Finite Group Databasebeta

← #11909911

Subgroups — #11909911

Order 1152.

2133 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3C3×#5570C211yesmaximal, characteristic, complemented
4Q8×#626C212yesmaximal, complemented
5#10595347C212yesmaximal, complemented
6#10594579C216yesmaximal, complemented
7#10594346C216yesmaximal, complemented
8#10593875C213yesmaximal
9#10593866C213yesmaximal, complemented
10#10593863C213yesmaximal, complemented
11#10593861C213yesmaximal, complemented
12#87024—31nomaximal
13#86753—31nomaximal
14C2×Q8×C3⋊D3C2211yescharacteristic
15C2×C3×D3×Q8C2212yes—
16C32×C4×Q8C2211yescharacteristic
17Q8×C3⋊Dic3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2213yes—
19#64096C2213yes—
20C42×C3⋊D3C2213yes—
21C4×#634C2213yes—
22C3×Q8×Dic3C2212yes—
23C3×#897C2216yes—
24C3×#890C2216yes—
25C3×C4×D12C2213yes—
26C3×#869C2213yes—
27C3×#869C2213yes—
28C3×C4×Dic6C2213yes—
29#63916C2211yescharacteristic
30C4×#626C2216yes—
31#63872C2216yes—
32#63872C2213yes—
33#63871C2216yes—
34#63871C2213yes—
35#63866C2216yes—
36#63863C2213yes—
37#63862C2216yes—
38#63858C22112yes—
39#63857C2216yes—
40#63855C2216yes—
41#63853C2216yes—
42#63849C2216yes—
43#63846C22112yes—
44#63843C2216yes—
45#63843C2216yes—
46Dic3×Dic6C2216yes—
47#63841C2216yes—
48C3×#557—31no—
49C3×D4×Q8—31no—
50Q8×#67—32no—
51#5812—32no—
52#5732—33no—
53#5728—33no—
54#5728—33no—
55#5721—33no—
56#5698—36no—
57#5694—36no—
58#5639—36no—
59#5625—36no—
60#5580—33no—
61Q8×D12—32no—
62Q8×D12D311yescharacteristic, complemented
63#5572—32no—
64C4×D3×Q8—31no—
65C4×D3×Q8—31no—
66C4×D3×Q8—61no—
67#5570—33no—
68#5570D311yescharacteristic, complemented
69#5557—33no—
70#5542—33no—
71C2×C32×Q8C2311yescharacteristic
72Q8×C3⋊D3—24no—
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×C4×C3⋊D3C2313yes—
75C2×C4×C3⋊D3C2313yes—
76C2×#634C2313yes—
77C3×D3×Q8—28no—
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3C2316yes—
80C2×C3×Dic6C2316yes—
81C2×C3×Dic6C2313yes—
82C2×#626C2312yes—
83C32×C4⋊C4C2313yes—
84C32×C42C2313yes—
85C4⋊(C3⋊Dic3)C2313yes—
86#3750C2316yes—
87C4×C3⋊Dic3C2313yes—
88C4×C3⋊Dic3C2313yes—
89C4×C3⋊Dic3C2313yes—
90C3×(C2×D3)⋊C4C2316yes—
91C3×C4⋊Dic3C2316yes—
92C3×C4⋊Dic3C2316yes—
93C3×C4⋊Dic3C2316yes—
94C3×C4⋊Dic3C2313yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4C2316yes—
97C3×C4×Dic3C2316yes—
98Dic3⋊Dic3C2316yes—
99Dic3⋊Dic3C2316yes—
100Dic3⋊Dic3C23112yes—
101Dic3⋊Dic3C2316yes—
102#3722C2316yes—
103(C2×D3)⋊Dic3C2316yes—
104(C2×D3)⋊Dic3C2312yes—
105(C2×D3)⋊Dic3C2316yes—
106Dic32C23112yes—
107#3523—91noSylow
108C22×C3×Q8—32no—
109C2×D3×Q8—31no—
110C2×D3×Q8—31no—
111C2×D3×Q8—61no—
112C2×D3×Q8C2×D312yes—
113C3×C4⋊Q8—33no—
114C3×C4⋊Q8—33no—
115C3×#125—36no—
116C3×C22⋊Q8—36no—
117C3×C4×Q8—21no—
118C3×C4×Q8—32no—
119C3×C4×Q8—33no—
