Finite Group Databasebeta

← #11787404

Subgroups — #11787404

Order 1152.

727 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63829C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic, complemented
3#10592828C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70377—31nomaximal
9#68946—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
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
23C2×#3711—21no—
24#63815—22no—
25#63815—22no—
26C2×D3×C3⋊C8—21no—
27#63647—21no—
28#63647—21no—
29C3×#825—22no—
30#63570—22no—
31C2×#950—31no—
32C2×#948—31no—
33C2×#907—31no—
34C2×#904—31no—
35C2×C3×#104—31no—
36C2×#825—31no—
37C2×#825D311yescharacteristic, complemented
38#5129—31no—
39#5129—31no—
40#5129—61no—
41C2×#805—31no—
42C3×#341—31no—
43#4558D311yescharacteristic, complemented
44#4550—31no—
45#4524—31no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×#634C2×C411yescharacteristic
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235D412yes—
60C3×#235D412yes—
61C2×C3×D12C2×C411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6C2×C411yescharacteristic
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)D411yescharacteristic
70C2×C3⋊(C3⋊C8)D411yescharacteristic
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C3×#208—21no—
74C3×#208D412yes—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C411yescharacteristic
79C2×C3×C3⋊C8C2×C411yescharacteristic
80#3719—22no—
81#3717—22no—
82#3716—22no—
83#3714—22no—
84#3711—24no—
85D3×C3⋊C8—24no—
86#1876—91noSylow
87C2×C3×#41—31no—
88C2×#235—31no—
89C2×#235—31no—
90C2×#235—61no—
91C2×#235C2×D311yescharacteristic
92C2×C3×M16—21no—
93C2×C3×M16—31no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C22×C3×C8—31no—
97C2×C3×C42—31no—
98#950—62no—
99#950—62no—
100#948—62no—
101#948—62no—
102C2×#216—31no—
103C2×#215—31no—
104C2×#214—31no—
105C2×#213—31no—
106C2×C4×Dic3C2×D311yescharacteristic
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109C22×C3⋊C8—31no—
110C22×C3⋊C8—31no—
111C22×C3⋊C8—61no—
112C22×C3⋊C8—61no—
113C22×C3⋊C8C2×D311yescharacteristic
114#907—62no—
115#907—62no—
116C2×Dic12—31no—
117#904—62no—
118#904—62no—
119C2×D24—31no—
120C2×#204—31no—
121C2×#204—31no—
122C2×ΓL(1,𝔽25)—61no—
123C2×D3×C8—61no—
124C3×#104—62no—
125#825—22no—
126#825—62no—
127(C2×D3)⋊C8—61no—
128(C2×D3)⋊C8—61no—
129(C2×D3)⋊C8—61no—
130(C2×D3)⋊C8—61no—
131(C2×D3)⋊C8—62no—
132(C2×D3)⋊C8—62no—
133#805—62no—
134C23×C32#4111yescharacteristic
135C22×C3⋊D3—21no—
136C22×C3×D3—21no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143#638—41no—
144#638—41no—
145C2×C3⋊Dic3—21no—
146C4⋊(C3⋊D3)—21no—
147C4⋊(C3⋊D3)—21no—
148C4×C3⋊D3—41no—
149C4×C3⋊D3—41no—
150#634—21no—
151#634—21no—
152C3×#67—22no—
153C3×#67—22no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C3×D12—21no—
159C3×D12C22⋊C412yes—
160C3×C4×D3—22no—
161C3×C4×D3—22no—
162C3×Dic6—21no—
163C3×Dic6C22⋊C412yes—
164C32×C8—41no—
165C3⋊(C3⋊C8)—21no—
166C3⋊(C3⋊C8)—21no—
167C3×C3⋊C8—21no—
168C3×C3⋊C8—21no—
169C3×C3⋊C8—22no—
170C2×#135—91no—
171C2×#131—91no—
172C2×#104—31no—
173C2×#104—91no—
174#408—91no—
175#341—31no—
176#336—91no—
177C3×#41—32no—
178C3×#41—32no—
179C3×#41—61no—
180C3×#41—61no—
181C2×C3×Q8—31no—
182C2×C3×D4—31no—
183C2×C3×D4—61no—
184C22×C3×C4—21no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C2×#67—21no—
190C2×#67—62no—
191C2×#67—61no—
192C2×#67—61no—
193C22×Dic3—21no—
194#235—21no—
195#235—21no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204#235—121no—
205#235—121no—
206#235—121no—
207#235—121no—
208#235D1212yes—
209#235#6712yes—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×D12C4×D311yescharacteristic
