Finite Group Databasebeta

← #11910007

Subgroups — #11910007

Order 1152.

3090 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2#10596205C213yesmaximal, complemented
3#10596204C213yesmaximal, complemented
4#10596168C213yesmaximal, complemented
5#10596166C213yesmaximal, complemented
6#10596165C213yesmaximal, complemented
7#10596162C213yesmaximal, complemented
8#10596056C213yesmaximal, complemented
9#10596051C213yesmaximal, complemented
10#10596048C211yesmaximal, characteristic, complemented
11#10596047C211yesmaximal, characteristic, complemented
12#10596047C211yesmaximal, characteristic, complemented
13#10596045C211yesmaximal, characteristic, complemented
14C4×#3832C211yesmaximal, characteristic, complemented
15#10596043C211yesmaximal, characteristic, complemented
16#87026—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C32×C4⋊Q8C2213yes—
21C32×#125C2213yes—
22C32×#125C2213yes—
23C32×C4×Q8C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C32×C4×Q8C2213yes—
27#64156C2216yes—
28#64156C2213yes—
29#64155C2213yes—
30Q8×C3⋊Dic3C2211yescharacteristic
31#64107C2213yes—
32#64107C2216yes—
33#64107C2211yescharacteristic
34#64106C2213yes—
35#64106C2213yes—
36#64104C2213yes—
37#64104C2216yes—
38#64104C2213yes—
39#64104C2213yes—
40#64104C2213yes—
41#64104C2213yes—
42#64103C2216yes—
43#64103C2216yes—
44#64103C2213yes—
45#64103C2213yes—
46#64102C2216yes—
47#64102C2213yes—
48#64102C2213yes—
49#64101C2216yes—
50#64101C2213yes—
51#64101C2213yes—
52C4⋊C4×C3⋊D3C2213yes—
53#64099C2213yes—
54#64096C2213yes—
55#64084C2213yes—
56#64084C2213yes—
57#64083C2213yes—
58C4×C4⋊(C3⋊D3)C2213yes—
59C4×C4⋊(C3⋊D3)C2213yes—
60C4×C4⋊(C3⋊D3)C2213yes—
61C4×C4⋊(C3⋊D3)C2213yes—
62C4×C4⋊(C3⋊D3)C2213yes—
63#64081C2213yes—
64#64081C2213yes—
65C42×C3⋊D3C2213yes—
66C4×#634C2213yes—
67C3×#557D314yescomplemented
68#5734—312no—
69#5733—312no—
70#5697—312no—
71#5695—312no—
72#5694—312no—
73#5691—312no—
74#5585—312no—
75#5580—312no—
76#5577—34no—
77#5576—34no—
78#5576—34no—
79#5574—34no—
80C4×#239—34no—
81#5572—34no—
82C2×C32×Q8C2313yes—
83C2×C32×Q8C2311yescharacteristic
84#3832—24no—
85#3832—24no—
86Q8×C3⋊D3—24no—
87C2×C4⋊(C3⋊D3)C2313yes—
88C2×C4⋊(C3⋊D3)C2313yes—
89C2×C4⋊(C3⋊D3)C2313yes—
90C2×C4⋊(C3⋊D3)C2313yes—
91C2×C4⋊(C3⋊D3)C2313yes—
92C2×C4⋊(C3⋊D3)C2316yes—
93C2×C4×C3⋊D3C2313yes—
94C2×C4×C3⋊D3C2313yes—
95C2×C4×C3⋊D3C2313yes—
96C2×C4×C3⋊D3C2313yes—
97C2×C4×C3⋊D3C2313yes—
98C2×C4×C3⋊D3C2316yes—
99C2×#634C2313yes—
100C32×C4⋊C4C2313yes—
101C32×C4⋊C4C2313yes—
102C32×C4⋊C4C2313yes—
103C32×C4⋊C4C2313yes—
104C32×C4⋊C4C2316yes—
105C32×C4⋊C4C2313yes—
106C32×C4⋊C4C2311yescharacteristic
107C32×C42C2313yes—
108C32×C42C2313yes—
109C32×C42C2313yes—
110#3752C2311yescharacteristic
111#3752C2313yes—
112#3752C2313yes—
113#3752C2313yes—
114#3752C2311yescharacteristic
115#3752C2311yescharacteristic
116#3752C2313yes—
