Finite Group Databasebeta

← #11784871

Subgroups — #11784871

Order 1152.

1689 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic, complemented
3C2×C3×#833C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal, complemented
5#10591106C212yesmaximal, complemented
6#70086—31nomaximal
7#69662—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×#638—22no—
10#64361—22no—
11#64361—24no—
12#64361C414yescomplemented
13C2×#3830—22no—
14C2×D4×C3⋊D3—22no—
15C2×#3828C2212yes—
16C2×C3×#217—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
18C2×C3×C4×Dic3C2211yescharacteristic, complemented
19C2×C3×#208C2212yescomplemented
20C3×#833—22no—
21#63570—24no—
22#63567—22no—
23#63564—22no—
24C2×#1004—31no—
25C2×#1004—31no—
26C2×#1004—61no—
27C2×C3×#100—31no—
28C3×#390—31no—
29#5221D311yescharacteristic, complemented
30C2×#833D311yescharacteristic, complemented
31C2×#825—32no—
32#5133—32no—
33#4966—32no—
34C2×#805—32no—
35C24×C32D412yes—
36C23×C3⋊D3—22no—
37C2×C32×D4—22no—
38C2×C32×D4—22no—
39C2×C32×D4C2×C412yes—
40C2×C32×D4D412yes—
41C22×C32×C4C2311yescharacteristic
42C2×#638—24no—
43C2×#638—28no—
44C2×#638—28no—
45C2×#638—22no—
46C22×C3⋊Dic3—22no—
47#3830—28no—
48#3830—28no—
49D4×C3⋊D3—28no—
50D4×C3⋊D3—28no—
51#3828—22no—
52#3828—22no—
53#3828C2×C414yes—
54#3828D414yes—
55C2×C4⋊(C3⋊D3)D412yes—
56C2×C4×C3⋊D3—22no—
57C2×#634D412yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C3×#217—44no—
61C3×C4⋊Dic3—22no—
62C3×C4×Dic3—22no—
63C3×#208—22no—
64C3×#208—22no—
65C2×C3×C3⋊C8—22no—
66#1792—91noSylow
67C22×C3×D4—21no—
68C22×C3×D4C2×D311yescharacteristic
69C22×C3×D4C2×D311yescharacteristic
70C22×#67—64no—
71C22×#67—62no—
72C22×#67—62no—
73#1004—34no—
74#1004—34no—
75#1004—64no—
76#1004—64no—
77#1004—64no—
78#1004—68no—
79#1004—64no—
80#1004—62no—
81#1004—62no—
82C2×#237—62no—
83C2×#237—62no—
84C2×#237—64no—
85C2×D3×D4—62no—
86C2×D3×D4—62no—
87C2×D3×D4—64no—
88C2×#235—32no—
89C2×#235—32no—
90C2×#235—62no—
91C2×C3×M16—32no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C22⋊C4—62no—
94C2×C3×C42—31no—
95C2×#217—22no—
96C2×C4⋊Dic3C2×D311yescharacteristic, complemented
97C2×C4×Dic3C2×D311yescharacteristic, complemented
98C2×#208C2×D312yescomplemented
99C3×#100—62no—
100#833—22no—
101#825—64no—
102#821—62no—
103#816—62no—
104#810—62no—
105#809—62no—
106#805—64no—
107C23×C32—22no—
108C23×C32—22no—
109C23×C32—42no—
110C23×C32—42no—
111C23×C32C22⋊C414yes—
112C23×C32C2×D411yescharacteristic
113C22×C3⋊D3—22no—
114C22×C3⋊D3—28no—
115C22×C3⋊D3—82no—
116C22×C3⋊D3—82no—
117C32×D4—24no—
118C32×D4—24no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D412yes—
122C2×C32×C4C2×D412yes—
123#638—216no—
124#638—24no—
125#638—24no—
126C2×C3⋊Dic3—28no—
127C2×C3⋊Dic3—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)C22⋊C414yescomplemented
130C4×C3⋊D3—24no—
131C4×C3⋊D3—24no—
132#634—22no—
133#634C22⋊C414yescomplemented
134C2×C3×Dic3—22no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3—41no—
139C3×C3⋊C8—42no—
140C2×H(5,𝔽2)—91no—
141C2×#104—92no—
142#417—92no—
143C2×#100—31no—
144#390—31no—
145C24×C3—22no—
146C24×C3D1212yes—
147C24×C3#6712yes—
148C23×D3—64no—
149C23×D3—62no—
150C23×D3—62no—
151C2×C3×D4—24no—
152C2×C3×D4—24no—
153C2×C3×D4—22no—
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4C4×D312yes—
160C2×C3×D4C4×D312yes—
161C2×C3×D4D1212yes—
162C2×C3×D4#6712yes—
163C22×C3×C4—21no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—64no—
169C2×#67—68no—
170C2×#67—64no—
171C2×#67—64no—
172C2×#67—616no—
173C2×#67—68no—
174C2×#67—68no—
175C2×#67—616no—
176C2×#67—68no—
