Finite Group Databasebeta

← #11788683

Subgroups — #11788683

Order 1152.

753 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64151C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic
3C2×C3×#836C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591106C211yesmaximal, characteristic
6#10589167C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70286—31nomaximal
9#70123—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C2×#3756—21no—
13#64151—22no—
14#64151C414yescomplemented
15C2×#3755—21no—
16C2×#3748C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3712—21no—
22#63817—22no—
23#63817—22no—
24C2×#3710—21no—
25C3×#836—22no—
26C3×#835—21no—
27C3×#835—21no—
28#63567—21no—
29#63564—21no—
30C2×#942—31no—
31C2×#942—31no—
32C2×#942—61no—
33C2×#907—31no—
34C2×#901—31no—
35C2×C3×#103—31no—
36C2×C3×#101—31no—
37C2×#836D311yescharacteristic, complemented
38C2×#835D311yescharacteristic, complemented
39#5133—31no—
40#4966—31no—
41#4558—31no—
42#4554—31no—
43#4552—31no—
44#4530—31no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8C2×C412yes—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—21no—
55#3828—21no—
56#3828C2×C412yes—
57#3828D412yes—
58C2×C4⋊(C3⋊D3)D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634D411yescharacteristic
61C22×C3×Dic3—21no—
62#3756—24no—
63#3755—24no—
64#3748—21no—
65#3748C2×C412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208D412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D411yescharacteristic
78C2×C3×C3⋊C8D411yescharacteristic
79#3712—24no—
80#3710—24no—
81#1908—91noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8C2×D311yescharacteristic
84C22×C3×Q8C2×D311yescharacteristic
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C22×C3×C8—31no—
91C2×C3×C4⋊C4—31no—
92C2×#216—61no—
93C2×#216—61no—
94C2×#216—62no—
95#942—34no—
96#942—34no—
97#942—64no—
98#942—62no—
99#942—62no—
100#942—64no—
101C2×#215—61no—
102C2×#215—61no—
103C2×#215—62no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109C2×#208C2×D311yescharacteristic
110C22×C3⋊C8C2×D311yescharacteristic
111#907—62no—
112#907—62no—
113#901—62no—
114#901—62no—
115C2×ΓL(1,𝔽25)—61no—
116C2×ΓL(1,𝔽25)—61no—
117C2×D3×C8—61no—
118C2×D3×C8—61no—
119C3×#103—61no—
120C3×#103—61no—
121C3×#101—62no—
122#836—22no—
123#835—21no—
124#835—21no—
125#821—61no—
126#816—61no—
127#810—61no—
128#809—61no—
129C23×C32#4111yescharacteristic
130C22×C3⋊D3—21no—
131C32×Q8—22no—
132C32×Q8—22no—
133C32×Q8—41no—
134C32×Q8—41no—
135C2×C32×C4—22no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144#638—22no—
145#638—22no—
146C2×C3⋊Dic3—21no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)C22⋊C412yes—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151#634—21no—
152#634C22⋊C412yes—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—81no—
155C3⋊(C3⋊C8)—22no—
156C3×C3⋊C8—21no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8—21no—
159C3×C3⋊C8—41no—
160C2×#137—91no—
161C2×#131—91no—
162#417—91no—
163C2×#103—31no—
164C2×#101—31no—
165#343—91no—
166#341—91no—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—22no—
170C2×C3×Q8—22no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—22no—
180C2×C3×Q8—41no—
181C2×C3×Q8—41no—
182C2×C3×Q8—41no—
183C2×C3×Q8C4×D312yes—
184C2×C3×Q8C4×D312yes—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—41no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—61no—
193C2×#67—61no—
194C2×#67—121no—
195C22×Dic3—21no—
196#235—32no—
197#235—32no—
198#235—32no—
199#235—32no—
200#235—62no—
201#235—62no—
202#235—61no—
203#235—61no—
204#235—61no—
205#235—61no—
206#235—121no—
207#235—121no—
208C2×D12—31no—
209C2×D12—31no—
210C2×D12—61no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—121no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C3×M16—32no—
218C3×M16—61no—
219C3×M16—61no—
220C3×M16—61no—
221C2×C3×C8—31no—
222C2×C3×C8—31no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229#216—64no—
230#216—64no—
231#216—68no—
232#215—64no—
233#215—64no—
234#215—68no—
235C4⋊Dic3—21no—
236C4⋊Dic3—21no—
237#208—21no—
238#208—21no—
239#208—21no—
240#208—32no—
241#208—32no—
242#208—62no—
243#208—62no—
244#208—61no—
245#208—61no—
246#208#6712yes—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8#6711yescharacteristic
255C2×C3⋊C8#6711yescharacteristic
256ΓL(1,𝔽25)—64no—
257ΓL(1,𝔽25)—64no—
258D3×C8—64no—
259D3×C8—64no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32C4×D411yescharacteristic
263C22×C32#12111yescharacteristic
264C22×C32#12311yescharacteristic
265C2×C3⋊D3—22no—
266C2×C3⋊D3—41no—
267C2×C3⋊D3—41no—
268C32×C4—42no—
269C32×C4C2×C22⋊C411yescharacteristic
270C32×C4C4×D411yescharacteristic
271C32×C4#12011yescharacteristic
272C32×C4#12111yescharacteristic
273C3⋊Dic3—22no—
274C3×Dic3—81no—
275C2×#41—91no—
276C22×Q8D3211yescharacteristic
277#137—94no—
278#137—182no—
279C2×Q16—181no—
280C2×SD16—181no—
281#131—182no—
