Finite Group Databasebeta

← #11801155

Subgroups — #11801155

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#624C211yesmaximal, characteristic
2C4×#3752C211yesmaximal, characteristic
3C3×#4932C211yesmaximal, characteristic, complemented
4C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10591371C212yesmaximal
6#10591367C212yesmaximal
7C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8C4×#3722C211yesmaximal, characteristic
9#10591248C212yesmaximal, complemented
10#10591245C212yesmaximal, complemented
11#10591222C211yesmaximal, characteristic, complemented
12#73752—31nomaximal
13#73413—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#624C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×#3752C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×#3722C2212yes—
27C2×Dic32C2211yescharacteristic
28C2×Dic32C2211yescharacteristic
29C4×#624C418yescomplemented
30#63658C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C42×D3—31no—
39C2×C42×D3—31no—
40C3×C4×C4⋊C4—31no—
41C3×#376—31no—
42#4987—32no—
43#4977—32no—
44C4×(C2×D3)⋊C4—31no—
45C4×(C2×D3)⋊C4—31no—
46C4×(C2×D3)⋊C4—31no—
47C4×(C2×D3)⋊C4—31no—
48C4×(C2×D3)⋊C4—61no—
49C4×C4⋊Dic3—31no—
50#4932—31no—
51#4932—31no—
52#4932D311yescharacteristic, complemented
53C4×Dic3⋊C4—31no—
54C4×Dic3⋊C4D311yescharacteristic, complemented
55#4667—32no—
56#4664—32no—
57#4664—32no—
58#4651—32no—
59#4651—32no—
60#4650—32no—
61C23×C3⋊D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3C2×C414yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×#624—24no—
76C2×#624—24no—
77C2×#624C2×C414yes—
78C2×#624C2×C414yes—
79C32×C42—22no—
80#3752—24no—
81C4×C3⋊Dic3—22no—
82C3×Dic3⋊C4—24no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3C2×C414yes—
86C3×C4×Dic3C2×C414yes—
87Dic3⋊Dic3—24no—
88#3722—24no—
89Dic32C2×C414yes—
90Dic32C2×C414yes—
91#2283—91noSylow
92C22×C4×D3—31no—
93C22×C4×D3—31no—
94C22×C4×D3—31no—
95C22×C4×D3—31no—
96C22×C4×D3—31no—
97C22×C4×D3—31no—
98C22×C4×D3—61no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C42—21no—
101C2×C3×C42—31no—
102C2×C3×C42—31no—
103C2×C3×C42—31no—
104C2×C3×C42—31no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—62no—
112C2×C4⋊Dic3—32no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4C2×D312yes—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—61no—
122C2×C4×Dic3C2×D311yescharacteristic
123C2×C4×Dic3C2×D311yescharacteristic
124C2×C4×Dic3C2×D311yescharacteristic
125C2×C4×Dic3C2×D311yescharacteristic
126C42×D3—38no—
127C42×D3—38no—
128C3×#95—32no—
129C3×#95—32no—
130C3×#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—62no—
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3C22×C412yes—
150C22×C3⋊D3#4114yes—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4#4112yes—
156C2×C32×C4#4112yes—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3C22×C412yes—
163C4×C3⋊D3—28no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3#4114yes—
178#624—28no—
179#624—28no—
180C22×C42—91no—
181#383—92no—
182#382—92no—
183#381—92no—
184#380—92no—
185C4×C4⋊C4—31no—
186C4×C4⋊C4—91no—
187C4×C22⋊C4—91no—
188C4×C22⋊C4—91no—
189#376—31no—
190#376—91no—
191C23×D3—31no—
192C23×D3—31no—
193C23×D3—61no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4C22×D312yes—
