Finite Group Databasebeta

← #11788632

Subgroups — #11788632

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×#64158C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic, complemented
3C3×#5232C211yesmaximal, characteristic, complemented
4C2×#63564C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72018—31nomaximal
9#70303—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12#64158—22no—
13#64158C414yescomplemented
14C2×#3755—21no—
15C2×#3753—21no—
16C2×#3748C2211yescharacteristic
17C3×#948—22no—
18C3×#948—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208—21no—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C22×C3×C3⋊C8—21no—
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#835—21no—
26C3×#832—21no—
27#63564—21no—
28#63564—21no—
29#63559—22no—
30C2×C3×#131—31no—
31C2×#949—31no—
32C2×#949—31no—
33C2×#949—61no—
34C2×#948D311yescharacteristic, complemented
35C3×#417—31no—
36#5232D311yescharacteristic, complemented
37C2×#823—31no—
38C2×#823—31no—
39C2×#821—31no—
40C2×#809—31no—
41#4558—31no—
42#4554—31no—
43#4552—31no—
44#4530—31no—
45C23×C3⋊D3—21no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41C2×C412yes—
49C32×#41D412yes—
50C2×C32×Q8D411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2×C412yes—
61C22×C3×Dic3—21no—
62#3755—24no—
63#3753—24no—
64#3748—21no—
65#3748C2×C412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—24no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208D412yes—
74C2×C3×C3⋊C8—24no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8D411yescharacteristic
80C2×C3×C3⋊C8D411yescharacteristic
81#1907—91noSylow
82C2×C3×#41—21no—
83C2×C3×#41C2×D311yescharacteristic
84C2×C3×#41C2×D311yescharacteristic
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C3×#131—62no—
89C3×#131—62no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16—61no—
93C22×C3×C8—31no—
94C22×C3×C8—61no—
95C2×C3×C4⋊C4—31no—
96#949—34no—
97#949—34no—
98#949—64no—
99#949—64no—
100#949—62no—
101#949—62no—
102#948—22no—
103#948—22no—
104C2×#215—62no—
105C2×#215—61no—
106C2×#215—61no—
107C2×#213—62no—
108C2×#213—61no—
109C2×#213—61no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×#208—21no—
112C2×#208—31no—
113C2×#208—31no—
114C2×#208—61no—
115C2×#208C2×D311yescharacteristic
116C2×#208C2×D311yescharacteristic
117C22×C3⋊C8—21no—
118C22×C3⋊C8C2×D311yescharacteristic
119C3×#103—61no—
120C3×#102—61no—
121#835—21no—
122#832—21no—
123#823—62no—
124#823—62no—
125#821—61no—
126#821—61no—
127#809—61no—
128#809—61no—
129C23×C32—21no—
130C23×C32#4111yescharacteristic
131C22×C3⋊D3—22no—
132C22×C3⋊D3—41no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3—81no—
135C22×C3⋊D3—81no—
136C32×Q8—21no—
137C32×Q8C22⋊C412yes—
138C32×D4—22no—
139C32×D4—22no—
140C32×D4—21no—
141C32×D4C22⋊C412yes—
142C2×C32×C4—21no—
143C2×C32×C4—22no—
144C2×C32×C4—22no—
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)—41no—
154C4⋊(C3⋊D3)—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—81no—
157C3⋊(C3⋊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—31no—
164#417—31no—
165C2×#102—91no—
166C2×#100—91no—
167#343—91no—
168#341—91no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—41no—
179C3×#41—41no—
180C3×#41C4×D312yes—
181C3×#41C4×D312yes—
182C3×#41D1212yes—
183C3×#41#6712yes—
184C2×C3×Q8—21no—
185C2×C3×Q8D1211yescharacteristic
186C2×C3×Q8#6711yescharacteristic
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—41no—