177C2×#67—68no—
178C2×#67—62no—
179C2×#67—62no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—64no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185#237—68no—
186#237—68no—
187#237—616no—
188#237—616no—
189#237—68no—
190#237—68no—
191D3×D4—68no—
192D3×D4—68no—
193D3×D4—616no—
194D3×D4—616no—
195D3×D4—68no—
196D3×D4—68no—
197#235—34no—
198#235—34no—
199#235—34no—
200#235—34no—
201#235—64no—
202#235—64no—
203#235—64no—
204#235—64no—
205#235—62no—
206#235—62no—
207#235—62no—
208#235—62no—
209C2×D12—32no—
210C2×D12—32no—
211C2×D12—62no—
212C2×C4×D3—64no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×Dic6—32no—
216C2×Dic6—32no—
217C2×Dic6—62no—
218C3×M16—62no—
219C3×M16—62no—
220C2×C3×C8—62no—
221C3×C4⋊C4—62no—
222C3×C22⋊C4—124no—
223C3×C42—62no—
224#217—44no—
225C4⋊Dic3—22no—
226C4×Dic3—22no—
227#208—22no—
228#208—22no—
229C2×C3⋊C8—22no—
230C22×C32—24no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32—42no—
234C22×C32—42no—
235C22×C32—44no—
236C22×C32—82no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32#12011yescharacteristic
239C22×C32#12011yescharacteristic
240C2×C3⋊D3—24no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—88no—
244C32×C4C2×C22⋊C412yes—
245C32×C4#12012yes—
246C3⋊Dic3—24no—
247C3×Dic3—42no—
248C3×Dic3—81no—
249H(5,𝔽2)—94no—
250H(5,𝔽2)—184no—
251H(5,𝔽2)—182no—
252C2×#41—92no—
253C2×#41—182no—
254C22×D4—182no—
255C22×D4—182no—
256C22×D4D3211yescharacteristic
257C2×M16—32no—
258C2×C4⋊C4—31no—
259C2×C22⋊C4—62no—
260C2×C42—31no—
261#104—184no—
262#103—182no—
263#102—182no—
264#100—62no—
265C23×C3—24no—
266C23×C3—24no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—24no—
272C23×C3—21no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—42no—
276C23×C3—42no—
277C23×C3—82no—
278C23×C3—82no—
279C23×C3(C2×D3)⋊C414yes—
280C23×C3(C2×D3)⋊C414yes—
281C23×C3C2×D1211yescharacteristic
282C23×C3C2×#6711yescharacteristic
283C22×D3—64no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—616no—
287C22×D3—68no—
288C22×D3—68no—
289C22×D3—244no—
290C22×D3—244no—
291C22×D3—242no—
292C22×D3—242no—
293C22×D3—242no—
294C22×D3—242no—
295C3×D4—28no—
296C3×D4—28no—
297C3×D4—24no—
298C3×D4—24no—
299C3×D4—24no—
300C3×D4—24no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—62no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—122no—
309C2×C3×C4—121no—
310C2×C3×C4C2×C4×D311yescharacteristic
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4D3×D412yes—
314C2×C3×C4D3×D412yes—
315C2×C3×C4D3×D412yes—
316C2×C3×C4D3×D412yes—
317C2×C3×C4C2×#6711yescharacteristic
318#67—68no—
319#67—68no—
320#67—632no—
321#67—616no—
322#67—616no—
323#67—64no—
324#67—64no—
325#67—64no—
326#67—64no—
327C2×Dic3—22no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—42no—
331C2×Dic3—41no—
332C2×Dic3—64no—
333C2×Dic3—616no—
334C2×Dic3—68no—
335C2×Dic3—68no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338D12—34no—
339D12—34no—
340D12—64no—
341D12—64no—
342D12—62no—
343D12—62no—
344C4×D3—68no—
345C4×D3—68no—
346C4×D3—64no—
347C4×D3—64no—
348C4×D3—64no—
349C4×D3—64no—
350Dic6—34no—
351Dic6—34no—
352Dic6—64no—
353Dic6—64no—
354Dic6—62no—
355Dic6—62no—
356C3×C8—122no—
357C3⋊C8—42no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—44no—
361C2×C32#37911yescharacteristic
362C2×C32#45311yescharacteristic
363C2×C32#45511yescharacteristic
364C3⋊D3—44no—
365C24—182no—
366C24#62612yes—
367#41—94no—
368#41—94no—
369#41—188no—
370#41—188no—
371#41—182no—
372#41—182no—
373C2×Q8—92no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—92no—
377C2×D4—188no—