203C22×C3×C4C22×D312yes—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—32no—
209C22×Dic3—32no—
210C22×Dic3—61no—
211C22×Dic3—62no—
212C22×Dic3C22×D312yes—
213C22×Dic3C22×D312yes—
214C22×Dic3C22×D311yescharacteristic
215C22×Dic3C22×D311yescharacteristic
216C22×Dic3C22×D311yescharacteristic
217C22×Dic3C22×D311yescharacteristic
218C2×C4×D3—34no—
219C2×C4×D3—34no—
220C2×C4×D3—34no—
221C2×C4×D3—34no—
222C2×C4×D3—34no—
223C2×C4×D3—34no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×C4×D3—64no—
233C2×C4×D3—122no—
234C2×C4×D3—122no—
235C3×C4⋊C4—64no—
236C3×C42—22no—
237C3×C42—22no—
238C3×C42—34no—
239C3×C42—34no—
240C3×C42—42no—
241C3×C42—62no—
242C3×C42—62no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—68no—
248C4⋊Dic3—64no—
249Dic3⋊C4—24no—
250Dic3⋊C4—64no—
251C4×Dic3—22no—
252C4×Dic3—22no—
253C4×Dic3—34no—
254C4×Dic3—34no—
255C4×Dic3—34no—
256C4×Dic3—34no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—122no—
260C4×Dic3C4×D314yes—
261C4×Dic3C4×D314yes—
262C22×C32C23×C411yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C22×C32C2×#4111yescharacteristic
265C22×C32C2×#4112yes—
266C22×C32C2×#4112yes—
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—24no—
270C2×C3⋊D3—24no—
271C2×C3⋊D3#11714yes—
272C32×C4—42no—
273C32×C4#11714yes—
274C3⋊Dic3—22no—
275C3⋊Dic3—42no—
276C3×Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—22no—
279C3×Dic3—42no—
280C3×Dic3—42no—
281C3×Dic3#11714yes—
282C23×C4—91no—
283C23×C4—91no—
284C23×C4—91no—
285C2×C4⋊C4—32no—
286C2×C4⋊C4—92no—
287C2×C22⋊C4—92no—
288C2×C22⋊C4—92no—
289C2×C42—31no—
290C2×C42—31no—
291C2×C42—31no—
292C2×C42—31no—
293C2×C42—98no—
294C2×C42—91no—
295C2×C42—91no—
296C2×C42—91no—
297C2×C42D3211yescharacteristic
298#95—32no—
299#95—32no—
300#95—32no—
301#95—92no—
302#95—92no—
303#95—92no—
304#95—92no—
305#95—92no—
306C23×C3—21no—
307C23×C3C23×D311yescharacteristic
308C23×C3C23×D311yescharacteristic
309C22×D3—32no—
310C22×D3—32no—
311C22×D3—34no—
312C22×D3—34no—
313C22×D3—62no—
314C22×D3—64no—
315C22×D3—61no—
316C22×D3—62no—
317C22×D3—61no—
318C22×D3—61no—
319C22×D3—61no—
320C22×D3—62no—
321C22×D3—121no—
322C22×D3—121no—
323C22×D3—122no—
324C2×C3×C4—24no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—32no—
335C2×C3×C4—34no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4#23512yes—
353C2×C3×C4#23512yes—
354C2×C3×C4#23712yes—
355C2×C3×C4#23912yes—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—62no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—64no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—122no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—122no—
383C2×Dic3C2×C4×D312yes—
384C2×Dic3C2×C4×D312yes—
385C2×Dic3C2×C4×D312yes—
386C2×Dic3C2×C4×D312yes—
387C2×Dic3#23514yes—
388C4×D3—68no—
389C4×D3—68no—
390C4×D3—68no—
391C4×D3—68no—
392C4×D3—68no—
393C4×D3—68no—
394C4×D3—128no—
395C2×C32C2×#11711yescharacteristic
396C2×C32C2×#11711yescharacteristic
397C2×C32C2×#11711yescharacteristic
398C2×C32#52912yes—
399C2×C32#52912yes—
400C3⋊D3—24no—
401C24—91no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—31no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—94no—
409C22×C4—94no—
410C22×C4—91no—
411C22×C4—94no—
412C22×C4—92no—
413C22×C4—184no—
414C22×C4—184no—
415C22×C4—182no—
416C22×C4—182no—
