Finite Group Databasebeta

← #11785325

Subgroups — #11785325

Order 1152.

721 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C211yesmaximal, characteristic
2C4×#3750C211yesmaximal, characteristic, complemented
3C2×C3×#805C211yesmaximal, characteristic
4#10591120C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70355—31nomaximal
9#68770—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3750—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#67⋊Dic3—21no—
19#67⋊Dic3—21no—
20#63898C411yescharacteristic, complemented
21#63898C411yescharacteristic, complemented
22C4×D3×Dic3—21no—
23#63855—21no—
24#63843C411yescharacteristic, complemented
25#63843C411yescharacteristic, complemented
26#63658—21no—
27C3×#805—22no—
28#63572—21no—
29#63572—21no—
30#63568—22no—
31Dic3×#41—31no—
32#5522—31no—
33C2×C3×#104—31no—
34C2×#837—31no—
35C2×#825—31no—
36#5118—31no—
37#5118—31no—
38C4×Dic3⋊C4—31no—
39C4×Dic3⋊C4—31no—
40C4×Dic3⋊C4—61no—
41C2×#805D311yescharacteristic
42C3×#339—31no—
43#4555—31no—
44#4532—31no—
45#4523D311yescharacteristic, complemented
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×C3×#67—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×C42—21no—
62C32×C42—21no—
63#3750—24no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3C2×C411yescharacteristic
67C4×C3⋊Dic3C2×C411yescharacteristic
68C4×C3⋊Dic3D411yescharacteristic
69C4×C3⋊Dic3D411yescharacteristic
70C3×#217—21no—
71C3×C4⋊Dic3C2×C411yescharacteristic
72C3×C4⋊Dic3C2×C411yescharacteristic
73C3×C4×Dic3—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
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—31no—
90C2×C3×M16—31no—
91C3×#117—31no—
92C2×C3×C42—21no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C2×D311yescharacteristic
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×Dic3⋊C4—62no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—31no—
108C2×C4×Dic3—31no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3—61no—
113C2×#208C2×D311yescharacteristic
114C2×#208C2×D311yescharacteristic
115#893—31no—
116#893—31no—
117#887—31no—
118#887—31no—
119#67⋊C4—61no—
120#67⋊C4—61no—
121#872—61no—
122C42×D3—61no—
123C3×#104—62no—
124#837—62no—
125C3⋊#95—61no—
126C3⋊#95—61no—
127C3⋊#95—62no—
128#825—62no—
129Dic3⋊C8—61no—
130Dic3⋊C8—61no—
131Dic3⋊C8—61no—
132Dic3⋊C8—61no—
133#805—22no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—21no—
136C2×C32×C4—22no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×Q811yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—41no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3C22⋊C411yescharacteristic
151C2×C3⋊Dic3C22⋊C411yescharacteristic
152C2×C3⋊Dic3C22⋊C411yescharacteristic
153C2×C3⋊Dic3C22⋊C411yescharacteristic
154C3×#67—22no—
155C3×#67—22no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
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—
167C3×C3⋊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—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—21no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—62no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202#235—21no—
203#235—21no—
204#235Dic612yes—
205#235#6712yes—
206C2×D12C4×D311yescharacteristic
207C2×C4×D3—21no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×Dic6C4×D311yescharacteristic
211C3×M16—61no—
212C3×M16—61no—
213C3×M16—61no—