378C2×D4—188no—
379C2×D4—184no—
380C2×D4—188no—
381C2×D4—188no—
382C2×D4—182no—
383C2×D4#62412yes—
384C2×D4#62612yes—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—182no—
388C22×C4—182no—
389C22×C4C2×D3211yescharacteristic
390M16—62no—
391M16—62no—
392C2×C8—62no—
393C4⋊C4—62no—
394C22⋊C4—124no—
395C42—62no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—28no—
401C22×C3—24no—
402C22×C3—24no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—44no—
409C22×C3—44no—
410C22×C3—44no—
411C22×C3—44no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—84no—
417C22×C3—82no—
418C22×C3—82no—
419C22×C3—84no—
420C22×C3#88211yescharacteristic
421C22×C3#88211yescharacteristic
422C22×C3C2×(C2×D3)⋊C411yescharacteristic
423C22×C3C2×(C2×D3)⋊C411yescharacteristic
424C22×C3#93711yescharacteristic
425C22×C3#93711yescharacteristic
426C2×D3—68no—
427C2×D3—64no—
428C2×D3—64no—
429C2×D3—124no—
430C2×D3—124no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—2416no—
436C2×D3—248no—
437C2×D3—248no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—122no—
441C3×C4—241no—
442C3×C4D3×C22⋊C412yes—
443C3×C4D3×C22⋊C412yes—
444C3×C4#88212yes—
445C3×C4#93712yes—
446Dic3—42no—
447Dic3—68no—
448Dic3—64no—
449Dic3—64no—
450Dic3—81no—
451C32#179211yescharacteristic, complemented, Sylow
452C23—22no—
453C23—22no—
454C23—42no—
455C23—42no—
456C23—188no—
457C23—182no—
458C23—722no—
459C23—722no—
460C23#372214yes—
461C23C2×#62611yescharacteristic
462Q8—94no—
463Q8—182no—
464D4—24no—
465D4—24no—
466D4—94no—
467D4—1816no—
468D4—184no—
469D4—184no—
470D4—182no—
471C2×C4—62no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—122no—
475C2×C4—121no—
476C2×C4—188no—
477C2×C4—182no—
478C2×C4—184no—
479C2×C4—184no—
480C2×C4C2×#62411yescharacteristic
481C2×C4C2×#62611yescharacteristic
482C2×C4#381112yes—
483C2×C4#381112yes—
484C8—122no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—48no—
495C2×C3—44no—
496C2×C3—44no—
497C2×C3#474611yescharacteristic
498C2×C3#474711yescharacteristic
499C2×C3#495511yescharacteristic
500C2×C3#495511yescharacteristic
501C2×C3#506111yescharacteristic
502C2×C3#507711yescharacteristic
503D3—128no—
504D3—124no—
505D3—124no—
506C22—21no—
507C22—21no—
508C22—24no—
509C22—44no—
510C22—42no—
511C22—42no—
512C22—82no—
513C22—184no—
514C22—362no—
515C22—362no—
516C22—728no—
517C22C2×#372211yescharacteristic
518C22#6398111yescharacteristic
519C22#6398111yescharacteristic
520C4—122no—
521C4—184no—
522C4—241no—
523C4#6397412yes—
524C4#6398112yes—
525C3—21no—
526C3#6966211yescharacteristic, complemented
527C3#7008611yescharacteristic, complemented
528C2—21no—
529C2—21no—
530C2—44no—
531C2—364no—
532C2#1059151111yescharacteristic
533C2#1059151411yescharacteristic
534C2#1059171411yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC2×#64361C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1792
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5221C2semidirect
3. C2×C3×#833C2semidirect
4. C2×#63570C2semidirect
5. #10591106C2semidirect
12. #64361C4semidirect
17. C2×C3×C4⋊Dic3C22semidirect
18. C2×C3×C4×Dic3C22semidirect
19. C2×C3×#208C22semidirect
29. #5221D3semidirect
30. C2×#833D3semidirect
96. C2×C4⋊Dic3C2×D3semidirect
97. C2×C4×Dic3C2×D3semidirect
98. C2×#208C2×D3semidirect
129. C4⋊(C3⋊D3)C22⋊C4semidirect
133. #634C22⋊C4semidirect
451. C32#1792semidirect
526. C3#69662semidirect
527. C3#70086semidirect

Maximal subgroups

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

subgroupindex
C2×#643612
C3×#52212
C2×C3×#8332
C2×#635702
#105911062
#700863
#696623