Finite Group Databasebeta

← #11906283

Subgroups — #11906283

Order 1152.

2077 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2C3×#5570C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595422C212yesmaximal, complemented
5#10595339C212yesmaximal
6#10594325C216yesmaximal
7#10594318C216yesmaximal, complemented
8#10593882C213yesmaximal
9#10593866C213yesmaximal
10#10593864C213yesmaximal, complemented
11#10593856C213yesmaximal, complemented
12#87046—31nomaximal
13#87031—31nomaximal
14C2×Q8×C3⋊D3C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16Q8×C3⋊Dic3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2213yes—
18#64096C2213yes—
19C42×C3⋊D3C2213yes—
20C4×#634C2213yes—
21C3×Q8×Dic3C2212yes—
22C3×Q8×Dic3C2212yes—
23C3×#890C2216yes—
24C3×#888C2216yes—
25C3×#869C2213yes—
26C3×#869C2213yes—
27C3×C4×Dic6C2213yes—
28C3×C4×Dic6C2213yes—
29#63919C2213yes—
30#63918C2216yes—
31C4×#627C2216yes—
32#63874C2216yes—
33#63873C2213yes—
34#63872C2216yes—
35#63871C2216yes—
36#63871C2213yes—
37#63871C2211yescharacteristic
38#63870C2216yes—
39#63869C2216yes—
40#63865C2216yes—
41#63849C2216yes—
42#63847C22112yes—
43#63844C2216yes—
44#63844C2216yes—
45#63843C2216yes—
46#63843C2216yes—
47#63839C22112yes—
48C3×Q82—31no—
49C3×#557—31no—
50#5729—36no—
51#5728—33no—
52#5728—33no—
53#5722—33no—
54#5721—36no—
55#5721—33no—
56#5689—36no—
57#5685—36no—
58#5578—33no—
59#5578—33no—
60#5572—32no—
61#5572—32no—
62C4×D3×Q8—31no—
63C4×D3×Q8—31no—
64C4×D3×Q8—61no—
65#5570—32no—
66#5570D311yescharacteristic, complemented
67#5569—32no—
68#5567—33no—
69Q8×Dic6—33no—
70Q8×Dic6D311yescharacteristic, complemented
71C2×C32×Q8C2311yescharacteristic
72Q8×C3⋊D3Q818yescomplemented
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×C4×C3⋊D3C2313yes—
75C2×C4×C3⋊D3C2313yes—
76C2×#634C2313yes—
77C2×C3×Dic6C2313yes—
78C2×C3×Dic6C2311yescharacteristic
79C2×C3×Dic6C2316yes—
80C2×#627C2316yes—
81C32×C4⋊C4C2313yes—
82C32×C42C2313yes—
83C4⋊(C3⋊Dic3)C2313yes—
84#3750C2316yes—
85C4×C3⋊Dic3C2313yes—
86C4×C3⋊Dic3C2313yes—
87C4×C3⋊Dic3C2313yes—
88C3×C4⋊Dic3C2316yes—
89C3×C4⋊Dic3C2316yes—
90C3×C4⋊Dic3C2316yes—
91C3×C4⋊Dic3C2313yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4C2316yes—
94C3×Dic3⋊C4C2316yes—
95C3×C4×Dic3C2316yes—
96C3×C4×Dic3C2316yes—
97#3724C2316yes—
98#3724C2316yes—
99#3724C2316yes—
100Dic3⋊Dic3C23112yes—
101Dic3⋊Dic3C2316yes—
102Dic3⋊Dic3C2312yes—
103#3722C2316yes—
104#3722C2312yes—
105Dic32C23112yes—
106#3502—91noSylow
107C2×D3×Q8—31no—
108C2×D3×Q8—31no—
109C2×D3×Q8—61no—
110C3×C4⋊Q8—36no—
111C3×C4⋊Q8—33no—
112C3×C4⋊Q8—33no—
113C3×#125—36no—
114C3×C4×Q8—21no—
115C3×C4×Q8—32no—
116C3×C4×Q8—32no—
117C3×C4×Q8—33no—
118C3×C4×Q8—33no—