191C2×C3×D4D1211yescharacteristic
192C2×C3×D4#6711yescharacteristic
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—41no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3—21no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—121no—
217C2×D12—121no—
218C2×D12—121no—
219C3×M16—32no—
220C3×M16—64no—
221C3×M16—61no—
222C3×M16—61no—
223C3×M16—61no—
224C2×C3×C8—31no—
225C2×C3×C8—31no—
226C2×C3×C8—64no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233#215—68no—
234#215—64no—
235#215—64no—
236#213—68no—
237#213—64no—
238#213—64no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241#208—24no—
242#208—21no—
243#208—21no—
244#208—21no—
245#208—32no—
246#208—32no—
247#208—62no—
248#208—62no—
249#208—61no—
250#208—61no—
251#208#6712yes—
252C2×C3⋊C8—24no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—62no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8#6711yescharacteristic
261C2×C3⋊C8#6711yescharacteristic
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—22no—
265C22×C32—41no—
266C22×C32—41no—
267C22×C32C4×D411yescharacteristic
268C22×C32#12111yescharacteristic
269C22×C32#12311yescharacteristic
270C2×C3⋊D3—42no—
271C2×C3⋊D3—82no—
272C2×C3⋊D3—81no—
273C2×C3⋊D3—81no—
274C2×C3⋊D3—82no—
275C32×C4—22no—
276C32×C4C2×C22⋊C411yescharacteristic
277C32×C4C4×D411yescharacteristic
278C32×C4#12011yescharacteristic
279C32×C4#12111yescharacteristic
280C3×Dic3—81no—
281C2×#41D3211yescharacteristic
282C22×D4—91no—
283AGL(1,ℤ/8)—94no—
284AGL(1,ℤ/8)—182no—
285C2×SD16—181no—
286C2×D8—181no—
287#131—62no—
288#131—62no—
289C2×M16—31no—
290C2×M16—31no—
291C2×M16—61no—
292C2×M16—91no—
293C22×C8—31no—
294C22×C8—61no—
295C2×C4⋊C4—31no—
296#103—61no—
297#102—61no—
298#102—181no—
299#102—181no—
300#100—182no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—41no—
305C23×C3#23511yescharacteristic
306C23×C3#23711yescharacteristic
307C22×D3—62no—
308C22×D3—62no—
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—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—22no—
325C3×Q8—41no—
326C3×Q8(C2×D3)⋊C412yes—
327C3×Q8(C2×D3)⋊C412yes—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—21no—
333C3×D4—21no—
334C3×D4—22no—
335C3×D4—41no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4(C2×D3)⋊C412yes—
339C3×D4(C2×D3)⋊C412yes—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—41no—
355C2×C3×C4—121no—
356C2×C3×C4—241no—
357C2×C3×C4C2×C4×D311yescharacteristic
358C2×C3×C4C2×C4×D311yescharacteristic
359C2×C3×C4C2×D1211yescharacteristic
360C2×C3×C4C2×D1211yescharacteristic
361C2×C3×C4#23511yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×Dic3—41no—
370C2×Dic3—81no—
371D12—64no—
372D12—62no—
373D12—62no—
374D12—62no—
375D12—62no—
376D12—122no—
377D12—122no—
378D12—122no—
379D12—121no—
380D12—121no—
381D12—121no—
382D12—121no—
383C3×C8—61no—
384C3×C8—61no—
385C3×C8—62no—
386C3×C8—121no—
387C3⋊C8—21no—
388C3⋊C8—22no—
389C3⋊C8—21no—
390C3⋊C8—41no—
391C3⋊C8—64no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32—42no—
397C2×C32#38611yescharacteristic
398C2×C32#47111yescharacteristic
399C2×C32#47211yescharacteristic
400C3⋊D3—82no—
401C24—181no—
402#41—21no—
403#41—21no—
404#41#62412yes—
405#41#62612yes—
406C2×Q8#62611yescharacteristic
407C2×D4—21no—
408C2×D4—92no—
409C2×D4—181no—
410C2×D4—181no—
411C2×D4—181no—
412C2×D4—181no—
413C2×D4—181no—
414C2×D4#62611yescharacteristic
415C22×C4—21no—
416C22×C4—61no—
