Finite Group Databasebeta

← #11784783

Subgroups — #11784783

Order 1152.

1854 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic, complemented
3C2×#63664C211yesmaximal, characteristic, complemented
4C2×#63652C211yesmaximal, characteristic, complemented
5#10592825C211yesmaximal, characteristic, complemented
6C4×#3752C211yesmaximal, characteristic, complemented
7C2×#63632C211yesmaximal, characteristic, complemented
8#70380—34nomaximal
9C2×C32×#41C2211yescharacteristic
10#41×C3⋊D3—22no—
11#41×C3⋊D3—22no—
12#41×C3⋊D3—22no—
13#41×C3⋊D3—22no—
14C2×#3832C411yescharacteristic, complemented
15C2×Q8×C3⋊D3C411yescharacteristic, complemented
16C2×#3830—21no—
17C2×#3830C411yescharacteristic, complemented
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3C411yescharacteristic, complemented
20C2×#3828—21no—
21C2×#3828C2211yescharacteristic
22C22×C4×C3⋊D3—21no—
23C22×C4×C3⋊D3C2211yescharacteristic
24C2×C32×M16C2211yescharacteristic, complemented
25C2×C32×C42C2211yescharacteristic, complemented
26C2×#3752—21no—
27C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
28C2×#3748C2211yescharacteristic, complemented
29C32×#104—22no—
30#63664—22no—
31#63658—21no—
32#63652—22no—
33#63647—21no—
34#63647—21no—
35#63632—22no—
36C2×D3×#41—34no—
37C2×C3×#104D314yescomplemented
38C2×#837—34no—
39C2×#825—34no—
40#5126—34no—
41C4×(C2×D3)⋊C4—34no—
42C2×#805—34no—
43C23×C3⋊D3—21no—
44C23×C3⋊D3D411yescharacteristic
45C32×#41—21no—
46C32×#41—21no—
47C32×#41D412yes—
48C32×#41D412yes—
49C2×C32×Q8C2×C411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4C2×C411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—21no—
56C2×#638—21no—
57C2×#638—21no—
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3D411yescharacteristic
61#3832—22no—
62#3832—22no—
63Q8×C3⋊D3—22no—
64Q8×C3⋊D3—22no—
65#3830—24no—
66#3830—24no—
67#3830—22no—
68#3830—22no—
69D4×C3⋊D3—24no—
70D4×C3⋊D3—24no—
71D4×C3⋊D3—22no—
72D4×C3⋊D3—22no—
73#3828—24no—
74#3828—24no—
75#3828—21no—
76#3828—21no—
77#3828D412yes—
78#3828D412yes—
79C2×C4⋊(C3⋊D3)—21no—
80C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3C2×C411yescharacteristic
91C2×C4×C3⋊D3C2×C411yescharacteristic
92C2×C4×C3⋊D3D411yescharacteristic
93C2×C4×C3⋊D3D411yescharacteristic
94C2×#634—21no—
95C2×#634C2×C411yescharacteristic
96C32×M16—21no—
97C32×M16—21no—
98C2×C32×C8—21no—
99C32×C42—21no—
100C32×C42—21no—
101#3752—24no—
102C4×C3⋊Dic3—21no—
103C4×C3⋊Dic3—21no—
104#3748—21no—
105#3748—21no—
106C2×C3⋊(C3⋊C8)—21no—
107#1789—91noSylow
108C2×C3×#41C2×D314yes—
109D3×#41—68no—
110D3×#41—68no—
111D3×#41—68no—
112D3×#41—68no—
113C2×#239—34no—
114C2×D3×Q8—34no—
115C2×#237—34no—
116C2×#237—64no—
117C2×D3×D4—34no—
118C2×D3×D4—64no—
119C2×#235—34no—
120C2×#235—64no—
121C22×C4×D3—34no—
122C22×C4×D3—64no—
123C2×C3×M16C2×D314yescomplemented
124C2×C3×C42C2×D314yescomplemented
125C2×(C2×D3)⋊C4—64no—
126C2×C4×Dic3—34no—
127C2×#208—34no—
128C3×#104—28no—
129#837—68no—
130C3⋊#95—64no—
131#825—68no—
132(C2×D3)⋊C8—64no—
133(C2×D3)⋊C8—64no—
134#805—68no—
135C23×C32—21no—
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—24no—
138C22×C3⋊D3—21no—
139C22×C3⋊D3—21no—
