yes—
82C2×C4×D9C2×C414yescomplemented
83C2×C4×D9D414yes—
84C2×C4×D9D414yes—
85C2×Dic18—22no—
86C2×Dic18—22no—
87C2×Dic18C2×C414yescomplemented
88C9×C4⋊C4—22no—
89C9×C4⋊C4—22no—
90C9×C22⋊C4—42no—
91#3676—42no—
92(C2×D9)⋊C4—24no—
93(C2×D9)⋊C4—42no—
94(C2×D9)⋊C4—42no—
95C4⋊Dic9—22no—
96C4⋊Dic9—22no—
97Dic9⋊C4—24no—
98C4×Dic9—24no—
99#2311—91noSylow
100C23×C3×C4C2×D311yescharacteristic
101C22×#67—31no—
102C22×#67—31no—
103C2×#235—38no—
104C2×#235—64no—
105C2×#235—64no—
106C22×D12—31no—
107C22×C4×D3—31no—
108C22×C4×D3—31no—
109C22×C4×D3—32no—
110C22×Dic6—31no—
111C2×C3×C4⋊C4C2×D311yescharacteristic
112C2×C3×C4⋊C4C2×D311yescharacteristic
113C2×C3×C22⋊C4C2×D312yes—
114C2×#217—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×Dic3⋊C4—32no—
121C2×C4×Dic3—32no—
122#892—64no—
123D3×C4⋊C4—64no—
124C3×#95C2×D312yes—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C23×C9—21no—
129C23×C9—21no—
130C23×C9—21no—
131C23×C9—21no—
132C23×C9—21no—
133C23×C9—21no—
134C23×C9C22×C412yes—
135C23×C9C2411yescharacteristic
136C22×D9—21no—
137C22×D9—21no—
138C22×D9—21no—
139C22×D9—21no—
140C22×D9—21no—
141C22×D9—21no—
142C22×D9—21no—
143C22×D9—21no—
144C22×D9—21no—
145C22×D9—21no—
146C22×D9C22×C412yes—
147C22×D9C22×C412yes—
148C22×D9C2×D412yes—
149C22×D9C2×D412yes—
150C2×C4×C9—21no—
151C2×C4×C9—21no—
152C2×C4×C9—28no—
153C2×C4×C9—22no—
154C2×C4×C9—22no—
155C2×C4×C9—22no—
156C2×C4×C9—22no—
157C2×C4×C9—22no—
158C2×C4×C9—22no—
159C2×C4×C9C22×C412yes—
160C2×C4×C9C22×C412yes—
161C2×C4×C9C2×D412yes—
162C2×C4×C9C2×D412yes—
163#611—28no—
164#611—28no—
165C2×Dic9—21no—
166C2×Dic9—21no—
167C2×Dic9—22no—
168C2×Dic9—22no—
169C2×Dic9—22no—
170C2×Dic9—22no—
171C2×Dic9—22no—
172C2×Dic9—22no—
173C2×Dic9C22×C412yes—
174C2×Dic9C22×C412yes—
175C2×Dic9C2×D412yes—
176C2×Dic9C2×D412yes—
177D36—28no—
178C4×D9—28no—
179C4×D9—48no—
180C4×D9C22⋊C4116yescomplemented
181Dic18—28no—
182C22×#41—91no—
183C2×#117—91no—
184C22×C4⋊C4—91no—
185#391—92no—
186#390—92no—
187#386—92no—
188#386—92no—
189#380—91no—
190#380—91no—
191#380—91no—
192#380D911yescharacteristic, complemented
193C24×C3C22×D311yescharacteristic
194C23×D3—31no—
195C23×D3—31no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4C4×D314yes—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—34no—
204C2×#67—34no—
205C2×#67—62no—
206C2×#67—62no—
207C2×#67—62no—
208C2×#67—62no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—32no—
212C22×Dic3—32no—
213#235—632no—
214C2×D12—34no—
215C2×D12—62no—
216C2×D12—62no—
217C2×C4×D3—34no—
218C2×C4×D3—34no—
219C2×C4×D3—34no—
220C2×C4×D3—34no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—64no—
224C2×C4×D3—122no—
225C2×C4×D3—122no—
226C2×Dic6—34no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—22no—
231C3×C22⋊C4—42no—
232#217—122no—
233(C2×D3)⋊C4—64no—
234(C2×D3)⋊C4—122no—
235(C2×D3)⋊C4—122no—
236C4⋊Dic3—62no—
237C4⋊Dic3—62no—
238Dic3⋊C4—64no—
239C4×Dic3—64no—
240C22×C9—22no—
241C22×C9—22no—
242C22×C9—22no—
243C22×C9—41no—
244C22×C9—41no—
245C22×C9—41no—
246C22×C9—41no—
247C22×C9C23×C411yescharacteristic
248C22×C9C22×D411yescharacteristic
249C22×C9C22×D411yescharacteristic
250C22×C9H(5,𝔽2)11yescharacteristic