417C22×C4C2×D3211yescharacteristic
418SD16—184no—
419D8—184no—
420M16—32no—
421M16—64no—
422M16—61no—
423M16—61no—
424M16—61no—
425M16—92no—
426M16—181no—
427C2×C8—31no—
428C2×C8—31no—
429C2×C8—64no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8—181no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—42no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—81no—
454C22×C3—81no—
455C22×C3#67⋊C411yescharacteristic
456C22×C3#88611yescharacteristic
457C22×C3C4×#6711yescharacteristic
458C22×C3#92911yescharacteristic
459C22×C3#93011yescharacteristic
460C22×C3#93911yescharacteristic
461C2×D3—124no—
462C2×D3—122no—
463C2×D3—122no—
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—22no—
477C3×C4—22no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—42no—
483C3×C4—241no—
484C3×C4#67⋊C411yescharacteristic
485C3×C4#88211yescharacteristic
486C3×C4C2×(C2×D3)⋊C411yescharacteristic
487C3×C4C2×(C2×D3)⋊C411yescharacteristic
488C3×C4C4×#6711yescharacteristic
489C3×C4#93011yescharacteristic
490C3×C4#93911yescharacteristic
491C3×C4#95311yescharacteristic
492Dic3—81no—
493C32#190711yescharacteristic, complemented, Sylow
494C23—21no—
495C23—182no—
496C23—361no—
497C23—361no—
498C23—721no—
499C23—721no—
500C23#380411yescharacteristic
501Q8—21no—
502Q8#372212yes—
503D4—22no—
504D4—22no—
505D4—21no—
506D4—182no—
507D4—182no—
508D4—361no—
509D4—361no—
510D4#372212yes—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—121no—
515C2×C4—241no—
516C2×C4#380411yescharacteristic
517C2×C4C2×#62411yescharacteristic
518C2×C4C2×#62611yescharacteristic
519C2×C4C2×#62611yescharacteristic
520C2×C4D3×#6711yescharacteristic
521C2×C4D3×#6711yescharacteristic
522C8—61no—
523C8—61no—
524C8—62no—
525C8—121no—
526C8—182no—
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—42no—
537C2×C3—42no—
538C2×C3—82no—
539C2×C3#495811yescharacteristic
540C2×C3#514111yescharacteristic
541C2×C3#514211yescharacteristic
542C2×C3#519911yescharacteristic
543C2×C3#520311yescharacteristic
544C2×C3#521311yescharacteristic
545D3—244no—
546D3—242no—
547D3—242no—
548C22—21no—
549C22—21no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—362no—
554C22—722no—
555C22—722no—
556C22—721no—
557C22—721no—
558C22#6395211yescharacteristic
559C22#6396611yescharacteristic
560C22#6397811yescharacteristic
561C4—22no—
562C4—241no—
563C4#6395211yescharacteristic
564C4C2×#372211yescharacteristic
565C4#6397711yescharacteristic
566C4#6397811yescharacteristic
567C3—21no—
568C3#7030311yescharacteristic, complemented
569C3#7201811yescharacteristic, complemented
570C2—21no—
571C2—21no—
572C2—42no—
573C2—722no—
574C2#1059167711yescharacteristic
575C2#1059168011yescharacteristic
576C2#1059171111yescharacteristic
subgroupG/H
centerC22#63978
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#121
prime radicalC2×#64158C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1907
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
2. C2×C3×#948C2semidirect
3. C3×#5232C2semidirect
4. C2×#63564C2semidirect
5. C2×#63559C2semidirect
6. #10589167C2semidirect
7. #10589166C2semidirect
13. #64158C4semidirect
34. C2×#948D3semidirect
36. #5232D3semidirect
493. C32#1907semidirect
568. C3#70303semidirect
569. C3#72018semidirect

Maximal subgroups

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

subgroupindex
C2×#641582
C2×C3×#9482
C3×#52322
C2×#635642
C2×#635592
#105891672
#105891662
#720183
#703033