Finite Group Databasebeta

← #11791194

Subgroups — #11791194

Order 1152.

679 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63829C211yesmaximal, characteristic
2#10592809C211yesmaximal, characteristic, complemented
3C3×#5110C211yesmaximal, characteristic, complemented
4C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
5C2×#63577C211yesmaximal, characteristic, complemented
6C2×#63570C211yesmaximal, characteristic, complemented
7C2×#63569C211yesmaximal, characteristic, complemented
8#69999—31nomaximal
9#69795—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3719C411yescharacteristic, complemented
18C2×#3717C411yescharacteristic, complemented
19#63829—22no—
20#63829—22no—
21C2×#3716C411yescharacteristic, complemented
22C2×#3714C411yescharacteristic, complemented
23#63647—22no—
24C3×(C2×D3)⋊C8—22no—
25C3×C8×Dic3—22no—
26#63577—22no—
27#63570—22no—
28#63569—22no—
29C2×#950—31no—
30C2×#904—31no—
31C3×#408—31no—
32C2×C3×C4×C8—31no—
33C2×#837—31no—
34C2×#825—31no—
35C2×#822—31no—
36#5110—31no—
37#5110—31no—
38#5110—61no—
39#5110D311yescharacteristic, complemented
40C2×#819—31no—
41C2×C8×Dic3D311yescharacteristic, complemented
42C2×#805—31no—
43C2×#805—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634C2×C411yescharacteristic
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C2×C3×D12C2×C411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×Dic6C2×C411yescharacteristic
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8D412yes—
65#3748—21no—
66#3748—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3D412yes—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8C2×C411yescharacteristic
74C2×C3×C3⋊C8C2×C411yescharacteristic
75C2×C3×C3⋊C8D412yes—
76C2×C3×C3⋊C8D412yes—
77#3719—22no—
78#3717—22no—
79#3716—22no—
80#3714—22no—
81#1974—91noSylow
82C2×C3×#41—31no—
83C2×#235—31no—
84C2×#235—31no—
85C2×#235—61no—
86C2×#235C2×D311yescharacteristic
87C2×C3×M16—31no—
88C22×C3×C8—21no—
89C22×C3×C8—31no—
90C22×C3×C8C2×D311yescharacteristic
91C22×C3×C8C2×D311yescharacteristic
92C2×C3×C42—31no—
93#950—62no—
94#950—62no—
95C2×#216—31no—
96C2×#215—31no—
97C2×#214—31no—
98C2×#213—31no—
99C2×C4×Dic3C2×D311yescharacteristic
100C2×#208—31no—
101C2×#208—31no—
102C2×#208—61no—
103C2×#208C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105C2×Dic12—31no—
106#904—62no—
107#904—62no—
108C2×D24—31no—
109C2×#204—31no—
110C2×#204—31no—
111C3×C22⋊C8—62no—
112C3×C4×C8—62no—
113#837—62no—
114#825—62no—
115#822—62no—
116(C2×D3)⋊C8—22no—
117(C2×D3)⋊C8—64no—
118(C2×D3)⋊C8—62no—
119(C2×D3)⋊C8—62no—
120#819—62no—
121C8×Dic3—22no—
122#805—62no—
123#805—62no—
124C23×C32#4111yescharacteristic
125C22×C3⋊D3—21no—
126C22×C3×D3—21no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133#638—41no—
134#638—41no—
135C2×C3⋊Dic3—21no—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)—21no—
138C4×C3⋊D3—41no—
139C4×C3⋊D3—41no—
140#634—21no—
141#634—21no—
142C3×#67—41no—
143C3×#67—41no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—21no—
147C3×D12—21no—
148C3×D12—21no—
149C3×C4×D3—41no—
150C3×C4×D3—41no—
151C3×Dic6—21no—
152C3×Dic6—21no—
153C32×C8—22no—
154C3⋊(C3⋊C8)—41no—
155C3×C3⋊C8—41no—
156C3×C3⋊C8C22⋊C412yes—
157C3×C3⋊C8C22⋊C412yes—
158C2×#135—91no—
159C2×#108—91no—
160C2×#104—91no—
161C2×#104—91no—
162#408—31no—
163#408—91no—
164C2×C4×C8—31no—
165C3×#41—61no—
166C3×#41—61no—
167C3×#41—61no—
168C3×#41—61no—
169C2×C3×Q8—31no—
170C2×C3×D4—31no—
171C2×C3×D4—61no—
172C22×C3×C4—21no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—21no—
