Finite Group Databasebeta

← #11784802

Subgroups — #11784802

Order 1152.

1681 conjugacy classes of subgroups.

The subgroup lattice has 579 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C3×C4×#217C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4C2×#63570C214yesmaximal, complemented
5#69991—31nomaximal
6#69454—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638—21no—
9C2×#3828—21no—
10C2×#3828—21no—
11C2×#3828—28no—
12C2×#3828C412yescomplemented
13C2×#3828C2212yes—
14C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
15C22×C4×C3⋊D3—21no—
16C22×#634C411yescharacteristic, complemented
17C2×C3×#217—21no—
18C2×C3×C4×Dic3C2212yescomplemented
19C2×C3×#208C2212yescomplemented
20C3×C3⋊#95—21no—
21C3×#830—21no—
22C3×#830—21no—
23#63570—28no—
24C22×#235—31no—
25C22×#235—31no—
26C22×#235—61no—
27C3×#407—31no—
28C3×C4×C22⋊C4—31no—
29C4×#217D311yescharacteristic, complemented
30#5207D311yescharacteristic, complemented
31C2×#825—34no—
32C2×#805—34no—
33C24×C32D411yescharacteristic
34C23×C3⋊D3—21no—
35C22×C32×C4—24no—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4C2311yescharacteristic
42C2×#638—28no—
43C2×#638—22no—
44C2×#638—22no—
45C22×C3⋊Dic3—21no—
46#3828—28no—
47#3828—28no—
48#3828—24no—
49#3828—24no—
50#3828—24no—
51#3828D418yes—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—24no—
54C2×C4⋊(C3⋊D3)C2×C412yes—
55C2×C4×C3⋊D3—28no—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—22no—
58C2×#634—21no—
59C2×#634—24no—
60C2×#634C2×C412yes—
61C22×C3×Dic3—22no—
62C3×#217—24no—
63C3×C4×Dic3—24no—
64C3×#208—24no—
65C2×C3×C3⋊C8—22no—
66#1789—91noSylow
67C23×C3×C4—21no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C2×D311yescharacteristic
70C22×#67—62no—
71C22×#67—61no—
72C22×#67—61no—
73C2×#235—32no—
74C2×#235—32no—
75C2×#235—32no—
76C2×#235—32no—
77C2×#235—62no—
78C2×#235—62no—
79C2×#235—68no—
80C2×#235—68no—
81C2×#235—616no—
82C2×#235—62no—
83C2×#235—62no—
84C2×#235—61no—
85C2×#235—61no—
86C2×#235—61no—
87C2×#235—61no—
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C22×C4×D3—62no—
92C22×C4×D3—61no—
93C22×C4×D3—61no—
94C22×Dic6—31no—
95C22×Dic6—31no—
96C22×Dic6—61no—
97C2×C3×M16—32no—
98C2×C3×C22⋊C4—61no—
99C2×C3×C42—32no—
100C2×#217—21no—
101C2×C4×Dic3C2×D312yescomplemented
102C2×#208C2×D312yescomplemented
103C3×C22⋊C8—61no—
104C3×C22⋊C8—61no—
105C3×#95—61no—
106C3⋊#95—21no—
107#830—21no—
108#830—21no—
109#825—68no—
110#805—68no—
111C23×C32—22no—
112C23×C32—22no—
113C23×C32—41no—
114C23×C32C22⋊C411yescharacteristic
115C23×C32C22⋊C411yescharacteristic
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—24no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3—42no—
120C22×C3⋊D3—42no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4C22⋊C411yescharacteristic
127C2×C32×C4C22⋊C411yescharacteristic
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D414yes—
131#638—28no—
132#638—28no—
133C2×C3⋊Dic3—24no—
134C2×C3⋊Dic3—22no—
135C4⋊(C3⋊D3)—24no—
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)C22⋊C414yescomplemented
138C4×C3⋊D3—28no—
139C4×C3⋊D3—28no—
140#634—24no—
141#634—22no—
142#634C22⋊C414yescomplemented
143C2×C3×Dic3—24no—
144C2×C3×Dic3—42no—
145C2×C3×Dic3—42no—
146C3×C3⋊C8—42no—
147C22×#41—91no—
148C2×#104—94no—
149#407—31no—
150C4×C22⋊C4—31no—
151C24×C3—21no—
152C24×C3D1211yescharacteristic
153C24×C3#6711yescharacteristic
154C23×D3—62no—
155C23×D3—61no—
156C23×D3—61no—
157C22×C3×C4—28no—
158C22×C3×C4—24no—
159C22×C3×C4—24no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—62no—
167C22×C3×C4C4×D311yescharacteristic
168C22×C3×C4C4×D311yescharacteristic
169C22×C3×C4C4×D311yescharacteristic
170C22×C3×C4C4×D311yescharacteristic
171C22×C3×C4D1211yescharacteristic
