Finite Group Databasebeta

← #11787396

Subgroups — #11787396

Order 1152.

733 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×C3×#950C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic, complemented
3C2×#63664C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic, complemented
5#10591070C211yesmaximal, characteristic, complemented
6#10589166C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72087—31nomaximal
9#72010—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#950—22no—
15C3×#950—22no—
16C3×#948—22no—
17C3×#948—22no—
18C2×C3×#216C411yescharacteristic, complemented
19C2×C3×#215C411yescharacteristic, complemented
20C2×C3×#214C411yescharacteristic, complemented
21C2×C3×#213C411yescharacteristic, complemented
22C2×C3×#208—21no—
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27#63664—22no—
28#63568—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C2×C3×#135—31no—
32C2×C3×#131—31no—
33C2×#950D311yescharacteristic
34C2×#948D311yescharacteristic, complemented
35C2×#837—31no—
36C2×#837—31no—
37C2×#837—31no—
38C2×#837—61no—
39#5234—31no—
40C2×#825—31no—
41#5110—31no—
42#4558—31no—
43#4552—31no—
44#4550—31no—
45#4550—31no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41D412yes—
49C32×#41D412yes—
50C2×C32×Q8C2×C411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4C2×C411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C3×#67—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12C2×C411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6C2×C411yescharacteristic
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—21no—
66#3748—21no—
67#3748—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C3×#216—22no—
70C3×#215—22no—
71C3×#214—22no—
72C3×#213—22no—
73C3×#208—24no—
74C3×#208—21no—
75C3×#208D412yes—
76C2×C3×C3⋊C8—24no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8C2×C411yescharacteristic
83C2×C3×C3⋊C8C2×C411yescharacteristic
84C2×C3×C3⋊C8D411yescharacteristic
85C2×C3×C3⋊C8D411yescharacteristic
86#1876—91noSylow
87C2×C3×#41—21no—
88C2×C3×#41—31no—
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×#41C2×D311yescharacteristic
91C2×#235C2×D311yescharacteristic
92C3×#135—62no—
93C3×#135—62no—
94C2×C3×Q16—31no—
95C2×C3×SD16—31no—
96C2×C3×SD16—31no—
97C2×C3×D8—31no—
98C3×#131—62no—
99C3×#131—62no—
100C2×C3×M16—31no—
101C2×C3×M16—61no—
102C22×C3×C8—31no—
103C22×C3×C8—31no—
104C22×C3×C8—61no—
105#950—22no—
106#950—22no—
107#948—22no—
108#948—22no—
109C2×#216Dic311yescharacteristic, complemented
110C2×#215Dic311yescharacteristic, complemented
111C2×#214Dic311yescharacteristic, complemented
112C2×#213Dic311yescharacteristic, complemented
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—61no—
116C2×#208—21no—
117C2×#208—31no—
118C2×#208—31no—
119C2×#208—61no—
120C2×#208C2×D311yescharacteristic
121C22×C3⋊C8—21no—
122C22×C3⋊C8C2×D311yescharacteristic
123C22×C3⋊C8C2×D311yescharacteristic
124#837—64no—
125#837—62no—
126#837—62no—
127#837—62no—
128#830—61no—
129#830—61no—
130#825—62no—
131(C2×D3)⋊C8—61no—
132(C2×D3)⋊C8—61no—
133C23×C32—21no—
134C23×C32#4111yescharacteristic
135C22×C3×D3—21no—
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
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—41no—
153C2×C3⋊Dic3—41no—
154C3×#67—41no—
155C3×#67—41no—
156C2×C3×Dic3—21no—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—41no—
160C3×C4×D3—41no—
161C3×Dic6—21no—
162C3×Dic6—21no—
163C3⋊(C3⋊C8)—41no—
164C3×C3⋊C8—21no—
165C3×C3⋊C8—21no—
166C3×C3⋊C8—21no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—21no—
169C2×#135—31no—
170C2×#131—31no—
171C2×#104—91no—
172C2×#104—91no—
173#408—91no—
174#341—91no—
175#336—91no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—22no—
181C3×#41—22no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—61no—
185C3×#41—61no—
186C3×#41—61no—
187C3×#41—61no—