214C3×M16—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—31no—
218C3×C4⋊C4—31no—
219C3×C22⋊C4—61no—
220C3×C42—21no—
221C3×C42—21no—
222C3×C42—21no—
223C3×C42—21no—
224C3×C42—41no—
225C3×C42—41no—
226C3×C42—61no—
227#217—21no—
228#217—61no—
229#217—61no—
230(C2×D3)⋊C4—61no—
231(C2×D3)⋊C4—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3C4×D311yescharacteristic
235C4⋊Dic3C4×D311yescharacteristic
236Dic3⋊C4—61no—
237Dic3⋊C4—61no—
238Dic3⋊C4—64no—
239Dic3⋊C4—64no—
240Dic3⋊C4—68no—
241C4×Dic3—21no—
242C4×Dic3—31no—
243C4×Dic3—31no—
244C4×Dic3—31no—
245C4×Dic3—31no—
246C4×Dic3—31no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—61no—
259C4×Dic3—61no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262C4×Dic3—121no—
263C4×Dic3—121no—
264#208—21no—
265#208—21no—
266#208—21no—
267#208—21no—
268C2×C3⋊C8—21no—
269C2×C3⋊C8—21no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32C2×C22⋊C411yescharacteristic
273C22×C32#12111yescharacteristic
274C22×C32C22⋊Q811yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—42no—
279C32×C4C2×C4⋊C411yescharacteristic
280C32×C4#11711yescharacteristic
281C32×C4#12111yescharacteristic
282C32×C4C22⋊Q811yescharacteristic
283C3⋊Dic3—21no—
284C3⋊Dic3—21no—
285C3⋊Dic3—21no—
286C3⋊Dic3—42no—
287C3⋊Dic3#10412yescomplemented
288C3×Dic3—22no—
289C3×Dic3—41no—
290C3×Dic3—41no—
291C2×#41—31no—
292C2×M16—31no—
293C2×M16—31no—
294C4×Q8—91no—
295C4×Q8—91no—
296C4×D4—91no—
297C4×D4—91no—
298C4×D4—181no—
299C4×D4—181no—
300#117—31no—
301#117—181no—
302C2×C4⋊C4—181no—
303C2×C42—91no—
304C2×C42—91no—
305C2×C42—181no—
306C2×C42D3211yescharacteristic
307C4⋊C8—181no—
308C4⋊C8—181no—
309#104—62no—
310#104—182no—
311#95—181no—
312C23×C3—21no—
313C23×C3—61no—
314C23×C3D3×D411yescharacteristic
315C23×C3D3×D411yescharacteristic
316C22×D3—21no—
317C3×Q8—32no—
318C3×Q8—61no—
319C3×D4—32no—
320C3×D4—62no—
321C3×D4—62no—
322C3×D4—61no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4C2×Dic611yescharacteristic
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4#23511yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4#23711yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4D3×Q811yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355#67—22no—
356#67—22no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—31no—
364C2×Dic3—31no—
365C2×Dic3—31no—
366C2×Dic3—31no—
367C2×Dic3—31no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389D12—21no—
390D12Dic3⋊C412yescomplemented
391C4×D3—22no—
392C4×D3—22no—
393C4×D3—122no—
394C4×D3—122no—
395Dic6—21no—
396Dic6Dic3⋊C412yescomplemented
397C3×C8—121no—
398C3×C8—121no—
399C3⋊C8—41no—
400C3⋊C8—41no—
401C2×C32—21no—
402C2×C32—21no—
403C2×C32#38011yescharacteristic
404C2×C32C2×#10411yescharacteristic
405C2×C32#42111yescharacteristic
406C3×D3—42no—
407#41—32no—
408#41—32no—
409#41—61no—
410#41—61no—
411C2×Q8—31no—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—21no—
415C22×C4—61no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—181no—
419C22×C4—181no—
420C22×C4—181no—
421C22×C4C2×D3211yescharacteristic
422M16—61no—
423M16—61no—
424M16—61no—
425M16—61no—
426C2×C8—61no—
427C2×C8—61no—
428C4⋊C4—31no—
429C4⋊C4—31no—
430C4⋊C4—184no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C22⋊C4—61no—
434C22⋊C4—181no—
435C22⋊C4—181no—
436C42—21no—
437C42—21no—
438C42—61no—
439C42—91no—
440C42—91no—
