Finite Group Databasebeta

← #11808149

Subgroups — #11808149

Order 1152.

3185 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic
2C2×#63974C212yesmaximal, complemented
3C2×#63974C212yesmaximal, complemented
4C2×#63883C211yesmaximal, characteristic, complemented
5C3×#5222C212yesmaximal, complemented
6#10591712C214yesmaximal, complemented
7#10591370C211yesmaximal, characteristic, complemented
8#10591321C212yesmaximal, complemented
9D3×#394—32nomaximal
10C24×C3⋊D3C2212yes—
11C22×C32×D4C2211yescharacteristic
12C22×#638C2212yes—
13C2×D4×C3⋊D3—24no—
14C2×D4×C3⋊D3—28no—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#624C2211yescharacteristic
18C22×#624C2212yes—
19C22×#624C2211yescharacteristic
20C2×C3×#217C2214yescomplemented
21C2×C3×#217C2214yescomplemented
22C2×C3×Dic3⋊C4C2212yescomplemented
23#63974—28no—
24#63974—28no—
25C2×Dic3⋊Dic3C2212yescomplemented
26C2×#3722C2214yescomplemented
27C2×#3722C2214yescomplemented
28#63883—24no—
29C3×C3⋊#95C2212yescomplemented
30#63579C2212yescomplemented
31C22×D3×D4—32no—
32C22×D3×D4—61no—
33C2×D3×C4⋊C4—32no—
34C2×D3×C22⋊C4—34no—
35C2×D3×C22⋊C4—34no—
36C3×#394—32no—
37#5222D312yescomplemented
38#4991—32no—
39#4961—34no—
40#4959—34no—
41#4672—32no—
42D3×#95—32no—
43C24×C32C2312yes—
44C23×C3⋊D3—24no—
45C23×C3⋊D3—24no—
46C23×C3⋊D3—24no—
47C23×C3⋊D3—24no—
48C23×C3⋊D3—24no—
49C23×C3⋊D3—24no—
50C23×C3⋊D3D418yes—
51C23×C3⋊D3C2312yes—
52C23×C3⋊D3C2311yescharacteristic
53C2×C32×D4—24no—
54C2×C32×D4—22no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—24no—
57C2×#638—24no—
58C2×#638—24no—
59C22×C3⋊Dic3C2311yescharacteristic
60D4×C3⋊D3—232no—
61C2×C4⋊(C3⋊D3)—24no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4×C3⋊D3—24no—
64C2×C4×C3⋊D3D414yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2314yes—
67C22×C3×Dic3C2312yes—
68C2×#624—22no—
69C2×#624—22no—
70C2×#624—22no—
71C2×#624—24no—
72C2×#624—24no—
73C2×#624—24no—
74C2×#624—24no—
75C2×#624D414yescomplemented
76C3×#217—28no—
77C3×#217—28no—
78C3×Dic3⋊C4—24no—
79Dic3⋊Dic3—24no—
80#3722—28no—
81#3722—28no—
82C2×#394—91noSylow
83C24×D3—34no—
84C24×D3—62no—
85C22×C3×D4—21no—
86C22×C3×D4C2×D312yes—
87C22×#67—34no—
88C22×#67—62no—
89C2×D3×D4—68no—
90C2×D3×D4—616no—
91C2×D3×D4—68no—
92C2×D3×D4—616no—
93C22×D12—32no—
94C22×D12—61no—
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—34no—
98C22×C4×D3—32no—
99C22×C4×D3—61no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C22⋊C4—34no—
102C2×C3×C22⋊C4—34no—
103C2×#217C2×D314yescomplemented
104C2×#217C2×D314yescomplemented
105C2×(C2×D3)⋊C4—34no—
106C2×(C2×D3)⋊C4—34no—
107C2×(C2×D3)⋊C4—34no—
108C2×(C2×D3)⋊C4—34no—
109C2×C4⋊Dic3—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4C2×D312yescomplemented
112D3×C4⋊C4—68no—
113D3×C22⋊C4—616no—
114D3×C22⋊C4—616no—
115C3×#95—32no—
116C3⋊#95—34no—
117C3⋊#95C2×D312yescomplemented
118C23×C32—22no—
119C23×C32—22no—
120C23×C32—22no—
121C23×C32—22no—
122C23×C32—22no—
123C23×C32—22no—
124C23×C32C2×D414yes—
125C23×C32C2411yescharacteristic