214C2×C4×D3—21no—
215C2×C4×D3—62no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×Dic6—31no—
219C2×Dic6—31no—
220C2×Dic6—61no—
221C2×Dic6C4×D311yescharacteristic
222C3×M16—21no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—21no—
226C3×M16—32no—
227C3×M16—41no—
228C3×M16—41no—
229C3×M16—61no—
230C2×C3×C8—22no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—31no—
234C2×C3×C8—31no—
235C2×C3×C8—61no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C3×C42—61no—
239C3×C42—61no—
240#216—62no—
241#215—62no—
242#214—62no—
243#213—62no—
244C4×Dic3—21no—
245C4×Dic3—21no—
246#208—21no—
247#208—64no—
248#208D1212yes—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—31no—
253C2×C3⋊C8—31no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—64no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—121no—
264C2×C3⋊C8—121no—
265C2×C3⋊C8C4×D311yescharacteristic
266C2×C3⋊C8C4×D311yescharacteristic
267Dic12—62no—
268D24—62no—
269#204—62no—
270#204—62no—
271ΓL(1,𝔽25)—64no—
272D3×C8—64no—
273C22×C32—21no—
274C22×C32—21no—
275C22×C32C4×D411yescharacteristic
276C22×C32#12111yescharacteristic
277C22×C32#12311yescharacteristic
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3×D3—22no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C32×C4C2×C22⋊C411yescharacteristic
285C32×C4C4×D411yescharacteristic
286C32×C4#12011yescharacteristic
287C32×C4#12111yescharacteristic
288C3⋊Dic3—41no—
289C3×Dic3—22no—
290C3×Dic3—42no—
291C2×#41—31no—
292C2×#41—91no—
293#135—182no—
294#135—182no—
295C2×Q16—91no—
296C2×SD16—91no—
297C2×SD16—91no—
298C2×D8—91no—
299#131—182no—
300#131—182no—
301C2×M16—31no—
302C2×M16—181no—
303C2×M16D3211yescharacteristic
304C22×C8—31no—
305C22×C8—91no—
306C22×C8—181no—
307C2×C42—31no—
308#104—62no—
309#104—182no—
310C22⋊C8—181no—
311C22⋊C8—181no—
312C23×C3—21no—
313C23×C3—61no—
314C23×C3#23711yescharacteristic
315C23×C3#23911yescharacteristic
316C22×D3—21no—
317C22×D3—62no—
318C22×D3—61no—
319C22×D3—61no—
320C3×Q8—32no—
321C3×Q8—61no—
322C3×D4—32no—
323C3×D4—62no—
324C3×D4—62no—
325C3×D4—61no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4C2×C4×D311yescharacteristic
339C2×C3×C4C2×C4×D311yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4#23511yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4#23711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350#67—22no—
351#67—22no—
352#67—122no—
353#67—122no—
354#67—121no—
355#67—121no—
356#67—121no—
357#67—121no—
358C2×Dic3—21no—
359C2×Dic3—22no—
360C2×Dic3—41no—
361C2×Dic3—41no—
362C2×Dic3—62no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365D12—21no—
366D12—61no—
367D12—61no—
368D12—61no—
369D12—61no—
370D12—121no—
371D12—121no—
372D12(C2×D3)⋊C412yes—
373C4×D3—22no—
374C4×D3—22no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—121no—
378C4×D3—121no—
379C4×D3—121no—
380C4×D3—121no—
381Dic6—21no—
382Dic6—61no—
383Dic6—61no—
384Dic6—61no—
385Dic6—61no—
386Dic6—121no—
387Dic6—121no—
388Dic6(C2×D3)⋊C412yes—
389C3×C8—42no—
390C3×C8—41no—
391C3×C8—41no—
392C3×C8—62no—
393C3×C8—61no—
394C3×C8—61no—
395C3⋊C8—21no—
396C3⋊C8—21no—
397C3⋊C8—22no—
398C3⋊C8—61no—
399C3⋊C8—61no—
400C3⋊C8—61no—
401C3⋊C8—61no—
402C3⋊C8—121no—
403C3⋊C8—121no—
404C2×C32—21no—
405C2×C32—21no—
406C2×C32#38611yescharacteristic
407C2×C32#44311yescharacteristic
408C2×C32#44411yescharacteristic
409C3⋊D3—81no—
410C3×D3—42no—
411#41—32no—
412#41—32no—
413#41—61no—
414#41—61no—
415#41—181no—
416#41—181no—
417#41—181no—
418#41—181no—
419C2×Q8—31no—
420C2×Q8—91no—
421C2×D4—31no—
422C2×D4—61no—
423C2×D4—91no—
