Finite Group Databasebeta

← #11785317

Subgroups — #11785317

Order 1152.

687 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C211yesmaximal, characteristic
2#10592817C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic
4C4×#3724C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70355—31nomaximal
9#68770—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17#67⋊Dic3—21no—
18#67⋊Dic3—21no—
19C2×#3724—21no—
20#63898C411yescharacteristic, complemented
21#63898C411yescharacteristic, complemented
22C4×D3×Dic3—21no—
23#63855—21no—
24#63843C411yescharacteristic, complemented
25#63843C411yescharacteristic, complemented
26#63641—21no—
27#63641—21no—
28C3×#825—22no—
29#63579—21no—
30#63569—22no—
31Dic3×#41—31no—
32#5522—31no—
33C2×C3×#104—31no—
34C2×#837—31no—
35C2×#825D311yescharacteristic
36#5118—31no—
37#5118—31no—
38#5118—61no—
39C4×Dic3⋊C4—31no—
40C4×Dic3⋊C4—31no—
41C2×#805—31no—
42C3×#339—31no—
43#4555D311yescharacteristic, complemented
44#4532—31no—
45#4523—31no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×C3×#67—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235D412yes—
55C3×#235Q812yes—
56C2×C3×D12C2×C411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×Dic6C2×C411yescharacteristic
59C2×D3×Dic3—21no—
60C2×D3×Dic3—21no—
61C32×M16—21no—
62C32×M16—21no—
63C2×C32×C8—21no—
64C4×C3⋊Dic3C2×C411yescharacteristic
65C4×C3⋊Dic3C2×C411yescharacteristic
66C4×C3⋊Dic3D411yescharacteristic
67C4×C3⋊Dic3D411yescharacteristic
68#3748—21no—
69#3748—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C3×#217—21no—
72C3×C4⋊Dic3C2×C411yescharacteristic
73C3×C4⋊Dic3C2×C411yescharacteristic
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79#3724—24no—
80Dic3⋊Dic3—21no—
81Dic3⋊Dic3—21no—
82(C2×D3)⋊Dic3—21no—
83(C2×D3)⋊Dic3—21no—
84Dic32—21no—
85Dic32—21no—
86#1806—91noSylow
87C2×C3×#41—31no—
88C2×#235C2×D311yescharacteristic
89C2×C3×M16—21no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C3×#117—31no—
93C2×C3×C42—31no—
94C2×C3×C42—31no—
95Q8×Dic3—31no—
96Q8×Dic3—31no—
97D4×Dic3—31no—
98D4×Dic3—31no—
99D4×Dic3—61no—
100D4×Dic3—61no—
101#926—61no—
102#926C2×D311yescharacteristic
103C2×Dic3⋊C4—61no—
104C2×Dic3⋊C4—61no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3C2×D311yescharacteristic
110C2×C4×Dic3C2×D311yescharacteristic
111C2×#208—31no—
112C2×#208—31no—
113C2×#208—61no—
114#893—31no—
115#893—31no—
116#887—31no—
117#887—31no—
118#67⋊C4—61no—
119#67⋊C4—61no—
120#872—61no—
121C42×D3—61no—
122C3×#104—62no—
123#837—62no—
124C3⋊#95—61no—
125C3⋊#95—61no—
126#825—22no—
127Dic3⋊C8—61no—
128Dic3⋊C8—61no—
129Dic3⋊C8—61no—
130Dic3⋊C8—61no—
131Dic3⋊C8—62no—
132Dic3⋊C8—62no—
133#805—62no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—21no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×Q811yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3C22⋊C411yescharacteristic
145C2×C3⋊Dic3C22⋊C411yescharacteristic
146C2×C3⋊Dic3C22⋊C411yescharacteristic
147C2×C3⋊Dic3C22⋊C411yescharacteristic
148C3×#67—22no—
149C3×#67—22no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C3×D12—21no—
160C3×D12C4⋊C412yescomplemented
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163C3×Dic6—21no—
164C3×Dic6C4⋊C412yescomplemented
165D3×Dic3—42no—
166D3×Dic3—42no—
167C32×C8—41no—
168C3⋊(C3⋊C8)—41no—
169C4×#41—91no—
170#423—91no—
171C2×#104—31no—
172C2×#104—91no—
173C4×C4⋊C4—91no—
174#339—31no—
175#339—91no—
176C3×#41—32no—
177C3×#41—32no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—31no—
181C2×C3×D4—31no—
182C2×C3×D4—61no—
183C22×C3×C4—21no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C2×#67—21no—
190C22×Dic3—21no—
191C22×Dic3—21no—