126C22×C3⋊D3—22no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—216no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3—216no—
134C22×C3⋊D3—216no—
135C22×C3⋊D3—48no—
136C22×C3⋊D3—48no—
137C22×C3⋊D3—48no—
138C22×C3⋊D3—48no—
139C22×C3⋊D3C2×D414yes—
140C22×C3⋊D3C2×D414yes—
141C22×C3⋊D3C2×D412yes—
142C22×C3⋊D3C2×D412yes—
143C22×C3⋊D3#4112yes—
144C22×C3⋊D3#4114yes—
145C32×D4—28no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D412yes—
148#638—216no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3C2×D412yes—
151C4⋊(C3⋊D3)—28no—
152C4×C3⋊D3—28no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3C2×D414yescomplemented
161#624—28no—
162#624—44no—
163#624—48no—
164C23×D4—91no—
165C22×C4⋊C4—91no—
166C22×C22⋊C4—92no—
167C22×C22⋊C4—92no—
168#394—32no—
169#394—92no—
170#394—94no—
171C2×#95—91no—
172C24×C3—22no—
173C24×C3C22×D314yes—
174C23×D3—32no—
175C23×D3—316no—
176C23×D3—34no—
177C23×D3—61no—
178C23×D3—68no—
179C23×D3—62no—
180C23×D3—68no—
181C23×D3—68no—
182C23×D3—68no—
183C23×D3—68no—
184C23×D3—68no—
185C23×D3—68no—
186C23×D3—68no—
187C23×D3—68no—
188C23×D3—124no—
189C23×D3—124no—
190C23×D3—124no—
191C23×D3—124no—
192C2×C3×D4—28no—
193C2×C3×D4—24no—
194C2×C3×D4—28no—
195C2×C3×D4—24no—
196C22×C3×C4—21no—
197C22×C3×C4—32no—
198C22×C3×C4—34no—
199C22×C3×C4—32no—
200C22×C3×C4C22×D312yes—
201C2×#67—68no—
202C2×#67—68no—
203C2×#67—68no—
204C2×#67—68no—
205C2×#67—68no—
206C2×#67—68no—
207C22×Dic3—32no—
208C22×Dic3—61no—
209C22×Dic3C22×D314yes—
210C22×Dic3C22×D312yes—
211C22×Dic3C22×D312yes—
212D3×D4—664no—
213D3×D4—664no—
214C2×D12—68no—
215C2×D12—68no—
216C2×D12—64no—
217C2×D12—64no—
218C2×C4×D3—38no—
219C2×C4×D3—38no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—68no—
224C2×C4×D3—68no—
225C2×C4×D3—68no—
226C2×C4×D3—68no—
227C2×C4×D3—68no—
228C2×C4×D3—64no—
229C2×C4×D3—68no—
230C3×C4⋊C4—64no—
231C3×C22⋊C4—68no—
232C3×C22⋊C4—68no—
233#217—28no—
234#217—28no—
235(C2×D3)⋊C4—68no—
236(C2×D3)⋊C4—68no—
237(C2×D3)⋊C4—68no—
238(C2×D3)⋊C4—68no—
239C4⋊Dic3—64no—
240Dic3⋊C4—24no—
241Dic3⋊C4—64no—
242C22×C32—24no—
243C22×C32—24no—
244C22×C32—24no—
245C22×C32—42no—
246C22×C32—42no—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32C22×D412yes—
250C22×C32C22×D411yescharacteristic
251C22×C32C22×D411yescharacteristic
252C22×C32C2×#4111yescharacteristic
253C22×C32C2×#4112yes—
254C2×C3⋊D3—24no—
255C2×C3⋊D3—24no—
256C2×C3⋊D3—24no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—42no—
261C2×C3⋊D3—432no—
262C2×C3⋊D3#12014yes—
263C2×C3⋊D3#12114yes—
264C2×C3⋊D3#12118yes—
265C2×C3⋊D3#12318yes—
266C2×C3⋊D3#12414yes—
267C32×C4—22no—
268C3⋊Dic3—22no—
269C3×Dic3—24no—
270C3×Dic3—42no—
271C3×Dic3—44no—
272C25—92no—
273C22×D4—92no—
274C22×D4—91no—
275C22×D4—184no—
276C22×D4—188no—
277C22×D4D3211yescharacteristic
278C23×C4—91no—
279C23×C4—91no—
280C23×C4—92no—
281C23×C4—91no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—92no—
284C2×C4⋊C4—184no—
285C2×C22⋊C4—34no—
286C2×C22⋊C4—34no—
287C2×C22⋊C4—94no—
288C2×C22⋊C4—94no—