178C2×#67—62no—
179C2×#67—61no—
180C2×#67—61no—
181C22×Dic3—21no—
182#235—21no—
183#235—21no—
184#235—21no—
185#235—21no—
186#235—61no—
187#235—61no—
188#235—61no—
189#235—61no—
190#235—61no—
191#235—61no—
192#235—61no—
193#235—61no—
194#235—121no—
195#235—121no—
196#235—121no—
197#235—121no—
198C2×D12—31no—
199C2×D12—31no—
200C2×D12—61no—
201C2×D12C4×D311yescharacteristic
202C2×C4×D3—21no—
203C2×C4×D3—62no—
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×Dic6—31no—
207C2×Dic6—31no—
208C2×Dic6—61no—
209C2×Dic6C4×D311yescharacteristic
210C3×M16—61no—
211C3×M16—61no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—22no—
217C2×C3×C8—31no—
218C2×C3×C8—31no—
219C2×C3×C8—32no—
220C2×C3×C8—32no—
221C2×C3×C8—41no—
222C2×C3×C8—41no—
223C2×C3×C8—61no—
224C2×C3×C8D1212yes—
225C2×C3×C8#6712yes—
226C3×C42—32no—
227C3×C42—61no—
228#216—62no—
229#215—62no—
230#214—62no—
231#213—62no—
232C4×Dic3—21no—
233C4×Dic3D1212yes—
234#208—21no—
235#208—21no—
236#208—61no—
237#208—61no—
238#208—61no—
239#208—61no—
240#208—121no—
241#208—121no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8C4×D311yescharacteristic
247C2×C3⋊C8C4×D311yescharacteristic
248C2×C3⋊C8D1212yes—
249C2×C3⋊C8#6712yes—
250Dic12—62no—
251D24—62no—
252#204—62no—
253#204—62no—
254C22×C32—22no—
255C22×C32C4×D411yescharacteristic
256C22×C32#12111yescharacteristic
257C22×C32#12411yescharacteristic
258C2×C3⋊D3—41no—
259C2×C3⋊D3—42no—
260C2×C3×D3—41no—
261C2×C3×D3—42no—
262C32×C4C2×C22⋊C411yescharacteristic
263C32×C4C4×D411yescharacteristic
264C32×C4#12111yescharacteristic
265C32×C4#12711yescharacteristic
266C3⋊Dic3—41no—
267C3×Dic3—24no—
268C3×Dic3—41no—
269C2×#41—31no—
270C2×#41—91no—
271#135—182no—
272#135—182no—
273C2×Q16—91no—
274C2×SD16—91no—
275C2×SD16—91no—
276C2×D8—91no—
277C2×M16—31no—
278C2×M16—91no—
279C22×C8—31no—
280C22×C8D3211yescharacteristic
281C2×C42—31no—
282#108—182no—
283#104—182no—
284#104—182no—
285C22⋊C8—62no—
286C22⋊C8—182no—
287C4×C8—62no—
288C23×C3—21no—
289C23×C3—61no—
290C23×C3#23511yescharacteristic
291C23×C3#23511yescharacteristic
292C22×D3—21no—
293C22×D3—62no—
294C22×D3—61no—
295C22×D3—61no—
296C3×Q8—61no—
297C3×Q8—61no—
298C3×D4—61no—
299C3×D4—61no—
300C3×D4—121no—
301C3×D4—121no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—64no—
309C2×C3×C4—62no—
310C2×C3×C4—61no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4C2×D1211yescharacteristic
317C2×C3×C4C2×D1211yescharacteristic
318C2×C3×C4#23511yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325#67—41no—
326#67—41no—
327#67—122no—
328#67—122no—
329#67—121no—
330#67—121no—
331#67—121no—
332#67—121no—
333C2×Dic3—24no—
334C2×Dic3—22no—
335C2×Dic3—21no—
336C2×Dic3—62no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339D12—21no—
340D12—21no—
341D12—61no—
342D12—61no—
343D12—61no—
344D12—61no—
345D12—121no—
346D12—121no—
347C4×D3—41no—
348C4×D3—41no—
349C4×D3—122no—
350C4×D3—122no—
351C4×D3—121no—
352C4×D3—121no—
353C4×D3—121no—
354C4×D3—121no—
355Dic6—21no—
356Dic6—21no—
357Dic6—61no—
358Dic6—61no—
359Dic6—61no—
360Dic6—61no—
361Dic6—121no—
362Dic6—121no—
363C3×C8—22no—
364C3×C8—22no—
365C3×C8—32no—
366C3×C8—32no—
367C3×C8—42no—
368C3×C8—121no—
369C3⋊C8—41no—
370C3⋊C8—122no—
371C3⋊C8—121no—
372C3⋊C8—121no—
373C3⋊C8(C2×D3)⋊C412yes—
374C3⋊C8(C2×D3)⋊C412yes—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32#39011yescharacteristic
378C2×C32#44312yes—
379C3⋊D3—81no—
380C3×D3—81no—
381#41—61no—
382#41—61no—
383#41—61no—
384#41—61no—
385#41—181no—
386#41—181no—
387#41—181no—