140C22×C3⋊D3—21no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—41no—
143C22×C3⋊D3—42no—
144C22×C3⋊D3—42no—
145C22×C3⋊D3C22⋊C411yescharacteristic
146C22×C3⋊D3C22⋊C411yescharacteristic
147C32×Q8—21no—
148C32×Q8C22⋊C412yescomplemented
149C32×D4—22no—
150C32×D4—22no—
151C32×D4—21no—
152C32×D4C22⋊C412yescomplemented
153C2×C32×C4—21no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—41no—
158C2×C32×C4—41no—
159C2×C32×C4C22×C411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165#638—24no—
166#638—24no—
167#638—22no—
168#638—22no—
169C2×C3⋊Dic3—24no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—41no—
175C2×C3⋊Dic3—41no—
176C2×C3⋊Dic3C22⋊C411yescharacteristic
177C2×C3⋊Dic3C22⋊C411yescharacteristic
178C4⋊(C3⋊D3)—24no—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)C22⋊C412yescomplemented
181C4×C3⋊D3—24no—
182C4×C3⋊D3—24no—
183C4×C3⋊D3—21no—
184C4×C3⋊D3—21no—
185C4×C3⋊D3—21no—
186C4×C3⋊D3—21no—
187C4×C3⋊D3—21no—
188C4×C3⋊D3—21no—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—22no—
191C4×C3⋊D3—21no—
192C4×C3⋊D3—21no—
193#634—24no—
194#634—21no—
195#634C22⋊C412yescomplemented
196C32×C8—41no—
197C3⋊(C3⋊C8)—41no—
198C22×#41—91no—
199C2×#104—91no—
200C2×#104—91no—
201C2×#104—91no—
202C2×#104C3⋊D311yescharacteristic, complemented
203#407—91no—
204C4×C22⋊C4—91no—
205C23×D3—34no—
206C23×D3—64no—
207C3×#41—24no—
208C3×#41—24no—
209C3×#41D1218yes—
210C3×#41#6718yes—
211C2×C3×Q8C4×D314yes—
212C2×C3×D4—24no—
213C2×C3×D4C4×D314yes—
214C22×C3×C4—24no—
215C22×C3×C4—24no—
216C22×C3×C4C22×D314yes—
217C2×#67—64no—
218C2×#67—64no—
219C2×#67—64no—
220C22×Dic3—34no—
221C22×Dic3—64no—
222C22×Dic3—64no—
223#239—68no—
224#239—68no—
225D3×Q8—68no—
226D3×Q8—68no—
227#237—68no—
228#237—616no—
229#237—616no—
230#237—68no—
231D3×D4—68no—
232D3×D4—616no—
233D3×D4—616no—
234D3×D4—68no—
235#235—38no—
236#235—38no—
237#235—616no—
238#235—616no—
239#235—64no—
240#235—64no—
241C2×D12—34no—
242C2×D12—64no—
243C2×C4×D3—34no—
244C2×C4×D3—34no—
245C2×C4×D3—34no—
246C2×C4×D3—34no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—616no—
250C2×C4×D3—616no—
251C2×C4×D3—64no—
252C2×C4×D3—64no—
253C2×C4×D3—64no—
254C2×C4×D3—64no—
255C2×C4×D3—64no—
256C2×Dic6—34no—
257C2×Dic6—64no—
258C3×M16—24no—
259C3×M16—24no—
260C2×C3×C8—24no—
261C3×C42—24no—
262C3×C42—24no—
263(C2×D3)⋊C4—616no—
264C4×Dic3—64no—
265C4×Dic3—64no—
266#208—64no—
267#208—64no—
268C2×C3⋊C8—64no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32—22no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32C2×C22⋊C411yescharacteristic
275C22×C32#12011yescharacteristic
276C22×C32#12011yescharacteristic
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—21no—
280C2×C3⋊D3—22no—
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—42no—
285C2×C3⋊D3—48no—
286C2×C3⋊D3—41no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3#10412yescomplemented
289C32×C4—22no—
290C32×C4—42no—
291C32×C4C2×C22⋊C411yescharacteristic
292C32×C4C2×C22⋊C411yescharacteristic
293C32×C4#12011yescharacteristic
294C32×C4#12011yescharacteristic
295C3⋊Dic3—21no—
296C3⋊Dic3—22no—
297C3⋊Dic3—21no—
298C3⋊Dic3—42no—
299C2×#41—91no—
300C2×#41—91no—
301C2×#41—91no—
302C2×#41—181no—