119C3×C4×Q8C2×D311yescharacteristic
120C3×C4×Q8C2×D311yescharacteristic
121#946—33no—
122#946—36no—
123#946—31no—
124Q8×Dic3—31no—
125Q8×Dic3—31no—
126Q8×Dic3—36no—
127Q8×Dic3—36no—
128Q8×Dic3—61no—
129Q8×Dic3C2×D312yes—
130Q8×Dic3C2×D312yes—
131#944—33no—
132#944—33no—
133#944—312no—
134#897—36no—
135#897—33no—
136#897—31no—
137#896—36no—
138#896—36no—
139#892—36no—
140#892—36no—
141D3×C4⋊C4—33no—
142D3×C4⋊C4—33no—
143D3×C4⋊C4—63no—
144#890—36no—
145#890—36no—
146#890—36no—
147#890C2×D316yes—
148#889—312no—
149#889—36no—
150#889—312no—
151#889—36no—
152#888—312no—
153#888—33no—
154#888—33no—
155#888—36no—
156#888C2×D316yes—
157#887—36no—
158#887—36no—
159#887—33no—
160#887—33no—
161#887—36no—
162#887—36no—
163#887—63no—
164#872—36no—
165#872—36no—
166C42×D3—33no—
167C42×D3—33no—
168C42×D3—63no—
169#870—36no—
170#869—36no—
171#869C2×D313yes—
172#869C2×D313yes—
173C4×Dic6—33no—
174C4×Dic6—33no—
175C4×Dic6—36no—
176C4×Dic6—36no—
177C4×Dic6—36no—
178C4×Dic6—36no—
179C4×Dic6—63no—
180C4×Dic6C2×D313yes—
181C4×Dic6C2×D313yes—
182C22×C3⋊D3C2411yescharacteristic
183C32×Q8C2×Q814yes—
184C2×C32×C4C2413yes—
185C2×C32×C4C2413yes—
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3C2411yescharacteristic
188C2×C3⋊Dic3C2413yes—
189C2×C3⋊Dic3C2413yes—
190C4×C3⋊D3—22no—
191C4×C3⋊D3—43no—
192C4×C3⋊D3C2×Q8112yes—
193#634C2×Q8112yes—
194C2×C3×Dic3C2416yes—
195C2×C3×Dic3C2416yes—
196C2×C3×Dic3C2412yes—
197C2×C3×Dic3C2412yes—
198C3×Dic6—22no—
199C3×Dic6—26no—
200C3×Dic6—46no—
201#627—46no—
202Q82—31no—
203Q82—93no—
204#557—31no—
205#557—92no—
206#557—93no—
207#557—96no—
208#544—96no—
209#533—93no—
210#533—93no—
211#519—92no—
212C2×C4×Q8—91no—
213C2×C3×Q8—21no—
214C2×C3×Q8—31no—
215C2×C3×Q8—33no—
216C2×C3×Q8—36no—
217C2×C3×Q8C22×D311yescharacteristic
218C2×C3×Q8C22×D311yescharacteristic
219D3×Q8—38no—
220D3×Q8—38no—
221D3×Q8—68no—
222C2×C4×D3—33no—
223C2×C4×D3—33no—
224C2×C4×D3—31no—
225C2×C4×D3—31no—
226C2×C4×D3—33no—
227C2×C4×D3—33no—
228C2×C4×D3—61no—
229C2×C4×D3—63no—
230C2×C4×D3—63no—
231C2×Dic6—33no—
232C2×Dic6—33no—
233C2×Dic6—36no—
234C2×Dic6—36no—
235C2×Dic6—63no—
236C2×Dic6C22×D311yescharacteristic
237C2×Dic6C22×D313yes—
238C2×Dic6C22×D316yes—
239C3×C4⋊C4—23no—
240C3×C4⋊C4—33no—
241C3×C4⋊C4—36no—
242C3×C4⋊C4—36no—
243C3×C4⋊C4—36no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—36no—
246C3×C4⋊C4—36no—
247C3×C4⋊C4C22×D313yes—
248C3×C4⋊C4C22×D313yes—
249C3×C42—23no—
250C3×C42—36no—
251C3×C42—36no—
252C3×C42C22×D313yes—
253C3×C42C22×D313yes—
254(C2×D3)⋊C4—32no—
255(C2×D3)⋊C4—32no—
256(C2×D3)⋊C4—36no—
257(C2×D3)⋊C4—36no—
258C4⋊Dic3—33no—
259C4⋊Dic3—33no—
260C4⋊Dic3—32no—
261C4⋊Dic3—36no—
262C4⋊Dic3—312no—
263C4⋊Dic3—63no—
264C4⋊Dic3C22×D316yes—