120C3×C4×Q8C2×D311yescharacteristic
121C3×C4×Q8C2×D311yescharacteristic
122C3×C4×D4—33no—
123#947—33no—
124#946—36no—
125#946—33no—
126Q8×Dic3—31no—
127Q8×Dic3—31no—
128Q8×Dic3—36no—
129Q8×Dic3—36no—
130Q8×Dic3—36no—
131Q8×Dic3—61no—
132Q8×Dic3C2×D312yes—
133#944—36no—
134#938—31no—
135#936—33no—
136C4×#67—36no—
137#926—36no—
138#926—36no—
139#924—36no—
140#898—312no—
141#898—36no—
142#897—36no—
143#897—36no—
144#897—33no—
145#897C2×D316yes—
146#895—31no—
147#894—36no—
148#892—36no—
149#892—36no—
150#892—36no—
151D3×C4⋊C4—33no—
152D3×C4⋊C4—33no—
153D3×C4⋊C4—63no—
154#890—312no—
155#890—36no—
156#890—33no—
157#890—36no—
158#890—33no—
159#890C2×D316yes—
160#889—312no—
161#887—36no—
162#887—36no—
163#887—33no—
164#887—33no—
165#887—63no—
166#883—36no—
167#879—312no—
168#879—36no—
169C4×D12—36no—
170C4×D12C2×D313yes—
171#872—36no—
172C42×D3—33no—
173C42×D3—33no—
174C42×D3—63no—
175#869—36no—
176#869C2×D313yes—
177#869C2×D313yes—
178C4×Dic6—36no—
179C4×Dic6—33no—
180C4×Dic6—33no—
181C4×Dic6—63no—
182C4×Dic6C2×D313yes—
183C22×C3⋊D3C2411yescharacteristic
184C22×C3×D3C2412yes—
185C32×Q8#4114yes—
186C2×C32×C4C2413yes—
187C2×C32×C4C2413yes—
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3C2413yes—
190C2×C3⋊Dic3C2411yescharacteristic
191C2×C3⋊Dic3C2413yes—
192C4×C3⋊D3—26no—
193C4×C3⋊D3—22no—
194C4×C3⋊D3—26no—
195#634—26no—
196C2×C3×Dic3C2416yes—
197C2×C3×Dic3C2416yes—
198C2×C3×Dic3C2412yes—
199C3×D12—22no—
200C3×C4×D3—212no—
201C3×Dic6—212no—
202C3×Dic6—26no—
203#626—24no—
204#557—31no—
205#557—93no—
206#556—93no—
207#552—96no—
208D4×Q8—31no—
209D4×Q8—92no—
210#541—96no—
211#533—93no—
212#529—93no—
213#519—92no—
214C2×C4×Q8—91no—
215C2×C3×Q8—21no—
216C2×C3×Q8—36no—
217C2×C3×Q8—33no—
218C2×C3×Q8—68no—
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×D4—31no—
222C22×C3×C4—36no—
223C2×#67—32no—
224D3×Q8—28no—
225D3×Q8—68no—
226D3×Q8—64no—
227D3×Q8—64no—
228C2×D12—32no—
229C2×D12C22×D311yescharacteristic
230C2×C4×D3—31no—
231C2×C4×D3—31no—
232C2×C4×D3—33no—
233C2×C4×D3—33no—
234C2×C4×D3—33no—
235C2×C4×D3—33no—
236C2×C4×D3—61no—
237C2×C4×D3—63no—
238C2×C4×D3—63no—
239C2×C4×D3C22×D316yes—
240C2×Dic6—33no—
241C2×Dic6—33no—
242C2×Dic6—63no—
243C2×Dic6C22×D316yes—
244C2×Dic6C22×D313yes—
245C3×C4⋊C4—23no—
246C3×C4⋊C4—33no—
247C3×C4⋊C4—36no—
248C3×C4⋊C4—36no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—36no—
251C3×C4⋊C4—36no—
252C3×C4⋊C4C22×D313yes—
253C3×C4⋊C4C22×D313yes—
254C3×C22⋊C4—36no—
255C3×C42—23no—
256C3×C42—36no—
257C3×C42C22×D313yes—
258C3×C42C22×D313yes—
259#217—36no—
260#217—32no—
261#217—36no—
262(C2×D3)⋊C4—32no—
263(C2×D3)⋊C4—36no—
264(C2×D3)⋊C4—36no—
265(C2×D3)⋊C4—36no—
266(C2×D3)⋊C4—36no—
267(C2×D3)⋊C4C22×D316yes—
268C4⋊Dic3—33no—
269C4⋊Dic3—33no—
270C4⋊Dic3—36no—
271C4⋊Dic3—312no—