117#3752C2313yes—
118#3752C2313yes—
119#3752C2316yes—
120#3752C2313yes—
121#3752C2316yes—
122#3752C2316yes—
123C4⋊(C3⋊Dic3)C2313yes—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2313yes—
126C4⋊(C3⋊Dic3)C2313yes—
127#3750C2313yes—
128#3750C2311yescharacteristic
129#3750C2313yes—
130#3750C2313yes—
131C4×C3⋊Dic3C2316yes—
132C4×C3⋊Dic3C2311yescharacteristic
133C4×C3⋊Dic3C2313yes—
134C4×C3⋊Dic3C2313yes—
135#3524—91noSylow
136C2×#239—34no—
137C2×#239—34no—
138C2×D3×Q8—34no—
139C3×C4⋊Q8C2×D3112yes—
140C3×#125C2×D3112yes—
141C3×#125C2×D3112yes—
142C3×C4×Q8C2×D314yes—
143C3×C4×Q8C2×D314yes—
144C3×C4×Q8C2×D314yes—
145C3×C4×Q8C2×D3112yes—
146#947—324no—
147#947—312no—
148#946—312no—
149Q8×Dic3—34no—
150#898—312no—
151#898—324no—
152#898—34no—
153#897—312no—
154#897—312no—
155#895—312no—
156#895—324no—
157#895—312no—
158#895—312no—
159#895—312no—
160#895—312no—
161#894—324no—
162#894—324no—
163#894—312no—
164#894—312no—
165#893—324no—
166#893—312no—
167#893—312no—
168#892—324no—
169#892—312no—
170#892—312no—
171D3×C4⋊C4—312no—
172#890—312no—
173#887—312no—
174#875—312no—
175#875—312no—
176#874—312no—
177C4×D12—312no—
178C4×D12—312no—
179C4×D12—312no—
180C4×D12—312no—
181C4×D12—312no—
182#872—312no—
183#872—312no—
184C42×D3—312no—
185C4×Dic6—312no—
186C22×C3⋊D3C2411yescharacteristic
187C22×C3⋊D3C2413yes—
188C22×C3⋊D3C2413yes—
189C32×Q8—43no—
190C32×Q8#4114yes—
191C2×C32×C4C2413yes—
192C2×C32×C4C2413yes—
193C2×C32×C4C2411yescharacteristic
194C2×C32×C4C2411yescharacteristic
195C2×C32×C4C2413yes—
196C2×C32×C4C2411yescharacteristic
197C2×C32×C4C2413yes—
198C2×C3⋊Dic3C2411yescharacteristic
199C2×C3⋊Dic3C2413yes—
200C2×C3⋊Dic3C2411yescharacteristic
201C2×C3⋊Dic3C2413yes—
202C2×C3⋊Dic3C2411yescharacteristic
203C4⋊(C3⋊D3)—26no—
204C4⋊(C3⋊D3)—26no—
205C4⋊(C3⋊D3)—43no—
206C4⋊(C3⋊D3)—43no—
207C4⋊(C3⋊D3)—43no—
208C4⋊(C3⋊D3)—46no—
209C4×C3⋊D3—26no—
210C4×C3⋊D3—26no—
211C4×C3⋊D3—26no—
212C4×C3⋊D3—43no—
213C4×C3⋊D3—46no—
214C4×C3⋊D3—43no—
215#634—26no—
216#559—93no—
217#557C3⋊D311yescharacteristic, complemented
218#555—93no—
219#553—93no—
220#552—93no—
221#550—91no—
222#548—91no—
223#548—91no—
224#542—93no—
225#540—93no—
226#529—93no—
227#529—93no—
228#520—91no—
229#519—91no—
230C4×#41—91no—
231C2×C3×Q8C22×D3112yes—
232C2×C3×Q8C22×D314yes—
233#239—616no—
234#239—616no—
235D3×Q8—616no—
236C2×D12—312no—
237C2×D12—312no—
238C2×D12—312no—
239C2×D12—312no—
240C2×D12—312no—
241C2×D12—324no—
242C2×C4×D3—312no—
243C2×C4×D3—312no—
244C2×C4×D3—312no—
245C2×C4×D3—312no—
246C2×C4×D3—312no—
247C2×C4×D3—324no—
248C2×Dic6—312no—
249C3×C4⋊C4C22×D3112yes—
250C3×C4⋊C4C22×D3112yes—
251C3×C4⋊C4C22×D3112yes—
252C3×C4⋊C4C22×D3112yes—
253C3×C4⋊C4C22×D3124yes—
254C3×C4⋊C4C22×D3112yes—
255C3×C4⋊C4C22×D314yes—
256C3×C42C22×D3112yes—
257C3×C42C22×D3112yes—
258C3×C42C22×D3112yes—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—312no—
