Finite Group Databasebeta

← #11788643

Subgroups — #11788643

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3#10591106C211yesmaximal, characteristic, complemented
4C2×#63564C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#69006—31nomaximal
9#68948—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64117—22no—
14#64117C414yescomplemented
15C2×#3745—21no—
16C2×#3744—21no—
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—
25#63567—21no—
26#63564—21no—
27#63564—21no—
28#63564—21no—
29#63559—22no—
30C2×#908—31no—
31C2×#908—31no—
32C2×#908—61no—
33C2×#907—31no—
34C2×#901—31no—
35#5133—31no—
36C2×#823—31no—
37C2×#823—31no—
38C2×#821—31no—
39#4966—31no—
40C2×#809—31no—
41C3×#343—31no—
42C3×#341—31no—
43#4558D311yescharacteristic, complemented
44#4554D311yescharacteristic, complemented
45C23×C3⋊D3—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48#3828—21no—
49#3828—21no—
50#3828C2×C412yes—
51#3828D412yes—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2×C412yes—
58C2×C4⋊(C3⋊D3)D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634D411yescharacteristic
61C22×C3×Dic3—21no—
62C32×M16—21no—
63C32×M16C2×C412yes—
64C2×C32×C8—21no—
65#3745—24no—
66#3744—24no—
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#1907—91noSylow
82C2×#235—31no—
83C2×#235—31no—
84C2×#235—61no—
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C2×C3×M16—21no—
89C2×C3×M16—31no—
90C2×C3×M16—31no—
91C2×C3×M16C2×D311yescharacteristic
92C2×C3×M16C2×D311yescharacteristic
93C22×C3×C8—31no—
94C2×C3×C4⋊C4—31no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×#208C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C22×C3⋊C8C2×D311yescharacteristic
99#908—34no—
100#908—34no—
101#908—64no—
102#908—62no—
103#908—62no—
104#908—64no—
105#907—62no—
106#907—62no—
107C2×D24—61no—
108C2×D24—61no—
109C2×D24—62no—
110C2×#204—61no—
111C2×#204—61no—
112C2×#204—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—
119#823—62no—
120#823—62no—
121#821—61no—
122#821—61no—
123#821—61no—
124#816—61no—
125#810—61no—
126#809—61no—
127#809—61no—
128#809—61no—
129C23×C32#4111yescharacteristic
130C22×C3⋊D3—21no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—41no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3—81no—
135C22×C3⋊D3—81no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142#638—22no—
143#638—22no—
144C2×C3⋊Dic3—21no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)—41no—
149C4⋊(C3⋊D3)—41no—
150C4⋊(C3⋊D3)C22⋊C412yes—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153#634—21no—
154#634C22⋊C412yes—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—81no—
157C32×C8—22no—
158C3×C3⋊C8—21no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—21no—
161C3×C3⋊C8—41no—
162C2×AGL(1,ℤ/8)—91no—
163C2×#131—91no—
164#417—91no—
165C2×#102—91no—
166C2×#100—91no—
167#343—31no—
168#341—31no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C22×C3×C4—21no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C2×#67—61no—
177C2×#67—61no—
178C2×#67—121no—
179C22×Dic3—21no—
180#235—32no—
181#235—32no—
182#235—32no—
183#235—32no—
184#235—62no—
185#235—62no—
186#235—61no—
187#235—61no—
188#235—61no—
189#235—61no—
190#235—121no—
191#235—121no—
192C2×D12—31no—
193C2×D12—31no—
194C2×D12—32no—
195C2×D12—32no—
196C2×D12—61no—
197C2×D12—62no—
198C2×D12—62no—
199C2×D12—62no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—121no—