188C3×#41D1212yes—
189C3×#41#6712yes—
190C3×#41#6712yes—
191C3×#41#6712yes—
192C2×C3×Q8—21no—
193C2×C3×Q8—31no—
194C2×C3×Q8C4×D311yescharacteristic
195C2×C3×Q8C2×Dic311yescharacteristic
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—31no—
200C2×C3×D4—41no—
201C2×C3×D4—61no—
202C2×C3×D4C4×D311yescharacteristic
203C2×C3×D4C2×Dic311yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—41no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—21no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3—121no—
215#235—21no—
216#235—21no—
217#235—21no—
218#235—21no—
219C2×D12C2×Dic311yescharacteristic
220C2×C4×D3—21no—
221C2×Dic6C2×Dic311yescharacteristic
222C3×Q16—62no—
223C3×SD16—62no—
224C3×SD16—62no—
225C3×D8—62no—
226C3×M16—32no—
227C3×M16—64no—
228C3×M16—61no—
229C2×C3×C8—31no—
230C2×C3×C8—31no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C2×C3×C8—64no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239#216—22no—
240#215—22no—
241#214—22no—
242#213—22no—
243C4×Dic3—62no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249#208—24no—
250#208—21no—
251#208—62no—
252#208—61no—
253#208—61no—
254#208—61no—
255#208—61no—
256#208—121no—
257#208#6712yes—
258C2×C3⋊C8—24no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—121no—
267C2×C3⋊C8C2×Dic311yescharacteristic
268C2×C3⋊C8C2×Dic311yescharacteristic
269C2×C3⋊C8#6711yescharacteristic
270C2×C3⋊C8#6711yescharacteristic
271C22×C32—21no—
272C22×C32—21no—
273C22×C32—22no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32C4×D411yescharacteristic
277C22×C32#12111yescharacteristic
278C22×C32#12311yescharacteristic
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C32×C4—22no—
283C32×C4C2×C22⋊C411yescharacteristic
284C32×C4C4×D411yescharacteristic
285C32×C4#12011yescharacteristic
286C32×C4#12111yescharacteristic
287C3⋊Dic3—42no—
288C3×Dic3—41no—
289C2×#41—31no—
290C2×#41D3211yescharacteristic
291#135—62no—
292#135—62no—
293C2×Q16—31no—
294C2×SD16—31no—
295C2×SD16—31no—
296C2×D8—31no—
297#131—62no—
298#131—62no—
299C2×M16—31no—
300C2×M16—61no—
301C2×M16—91no—
302C22×C8—31no—
303C22×C8—31no—
304C22×C8—61no—
305C2×C42—91no—
306#104—182no—
307#104—182no—
308C22⋊C8—181no—
309C22⋊C8—181no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—41no—
314C23×C3—61no—
315C23×C3#23511yescharacteristic
316C23×C3#23711yescharacteristic
317C22×D3—21no—
318C3×Q8—21no—
319C3×Q8—21no—
320C3×Q8—22no—
321C3×Q8—41no—
322C3×Q8—61no—
323C3×Q8—61no—
324C3×Q8(C2×D3)⋊C412yes—
325C3×Q8#21712yes—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—22no—
333C3×D4—41no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—61no—
337C3×D4—61no—
338C3×D4—121no—
339C3×D4—121no—
340C3×D4(C2×D3)⋊C412yes—
341C3×D4#21712yes—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—41no—
357C2×C3×C4—61no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4C2×C4×D311yescharacteristic
361C2×C3×C4C2×D1211yescharacteristic
362C2×C3×C4#23511yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4#23711yescharacteristic
366C2×C3×C4C22×Dic311yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372#67—41no—
373#67—41no—
374C2×Dic3—21no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—122no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384D12—21no—
385D12—21no—
386C4×D3—41no—
387C4×D3—41no—
388Dic6—21no—
389Dic6—21no—
390C3×C8—61no—
391C3×C8—61no—
392C3×C8—61no—
393C3×C8—61no—
394C3×C8—62no—
395C3⋊C8—21no—
396C3⋊C8—21no—
397C3⋊C8—21no—
398C3⋊C8—22no—
399C3⋊C8—21no—
400C3⋊C8—122no—
401C3⋊C8—121no—
402C3⋊C8—121no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32—42no—
406C2×C32#38611yescharacteristic
407C2×C32#44311yescharacteristic
408C2×C32#44411yescharacteristic
409C3×D3—81no—
410#41—21no—
411#41—21no—
412#41—61no—
413#41—61no—
414#41—61no—
415#41—61no—
416#41#62512yes—
417#41#62612yes—
418C2×Q8—31no—