272C4⋊Dic3—36no—
273C4⋊Dic3—36no—
274C4⋊Dic3—63no—
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D313yes—
277C4⋊Dic3C22×D316yes—
278C4⋊Dic3C22×D316yes—
279C4⋊Dic3C22×D316yes—
280Dic3⋊C4—36no—
281Dic3⋊C4—36no—
282Dic3⋊C4—36no—
283Dic3⋊C4—36no—
284Dic3⋊C4—312no—
285Dic3⋊C4—36no—
286Dic3⋊C4—66no—
287Dic3⋊C4C22×D316yes—
288C4×Dic3—33no—
289C4×Dic3—33no—
290C4×Dic3—33no—
291C4×Dic3—33no—
292C4×Dic3—33no—
293C4×Dic3—33no—
294C4×Dic3—312no—
295C4×Dic3—312no—
296C4×Dic3—63no—
297C4×Dic3—63no—
298C4×Dic3—63no—
299C4×Dic3C22×D316yes—
300C22×C32C2511yescharacteristic
301C2×C3⋊D3—21no—
302C2×C3⋊D3—21no—
303C2×C3⋊D32−1+412yes—
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C32×C4—23no—
308C32×C4C2×#4116yes—
309C32×C42−1+412yes—
310C3⋊Dic3—23no—
311C3⋊Dic3—21no—
312C3⋊Dic3—23no—
313C3×Dic3—26no—
314C3×Dic3—22no—
315C3×Dic3—26no—
316C22×Q8—32no—
317C22×Q8—91no—
318C4⋊Q8—33no—
319C4⋊Q8—33no—
320C4⋊Q8—96no—
321#126—96no—
322#126—912no—
323#125—36no—
324#125—93no—
325#125—96no—
326#125—912no—
327#124—93no—
328#123—96no—
329C22⋊Q8—36no—
330C22⋊Q8—96no—
331C22⋊Q8—93no—
332C22⋊Q8—96no—
333#121—91no—
334C4×Q8—32no—
335C4×Q8—33no—
336C4×Q8—96no—
337C4×Q8—96no—
338C4×Q8—96no—
339C4×Q8—91no—
340C4×Q8—93no—
341C4×Q8—93no—
342C4×Q8D3211yescharacteristic
343C4×D4—33no—
344C4×D4—96no—
345#117—96no—
346#117—96no—
347#117—96no—
348C2×C4⋊C4—93no—
349C2×C42—93no—
350C23×C3—32no—
351C22×D3—31no—
352C22×D3—31no—
353C22×D3—61no—
354C22×D3C23×D312yes—
355C3×Q8—24no—
356C3×Q8—612no—
357C3×Q8—66no—
358C3×Q8#23714yes—
359C3×Q8#23914yes—
360C3×D4—62no—
361C2×C3×C4—21no—
362C2×C3×C4—23no—
363C2×C3×C4—23no—
364C2×C3×C4—36no—
365C2×C3×C4—36no—
366C2×C3×C4—32no—
367C2×C3×C4—612no—
368C2×C3×C4C23×D313yes—
369C2×C3×C4C23×D313yes—
370C2×C3×C4C23×D313yes—
371C2×C3×C4C23×D313yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—64no—
375C2×Dic3—31no—
376C2×Dic3—33no—
377C2×Dic3—33no—
378C2×Dic3—31no—
379C2×Dic3—33no—
380C2×Dic3—33no—
381C2×Dic3—61no—
382C2×Dic3—63no—
383C2×Dic3—63no—
384C2×Dic3C23×D316yes—
385C2×Dic3C23×D316yes—
386C2×Dic3C23×D312yes—
387D12—22no—
388D12—64no—
389C4×D3—212no—
390C4×D3—66no—
391C4×D3—66no—
392C4×D3—64no—
393C4×D3—612no—
394C4×D3—66no—
395C4×D3—66no—
396C4×D3—62no—
397C4×D3—62no—
398C4×D3—126no—
399Dic6—212no—
400Dic6—26no—
401Dic6—612no—
402Dic6—66no—
403Dic6—66no—
404C2×C32C22×#4111yescharacteristic
405C2×C32C2×2−1+411yescharacteristic
406C2×C32C2×2−1+411yescharacteristic
407C3⋊D3—22no—
408C3×D3—42no—
409C2×Q8—33no—
410C2×Q8—36no—
411C2×Q8—68no—
412C2×Q8—93no—
413C2×Q8—184no—
414C2×Q8C2×D3211yescharacteristic
415C2×D4—31no—
416C2×D4—92no—
417C22×C4—36no—
418C22×C4—91no—
419C22×C4—93no—
420C22×C4—93no—
421C4⋊C4—36no—
422C4⋊C4—36no—
423C4⋊C4—36no—
424C4⋊C4—33no—
425C4⋊C4—31no—
426C4⋊C4—36no—
427C4⋊C4—96no—