261(C2×D3)⋊C4—312no—
262(C2×D3)⋊C4—312no—
263(C2×D3)⋊C4—34no—
264(C2×D3)⋊C4—34no—
265(C2×D3)⋊C4—312no—
266(C2×D3)⋊C4—312no—
267(C2×D3)⋊C4—312no—
268(C2×D3)⋊C4—324no—
269(C2×D3)⋊C4—312no—
270(C2×D3)⋊C4—324no—
271(C2×D3)⋊C4—324no—
272C4⋊Dic3—312no—
273C4⋊Dic3—34no—
274C4⋊Dic3—312no—
275C4⋊Dic3—312no—
276Dic3⋊C4—312no—
277Dic3⋊C4—34no—
278Dic3⋊C4—312no—
279Dic3⋊C4—312no—
280C4×Dic3—324no—
281C4×Dic3—34no—
282C4×Dic3—312no—
283C4×Dic3—312no—
284C22×C32C2511yescharacteristic
285C2×C3⋊D3—21no—
286C2×C3⋊D3—23no—
287C2×C3⋊D3—23no—
288C2×C3⋊D3—23no—
289C2×C3⋊D3—23no—
290C2×C3⋊D3—23no—
291C2×C3⋊D3—21no—
292C2×C3⋊D3—23no—
293C2×C3⋊D3—21no—
294C32×C4—21no—
295C32×C4—23no—
296C32×C4—23no—
297C32×C4—21no—
298C32×C4—23no—
299C32×C4—21no—
300C32×C4C2×#4116yes—
301C3⋊Dic3—23no—
302C3⋊Dic3—21no—
303C3⋊Dic3—21no—
304C3⋊Dic3—21no—
305C3⋊Dic3—23no—
306C2×#41—91no—
307C2×#41—91no—
308C22×Q8—91no—
309C4⋊Q8C2×C3⋊D313yes—
310#127—93no—
311#126—91no—
312#126—93no—
313#126—96no—
314#125—93no—
315#125C2×C3⋊D313yes—
316#125C2×C3⋊D313yes—
317#124—93no—
318#124—96no—
319#124—93no—
320#124—93no—
321#123—96no—
322#123—93no—
323#123—93no—
324#123—96no—
325C22⋊Q8—93no—
326C22⋊Q8—93no—
327C22⋊Q8—93no—
328#121—93no—
329#121—93no—
330#121—93no—
331#121—93no—
332#121—96no—
333#121—93no—
334C4×Q8—91no—
335C4×Q8—93no—
336C4×Q8—93no—
337C4×Q8C2×C3⋊D311yescharacteristic
338C4×Q8C2×C3⋊D311yescharacteristic
339C4×Q8C2×C3⋊D311yescharacteristic
340C4×Q8C2×C3⋊D313yes—
341C4×D4—93no—
342C4×D4—93no—
343C4×D4—96no—
344C4×D4—93no—
345C4×D4—93no—
346C4×D4—93no—
347C4×D4—93no—
348C4×D4—93no—
349#117—93no—
350#117—93no—
351#117—96no—
352#117—93no—
353#117—93no—
354C2×C4⋊C4—93no—
355C2×C42—93no—
356C22×D3—34no—
357C22×D3—312no—
358C22×D3—312no—
359C3×Q8—412no—
360C3×Q8#239116yes—
361C2×C3×C4C23×D3112yes—
362C2×C3×C4C23×D3112yes—
363C2×C3×C4C23×D314yes—
364C2×C3×C4C23×D314yes—
365C2×C3×C4C23×D3112yes—
366C2×C3×C4C23×D314yes—
367C2×C3×C4C23×D3112yes—
368C2×Dic3—34no—
369C2×Dic3—312no—
370C2×Dic3—34no—
371C2×Dic3—312no—
372C2×Dic3—34no—
373D12—624no—
374D12—624no—
375D12—1212no—
376D12—1224no—
377D12—1212no—
378D12—1212no—
379C4×D3—624no—
380C4×D3—624no—
381C4×D3—624no—
382C4×D3—1212no—
383C4×D3—1212no—
384C4×D3—1224no—
385Dic6—624no—
386C2×C32C22×#4111yescharacteristic
387C2×C32#58511yescharacteristic
388C2×C32#58511yescharacteristic
389C3⋊D3—41no—
390C3⋊D3—43no—
391C3⋊D3—43no—
392#41—184no—
393#41—184no—
394C2×Q8—93no—
395C2×Q8—184no—
396C2×Q8C22×C3⋊D313yes—
397C2×Q8C22×C3⋊D311yescharacteristic
398C2×D4—93no—
399C2×D4—93no—
400C2×D4—93no—
401C2×D4—93no—
402C2×D4—96no—
403C2×D4—93no—
404C22×C4—93no—
405C22×C4—93no—
406C22×C4—93no—
407C22×C4—93no—
408C22×C4—93no—
409C22×C4—96no—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—91no—
413C4⋊C4—93no—
414C4⋊C4—93no—
415C4⋊C4—93no—
416C4⋊C4—91no—