388#41—181no—
389C2×Q8—31no—
390C2×Q8—91no—
391C2×D4—31no—
392C2×D4—61no—
393C2×D4—91no—
394C2×D4—181no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—181no—
398C22×C4C2×D3211yescharacteristic
399Q16—182no—
400SD16—182no—
401SD16—182no—
402D8—182no—
403M16—61no—
404M16—61no—
405M16—181no—
406M16—181no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8—32no—
412C2×C8—32no—
413C2×C8—61no—
414C2×C8—181no—
415C2×C8#62612yes—
416C42—32no—
417C42—61no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—42no—
424C22×C3—121no—
425C22×C3—122no—
426C22×C3C4×D1211yescharacteristic
427C22×C3#87511yescharacteristic
428C22×C3#88411yescharacteristic
429C22×C3#88511yescharacteristic
430C22×C3C4×#6711yescharacteristic
431C22×C3#93011yescharacteristic
432C2×D3—42no—
433C2×D3—41no—
434C2×D3—122no—
435C2×D3—124no—
436C2×D3—122no—
437C2×D3—121no—
438C2×D3—122no—
439C2×D3—121no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—64no—
445C3×C4—121no—
446C3×C4C4×D1211yescharacteristic
447C3×C4#87411yescharacteristic
448C3×C4D3×C22⋊C411yescharacteristic
449C3×C4#67⋊C411yescharacteristic
450C3×C4C2×(C2×D3)⋊C411yescharacteristic
451C3×C4#93011yescharacteristic
452C3×C4#93911yescharacteristic
453C3×C4#94011yescharacteristic
454Dic3—24no—
455Dic3—41no—
456Dic3—122no—
457Dic3—121no—
458Dic3—121no—
459C32#197411yescharacteristic, complemented, Sylow
460C23—61no—
461C23—181no—
462C23#379811yescharacteristic
463Q8—61no—
464Q8—61no—
465Q8—181no—
466Q8—181no—
467D4—61no—
468D4—61no—
469D4—121no—
470D4—121no—
471D4—181no—
472D4—181no—
473D4—361no—
474D4—361no—
475C2×C4—64no—
476C2×C4—62no—
477C2×C4—61no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—181no—
481C2×C4—361no—
482C2×C4—361no—
483C2×C4C4×D3211yescharacteristic
484C2×C4D3×D1211yescharacteristic
485C2×C4D3×D1211yescharacteristic
486C2×C4#380411yescharacteristic
487C2×C4C2×#62611yescharacteristic
488C2×C4D3×#6711yescharacteristic
489C8—22no—
490C8—32no—
491C8—32no—
492C8—121no—
493C8—361no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—22no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3—241no—
503C2×C3#470012yes—
504C2×C3#493911yescharacteristic
505C2×C3#495711yescharacteristic
506C2×C3#514412yes—
507D3—81no—
508D3—242no—
509D3—241no—
510D3—241no—
511C22—22no—
512C22—121no—
513C22—122no—
514C22—361no—
515C22—362no—
516C22#6385211yescharacteristic
517C22C4×#62611yescharacteristic
518C22#6390611yescharacteristic
519C4—64no—
520C4—121no—
521C4—361no—
522C4#6388011yescharacteristic
523C4#6391111yescharacteristic
524C4D3×(C2×D3)⋊C411yescharacteristic
525C4#6397811yescharacteristic
526C3—21no—
527C3#6979511yescharacteristic, complemented
528C3#6999911yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—241no—
532C2—721no—
533C2#1059092312yes—
534C2#1059138311yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×#63829C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1974
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10592809C2semidirect
3. C3×#5110C2semidirect
4. C2×C3×C8×Dic3C2semidirect
5. C2×#63577C2semidirect
6. C2×#63570C2semidirect
7. C2×#63569C2semidirect
17. C2×#3719C4semidirect
18. C2×#3717C4semidirect
21. C2×#3716C4semidirect
22. C2×#3714C4semidirect
39. #5110D3semidirect
41. C2×C8×Dic3D3semidirect
459. C32#1974semidirect
527. C3#69795semidirect
528. C3#69999semidirect

Maximal subgroups

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

subgroupindex
C2×#638292
#105928092
C3×#51102
C2×C3×C8×Dic32
C2×#635772
C2×#635702
C2×#635692
#699993
#697953