192C22×Dic3—31no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—31no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—61no—
200#235—21no—
201#235—21no—
202#235Dic612yes—
203#235#6712yes—
204C2×D12C4×D311yescharacteristic
205C2×C4×D3—21no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×Dic6C4×D311yescharacteristic
209C3×M16—21no—
210C3×M16—21no—
211C3×M16—21no—
212C3×M16—21no—
213C3×M16—41no—
214C3×M16—41no—
215C2×C3×C8—22no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—31no—
220C3×C22⋊C4—61no—
221C3×C42—61no—
222C3×C42—61no—
223C3×C42—61no—
224C3×C42—61no—
225C3×C42—61no—
226#217—21no—
227#217—61no—
228#217—61no—
229(C2×D3)⋊C4—61no—
230(C2×D3)⋊C4—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3C4×D311yescharacteristic
234C4⋊Dic3C4×D311yescharacteristic
235Dic3⋊C4—61no—
236Dic3⋊C4—61no—
237Dic3⋊C4—64no—
238Dic3⋊C4—64no—
239C4×Dic3—21no—
240C4×Dic3—21no—
241C4×Dic3—21no—
242C4×Dic3—21no—
243C4×Dic3—21no—
244C4×Dic3—31no—
245C4×Dic3—31no—
246C4×Dic3—31no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—31no—
251C4×Dic3—31no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—61no—
259C4×Dic3—61no—
260#208—61no—
261#208—61no—
262#208—61no—
263#208—61no—
264#208—121no—
265#208—121no—
266C2×C3⋊C8—62no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32C2×C22⋊C411yescharacteristic
272C22×C32#12111yescharacteristic
273C22×C32C22⋊Q811yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C32×C4C2×C4⋊C411yescharacteristic
278C32×C4#11711yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4C22⋊Q811yescharacteristic
281C3⋊Dic3—21no—
282C3⋊Dic3—21no—
283C3⋊Dic3—21no—
284C3⋊Dic3#10412yescomplemented
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C2×#41—31no—
291C2×M16—91no—
292C2×M16D3211yescharacteristic
293C4×Q8—91no—
294C4×Q8—91no—
295C4×D4—91no—
296C4×D4—91no—
297C4×D4—181no—
298C4×D4—181no—
299#117—31no—
300#117—181no—
301C2×C4⋊C4—181no—
302C2×C42—31no—
303C2×C42—31no—
304C2×C42—91no—
305C2×C42—181no—
306C4⋊C8—181no—
307C4⋊C8—181no—
308#104—62no—
309#104—182no—
310#95—181no—
311C23×C3—21no—
312C23×C3—61no—
313C23×C3D3×D411yescharacteristic
314C23×C3D3×D411yescharacteristic
315C22×D3—21no—
316C3×Q8—32no—
317C3×Q8—61no—
318C3×D4—32no—
319C3×D4—62no—
320C3×D4—62no—
321C3×D4—61no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—121no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4C2×Dic611yescharacteristic
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4C2×C4×D311yescharacteristic
342C2×C3×C4#23511yescharacteristic
343C2×C3×C4#23511yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4#23711yescharacteristic
348C2×C3×C4#23711yescharacteristic
349C2×C3×C4D3×Q811yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351#67—22no—
352#67—22no—
353C2×Dic3—21no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—31no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—31no—
364C2×Dic3—31no—
365C2×Dic3—31no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—41no—
369C2×Dic3—41no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—122no—
382D12—21no—
383D12Dic3⋊C412yescomplemented
384C4×D3—22no—
385C4×D3—22no—
386C4×D3—122no—
387C4×D3—122no—
388Dic6—21no—
389Dic6Dic3⋊C412yescomplemented
390C3×C8—42no—
391C3×C8—41no—
392C3×C8—41no—
393C3⋊C8—122no—
394C3⋊C8—121no—
395C3⋊C8—121no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32#38011yescharacteristic
399C2×C32C2×#10411yescharacteristic
400C2×C32#42111yescharacteristic
401C3×D3—42no—
402#41—32no—
403#41—32no—
404#41—61no—
405#41—61no—
406C2×Q8—31no—
407C2×D4—31no—
408C2×D4—61no—
409C22×C4—61no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4—181no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417M16—21no—