211C2×D12—121no—
212C2×D12—121no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—121no—
216C2×Dic6—31no—
217C2×Dic6—31no—
218C2×Dic6—61no—
219C3×M16—22no—
220C3×M16—21no—
221C3×M16—21no—
222C3×M16—22no—
223C3×M16—32no—
224C3×M16—61no—
225C3×M16—61no—
226C3×M16—61no—
227C3×M16C4×D312yes—
228C3×M16C4×D312yes—
229C2×C3×C8—22no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—31no—
233C2×C3×C8—31no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242#208—21no—
243#208—21no—
244#208—21no—
245#208D1212yes—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8D1211yescharacteristic
251C2×C3⋊C8D1211yescharacteristic
252D24—64no—
253D24—64no—
254D24—68no—
255#204—64no—
256#204—64no—
257#204—68no—
258ΓL(1,𝔽25)—64no—
259ΓL(1,𝔽25)—64no—
260D3×C8—64no—
261D3×C8—64no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32C4×D411yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12311yescharacteristic
267C2×C3⋊D3—22no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—41no—
270C2×C3⋊D3—41no—
271C2×C3⋊D3—82no—
272C2×C3⋊D3—81no—
273C2×C3⋊D3—81no—
274C2×C3⋊D3—82no—
275C32×C4C2×C22⋊C411yescharacteristic
276C32×C4C4×D411yescharacteristic
277C32×C4#12011yescharacteristic
278C32×C4#12111yescharacteristic
279C3⋊Dic3—22no—
280C3×Dic3—81no—
281C2×#41—91no—
282C22×D4—91no—
283AGL(1,ℤ/8)—94no—
284AGL(1,ℤ/8)—182no—
285C2×SD16—181no—
286C2×D8—181no—
287#131—182no—
288#131—182no—
289C2×M16—31no—
290C2×M16—31no—
291C2×M16—181no—
292C2×M16D3211yescharacteristic
293C22×C8—31no—
294C22×C8—181no—
295C2×C4⋊C4—31no—
296#103—181no—
297#102—181no—
298#102—181no—
299#102—181no—
300#100—182no—
301C23×C3—21no—
302C23×C3#23511yescharacteristic
303C23×C3#23911yescharacteristic
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—121no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—121no—
313C22×D3—121no—
314C22×D3—121no—
315C22×D3—121no—
316C22×D3—242no—
317C22×D3—242no—
318C22×D3—241no—
319C22×D3—241no—
320C22×D3—241no—
321C22×D3—241no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—121no—
329C2×C3×C4—241no—
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4#23511yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4#23911yescharacteristic
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—64no—
357D12—62no—
358D12—62no—
359D12—62no—
360D12—61no—
361D12—62no—
362D12—61no—
363D12—122no—
364D12—121no—
365D12—122no—
366D12—122no—
367D12—121no—
368D12—121no—
369D12—121no—
370D12—121no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—122no—
376C4×D3—122no—
377Dic6—32no—
378Dic6—32no—
379Dic6—62no—
380Dic6—61no—
381Dic6—61no—
382Dic6—121no—
383C3×C8—24no—
384C3×C8—22no—
385C3×C8—22no—
386C3×C8—61no—
387C3×C8—62no—
388C3×C8—61no—
389C3×C8—121no—
390C3⋊C8—21no—
391C3⋊C8—22no—
392C3⋊C8—21no—
393C3⋊C8—41no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32#38611yescharacteristic
397C2×C32#47111yescharacteristic
398C2×C32#47211yescharacteristic
399C3⋊D3—42no—
400C3⋊D3—82no—
401C24—181no—
402#41—92no—
403#41—92no—
404#41—181no—
405#41—181no—
406C2×Q8—91no—
407C2×D4—92no—
408C2×D4—91no—
409C2×D4—181no—
410C2×D4—181no—
411C2×D4—181no—
412C2×D4—181no—
413C2×D4—181no—
414C2×D4—181no—
415C22×C4—61no—
416C22×C4—181no—
417C22×C4C2×D3211yescharacteristic
418SD16—184no—
419D8—184no—
420M16—21no—
421M16—32no—
422M16—61no—
423M16—61no—
424M16—61no—
425M16—184no—
426M16#62412yes—