172C22×C3×C4D1211yescharacteristic
173C22×C3×C4D1211yescharacteristic
174C22×C3×C4#6711yescharacteristic
175C22×C3×C4#6711yescharacteristic
176C22×C3×C4#6711yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C2×#67—616no—
180C2×#67—68no—
181C2×#67—68no—
182C2×#67—64no—
183C2×#67—64no—
184C2×#67—62no—
185C2×#67—62no—
186C2×#67—62no—
187C2×#67—62no—
188C22×Dic3—22no—
189C22×Dic3—62no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192#235—38no—
193#235—38no—
194#235—68no—
195#235—64no—
196#235—64no—
197#235—64no—
198#235—64no—
199#235—68no—
200#235—68no—
201#235—616no—
202#235—616no—
203#235—68no—
204#235—68no—
205#235—68no—
206#235—68no—
207#235—68no—
208#235—64no—
209#235—64no—
210C2×D12—32no—
211C2×D12—32no—
212C2×D12—62no—
213C2×D12—64no—
214C2×D12—64no—
215C2×D12—68no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×C4×D3—616no—
220C2×C4×D3—68no—
221C2×C4×D3—68no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×Dic6—32no—
229C2×Dic6—32no—
230C2×Dic6—62no—
231C2×Dic6—64no—
232C2×Dic6—64no—
233C2×Dic6—68no—
234C2×Dic6—62no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C3×M16—64no—
238C2×C3×C8—62no—
239C3×C22⋊C4—64no—
240C3×C42—64no—
241#217—24no—
242C4×Dic3—24no—
243#208—24no—
244C2×C3⋊C8—22no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—21no—
250C22×C32—21no—
251C22×C32—21no—
252C22×C32—44no—
253C22×C32#10412yescomplemented
254C22×C32C2×C22⋊C411yescharacteristic
255C22×C32#12012yes—
256C2×C3⋊D3—24no—
257C2×C3⋊D3—48no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4C2×C22⋊C412yes—
263C32×C4#12012yes—
264C3⋊Dic3—24no—
265C3×Dic3—44no—
266C2×#41—92no—
267C2×#41—92no—
268C2×#41—188no—
269C2×#41—181no—
270C2×#41—181no—
271C22×Q8—91no—
272C22×D4—91no—
273C22×D4—181no—
274C23×C4—181no—
275C23×C4D3211yescharacteristic
276C2×M16—32no—
277C2×C22⋊C4—61no—
278C2×C42—32no—
279#104—188no—
280C22⋊C8—61no—
281C22⋊C8—61no—
282#95—61no—
283C23×C3—24no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—42no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—42no—
295C23×C3(C2×D3)⋊C411yescharacteristic
296C23×C3(C2×D3)⋊C411yescharacteristic
297C23×C3(C2×D3)⋊C411yescharacteristic
298C23×C3(C2×D3)⋊C411yescharacteristic
299C23×C3C2×D1211yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C22×D3—68no—
302C22×D3—64no—
303C22×D3—64no—
304C22×D3—64no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—124no—
308C22×D3—122no—
309C22×D3—122no—
310C22×D3—124no—
311C22×D3—122no—
312C22×D3—122no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—24no—
333C2×C3×C4—64no—
334C2×C3×C4—122no—
335C2×C3×C4—122no—
336C2×C3×C4(C2×D3)⋊C411yescharacteristic
337C2×C3×C4(C2×D3)⋊C411yescharacteristic
338C2×C3×C4(C2×D3)⋊C411yescharacteristic
339C2×C3×C4(C2×D3)⋊C411yescharacteristic
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4C2×C4×D311yescharacteristic
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4D3×D414yes—
344C2×C3×C4D3×D414yes—
345C2×C3×C4C2×#6711yescharacteristic
346#67—616no—
347#67—68no—
348#67—68no—
349#67—616no—
350#67—68no—
351#67—68no—
352C2×Dic3—24no—
353C2×Dic3—42no—
354C2×Dic3—42no—
355C2×Dic3—68no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361D12—34no—
362D12—34no—
363D12—64no—
364D12—68no—
365D12—64no—
366D12—64no—
367D12—64no—
368D12—62no—
369D12—62no—
370C4×D3—616no—
371C4×D3—68no—
372C4×D3—68no—
373C4×D3—616no—
374C4×D3—68no—
375C4×D3—68no—
376Dic6—34no—
377Dic6—34no—
378Dic6—64no—
379Dic6—68no—
380Dic6—64no—
381Dic6—64no—
382Dic6—64no—
383Dic6—62no—
384Dic6—62no—
385C3×C8—122no—
386C3⋊C8—42no—
387C2×C32—22no—
388C2×C32—22no—
389C2×C32—41no—
390C2×C32#37911yescharacteristic
391C2×C32C2×#10411yescharacteristic
392C2×C32#42111yescharacteristic
393C3⋊D3—44no—
394C24—181no—