265C4⋊Dic3C22×D316yes—
266C4⋊Dic3C22×D311yescharacteristic
267C4⋊Dic3C22×D313yes—
268C4⋊Dic3C22×D316yes—
269Dic3⋊C4—36no—
270Dic3⋊C4—36no—
271Dic3⋊C4—32no—
272Dic3⋊C4—36no—
273Dic3⋊C4—36no—
274Dic3⋊C4—36no—
275Dic3⋊C4—36no—
276Dic3⋊C4—36no—
277Dic3⋊C4—312no—
278Dic3⋊C4—36no—
279Dic3⋊C4—36no—
280Dic3⋊C4—66no—
281Dic3⋊C4C22×D316yes—
282Dic3⋊C4C22×D316yes—
283C4×Dic3—33no—
284C4×Dic3—33no—
285C4×Dic3—33no—
286C4×Dic3—33no—
287C4×Dic3—33no—
288C4×Dic3—33no—
289C4×Dic3—312no—
290C4×Dic3—312no—
291C4×Dic3—63no—
292C4×Dic3—63no—
293C4×Dic3—63no—
294C4×Dic3C22×D316yes—
295C4×Dic3C22×D316yes—
296C22×C32C2511yescharacteristic
297C2×C3⋊D3—21no—
298C2×C3⋊D3—21no—
299C2×C3⋊D3C22×Q812yes—
300C32×C4—23no—
301C32×C4C22×Q816yes—
302C32×C42−1+412yes—
303C3⋊Dic3—21no—
304C3⋊Dic3—23no—
305C3⋊Dic3C22×Q816yes—
306C3×Dic3—22no—
307C3×Dic3—26no—
308C3×Dic3—22no—
309C3×Dic3—26no—
310C22×Q8—91no—
311C4⋊Q8—36no—
312C4⋊Q8—33no—
313C4⋊Q8—33no—
314C4⋊Q8—96no—
315C4⋊Q8—93no—
316C4⋊Q8—912no—
317C4⋊Q8—93no—
318#125—36no—
319#125—96no—
320#125—96no—
321#125—96no—
322#125—912no—
323C22⋊Q8—96no—
324C22⋊Q8—91no—
325C22⋊Q8—93no—
326C22⋊Q8—96no—
327C4×Q8—32no—
328C4×Q8—32no—
329C4×Q8—33no—
330C4×Q8—33no—
331C4×Q8—96no—
332C4×Q8—96no—
333C4×Q8—96no—
334C4×Q8—96no—
335C4×Q8—96no—
336C4×Q8—91no—
337C4×Q8—93no—
338C4×Q8—93no—
339C4×Q8D3211yescharacteristic
340#117—96no—
341#117—96no—
342C2×C4⋊C4—93no—
343C2×C42—93no—
344C22×D3—31no—
345C22×D3—31no—
346C22×D3—61no—
347C3×Q8—24no—
348C3×Q8—66no—
349C3×Q8—62no—
350C3×Q8—126no—
351C3×Q8D3×Q814yes—
352C3×Q8D3×Q814yes—
353C2×C3×C4—21no—
354C2×C3×C4—23no—
355C2×C3×C4—23no—
356C2×C3×C4—36no—
357C2×C3×C4—36no—
358C2×C3×C4—32no—
359C2×C3×C4—32no—
360C2×C3×C4C23×D313yes—
361C2×C3×C4C23×D313yes—
362C2×C3×C4C23×D313yes—
363C2×C3×C4C23×D313yes—
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×Dic3—33no—
367C2×Dic3—33no—
368C2×Dic3—31no—
369C2×Dic3—31no—
370C2×Dic3—33no—
371C2×Dic3—33no—
372C2×Dic3—61no—
373C2×Dic3—63no—
374C2×Dic3—63no—
375C2×Dic3C23×D316yes—
376C2×Dic3C23×D316yes—
377C2×Dic3C23×D312yes—
378C2×Dic3C23×D312yes—
379C4×D3—312no—
380C4×D3—312no—
381C4×D3—612no—
382C4×D3—64no—
383C4×D3—62no—
384C4×D3—62no—
385C4×D3—123no—
386C4×D3—123no—
387C4×D3—126no—
388Dic6—22no—
389Dic6—26no—
390Dic6—312no—
391Dic6—312no—
392Dic6—46no—
393Dic6—612no—
394Dic6—126no—
395Dic6—126no—
396C2×C32C23×Q811yescharacteristic
397C2×C32C2×2−1+411yescharacteristic
398C2×C32#58511yescharacteristic
399C3⋊D3—22no—
400C2×Q8—31no—
401C2×Q8—33no—
402C2×Q8—36no—
403C2×Q8—96no—
404C2×Q8—98no—
405C2×Q8—93no—
406C2×Q8C2×D3211yescharacteristic
407C22×C4—93no—
408C22×C4—91no—
409C22×C4—93no—
410C4⋊C4—36no—
411C4⋊C4—36no—
412C4⋊C4—31no—
413C4⋊C4—33no—