303C2×#41—181no—
304C2×#41—182no—
305C2×#41—182no—
306C2×#41—182no—
307C2×#41—182no—
308C2×#41C2×C3⋊D311yescharacteristic
309C22×Q8—91no—
310C22×D4—91no—
311C22×D4—181no—
312C23×C4—91no—
313C23×C4—181no—
314C2×M16—91no—
315C2×M16C2×C3⋊D311yescharacteristic, complemented
316C2×C22⋊C4—181no—
317C2×C42—91no—
318C2×C42C2×C3⋊D311yescharacteristic, complemented
319#104—22no—
320#104—182no—
321#104—182no—
322#104—182no—
323C22⋊C8—181no—
324C22⋊C8—181no—
325#95—181no—
326C23×C3—24no—
327C23×C3D3×D414yes—
328C22×D3—34no—
329C22×D3—34no—
330C22×D3—68no—
331C22×D3—616no—
332C22×D3—64no—
333C22×D3—64no—
334C22×D3—64no—
335C22×D3—128no—
336C22×D3—124no—
337C22×D3—128no—
338C3×Q8—24no—
339C3×Q8(C2×D3)⋊C418yescomplemented
340C3×D4—28no—
341C3×D4—28no—
342C3×D4—24no—
343C3×D4(C2×D3)⋊C418yescomplemented
344C2×C3×C4—24no—
345C2×C3×C4—28no—
346C2×C3×C4—28no—
347C2×C3×C4—28no—
348C2×C3×C4—44no—
349C2×C3×C4—44no—
350C2×C3×C4C2×C4×D314yes—
351C2×C3×C4C2×D1214yes—
352C2×C3×C4D3×D414yes—
353C2×C3×C4D3×D414yes—
354C2×C3×C4D3×D414yes—
355C2×C3×C4C2×#6714yes—
356#67—616no—
357#67—616no—
358#67—68no—
359#67—68no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—616no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—68no—
367C2×Dic3—124no—
368C2×Dic3—124no—
369D12—38no—
370D12—616no—
371D12—64no—
372C4×D3—616no—
373C4×D3—616no—
374C4×D3—64no—
375C4×D3—64no—
376C4×D3—64no—
377C4×D3—64no—
378C4×D3—68no—
379C4×D3—64no—
380C4×D3—64no—
381C4×D3—64no—
382C4×D3—64no—
383C4×D3—68no—
384Dic6—38no—
385Dic6—616no—
386Dic6—64no—
387C3×C8—44no—
388C3⋊C8—124no—
389C2×C32—21no—
390C2×C32—21no—
391C2×C32—42no—
392C2×C32#37911yescharacteristic
393C2×C32C2×#10411yescharacteristic
394C2×C32#42111yescharacteristic
395C3⋊D3—22no—
396C3⋊D3—41no—
397C3⋊D3—42no—
398C24—91no—
399C24—181no—
400#41—21no—
401#41—21no—
402#41—92no—
403#41—92no—
404#41—184no—
405#41—184no—
406#41—182no—
407#41—184no—
408#41—184no—
409#41—182no—
410#41—182no—
411#41—182no—
412#41—181no—
413#41—181no—
414#41C4⋊(C3⋊D3)12yes—
415#41#63812yes—
416C2×Q8—91no—
417C2×Q8—181no—
418C2×Q8—182no—
419C2×Q8—182no—
420C2×Q8C4×C3⋊D311yescharacteristic
421C2×D4—21no—
422C2×D4—91no—
423C2×D4—181no—
424C2×D4—181no—
425C2×D4—182no—
426C2×D4—184no—
427C2×D4—184no—
428C2×D4—181no—
429C2×D4—181no—
430C2×D4—182no—
431C2×D4C4×C3⋊D311yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—181no—
440C22×C4—181no—
441C22×C4—184no—
442C22×C4—184no—
443C22×C4—181no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—181no—
447C22×C4—181no—
448C22×C4—181no—
449C22×C4—181no—
450C22×C4C22×C3⋊D311yescharacteristic
451M16—21no—
452M16—21no—
453M16—181no—
454M16—181no—
455C2×C8—21no—
456C2×C8—181no—
457C22⋊C4—184no—
458C42—21no—
459C42—21no—
460C42—181no—
461C42—181no—
462C22×C3—24no—
463C22×C3—24no—
464C22×C3—28no—
465C22×C3—44no—
466C22×C3—44no—
467C22×C3D3×C22⋊C414yes—
468C22×C3#88214yes—
469C22×C3#93714yes—
470C2×D3—38no—
471C2×D3—64no—
472C2×D3—64no—
473C2×D3—68no—
474C2×D3—64no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—128no—
478C2×D3—128no—
479C2×D3—1232no—
480C2×D3—124no—
481C2×D3—124no—
482C3×C4—28no—
483C3×C4—48no—
484C3×C4D3×C22⋊C414yes—