395C24#62611yescharacteristic
396#41—98no—
397#41—184no—
398#41—184no—
399#41—188no—
400#41—188no—
401#41—184no—
402C2×Q8—92no—
403C2×Q8—184no—
404C2×Q8—181no—
405C2×D4—92no—
406C2×D4—184no—
407C2×D4—188no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—181no—
411C22×C4—24no—
412C22×C4—62no—
413C22×C4—188no—
414C22×C4—181no—
415C22×C4—182no—
416C22×C4—182no—
417C22×C4#62411yescharacteristic
418C22×C4#62411yescharacteristic
419C22×C4#62611yescharacteristic
420C22×C4#62611yescharacteristic
421C22×C4#62611yescharacteristic
422C22×C4C2×D3211yescharacteristic
423M16—64no—
424C2×C8—62no—
425C22⋊C4—64no—
426C42—64no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—44no—
452C22×C3—44no—
453C22×C3—48no—
454C22×C3#80512yescomplemented
455C22×C3#82512yescomplemented
456C22×C3#88212yes—
457C22×C3C2×(C2×D3)⋊C411yescharacteristic
458C22×C3C2×(C2×D3)⋊C411yescharacteristic
459C22×C3#93712yes—
460C2×D3—68no—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—1216no—
464C2×D3—128no—
465C2×D3—128no—
466C2×D3—124no—
467C2×D3—124no—
468C2×D3—122no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—22no—
480C3×C4—124no—
481C3×C4D3×C22⋊C412yes—
482C3×C4D3×C22⋊C412yes—
483C3×C4#88212yes—
484C3×C4#93712yes—
485Dic3—44no—
486Dic3—68no—
487Dic3—64no—
488Dic3—64no—
489C32#178911yescharacteristic, complemented, Sylow
490C23—22no—
491C23—22no—
492C23—41no—
493C23—184no—
494C23—182no—
495C23—362no—
496C23—362no—
497C23#372211yescharacteristic
498C23#372211yescharacteristic
499C23C2×#62611yescharacteristic
500Q8—94no—
501Q8—184no—
502Q8—182no—
503D4—94no—
504D4—184no—
505D4—188no—
506D4—188no—
507D4—182no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—64no—
514C2×C4—122no—
515C2×C4—122no—
516C2×C4—188no—
517C2×C4—184no—
518C2×C4—182no—
519C2×C4—188no—
520C2×C4#372211yescharacteristic
521C2×C4#372211yescharacteristic
522C2×C4C2×#62411yescharacteristic
523C2×C4C2×#62611yescharacteristic
524C2×C4#381114yes—
525C8—122no—
526C2×C3—24no—
527C2×C3—22no—
528C2×C3—22no—
529C2×C3—22no—
530C2×C3—22no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—42no—
535C2×C3—42no—
536C2×C3—41no—
537C2×C3—41no—
538C2×C3C2×#80511yescharacteristic
539C2×C3#495511yescharacteristic
540C2×C3#495511yescharacteristic
541C2×C3#500511yescharacteristic
542C2×C3C2×#82511yescharacteristic
543C2×C3#513911yescharacteristic
544D3—128no—
545D3—124no—
546D3—124no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—44no—
555C22—184no—
556C22—368no—
557C22—362no—
558C22—362no—
559C22#6357012yescomplemented
560C22C2×#372211yescharacteristic
561C22#6398112yes—
562C4—21no—
563C4—21no—
564C4—124no—
565C4—184no—
566C4#6397412yes—
567C4#6398112yes—
568C3—21no—
569C3#6945411yescharacteristic, complemented
570C3#6999111yescharacteristic, complemented
571C2—22no—
572C2—22no—
573C2—41no—
574C2—364no—
575C2C2×#6357011yescharacteristic
576C2#1059111311yescharacteristic
577C2#1059171411yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3828C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1789
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×#217C2semidirect
3. C3×#5207C2semidirect
4. C2×#63570C2semidirect
12. C2×#3828C4semidirect
14. C22×C4⋊(C3⋊D3)C4semidirect
16. C22×#634C4semidirect
18. C2×C3×C4×Dic3C22semidirect
19. C2×C3×#208C22semidirect
29. C4×#217D3semidirect
30. #5207D3semidirect
101. C2×C4×Dic3C2×D3semidirect
102. C2×#208C2×D3semidirect
137. C4⋊(C3⋊D3)C22⋊C4semidirect
142. #634C22⋊C4semidirect
253. C22×C32#104semidirect
454. C22×C3#805semidirect
455. C22×C3#825semidirect
489. C32#1789semidirect
559. C22#63570semidirect
569. C3#69454semidirect
570. C3#69991semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C3×C4×#2172
C3×#52072
C2×#635702
#699913
#694543