282#131—182no—
283C2×M16—31no—
284C2×M16—31no—
285C2×M16—91no—
286C2×M16—181no—
287C22×C8—31no—
288C22×C8—181no—
289C2×C4⋊C4—31no—
290#103—61no—
291#103—61no—
292#103—181no—
293#102—181no—
294#101—62no—
295C23×C3—21no—
296C23×C3#23511yescharacteristic
297C23×C3#23711yescharacteristic
298C22×D3—61no—
299C22×D3—61no—
300C22×D3—121no—
301C3×Q8—24no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—42no—
307C3×Q8—42no—
308C3×Q8—42no—
309C3×Q8—41no—
310C3×Q8—41no—
311C3×Q8—41no—
312C3×Q8—41no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—121no—
329C2×C3×C4—241no—
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4#23711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342#67—62no—
343#67—62no—
344#67—62no—
345#67—62no—
346#67—122no—
347#67—122no—
348C2×Dic3—41no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—81no—
352C2×Dic3—121no—
353D12—32no—
354D12—32no—
355D12—62no—
356D12—61no—
357D12—61no—
358D12—121no—
359C4×D3—62no—
360C4×D3—62no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—122no—
364C4×D3—122no—
365Dic6—32no—
366Dic6—32no—
367Dic6—62no—
368Dic6—61no—
369Dic6—61no—
370Dic6—121no—
371C3×C8—61no—
372C3×C8—62no—
373C3×C8—61no—
374C3×C8—121no—
375C3⋊C8—21no—
376C3⋊C8—22no—
377C3⋊C8—21no—
378C3⋊C8—41no—
379C3⋊C8—64no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C2×C32—21no—
383C2×C32—21no—
384C2×C32#38611yescharacteristic
385C2×C32#47111yescharacteristic
386C2×C32#47311yescharacteristic
387C3⋊D3—42no—
388#41—92no—
389#41—92no—
390#41—181no—
391#41—181no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—91no—
398C2×Q8#62412yes—
399C2×D4—91no—
400C2×D4—181no—
401C22×C4—21no—
402C22×C4—61no—
403C22×C4—181no—
404C22×C4C2×D3211yescharacteristic
405Q16—184no—
406SD16—184no—
407M16—32no—
408M16—61no—
409M16—61no—
410M16—61no—
411M16—92no—
412M16—184no—
413M16—181no—
414C2×C8—31no—
415C2×C8—31no—
416C2×C8—61no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—61no—
420C2×C8—184no—
421C2×C8—181no—
422C4⋊C4—61no—
423C4⋊C4—61no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3#67⋊C411yescharacteristic
434C22×C3#88311yescharacteristic
435C22×C3#88311yescharacteristic
436C22×C3#88411yescharacteristic
437C22×C3C4×#6711yescharacteristic
438C22×C3#93811yescharacteristic
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—122no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—241no—
447C2×D3—241no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—44no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—241no—
456C3×C4D3×C22⋊C411yescharacteristic
457C3×C4D3×C22⋊C411yescharacteristic
458C3×C4#67⋊C411yescharacteristic
459C3×C4#88411yescharacteristic
460C3×C4C4×#6711yescharacteristic
461C3×C4#93711yescharacteristic
462C3×C4#93711yescharacteristic
463C3×C4#93811yescharacteristic
464Dic3—62no—
465Dic3—62no—
466Dic3—81no—
467Dic3—122no—
468C32#190811yescharacteristic, complemented, Sylow
469C23—181no—
470C23#380411yescharacteristic
471Q8—22no—
472Q8—22no—
473Q8—41no—
474Q8—41no—
475Q8—92no—
476Q8—181no—
477D4—92no—
478D4—182no—
479D4—182no—
480D4—181no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—121no—
485C2×C4—181no—
486C2×C4—182no—
487C2×C4—182no—
488C2×C4—241no—
489C2×C4#380411yescharacteristic
490C2×C4C2×#62411yescharacteristic
491C2×C4D3×#6711yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C2×C4#381111yescharacteristic
494C2×C4#381111yescharacteristic
495C8—61no—
496C8—61no—
497C8—62no—
498C8—121no—
499C8—182no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—41no—
508C2×C3—41no—
509C2×C3#475411yescharacteristic
510C2×C3#475511yescharacteristic
511C2×C3#495611yescharacteristic
512C2×C3#495611yescharacteristic
513C2×C3#517711yescharacteristic
514C2×C3#519211yescharacteristic
515D3—122no—
516D3—122no—
517D3—242no—
518C22—21no—
519C22—21no—
520C22—182no—
521C22—361no—
522C22—361no—
523C22#6395211yescharacteristic
524C22#6395811yescharacteristic
525C22#6397511yescharacteristic
526C4—42no—
527C4—182no—
528C4—241no—
529C4#6395211yescharacteristic
530C4#6395811yescharacteristic
531C4#6397411yescharacteristic
532C4#6398311yescharacteristic
533C3—21no—
534C3#7012311yescharacteristic, complemented
535C3#7028611yescharacteristic, complemented
536C2—21no—
537C2—21no—
538C2—362no—
539C2#1059154211yescharacteristic
540C2#1059154311yescharacteristic
541C2#1059172211yescharacteristic
subgroupG/H
centerC22#63958
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#121
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1908
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#836C2semidirect
4. C2×C3×#835C2semidirect
6. #10589167C2semidirect
7. #10589166C2semidirect
14. #64151C4semidirect
37. C2×#836D3semidirect
38. C2×#835D3semidirect
468. C32#1908semidirect
534. C3#70123semidirect
535. C3#70286semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
C2×#638172
C2×C3×#8362
C2×C3×#8352
#105911062
#105891672
#105891662
#702863
#701233