414C4⋊C4—36no—
415C4⋊C4—36no—
416C4⋊C4—36no—
417C4⋊C4—96no—
418C4⋊C4—96no—
419C4⋊C4—92no—
420C4⋊C4—96no—
421C4⋊C4—96no—
422C4⋊C4—912no—
423C4⋊C4—96no—
424C4⋊C4—93no—
425C4⋊C4C2×D3213yes—
426C22⋊C4—92no—
427C22⋊C4—96no—
428C42—36no—
429C42—36no—
430C42—912no—
431C42—93no—
432C42—93no—
433C42—93no—
434C42C2×D3213yes—
435C22×C3—21no—
436C22×C3C24×D311yescharacteristic
437C22×C3C24×D311yescharacteristic
438C2×D3—32no—
439C2×D3—32no—
440C2×D3—62no—
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—61no—
444C2×D3—61no—
445C2×D3—61no—
446C2×D3—61no—
447C3×C4—23no—
448C3×C4—23no—
449C3×C4—26no—
450C3×C4—22no—
451C3×C4—43no—
452C3×C4—66no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—66no—
456C3×C4C2×D3×Q816yes—
457C3×C4C2×D3×Q816yes—
458C3×C4#100712yes—
459C3×C4#101012yes—
460Dic3—22no—
461Dic3—26no—
462Dic3—26no—
463Dic3—22no—
464Dic3—36no—
465Dic3—36no—
466Dic3—66no—
467Dic3—62no—
468Dic3—61no—
469Dic3—61no—
470Dic3—63no—
471Dic3—63no—
472Dic3—123no—
473C32#350211yescharacteristic, complemented, Sylow
474C23—91no—
475Q8—62no—
476Q8—66no—
477Q8—912no—
478Q8—126no—
479Q8—366no—
480Q8#379714yes—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—36no—
484C2×C4—36no—
485C2×C4—93no—
486C2×C4—912no—
487C2×C4—91no—
488C2×C4—93no—
489C2×C4—182no—
490C2×C4—363no—
491C2×C4C22×D3213yes—
492C2×C4C22×D3213yes—
493C2×C4C22×D3211yescharacteristic
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3C22×D3×Q811yescharacteristic
498C2×C3C22×D3×Q811yescharacteristic
499C2×C3C2×#100711yescharacteristic
500C2×C3C2×#101011yescharacteristic
501C2×C3#596611yescharacteristic
502C2×C3#596811yescharacteristic
503D3—64no—
504D3—62no—
505D3—62no—
506C22—92no—
507C22—181no—
508C22—181no—
509C22C23×D3211yescharacteristic
510C4—23no—
511C4—62no—
512C4—66no—
513C4—66no—
514C4—62no—
515C4—96no—
516C4—181no—
517C4—183no—
518C4C2×#379716yes—
519C4#6431512yes—
520C3—21no—
521C3#8703111yescharacteristic, complemented
522C3#8704611yescharacteristic, complemented
523C2—182no—
524C2C22×#379711yescharacteristic
525C2C2×#6431511yescharacteristic
526C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC22×C3⋊D3C24
hypercenterC4×Q8D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5570C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595422C2semidirect
7. #10594318C2semidirect
10. #10593864C2semidirect
11. #10593856C2semidirect
66. #5570D3semidirect
70. Q8×Dic6D3semidirect
72. Q8×C3⋊D3Q8semidirect
473. C32#3502semidirect
521. C3#87031semidirect
522. C3#87046semidirect

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×#55702
C3×Q8×Dic62
#105954222
#105953392
#105943252
#105943182
#105938822
#105938662
#105938642
#105938562
#870463
#870313