289C2×C22⋊C4—188no—
290C2×C22⋊C4—188no—
291#95—32no—
292#95—92no—
293C23×C3—24no—
294C23×C3—24no—
295C23×C3—24no—
296C23×C3—24no—
297C23×C3—24no—
298C23×C3—24no—
299C23×C3—24no—
300C23×C3—24no—
301C23×C3—21no—
302C23×C3—24no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—42no—
307C23×C3D3×D418yes—
308C23×C3C23×D312yes—
309C22×D3—34no—
310C22×D3—34no—
311C22×D3—38no—
312C22×D3—34no—
313C22×D3—38no—
314C22×D3—38no—
315C22×D3—62no—
316C22×D3—64no—
317C22×D3—62no—
318C22×D3—62no—
319C22×D3—64no—
320C22×D3—64no—
321C22×D3—632no—
322C22×D3—632no—
323C22×D3—632no—
324C22×D3—64no—
325C22×D3—64no—
326C22×D3—632no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3—64no—
330C22×D3—64no—
331C22×D3—64no—
332C22×D3—64no—
333C22×D3—1216no—
334C22×D3—1216no—
335C22×D3—122no—
336C22×D3—122no—
337C22×D3—122no—
338C22×D3—122no—
339C22×D3—1216no—
340C22×D3—1216no—
341C22×D3—1216no—
342C22×D3—1216no—
343C22×D3—1216no—
344C22×D3—1216no—
345C22×D3—1216no—
346C22×D3—1216no—
347C3×D4—216no—
348C3×D4—216no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—22no—
352C2×C3×C4—34no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—64no—
357C2×C3×C4—64no—
358C2×C3×C4—64no—
359C2×C3×C4—64no—
360C2×C3×C4D3×D414yes—
361#67—632no—
362#67—632no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—24no—
367C2×Dic3—24no—
368C2×Dic3—24no—
369C2×Dic3—24no—
370C2×Dic3—34no—
371C2×Dic3—62no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3D3×D414yescomplemented
375D12—616no—
376D12—616no—
377C4×D3—616no—
378C4×D3—616no—
379C4×D3—616no—
380C4×D3—128no—
381C4×D3—1216no—
382C2×C32—44no—
383C2×C32C2×#12011yescharacteristic
384C2×C32C2×#12111yescharacteristic
385C2×C32C2×#12112yes—
386C2×C32C2×#12312yes—
387C2×C32C2×#12411yescharacteristic
388C3⋊D3—44no—
389C3⋊D3#39418yescomplemented
390C24—91no—
391C24—92no—
392C24—98no—
393C24—184no—
394C24—184no—
395C24—184no—
396C24—184no—
397C24—184no—
398C24—184no—
399C24C2×D3212yes—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—184no—
403C2×D4—184no—
404C2×D4—1832no—
405C2×D4—184no—
406C2×D4—184no—
407C2×D4—182no—
408C22×C4—32no—
409C22×C4—34no—
410C22×C4—32no—
411C22×C4—94no—
412C22×C4—91no—
413C22×C4—94no—
414C22×C4—184no—
415C22×C4—182no—
416C22×C4—182no—
417C22×C4—184no—
418C22×C4—184no—
419C22×C4—184no—
420C22×C4—182no—
421C22×C4—184no—
422C22×C4C2×D3211yescharacteristic
423C4⋊C4—64no—
424C4⋊C4—184no—
425C22⋊C4—68no—
426C22⋊C4—68no—
427C22⋊C4—188no—
428C22⋊C4—188no—
429C22×C3—28no—
430C22×C3—28no—
431C22×C3—28no—
432C22×C3—28no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—44no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3—44no—
445C22×C3—44no—
446C22×C3—44no—
447C22×C3—44no—
448C22×C3C2×D3×D412yes—
449C22×C3C2×D3×D414yes—
450C22×C3C2×D3×D412yes—
451C22×C3D3×#4112yes—
452C22×C3D3×#4114yes—
453C2×D3—316no—
454C2×D3—38no—
455C2×D3—38no—
456C2×D3—38no—
457C2×D3—316no—
458C2×D3—64no—
459C2×D3—64no—
460C2×D3—68no—
461C2×D3—68no—
462C2×D3—64no—
463C2×D3—68no—
464C2×D3—68no—
