Finite Group Databasebeta

← #11786742

Subgroups — #11786742

Order 1152.

719 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic
2C2×C3×#837C211yesmaximal, characteristic
3C3×#5232C211yesmaximal, characteristic
4#10591224C211yesmaximal, characteristic, complemented
5#10591130C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70364—31nomaximal
9#70298—31nomaximal
10C2×C32×#41C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12D4×C3⋊Dic3—21no—
13D4×C3⋊Dic3—22no—
14#64135—21no—
15#64135C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#837C414yescomplemented
23C3×#835—21no—
24C3×#832—21no—
25#63579—22no—
26#63575—21no—
27#63573—21no—
28#5827—31no—
29#5827—31no—
30#5827—61no—
31C2×C3×#104—31no—
32C3×#417—31no—
33C2×#837D311yescharacteristic
34#5232D311yescharacteristic
35#5121—31no—
36#4977—31no—
37#4964—31no—
38#4936—31no—
39#4555—31no—
40#4554—31no—
41#4554—31no—
42#4523—31no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41C2×C412yes—
46C32×#41Q812yes—
47C2×C32×Q8D411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—22no—
53C22×C3⋊Dic3D412yes—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56#3757—22no—
57#3757—21no—
58C4⋊(C3⋊Dic3)—22no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)D411yescharacteristic
62C4⋊(C3⋊Dic3)D411yescharacteristic
63C4×C3⋊Dic3—22no—
64C4×C3⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C412yescomplemented
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yescomplemented
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#1860—91noSylow
76C2×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C2×D311yescharacteristic
79C2×C3×M16—31no—
80C2×C3×M16—31no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C42—31no—
83Q8×Dic3—62no—
84Q8×Dic3—61no—
85Q8×Dic3—61no—
86D4×Dic3—62no—
87D4×Dic3—62no—
88D4×Dic3—64no—
89D4×Dic3—62no—
90D4×Dic3—61no—
91D4×Dic3—61no—
92#926—31no—
93#926—31no—
94#926—61no—
95#926—61no—
96#926—61no—
97#926—62no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3—62no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4×Dic3C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107C2×#208C2×D311yescharacteristic
108C3×#104—34no—
109C3×#103—61no—
110C3×#102—61no—
111#837Dic314yescomplemented
112#835—21no—
113#832—21no—
114C3⋊#95—62no—
115C3⋊#95—62no—
116#818—61no—
117#817—61no—
118#808—61no—
119#807—61no—
120C23×C32—21no—
121C23×C32C2×D411yescharacteristic
122C32×Q8—21no—
123C32×Q8C4⋊C412yes—
124C32×D4—22no—
125C32×D4—22no—
126C32×D4—21no—
127C32×D4C4⋊C412yes—
128C2×C32×C4—21no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×Q811yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—42no—
141C2×C3⋊Dic3—82no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149#520—91no—
150#428—91no—
151C2×#104—31no—
152#417—31no—
153#382—91no—
154#343—91no—
155#339—91no—
156C3×#41—22no—
157C3×#41—22no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—21no—
162C3×#41—22no—
163C3×#41—22no—
164C3×#41Dic612yes—
165C3×#41Dic612yes—
166C3×#41C4×D312yes—
167C3×#41C2×Dic312yes—
168C2×C3×Q8—21no—
169C2×C3×Q8D1211yescharacteristic
170C2×C3×Q8#6711yescharacteristic
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4D1211yescharacteristic
176C2×C3×D4#6711yescharacteristic
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—62no—
190C22×Dic3—64no—
191C22×Dic3—62no—
192C22×Dic3—62no—
193C3×M16—32no—
194C3×M16—61no—
195C3×M16—61no—
196C3×M16—61no—
197C2×C3×C8—61no—
198C2×C3×C8—61no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C42—32no—
202C3×C42—61no—
203#217—64no—
204#217—62no—
205#217—62no—
206#217—62no—
207#217—61no—
208#217—61no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3—31no—
212C4⋊Dic3—31no—
213C4⋊Dic3—31no—
214C4⋊Dic3—31no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—62no—
218C4⋊Dic3—64no—
219C4⋊Dic3—62no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4×Dic3—21no—
227C4×Dic3—64no—
228C4×Dic3—62no—
229C4×Dic3—62no—
230C4×Dic3—62no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233C4×Dic3C2×Dic312yescomplemented
234#208—21no—
235#208—21no—
236#208—21no—
237#208C2×Dic312yescomplemented
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C22×C32—22no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—41no—
244C22×C32—41no—
245C22×C32C4×D411yescharacteristic
246C22×C32#12011yescharacteristic
247C22×C32C22⋊Q811yescharacteristic
248C32×C4—22no—
249C32×C4C2×C4⋊C411yescharacteristic
250C32×C4C4×D411yescharacteristic
251C32×C4C22⋊Q811yescharacteristic
252C32×C4#12311yescharacteristic
253C3⋊Dic3—41no—
254C3⋊Dic3—42no—
255C3⋊Dic3—41no—
256C3×Dic3—42no—
257C3×Dic3—81no—
258C2×#41D3211yescharacteristic
259C2×M16—31no—
260C2×M16—31no—
261C4×Q8—181no—
262C4×D4—182no—
263C4×D4—181no—
264#117—91no—
265#117—181no—
266C2×C4⋊C4—31no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—181no—
269C2×C42—31no—
270#107—181no—
271#106—181no—
272#104—34no—
273#103—61no—
274#102—61no—
275#95—182no—
276C23×C3—22no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3D3×D411yescharacteristic
281C23×C3D3×D411yescharacteristic
282C3×Q8—22no—