251C22×C9H(5,𝔽2)11yescharacteristic
252C22×C92−1+411yescharacteristic
253C22×C92−1+411yescharacteristic
254C2×D9—22no—
255C2×D9—22no—
256C2×D9—22no—
257C2×D9—22no—
258C2×D9—22no—
259C2×D9—22no—
260C2×D9—22no—
261C2×D9—22no—
262C2×D9—22no—
263C2×D9—41no—
264C2×D9—41no—
265C2×D9—41no—
266C2×D9—41no—
267C2×D9C2×C22⋊C414yes—
268C4×C9—22no—
269C4×C9—42no—
270C4×C9—42no—
271C4×C9C2×C22⋊C414yes—
272Dic9—22no—
273Dic9—42no—
274Dic9—42no—
275Dic9C2×C22⋊C414yes—
276C2×#41—98no—
277C2×#41—184no—
278C2×#41—184no—
279C22×Q8—91no—
280C22×D4—91no—
281C22×D4—91no—
282C22×D4—91no—
283C23×C4—91no—
284C23×C4—91no—
285C23×C4—92no—
286C23×C4C2×D911yescharacteristic
287#117—184no—
288C2×C4⋊C4—91no—
289C2×C4⋊C4—92no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4—184no—
292C2×C4⋊C4C2×D911yescharacteristic
293C2×C4⋊C4C2×D911yescharacteristic
294C2×C22⋊C4—92no—
295C2×C22⋊C4—92no—
296C2×C22⋊C4—92no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4C2×D912yes—
299C2×C42—92no—
300#95—92no—
301#95—92no—
302#95—92no—
303#95C2×D912yes—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3C2×C4×D312yes—
311C23×C3C23×D311yescharacteristic
312C22×D3—32no—
313C22×D3—32no—
314C22×D3—32no—
315C22×D3—32no—
316C22×D3—61no—
317C22×D3—61no—
318C22×D3—61no—
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—61no—
322C22×D3—61no—
323C22×D3—61no—
324C22×D3—61no—
325C22×D3—61no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—28no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4C2×C4×D312yes—
336C2×C3×C4C2×C4×D312yes—
337C2×C3×C4D3×D412yes—
338C2×C3×C4D3×D412yes—
339#67—68no—
340#67—68no—
341C2×Dic3—32no—
342C2×Dic3—32no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353D12—68no—
354C4×D3—316no—
355C4×D3—68no—
356C4×D3—128no—
357Dic6—68no—
358C2×C9—42no—
359C2×C9C22×C22⋊C411yescharacteristic
360C2×C9#52011yescharacteristic
361C2×C9#52011yescharacteristic
362C2×C9#53511yescharacteristic
363C2×C9#53611yescharacteristic
364C2×C9#53711yescharacteristic
365C2×C9#53711yescharacteristic
366D9—24no—
367D9—42no—
368C24—91no—
369C24—91no—
370C24C22×D911yescharacteristic
371#41—1832no—
372C2×Q8—94no—
373C2×Q8—182no—
374C2×Q8—182no—
375C2×D4—94no—
376C2×D4—94no—
377C2×D4—94no—
378C2×D4—182no—
379C2×D4—182no—
380C2×D4—182no—
381C2×D4—182no—
382C2×D4—182no—
383C2×D4—182no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—91no—
387C22×C4—94no—
388C22×C4—94no—
389C22×C4—94no—
390C22×C4—91no—
391C22×C4—94no—
392C22×C4—92no—
393C22×C4—92no—
394C22×C4—184no—
395C22×C4—182no—
396C22×C4—182no—
397C22×C4—362no—
398C22×C4—362no—
399C22×C4C4×D914yescomplemented
400C22×C4C22×D912yes—
401C22×C4C22×D912yes—
402C22×C4C22×D911yescharacteristic
403C22×C4C22×D911yescharacteristic
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—184no—
407C4⋊C4—182no—
408C4⋊C4—182no—
409C22⋊C4—42no—
410C22⋊C4—184no—
411C22⋊C4—362no—
412C22⋊C4—362no—
413C22⋊C4—362no—
414C42—184no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3C22×C4×D311yescharacteristic
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C2×D3×D411yescharacteristic
425C22×C3#100411yescharacteristic
426C22×C3#100711yescharacteristic
427C22×C3#100911yescharacteristic