485C3×C4#88214yes—
486C3×C4C2×(C2×D3)⋊C414yes—
487C3×C4#93714yes—
488Dic3—68no—
489Dic3—64no—
490Dic3—64no—
491Dic3—128no—
492C32#178911yescharacteristic, complemented, Sylow
493C23—21no—
494C23—91no—
495C23—91no—
496C23—182no—
497C23—184no—
498C23—181no—
499C23—181no—
500C23—181no—
501C23—361no—
502C23—362no—
503C23—362no—
504C23D4×C3⋊D311yescharacteristic
505Q8—21no—
506Q8—92no—
507Q8—184no—
508Q8—181no—
509Q8#375212yescomplemented
510D4—22no—
511D4—22no—
512D4—21no—
513D4—92no—
514D4—184no—
515D4—184no—
516D4—184no—
517D4—182no—
518D4—182no—
519D4—181no—
520D4#375212yescomplemented
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—91no—
528C2×C4—91no—
529C2×C4—184no—
530C2×C4—184no—
531C2×C4—184no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—182no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—361no—
547C2×C4—361no—
548C2×C4C2×C4×C3⋊D311yescharacteristic
549C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
550C2×C4D4×C3⋊D311yescharacteristic
551C2×C4D4×C3⋊D311yescharacteristic
552C2×C4D4×C3⋊D311yescharacteristic
553C2×C4C2×#63811yescharacteristic
554C8—41no—
555C8—361no—
556C2×C3—24no—
557C2×C3—24no—
558C2×C3—48no—
559C2×C3D3×#10414yes—
560C2×C3#482114yes—
561C2×C3#495514yes—
562D3—68no—
563D3—124no—
564D3—128no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—92no—
571C22—181no—
572C22—181no—
573C22—181no—
574C22—181no—
575C22—182no—
576C22—181no—
577C22—362no—
578C22—362no—
579C22—368no—
580C22—361no—
581C22—361no—
582C22C22⋊C4×C3⋊D311yescharacteristic
583C22#6409111yescharacteristic
584C22#6414611yescharacteristic
585C4—22no—
586C4—42no—
587C4—181no—
588C4—181no—
589C4—182no—
590C4—362no—
591C4C22⋊C4×C3⋊D311yescharacteristic
592C4#6409111yescharacteristic
593C4C2×#375211yescharacteristic
594C4#6414611yescharacteristic
595C3#7038014yescomplemented
596C2—21no—
597C2—21no—
598C2—42no—
599C2—182no—
600C2—361no—
601C2—362no—
602C2C3⋊D3×#10411yescharacteristic
603C2#1059252011yescharacteristic
604C2#1059265411yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radicalC2×#41×C3⋊D3C2
cosocleC22×C32×C4C23
hypercenterC2×#104C3⋊D3
hypocenterC32#1789
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C32×#104C2semidirect
3. C2×#63664C2semidirect
4. C2×#63652C2semidirect
5. #10592825C2semidirect
6. C4×#3752C2semidirect
7. C2×#63632C2semidirect
14. C2×#3832C4semidirect
15. C2×Q8×C3⋊D3C4semidirect
17. C2×#3830C4semidirect
19. C2×D4×C3⋊D3C4semidirect
24. C2×C32×M16C22semidirect
25. C2×C32×C42C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
28. C2×#3748C22semidirect
37. C2×C3×#104D3semidirect
123. C2×C3×M16C2×D3semidirect
124. C2×C3×C42C2×D3semidirect
148. C32×Q8C22⋊C4semidirect
152. C32×D4C22⋊C4semidirect
180. C4⋊(C3⋊D3)C22⋊C4semidirect
195. #634C22⋊C4semidirect
202. C2×#104C3⋊D3semidirect
288. C2×C3⋊D3#104semidirect
315. C2×M16C2×C3⋊D3semidirect
318. C2×C42C2×C3⋊D3semidirect
339. C3×Q8(C2×D3)⋊C4semidirect
343. C3×D4(C2×D3)⋊C4semidirect
492. C32#1789semidirect
509. Q8#3752semidirect
520. D4#3752semidirect
595. C3#70380semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×C32×#1042
C2×#636642
C2×#636522
#105928252
C4×#37522
C2×#636322
#703803