427C2×C8—21no—
428C2×C8—31no—
429C2×C8—31no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8—184no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3C4×D1211yescharacteristic
447C22×C3#88411yescharacteristic
448C22×C3#89311yescharacteristic
449C22×C3#89411yescharacteristic
450C22×C3#89411yescharacteristic
451C22×C3#89511yescharacteristic
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—122no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—124no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—241no—
463C2×D3—241no—
464C2×D3—242no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—242no—
468C2×D3—244no—
469C2×D3—244no—
470C2×D3—241no—
471C2×D3—241no—
472C2×D3—241no—
473C2×D3—241no—
474C2×D3—242no—
475C2×D3—242no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—241no—
481C3×C4C4×D1211yescharacteristic
482C3×C4D3×C22⋊C411yescharacteristic
483C3×C4D3×C22⋊C411yescharacteristic
484C3×C4#88211yescharacteristic
485C3×C4#88211yescharacteristic
486C3×C4#88411yescharacteristic
487C3×C4#89311yescharacteristic
488C3×C4#89511yescharacteristic
489Dic3—62no—
490Dic3—62no—
491Dic3—81no—
492Dic3—122no—
493C32#190711yescharacteristic, complemented, Sylow
494C23—181no—
495C23—182no—
496C23—361no—
497C23—361no—
498C23—721no—
499C23—721no—
500C23#379911yescharacteristic
501Q8—92no—
502Q8—181no—
503D4—92no—
504D4—182no—
505D4—182no—
506D4—182no—
507D4—181no—
508D4—182no—
509D4—361no—
510D4—361no—
511C2×C4—121no—
512C2×C4—181no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—241no—
516C2×C4#379911yescharacteristic
517C2×C4D3×D1211yescharacteristic
518C2×C4D3×D1211yescharacteristic
519C2×C4C2×#62411yescharacteristic
520C2×C4#381111yescharacteristic
521C2×C4#381111yescharacteristic
522C8—22no—
523C8—61no—
524C8—61no—
525C8—62no—
526C8—121no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—41no—
535C2×C3—41no—
536C2×C3#466511yescharacteristic
537C2×C3#466511yescharacteristic
538C2×C3#474911yescharacteristic
539C2×C3#475411yescharacteristic
540C2×C3#489711yescharacteristic
541C2×C3#489811yescharacteristic
542D3—122no—
543D3—122no—
544D3—242no—
545D3—244no—
546D3—242no—
547D3—242no—
548C22—21no—
549C22—21no—
550C22—182no—
551C22—361no—
552C22—361no—
553C22—362no—
554C22—722no—
555C22—722no—
556C22—721no—
557C22—721no—
558C22#6389411yescharacteristic
559C22#6389711yescharacteristic
560C22#6391011yescharacteristic
561C4—182no—
562C4—241no—
563C4#6389411yescharacteristic
564C4#6391011yescharacteristic
565C4#6392311yescharacteristic
566C4#6397411yescharacteristic
567C3—21no—
568C3#6894811yescharacteristic, complemented
569C3#6900611yescharacteristic, complemented
570C2—21no—
571C2—21no—
572C2—362no—
573C2—722no—
574C2#1059098711yescharacteristic
575C2#1059099011yescharacteristic
576C2#1059138011yescharacteristic
subgroupG/H
centerC22#63910
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#64117C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1907
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. #10591106C2semidirect
4. C2×#63564C2semidirect
5. C2×#63559C2semidirect
6. C3×#4558C2semidirect
7. C3×#4554C2semidirect
14. #64117C4semidirect
43. #4558D3semidirect
44. #4554D3semidirect
493. C32#1907semidirect
568. C3#68948semidirect
569. C3#69006semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
C2×#638172
#105911062
C2×#635642
C2×#635592
C3×#45582
C3×#45542
#690063
#689483