424C2×D4—181no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4—181no—
428C22×C4C2×D3211yescharacteristic
429Q16—182no—
430SD16—182no—
431SD16—182no—
432D8—182no—
433M16—21no—
434M16—21no—
435M16—32no—
436M16—61no—
437M16—184no—
438C2×C8—21no—
439C2×C8—31no—
440C2×C8—31no—
441C2×C8—61no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—91no—
445C2×C8—91no—
446C2×C8—184no—
447C2×C8—181no—
448C2×C8—181no—
449C42—61no—
450C42—61no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3#67⋊C411yescharacteristic
464C22×C3#88611yescharacteristic
465C22×C3#89311yescharacteristic
466C22×C3#89411yescharacteristic
467C22×C3#89511yescharacteristic
468C22×C3#93911yescharacteristic
469C2×D3—22no—
470C2×D3—41no—
471C2×D3—41no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—121no—
476C2×D3—121no—
477C2×D3—121no—
478C2×D3—121no—
479C2×D3—121no—
480C2×D3—121no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—62no—
486C3×C4—122no—
487C3×C4C4×D1211yescharacteristic
488C3×C4D3×C22⋊C411yescharacteristic
489C3×C4#67⋊C411yescharacteristic
490C3×C4#88211yescharacteristic
491C3×C4#88211yescharacteristic
492C3×C4#88411yescharacteristic
493C3×C4C2×(C2×D3)⋊C411yescharacteristic
494C3×C4#93911yescharacteristic
495Dic3—22no—
496Dic3—42no—
497Dic3—122no—
498Dic3—121no—
499Dic3—121no—
500C32#187611yescharacteristic, complemented, Sylow
501C23—61no—
502C23—181no—
503C23#379611yescharacteristic
504Q8—32no—
505Q8—61no—
506Q8—181no—
507Q8—181no—
508D4—32no—
509D4—62no—
510D4—62no—
511D4—61no—
512D4—181no—
513D4—181no—
514D4—361no—
515D4—361no—
516C2×C4—61no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4—181no—
523C2×C4—361no—
524C2×C4—361no—
525C2×C4C4×D3211yescharacteristic
526C2×C4D3×D1211yescharacteristic
527C2×C4D3×D1211yescharacteristic
528C2×C4#380411yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4#381111yescharacteristic
531C8—41no—
532C8—61no—
533C8—61no—
534C8—62no—
535C8—181no—
536C8—181no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—41no—
545C2×C3—41no—
546C2×C3—122no—
547C2×C3#466511yescharacteristic
548C2×C3#482311yescharacteristic
549C2×C3#482411yescharacteristic
550C2×C3#489411yescharacteristic
551C2×C3#489511yescharacteristic
552C2×C3#495811yescharacteristic
553D3—42no—
554D3—242no—
555D3—241no—
556D3—241no—
557C22—21no—
558C22—21no—
559C22—62no—
560C22—121no—
561C22—121no—
562C22—361no—
563C22—361no—
564C22—361no—
565C22#6388111yescharacteristic
566C22#6388611yescharacteristic
567C22#6389011yescharacteristic
568C4—62no—
569C4—122no—
570C4—361no—
571C4#6388011yescharacteristic
572C4D3×(C2×D3)⋊C411yescharacteristic
573C4#6392311yescharacteristic
574C4#6397111yescharacteristic
575C3—21no—
576C3#6894611yescharacteristic, complemented
577C3#7037711yescharacteristic, complemented
578C2—21no—
579C2—21no—
580C2—122no—
581C2—721no—
582C2#1059097711yescharacteristic
583C2#1059097811yescharacteristic
584C2#1059136411yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×#63829C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1876
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63815C2semidirect
3. #10592828C2semidirect
4. C2×C3×#825C2semidirect
5. C2×#63570C2semidirect
6. C3×#4558C2semidirect
7. #10589155C2semidirect
17. C2×#3719C4semidirect
18. C2×#3717C4semidirect
21. C2×#3716C4semidirect
22. C2×#3714C4semidirect
37. C2×#825D3semidirect
43. #4558D3semidirect
500. C32#1876semidirect
576. C3#68946semidirect
577. C3#70377semidirect

Maximal subgroups

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

subgroupindex
C2×#638292
C2×#638152
#105928282
C2×C3×#8252
C2×#635702
C3×#45582
#105891552
#703773
#689463