Finite Group Databasebeta

← #11801147

Subgroups — #11801147

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic32C211yesmaximal, characteristic
2#10592642C211yesmaximal, characteristic
3C3×#4942C211yesmaximal, characteristic
4C3×Dic3×C22⋊C4C211yesmaximal, characteristic
5#10591716C211yesmaximal, characteristic
6Dic3×#217C211yesmaximal, characteristic
7#10591697C211yesmaximal, characteristic
8#10591248C212yesmaximal, complemented
9#10591245C212yesmaximal, complemented
10Dic3×Dic3⋊C4C212yesmaximal, complemented
11#10591239C212yesmaximal, complemented
12#73863—31nomaximal
13#73437—31nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic32C418yescomplemented
25C2×Dic32C2212yes—
26C2×Dic32C2211yescharacteristic
27C2×Dic32C2211yescharacteristic
28C2×Dic32C2211yescharacteristic
29C2×Dic32C2211yescharacteristic
30#63658C2212yes—
31#63658C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C22×C4×Dic3—31no—
39C22×C4×Dic3—31no—
40C3×#380—31no—
41C3×C4×C22⋊C4—31no—
42#5212—31no—
43C4×#217—31no—
44#4977—32no—
45Dic3×C4⋊C4—32no—
46#4943—31no—
47#4943—31no—
48#4943—31no—
49#4943—31no—
50#4943—61no—
51#4942—31no—
52#4942D311yescharacteristic
53Dic3×C22⋊C4—31no—
54Dic3×C22⋊C4D311yescharacteristic
55#4932—32no—
56C4×Dic3⋊C4—32no—
57#4651—32no—
58#4651—32no—
59#4650—32no—
60#4648—32no—
61C24×C32C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3—22no—
65C22×C3⋊Dic3C2×C414yes—
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3—24no—
70C22×C3×Dic3—24no—
71C22×C3×Dic3C2×C414yes—
72C22×C3×Dic3C2×C414yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C32×C22⋊C4—22no—
80#3757—22no—
81C3×#217—22no—
82C3×#217—22no—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3—24no—
85Dic3⋊Dic3—24no—
86Dic32—24no—
87Dic32C2×C414yes—
88Dic32C2×C414yes—
89Dic32C2×C414yes—
90Dic32C2×C414yes—
91#2283—91noSylow
92C23×C3×C4—31no—
93C23×C3×C4—31no—
94C23×Dic3—31no—
95C23×Dic3—31no—
96C23×Dic3—61no—
97C23×Dic3C2×D311yescharacteristic
98C23×Dic3C2×D311yescharacteristic
99C2×C3×C4⋊C4—32no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C22⋊C4C2×D311yescharacteristic
104C2×C3×C22⋊C4C2×D311yescharacteristic
105C2×C3×C42—32no—
106C2×#217—31no—
107C2×#217—31no—
108C2×#217—61no—
109C2×#217C2×D311yescharacteristic
110C2×#217C2×D311yescharacteristic
111C2×C4⋊Dic3—32no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4C2×D312yes—
114C2×C4×Dic3—38no—
115C2×C4×Dic3—38no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3C2×D312yes—
127C3×#95—32no—
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⋊#95—62no—
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C23×C32—22no—
146C23×C32—22no—
147C23×C32C22×C412yes—
148C23×C32#4112yes—
149C23×C32#4112yes—
150C23×C32C2411yescharacteristic
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C3⋊Dic3—28no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3C22×C412yes—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—28no—
167C2×C3×Dic3—28no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3#4114yes—
179C2×C3×Dic3#4114yes—
180C22×C42—91no—
181#383—92no—
182#382—92no—
183#381—91no—
184#381—91no—
185#380—31no—
186#380—91no—
187C4×C4⋊C4—92no—
188C4×C22⋊C4—31no—
189C4×C22⋊C4—91no—
190#376—92no—
191C24×C3—21no—
192C24×C3C22×D311yescharacteristic
193C24×C3C22×D311yescharacteristic
194C22×C3×C4—22no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—34no—
198C22×C3×C4—34no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—32no—
202C22×C3×C4—32no—
203C22×C3×C4—64no—
204C22×C3×C4—64no—
205C22×C3×C4C22×D312yes—
206C22×C3×C4C22×D312yes—
207C22×Dic3—24no—
208C22×Dic3—24no—
209C22×Dic3—34no—
210C22×Dic3—34no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—64no—
220C22×Dic3—62no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—122no—
226C22×Dic3—122no—
227C22×Dic3C4×D314yes—
228C22×Dic3C4×D314yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D311yescharacteristic
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D311yescharacteristic
235C3×C4⋊C4—64no—
236C3×C22⋊C4—22no—
237C3×C22⋊C4—22no—
238C3×C22⋊C4—42no—
239C3×C22⋊C4—62no—
240C3×C22⋊C4—62no—
241C3×C42—64no—
242#217—22no—
243#217—22no—
244#217—62no—
245#217—62no—
246#217—122no—
247C4⋊Dic3—64no—
248Dic3⋊C4—24no—
249Dic3⋊C4—64no—
250C4×Dic3—24no—
251C4×Dic3—34no—
252C4×Dic3—34no—
253C4×Dic3—34no—
254C4×Dic3—34no—
255C4×Dic3—34no—
256C4×Dic3—34no—
257C4×Dic3—34no—
258C4×Dic3—34no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C22×C32—22no—
262C22×C32—22no—
263C22×C32—24no—
264C22×C32—24no—
265C22×C32#11714yes—
266C22×C32C23×C411yescharacteristic
267C22×C32C2×#4111yescharacteristic
268C22×C32C2×#4111yescharacteristic