417C22×C4C2×D3212yes—
418C22×C4C2×D3211yescharacteristic
419C4⋊C4—64no—
420C4⋊C4—184no—
421C22⋊C4—184no—
422C22⋊C4—184no—
423C42—22no—
424C42—34no—
425C42—34no—
426C42—62no—
427C42—62no—
428C42—94no—
429C42—94no—
430C42—182no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—21no—
436C22×C3C22×C4×D311yescharacteristic
437C22×C3C22×C4×D311yescharacteristic
438C22×C3C2×#23511yescharacteristic
439C22×C3C2×#23512yes—
440C22×C3C2×#23511yescharacteristic
441C22×C3C2×#23711yescharacteristic
442C22×C3C2×#23911yescharacteristic
443C22×C3D3×#4112yes—
444C22×C3D3×#4112yes—
445C22×C3D3×#4112yes—
446C2×D3—34no—
447C2×D3—34no—
448C2×D3—64no—
449C2×D3—62no—
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—64no—
454C2×D3—64no—
455C2×D3—64no—
456C2×D3—64no—
457C2×D3—122no—
458C2×D3—124no—
459C2×D3—124no—
460C2×D3—122no—
461C3×C4—24no—
462C3×C4—34no—
463C3×C4—44no—
464C3×C4—42no—
465C3×C4—42no—
466C3×C4—62no—
467C3×C4—62no—
468C3×C4—62no—
469C3×C4—122no—
470C3×C4—122no—
471C3×C4#87214yes—
472C3×C4#89214yes—
473Dic3—22no—
474Dic3—22no—
475Dic3—22no—
476Dic3—42no—
477Dic3—42no—
478Dic3—62no—
479Dic3—62no—
480Dic3—122no—
481Dic3—124no—
482Dic3—122no—
483Dic3—122no—
484Dic3#87214yes—
485C32#228311yescharacteristic, complemented, Sylow
486C23—92no—
487C23—94no—
488C23—181no—
489C23—182no—
490C23—181no—
491C23C22×D3211yescharacteristic
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—32no—
496C2×C4—34no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—92no—
510C2×C4—188no—
511C2×C4—188no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4—188no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4#379912yes—
519C2×C4C4×D3212yes—
520C2×C4#380412yes—
521C2×C3—22no—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3C2×#87211yescharacteristic
527C2×C3C2×#87211yescharacteristic
528C2×C3C2×#89211yescharacteristic
529C2×C3D3×#11711yescharacteristic
530C2×C3D3×#11711yescharacteristic
531C2×C3D3×#11711yescharacteristic
532C2×C3#552812yes—
533C2×C3#552812yes—
534C2×C3#555712yes—
535C2×C3#558012yes—
536D3—64no—
537D3—64no—
538D3—124no—
539C22—94no—
540C22—184no—
541C22—184no—
542C22—182no—
543C22—182no—
544C22C2×#379911yescharacteristic
545C22C2×C4×D3211yescharacteristic
546C22D3×#23512yes—
547C22#6430612yes—
548C22C2×#380411yescharacteristic
549C4—34no—
550C4—42no—
551C4—62no—
552C4—62no—
553C4—62no—
554C4—122no—
555C4—122no—
556C4—182no—
557C4—362no—
558C4#6383614yes—
559C3—21no—
560C3#7341311yescharacteristic, complemented
561C3#7375211yescharacteristic, complemented
562C2—184no—
563C2#1059393412yes—
564C2D3×#87211yescharacteristic
565C2#1059399211yescharacteristic
566C2C2×#6383611yescharacteristic
567C2#1059483612yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2283
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×#4932C2semidirect
4. C3×C4×Dic3⋊C4C2semidirect
7. C4×Dic3⋊Dic3C2semidirect
9. #10591248C2semidirect
10. #10591245C2semidirect
11. #10591222C2semidirect
29. C4×#624C4semidirect
52. #4932D3semidirect
54. C4×Dic3⋊C4D3semidirect
485. C32#2283semidirect
560. C3#73413semidirect
561. C3#73752semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6242
C4×#37522
C3×#49322
C3×C4×Dic3⋊C42
#105913712
#105913672
C4×Dic3⋊Dic32
C4×#37222
#105912482
#105912452
#105912222
#737523
#734133