465C2×D3—68no—
466C2×D3—68no—
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—1264no—
470C2×D3—1264no—
471C2×D3—124no—
472C2×D3—124no—
473C2×D3—124no—
474C2×D3—124no—
475C2×D3—124no—
476C2×D3—124no—
477C2×D3—124no—
478C2×D3—124no—
479C3×C4—24no—
480C3×C4—24no—
481C3×C4—64no—
482C3×C4—122no—
483C3×C4—124no—
484Dic3—24no—
485Dic3—42no—
486Dic3—44no—
487Dic3—64no—
488Dic3—64no—
489C32C2×#39411yescharacteristic, complemented, Sylow
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—92no—
497C23—92no—
498C23—94no—
499C23—92no—
500C23—94no—
501C23—94no—
502C23—1816no—
503C23—1816no—
504C23—1816no—
505C23—182no—
506C23—182no—
507C23—182no—
508C23—182no—
509C23—182no—
510C23—182no—
511C23—368no—
512C23—368no—
513C23—368no—
514C23—368no—
515C23#381114yes—
516C23C22×D3211yescharacteristic
517D4—28no—
518D4—188no—
519D4—1816no—
520C2×C4—22no—
521C2×C4—34no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—64no—
525C2×C4—64no—
526C2×C4—64no—
527C2×C4—64no—
528C2×C4—62no—
529C2×C4—92no—
530C2×C4—188no—
531C2×C4—188no—
532C2×C4—182no—
533C2×C4—364no—
534C2×C4—368no—
535C2×C4#381112yes—
536C2×C3—22no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—22no—
541C2×C3—48no—
542C2×C3—48no—
543C2×C3D3×#12012yes—
544C2×C3D3×#12112yes—
545C2×C3D3×#12114yes—
546C2×C3D3×#12314yes—
547C2×C3D3×#12412yes—
548D3—316no—
549D3—68no—
550D3—128no—
551D3—128no—
552C22—24no—
553C22—24no—
554C22—24no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—98no—
560C22—94no—
561C22—94no—
562C22—94no—
563C22—98no—
564C22—184no—
565C22—184no—
566C22—184no—
567C22—3632no—
568C22—362no—
569C22—362no—
570C22—362no—
571C22—362no—
572C22D32×D411yescharacteristic
573C22#6431211yescharacteristic
574C22#6431212yes—
575C22C2×#381112yes—
576C22C2×#381111yescharacteristic
577C4—22no—
578C4—64no—
579C4—122no—
580C4—124no—
581C4—182no—
582C3—21no—
583C3D3×#39412yescomplemented
584C2—44no—
585C2—98no—
586C2—364no—
587C2#1059516912yes—
588C2#1059517011yescharacteristic
589C2#1059528211yescharacteristic
590C2#1059529812yes—
591C2#1059552711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC22×D4×C3⋊D3C2
hypercenterC22×D4D32
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63974C2semidirect
3. C2×#63974C2semidirect
4. C2×#63883C2semidirect
5. C3×#5222C2semidirect
6. #10591712C2semidirect
7. #10591370C2semidirect
8. #10591321C2semidirect
20. C2×C3×#217C22semidirect
21. C2×C3×#217C22semidirect
22. C2×C3×Dic3⋊C4C22semidirect
25. C2×Dic3⋊Dic3C22semidirect
26. C2×#3722C22semidirect
27. C2×#3722C22semidirect
29. C3×C3⋊#95C22semidirect
30. #63579C22semidirect
37. #5222D3semidirect
75. C2×#624D4semidirect
103. C2×#217C2×D3semidirect
104. C2×#217C2×D3semidirect
111. C2×Dic3⋊C4C2×D3semidirect
117. C3⋊#95C2×D3semidirect
160. C2×C3×Dic3C2×D4semidirect
374. C2×Dic3D3×D4semidirect
389. C3⋊D3#394semidirect
489. C32C2×#394semidirect
583. C3D3×#394semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C2×#639742
C2×#638832
C3×#52222
#105917122
#105913702
#105913212
D3×#3943