418M16—21no—
419M16—181no—
420M16—181no—
421C2×C8—21no—
422C2×C8—181no—
423C4⋊C4—31no—
424C4⋊C4—31no—
425C4⋊C4—181no—
426C4⋊C4—181no—
427C4⋊C4—184no—
428C22⋊C4—61no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C42—61no—
432C42—61no—
433C42—61no—
434C42—61no—
435C42—61no—
436C42—91no—
437C42—91no—
438C42—91no—
439C42—91no—
440C42—181no—
441C42—181no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—62no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3#87811yescharacteristic
455C22×C3D3×C22⋊C411yescharacteristic
456C22×C3D3×C22⋊C411yescharacteristic
457C22×C3#88411yescharacteristic
458C22×C3#89611yescharacteristic
459C22×C3#93911yescharacteristic
460C2×D3—22no—
461C2×D3—41no—
462C2×D3—41no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—62no—
468C3×C4—122no—
469C3×C4—122no—
470C3×C4—121no—
471C3×C4—121no—
472C3×C4#87211yescharacteristic
473C3×C4#87711yescharacteristic
474C3×C4#87811yescharacteristic
475C3×C4#88411yescharacteristic
476C3×C4D3×C4⋊C411yescharacteristic
477C3×C4#89611yescharacteristic
478C3×C4C2×Dic3⋊C411yescharacteristic
479C3×C4#93911yescharacteristic
480Dic3—22no—
481Dic3—32no—
482Dic3—32no—
483Dic3—42no—
484Dic3—42no—
485Dic3—41no—
486Dic3—41no—
487Dic3—62no—
488Dic3—62no—
489Dic3—61no—
490Dic3—61no—
491Dic3—61no—
492Dic3—61no—
493Dic3—61no—
494Dic3—61no—
495Dic3—121no—
496Dic3—121no—
497C32#180611yescharacteristic, complemented, Sylow
498C23—61no—
499C23#380211yescharacteristic
500Q8—32no—
501Q8—61no—
502D4—32no—
503D4—62no—
504D4—62no—
505D4—61no—
506C2×C4—61no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—91no—
514C2×C4—91no—
515C2×C4—91no—
516C2×C4—91no—
517C2×C4—121no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—121no—
521C2×C4—182no—
522C2×C4—362no—
523C2×C4—362no—
524C2×C4—361no—
525C2×C4D3×Dic611yescharacteristic
526C2×C4#379511yescharacteristic
527C2×C4C4×D3211yescharacteristic
528C2×C4#380411yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4#381111yescharacteristic
531C8—41no—
532C8—361no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—41no—
541C2×C3—41no—
542C2×C3—122no—
543C2×C3#466711yescharacteristic
544C2×C3D3×#10411yescharacteristic
545C2×C3D3×#10411yescharacteristic
546C2×C3#482111yescharacteristic
547C2×C3#482111yescharacteristic
548C2×C3#494211yescharacteristic
549D3—42no—
550C22—21no—
551C22—21no—
552C22—62no—
553C22—121no—
554C22—121no—
555C22#6388511yescharacteristic
556C22#6389911yescharacteristic
557C22#6392111yescharacteristic
558C4—62no—
559C4—92no—
560C4—122no—
561C4—122no—
562C4—121no—
563C4—121no—
564C4—181no—
565C4—181no—
566C4—181no—
567C4D3×Dic3⋊C411yescharacteristic
568C4#6387711yescharacteristic
569C4#6389611yescharacteristic
570C4#6397111yescharacteristic
571C3—21no—
572C3#6877011yescharacteristic, complemented
573C3#7035511yescharacteristic, complemented
574C2—21no—
575C2—21no—
576C2—122no—
577C2#1059100811yescharacteristic
578C2#1059100911yescharacteristic
579C2#1059136911yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592817C2semidirect
4. C4×#3724C2semidirect
6. C3×#4555C2semidirect
7. #10589161C2semidirect
20. #63898C4semidirect
21. #63898C4semidirect
24. #63843C4semidirect
25. #63843C4semidirect
43. #4555D3semidirect
160. C3×D12C4⋊C4semidirect
164. C3×Dic6C4⋊C4semidirect
284. C3⋊Dic3#104semidirect
383. D12Dic3⋊C4semidirect
389. Dic6Dic3⋊C4semidirect
497. C32#1806semidirect
572. C3#68770semidirect
573. C3#70355semidirect

Maximal subgroups

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

subgroupindex
#105949582
#105928172
C2×C3×#8252
C4×#37242
C2×#635692
C3×#45552
#105891612
#703553
#687703