428C4⋊C4—96no—
429C4⋊C4—96no—
430C4⋊C4—912no—
431C4⋊C4—93no—
432C4⋊C4—96no—
433C4⋊C4C2×D3213yes—
434C22⋊C4—36no—
435C22⋊C4—96no—
436C22⋊C4—92no—
437C22⋊C4—96no—
438C22⋊C4—96no—
439C42—36no—
440C42—912no—
441C42—93no—
442C42—93no—
443C42—93no—
444C42C2×D3213yes—
445C22×C3—21no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—62no—
449C22×C3C24×D311yescharacteristic
450C22×C3C24×D311yescharacteristic
451C2×D3—22no—
452C2×D3—22no—
453C2×D3—22no—
454C2×D3—32no—
455C2×D3—32no—
456C2×D3—62no—
457C2×D3—62no—
458C2×D3—62no—
459C2×D3—61no—
460C2×D3—61no—
461C2×D3—61no—
462C2×D3—61no—
463C3×C4—23no—
464C3×C4—23no—
465C3×C4—26no—
466C3×C4—22no—
467C3×C4—43no—
468C3×C4—66no—
469C3×C4—66no—
470C3×C4—62no—
471C3×C4C2×#23716yes—
472C3×C4C2×#23916yes—
473C3×C4#100712yes—
474C3×C4#101012yes—
475Dic3—26no—
476Dic3—26no—
477Dic3—22no—
478Dic3—66no—
479Dic3—62no—
480Dic3—63no—
481Dic3—63no—
482Dic3—61no—
483Dic3—61no—
484Dic3—63no—
485Dic3—63no—
486Dic3—123no—
487C32#352311yescharacteristic, complemented, Sylow
488C23—32no—
489C23—91no—
490Q8—612no—
491Q8—66no—
492Q8—186no—
493Q8#379614yes—
494D4—62no—
495D4—184no—
496C2×C4—32no—
497C2×C4—36no—
498C2×C4—36no—
499C2×C4—612no—
500C2×C4—91no—
501C2×C4—93no—
502C2×C4—93no—
503C2×C4—186no—
504C2×C4—186no—
505C2×C4—182no—
506C2×C4C22×D3213yes—
507C2×C4C22×D3213yes—
508C2×C4C22×D3211yescharacteristic
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—122no—
513C2×C3C22×#23711yescharacteristic
514C2×C3C22×#23911yescharacteristic
515C2×C3C2×#100711yescharacteristic
516C2×C3C2×#101011yescharacteristic
517C2×C3D3×2−1+411yescharacteristic
518C2×C3D3×2−1+411yescharacteristic
519D3—42no—
520D3—64no—
521D3—62no—
522D3—62no—
523C22—62no—
524C22—62no—
525C22—62no—
526C22—92no—
527C22—181no—
528C22—181no—
529C22C23×D3211yescharacteristic
530C4—23no—
531C4—66no—
532C4—66no—
533C4—62no—
534C4—183no—
535C4—181no—
536C4—183no—
537C4C2×#379616yes—
538C4#6431512yes—
539C3—21no—
540C3#8675311yescharacteristic, complemented
541C3#8702411yescharacteristic, complemented
542C2—122no—
543C2—182no—
544C2C22×#379611yescharacteristic
545C2C2×#6431511yescharacteristic
546C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radical#63916C22
hypercenterC4×Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×Q8×D12C2semidirect
3. C3×#5570C2semidirect
4. Q8×#626C2semidirect
5. #10595347C2semidirect
6. #10594579C2semidirect
7. #10594346C2semidirect
9. #10593866C2semidirect
10. #10593863C2semidirect
11. #10593861C2semidirect
62. Q8×D12D3semidirect
68. #5570D3semidirect
487. C32#3523semidirect
540. C3#86753semidirect
541. C3#87024semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×Q8×D122
C3×#55702
Q8×#6262
#105953472
#105945792
#105943462
#105938752
#105938662
#105938632
#105938612
#870243
#867533