428C22×C3#101011yescharacteristic
429C2×D3—34no—
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—62no—
436C2×D3—62no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C3×C4—22no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4D3×C22⋊C414yes—
447Dic3—34no—
448Dic3—62no—
449Dic3—122no—
450Dic3—122no—
451C9#231111yescharacteristic, complemented, Sylow
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—92no—
459C23—92no—
460C23—92no—
461C23—92no—
462C23—181no—
463C23—181no—
464C23—181no—
465C23—181no—
466C23—181no—
467C23—181no—
468C23—181no—
469C23—181no—
470C23—181no—
471C23—181no—
472C23C2×C4×D912yes—
473C23C23×D911yescharacteristic
474Q8—188no—
475D4—188no—
476D4—188no—
477D4—188no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—28no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—916no—
491C2×C4—92no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—188no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—182no—
499C2×C4—182no—
500C2×C4—182no—
501C2×C4—368no—
502C2×C4C2×C4×D912yes—
503C2×C4C2×C4×D912yes—
504C2×C4D4×D912yes—
505C2×C4D4×D912yes—
506C2×C3—42no—
507C2×C3C2×D3×C22⋊C411yescharacteristic
508C2×C3#550411yescharacteristic
509C2×C3#552311yescharacteristic
510C2×C3#560711yescharacteristic
511C2×C3#560811yescharacteristic
512C2×C3#562811yescharacteristic
513C2×C3#562911yescharacteristic
514D3—64no—
515D3—122no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—94no—
524C22—182no—
525C22—182no—
526C22—182no—
527C22—182no—
528C22—182no—
529C22—182no—
530C22—182no—
531C22—182no—
532C22—182no—
533C22—361no—
534C22—361no—
535C22—361no—
536C22—361no—
537C22C22×C4×D911yescharacteristic
538C22C2×D4×D911yescharacteristic
539C22C2×D4×D911yescharacteristic
540C22#6371011yescharacteristic
541C22#6371311yescharacteristic
542C22#6371511yescharacteristic
543C22#6371611yescharacteristic
544C4—22no—
545C4—42no—
546C4—42no—
547C4—94no—
548C4—182no—
549C4—362no—
550C4—362no—
551C4C22⋊C4×D914yes—
552C3#7400311yescharacteristic
553C2—42no—
554C2—184no—
555C2—362no—
556C2C2×C22⋊C4×D911yescharacteristic
557C2#1058960611yescharacteristic
558C2#1058962511yescharacteristic
559C2#1058970911yescharacteristic
560C2#1058971011yescharacteristic
561C2#1058973011yescharacteristic
562C2#1058973111yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#380C2
prime radicalC22×#3697C2
cosocleC23×C9C24
hypercenter#380D9
hypocenterC9#2311
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#63454C2semidirect
3. C2×C4⋊C4×D9C2semidirect
4. C9×#380C2semidirect
5. #10588892C2semidirect
6. #10588667C2semidirect
7. #10588667C2semidirect
8. #10588637C2semidirect
9. #10588636C2semidirect
10. #10588345C2semidirect
11. #10588326C2semidirect
18. C2×#3697C4semidirect
57. C22×C4×C9C2×C4semidirect
67. C2×#611C2×C4semidirect
82. C2×C4×D9C2×C4semidirect
87. C2×Dic18C2×C4semidirect
180. C4×D9C22⋊C4semidirect
192. #380D9semidirect
399. C22×C4C4×D9semidirect
451. C9#2311semidirect

Maximal subgroups

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

subgroupindex
C22×#36972
C2×#634542
C2×C4⋊C4×D92
C9×#3802
#105888922
#105886672
#105886372
#105886362
#105883452
#105883262
#740033