419C2×Q8D3×Dic311yescharacteristic
420C2×D4—21no—
421C2×D4—31no—
422C2×D4—61no—
423C2×D4D3×Dic311yescharacteristic
424C22×C4—21no—
425C22×C4—61no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428Q16—62no—
429SD16—62no—
430SD16—62no—
431D8—62no—
432M16—32no—
433M16—64no—
434M16—61no—
435M16—181no—
436M16—181no—
437C2×C8—31no—
438C2×C8—31no—
439C2×C8—31no—
440C2×C8—31no—
441C2×C8—64no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8—61no—
447C2×C8—181no—
448C42—181no—
449C42—181no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—41no—
460C22×C3—41no—
461C22×C3—42no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—81no—
467C22×C3—81no—
468C22×C3—121no—
469C22×C3—121no—
470C22×C3—121no—
471C22×C3C4×#6711yescharacteristic
472C22×C3#92911yescharacteristic
473C22×C3#93011yescharacteristic
474C22×C3D4×Dic311yescharacteristic
475C22×C3#93511yescharacteristic
476C22×C3#93911yescharacteristic
477C2×D3—41no—
478C2×D3—41no—
479C2×D3—41no—
480C3×C4—22no—
481C3×C4—22no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—42no—
487C3×C4—121no—
488C3×C4C2×(C2×D3)⋊C411yescharacteristic
489C3×C4C4×#6711yescharacteristic
490C3×C4#93011yescharacteristic
491C3×C4D4×Dic311yescharacteristic
492C3×C4#93711yescharacteristic
493C3×C4#93911yescharacteristic
494C3×C4C2×#21711yescharacteristic
495C3×C4#95311yescharacteristic
496Dic3—41no—
497Dic3—122no—
498Dic3—122no—
499Dic3—124no—
500C32#187611yescharacteristic, complemented, Sylow
501C23—21no—
502C23—61no—
503C23#380411yescharacteristic
504Q8—21no—
505Q8—61no—
506Q8—61no—
507Q8(C2×D3)⋊Dic312yes—
508D4—22no—
509D4—22no—
510D4—21no—
511D4—61no—
512D4—61no—
513D4—121no—
514D4—121no—
515D4(C2×D3)⋊Dic312yes—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—61no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4—182no—
523C2×C4—361no—
524C2×C4—361no—
525C2×C4C2×D3×Dic311yescharacteristic
526C2×C4#380411yescharacteristic
527C2×C4C2×#62511yescharacteristic
528C2×C4C2×#62611yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4D3×#6711yescharacteristic
531C8—61no—
532C8—61no—
533C8—61no—
534C8—61no—
535C8—62no—
536C8—361no—
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—42no—
547C2×C3—42no—
548C2×C3—82no—
549C2×C3—241no—
550C2×C3#514411yescharacteristic
551C2×C3#514511yescharacteristic
552C2×C3#519611yescharacteristic
553C2×C3#519711yescharacteristic
554C2×C3#521311yescharacteristic
555C2×C3#522011yescharacteristic
556D3—81no—
557C22—21no—
558C22—21no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—121no—
563C22—121no—
564C22—121no—
565C22#6396111yescharacteristic
566C22Dic3×#6711yescharacteristic
567C22#6397811yescharacteristic
568C4—22no—
569C4—121no—
570C4—362no—
571C4C2×(C2×D3)⋊Dic311yescharacteristic
572C4Dic3×#6711yescharacteristic
573C4#6397611yescharacteristic
574C4#6397811yescharacteristic
575C3—21no—
576C3#7201011yescharacteristic, complemented
577C3#7208711yescharacteristic, complemented
578C2—21no—
579C2—21no—
580C2—42no—
581C2—241no—
582C2#1059167311yescharacteristic
583C2#1059167411yescharacteristic
584C2#1059171011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C4×D4
prime radicalC2×C3×#950C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1876
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#948C2semidirect
3. C2×#63664C2semidirect
4. C2×#63568C2semidirect
5. #10591070C2semidirect
6. #10589166C2semidirect
7. #10589156C2semidirect
18. C2×C3×#216C4semidirect
19. C2×C3×#215C4semidirect
20. C2×C3×#214C4semidirect
21. C2×C3×#213C4semidirect
34. C2×#948D3semidirect
109. C2×#216Dic3semidirect
110. C2×#215Dic3semidirect
111. C2×#214Dic3semidirect
112. C2×#213Dic3semidirect
500. C32#1876semidirect
576. C3#72010semidirect
577. C3#72087semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9502
C2×C3×#9482
C2×#636642
C2×#635682
#105910702
#105891662
#105891562
#720873
#720103