417C4⋊C4—93no—
418C4⋊C4C22×C3⋊D313yes—
419C4⋊C4C22×C3⋊D313yes—
420C4⋊C4C22×C3⋊D313yes—
421C4⋊C4C22×C3⋊D316yes—
422C4⋊C4C22×C3⋊D313yes—
423C4⋊C4C22×C3⋊D311yescharacteristic
424C4⋊C4C22×C3⋊D313yes—
425C22⋊C4—91no—
426C22⋊C4—93no—
427C22⋊C4—93no—
428C22⋊C4—93no—
429C22⋊C4—96no—
430C22⋊C4—93no—
431C22⋊C4—96no—
432C22⋊C4—91no—
433C22⋊C4—93no—
434C22⋊C4—91no—
435C22⋊C4—93no—
436C22⋊C4—96no—
437C22⋊C4—93no—
438C42—91no—
439C42—93no—
440C42—93no—
441C42—96no—
442C42C22×C3⋊D313yes—
443C42C22×C3⋊D313yes—
444C42C22×C3⋊D313yes—
445C22×C3C24×D314yes—
446C2×D3—64no—
447C2×D3—612no—
448C2×D3—612no—
449C2×D3—612no—
450C2×D3—64no—
451C2×D3—612no—
452C2×D3—612no—
453C2×D3—612no—
454C2×D3—64no—
455C3×C4—212no—
456C3×C4—212no—
457C3×C4—24no—
458C3×C4—24no—
459C3×C4—212no—
460C3×C4—24no—
461C3×C4C2×#239124yes—
462Dic3—612no—
463Dic3—64no—
464Dic3—64no—
465Dic3—64no—
466Dic3—612no—
467C32#352411yescharacteristic, complemented, Sylow
468C23—91no—
469C23—93no—
470C23—93no—
471Q8—43no—
472Q8—186no—
473Q8#383214yes—
474D4—186no—
475D4—186no—
476D4—363no—
477D4—366no—
478D4—363no—
479D4—363no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—93no—
483C2×C4—93no—
484C2×C4—91no—
485C2×C4—186no—
486C2×C4—186no—
487C2×C4—186no—
488C2×C4—363no—
489C2×C4—363no—
490C2×C4—366no—
491C2×C4C23×C3⋊D313yes—
492C2×C4C23×C3⋊D311yescharacteristic
493C2×C4C23×C3⋊D313yes—
494C2×C4C23×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C2×C4C23×C3⋊D313yes—
497C2×C4C23×C3⋊D313yes—
498C2×C3C22×#23914yes—
499C2×C3#596414yes—
500C2×C3#596814yes—
501D3—124no—
502D3—1212no—
503D3—1212no—
504C22—181no—
505C22—183no—
506C22—183no—
507C22—183no—
508C22—181no—
509C22—183no—
510C22—183no—
511C22—183no—
512C22—181no—
513C22C24×C3⋊D311yescharacteristic
514C4—23no—
515C4—23no—
516C4—21no—
517C4—21no—
518C4—23no—
519C4—21no—
520C4—181no—
521C4—181no—
522C4—183no—
523C4—181no—
524C4—183no—
525C4C2×#383216yes—
526C3#8702614yescomplemented
527C2—361no—
528C2—363no—
529C2—363no—
530C2C22×#383211yescharacteristic
531C2#1059675611yescharacteristic
532C2#1059676011yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#557C2
hypercenter#557C3⋊D3
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
2. #10596205C2semidirect
3. #10596204C2semidirect
4. #10596168C2semidirect
5. #10596166C2semidirect
6. #10596165C2semidirect
7. #10596162C2semidirect
8. #10596056C2semidirect
9. #10596051C2semidirect
10. #10596048C2semidirect
11. #10596047C2semidirect
12. #10596047C2semidirect
13. #10596045C2semidirect
14. C4×#3832C2semidirect
15. #10596043C2semidirect
67. C3×#557D3semidirect
217. #557C3⋊D3semidirect
467. C32#3524semidirect
526. C3#87026semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
#105962052
#105962042
#105961682
#105961662
#105961652
#105961622
#105960562
#105960512
#105960482
#105960472
#105960452
C4×#38322
#105960432
#870263