441C42—91no—
442C42—91no—
443C42—181no—
444C42—181no—
445C42—181no—
446C42—181no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—62no—
457C22×C3—121no—
458C22×C3—121no—
459C22×C3#87811yescharacteristic
460C22×C3D3×C22⋊C411yescharacteristic
461C22×C3D3×C22⋊C411yescharacteristic
462C22×C3#88411yescharacteristic
463C22×C3#89611yescharacteristic
464C22×C3#93911yescharacteristic
465C2×D3—22no—
466C2×D3—41no—
467C2×D3—41no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—44no—
473C3×C4—42no—
474C3×C4—42no—
475C3×C4—62no—
476C3×C4—121no—
477C3×C4—121no—
478C3×C4#87211yescharacteristic
479C3×C4#87711yescharacteristic
480C3×C4#87811yescharacteristic
481C3×C4#88411yescharacteristic
482C3×C4D3×C4⋊C411yescharacteristic
483C3×C4#89611yescharacteristic
484C3×C4C2×Dic3⋊C411yescharacteristic
485C3×C4#93911yescharacteristic
486Dic3—22no—
487Dic3—32no—
488Dic3—32no—
489Dic3—41no—
490Dic3—41no—
491Dic3—62no—
492Dic3—62no—
493Dic3—61no—
494Dic3—61no—
495Dic3—61no—
496Dic3—61no—
497Dic3—61no—
498Dic3—61no—
499Dic3—121no—
500Dic3—121no—
501Dic3—124no—
502Dic3—122no—
503Dic3—122no—
504C32#180611yescharacteristic, complemented, Sylow
505C23—61no—
506C23#381111yescharacteristic
507Q8—32no—
508Q8—61no—
509D4—32no—
510D4—62no—
511D4—62no—
512D4—61no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—61no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—91no—
522C2×C4—91no—
523C2×C4—91no—
524C2×C4—91no—
525C2×C4—182no—
526C2×C4—182no—
527C2×C4—362no—
528C2×C4—362no—
529C2×C4—361no—
530C2×C4—361no—
531C2×C4—361no—
532C2×C4D3×Dic611yescharacteristic
533C2×C4#379511yescharacteristic
534C2×C4C4×D3211yescharacteristic
535C2×C4#380211yescharacteristic
536C2×C4#380411yescharacteristic
537C2×C4D3×#6711yescharacteristic
538C8—121no—
539C8—121no—
540C2×C3—22no—
541C2×C3—22no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—122no—
550C2×C3#466711yescharacteristic
551C2×C3D3×#10411yescharacteristic
552C2×C3D3×#10411yescharacteristic
553C2×C3#482111yescharacteristic
554C2×C3#482111yescharacteristic
555C2×C3#494211yescharacteristic
556D3—42no—
557C22—21no—
558C22—21no—
559C22—62no—
560C22—121no—
561C22—121no—
562C22#6389611yescharacteristic
563C22#6392111yescharacteristic
564C22#6397111yescharacteristic
565C4—42no—
566C4—62no—
567C4—92no—
568C4—121no—
569C4—121no—
570C4—181no—
571C4—181no—
572C4—181no—
573C4—362no—
574C4D3×Dic3⋊C411yescharacteristic
575C4#6387711yescharacteristic
576C4#6388511yescharacteristic
577C4#6389911yescharacteristic
578C3—21no—
579C3#6877011yescharacteristic, complemented
580C3#7035511yescharacteristic, complemented
581C2—21no—
582C2—21no—
583C2—122no—
584C2#1059039311yescharacteristic
585C2#1059039411yescharacteristic
586C2#1059136911yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#3750C2semidirect
4. #10591120C2semidirect
6. C3×#4523C2semidirect
7. #10589160C2semidirect
20. #63898C4semidirect
21. #63898C4semidirect
24. #63843C4semidirect
25. #63843C4semidirect
45. #4523D3semidirect
160. C3×D12C4⋊C4semidirect
164. C3×Dic6C4⋊C4semidirect
287. C3⋊Dic3#104semidirect
390. D12Dic3⋊C4semidirect
396. Dic6Dic3⋊C4semidirect
504. C32#1806semidirect
579. C3#68770semidirect
580. C3#70355semidirect

Maximal subgroups

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

subgroupindex
#105949582
C4×#37502
C2×C3×#8052
#105911202
C2×#635682
C3×#45232
#105891602
#703553
#687703