283C3×Q8—21no—
284C3×Q8—21no—
285C3×Q8—22no—
286C3×Q8Dic3⋊C412yes—
287C3×Q8C4⋊Dic312yes—
288C3×D4—24no—
289C3×D4—24no—
290C3×D4—22no—
291C3×D4—22no—
292C3×D4—22no—
293C3×D4—22no—
294C3×D4—22no—
295C3×D4—21no—
296C3×D4—21no—
297C3×D4—22no—
298C3×D4Dic3⋊C412yes—
299C3×D4C4⋊Dic312yes—
300C2×C3×C4—22no—
301C2×C3×C4—24no—
302C2×C3×C4—24no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—62no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—122no—
319C2×C3×C4—121no—
320C2×C3×C4C2×Dic611yescharacteristic
321C2×C3×C4C2×Dic611yescharacteristic
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4C2×D1211yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4#23711yescharacteristic
327C2×C3×C4#23711yescharacteristic
328C2×C3×C4#23711yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4C22×Dic311yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×Dic3—22no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—42no—
336C2×Dic3—41no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—64no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—62no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—242no—
349C2×Dic3—244no—
350C2×Dic3—242no—
351C2×Dic3—242no—
352C3×C8—62no—
353C3×C8—121no—
354C3⋊C8—22no—
355C3⋊C8—41no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32—42no—
359C2×C32#38511yescharacteristic
360C2×C32#45411yescharacteristic
361C2×C32#45511yescharacteristic
362#41—21no—
363#41—21no—
364#41D3×Dic312yes—
365#41#62712yes—
366C2×Q8#62611yescharacteristic
367C2×D4—21no—
368C2×D4#62611yescharacteristic
369C22×C4—21no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—92no—
373C22×C4—182no—
374C22×C4C2×D3211yescharacteristic
375M16—32no—
376M16—61no—
377M16—61no—
378M16—61no—
379C2×C8—61no—
380C2×C8—61no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—182no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C22⋊C4—182no—
389C22⋊C4—181no—
390C42—32no—
391C42—61no—
392C42—182no—
393C42—181no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—24no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3#87811yescharacteristic
413C22×C3#87811yescharacteristic
414C22×C3#67⋊C411yescharacteristic
415C22×C3#88211yescharacteristic
416C22×C3D4×Dic311yescharacteristic
417C22×C3#93711yescharacteristic
418C3×C4—24no—
419C3×C4—22no—
420C3×C4—22no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—122no—
426C3×C4—241no—
427C3×C4#87811yescharacteristic
428C3×C4#87811yescharacteristic
429C3×C4#67⋊C411yescharacteristic
430C3×C4#88611yescharacteristic
431C3×C4C2×Dic3⋊C411yescharacteristic
432C3×C4C2×C4⋊Dic311yescharacteristic
433C3×C4D4×Dic311yescharacteristic
434C3×C4#93511yescharacteristic
435Dic3—42no—
436Dic3—81no—
437Dic3—124no—
438Dic3—122no—
439Dic3—122no—
440Dic3—121no—
441Dic3—122no—
442Dic3—121no—
443Dic3—122no—
444Dic3—121no—
445Dic3—121no—
446C32#186011yescharacteristic, complemented, Sylow
447C23—21no—
448C23#381111yescharacteristic
449Q8—21no—
450Q8Dic3⋊Dic312yes—
451D4—22no—
452D4—22no—
453D4—21no—
454D4Dic3⋊Dic312yes—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—62no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—122no—
462C2×C4—121no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—182no—
466C2×C4—362no—
467C2×C4—722no—
468C2×C4C2×D3×Dic311yescharacteristic
469C2×C4#380511yescharacteristic
470C2×C4#380511yescharacteristic
471C2×C4C2×#62611yescharacteristic
472C2×C4C2×#62711yescharacteristic
473C2×C4#381111yescharacteristic
474C8—62no—
475C8—121no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3—44no—
486C2×C3—42no—
487C2×C3—42no—
488C2×C3#482511yescharacteristic
489C2×C3#482711yescharacteristic
490C2×C3#494611yescharacteristic
491C2×C3#495011yescharacteristic
492C2×C3#520111yescharacteristic
493C2×C3#520211yescharacteristic
494C22—21no—
495C22—21no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22#67⋊Dic311yescharacteristic
500C22#6398111yescharacteristic
501C22#6398211yescharacteristic
502C4—22no—
503C4—122no—
504C4—241no—
505C4—361no—
506C4—362no—
507C4—361no—
508C4#6396211yescharacteristic
509C4C2×Dic3⋊Dic311yescharacteristic
510C4#67⋊Dic311yescharacteristic
511C4#6398211yescharacteristic
512C3—21no—
513C3#7029811yescharacteristic, complemented
514C3#7036411yescharacteristic, complemented
515C2—21no—
516C2—21no—
517C2—42no—
518C2#1059168611yescharacteristic
519C2#1059169011yescharacteristic
520C2#1059171911yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#120
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1860
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591224C2semidirect
5. #10591130C2semidirect
6. #10589168C2semidirect
7. #10589162C2semidirect
22. C3×#837C4semidirect
68. C3×C4×Dic3C2×C4semidirect
72. C3×#208C2×C4semidirect
111. #837Dic3semidirect
233. C4×Dic3C2×Dic3semidirect
237. #208C2×Dic3semidirect
446. C32#1860semidirect
513. C3#70298semidirect
514. C3#70364semidirect

Maximal subgroups

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

subgroupindex
#105962982
C2×C3×#8372
C3×#52322
#105912242
#105911302
#105891682
#105891622
#703643
#702983