269C22×C32C2×#4112yes—
270C22×C32C2×#4112yes—
271C32×C4—42no—
272C3⋊Dic3—22no—
273C3⋊Dic3—22no—
274C3⋊Dic3—42no—
275C3×Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C3×Dic3#11714yes—
280C3×Dic3#11714yes—
281C23×C4—31no—
282C23×C4—31no—
283C23×C4—91no—
284C2×C4⋊C4—32no—
285C2×C4⋊C4—92no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—31no—
288C2×C22⋊C4—91no—
289C2×C22⋊C4D3211yescharacteristic
290C2×C42—32no—
291C2×C42—91no—
292C2×C42—91no—
293C2×C42—91no—
294C2×C42—91no—
295C2×C42—98no—
296C2×C42—92no—
297#95—32no—
298#95—32no—
299#95—92no—
300#95—92no—
301#95—92no—
302#95—92no—
303#95—92no—
304#95—92no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—21no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3C2×C4×D312yes—
316C23×C3C2×C4×D312yes—
317C23×C3#23512yes—
318C23×C3#23512yes—
319C23×C3#23712yes—
320C23×C3#23912yes—
321C23×C3C23×D311yescharacteristic
322C23×C3C23×D311yescharacteristic
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—34no—
332C2×C3×C4—34no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—68no—
339C2×C3×C4—68no—
340C2×C3×C4—62no—
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×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—28no—
351C2×Dic3—28no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—68no—
365C2×Dic3—68no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3—128no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3C2×C4×D312yes—
389C2×Dic3C2×C4×D312yes—
390C2×Dic3C2×C4×D312yes—
391C2×Dic3C2×C4×D312yes—
392C2×Dic3#23714yes—
393C2×Dic3#23714yes—
394C2×C32—24no—
395C2×C32C2×#11711yescharacteristic
396C2×C32C2×#11711yescharacteristic
397C2×C32C2×#11711yescharacteristic
398C2×C32#52912yes—
399C2×C32#52912yes—
400C24C2×D3211yescharacteristic
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—34no—
406C22×C4—34no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—64no—
410C22×C4—64no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—94no—
414C22×C4—92no—
415C22×C4—182no—
416C22×C4—182no—
417C22×C4C2×D3212yes—
418C4⋊C4—64no—
419C4⋊C4—184no—
420C22⋊C4—22no—
421C22⋊C4—62no—
422C22⋊C4—62no—
423C22⋊C4—182no—
424C42—64no—
425C42—94no—
426C42—94no—
427C42—94no—
428C42—94no—
429C42—184no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—24no—
437C22×C3—24no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—21no—
443C22×C3—24no—
444C22×C3—44no—
445C22×C3—44no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3#87214yes—
449C22×C3#89214yes—
450C22×C3C22×C4×D311yescharacteristic
451C22×C3C22×C4×D311yescharacteristic
452C22×C3C2×#23511yescharacteristic
453C22×C3C2×#23511yescharacteristic
454C22×C3C2×#23712yes—
455C22×C3C2×#23712yes—
456C22×C3C2×#23711yescharacteristic
457C22×C3C2×#23911yescharacteristic
458C22×C3D3×#4112yes—
459C22×C3D3×#4112yes—
460C3×C4—34no—
461C3×C4—34no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—62no—
465C3×C4—62no—
466C3×C4—82no—
467C3×C4—122no—
468C3×C4—122no—
469Dic3—22no—
470Dic3—22no—
471Dic3—42no—
472Dic3—42no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—122no—
478Dic3—122no—
479Dic3—122no—
480Dic3—122no—
481Dic3—242no—
482Dic3#87714yes—
483Dic3#87714yes—
484C32#228311yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23#379912yes—
488C23C4×D3212yes—
489C23#380412yes—
490C23C22×D3211yescharacteristic
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—34no—
497C2×C4—34no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—68no—
501C2×C4—68no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—92no—
511C2×C4—92no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—188no—
517C2×C4—182no—
518C2×C4—182no—
519C2×C4—182no—
520C2×C3—24no—
521C2×C3—24no—
522C2×C3—22no—
523C2×C3—22no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—44no—
528C2×C3C2×#87211yescharacteristic
529C2×C3C2×#87711yescharacteristic
530C2×C3C2×#87711yescharacteristic
531C2×C3C2×#89211yescharacteristic
532C2×C3D3×#11711yescharacteristic
533C2×C3D3×#11711yescharacteristic
534C2×C3#553812yes—
535C2×C3#553812yes—
536C2×C3#560012yes—
537C2×C3#562412yes—
538C22—24no—
539C22—24no—
540C22—22no—
541C22—22no—
542C22#6383614yes—
543C22C2×#379911yescharacteristic
544C22C2×C4×D3211yescharacteristic
545C22D3×#23712yes—
546C22D3×#23712yes—
547C22C2×#380411yescharacteristic
548C4—34no—
549C4—34no—
550C4—42no—
551C4—62no—
552C4—62no—
553C4—122no—
554C4—122no—
555C4—182no—
556C4—182no—
557C4—362no—
558C3—21no—
559C3#7343711yescharacteristic, complemented
560C3#7386311yescharacteristic, complemented
561C2—24no—
562C2D3×#87711yescharacteristic
563C2D3×#87711yescharacteristic
564C2#1059421612yes—
565C2C2×#6383611yescharacteristic
566C2#1059518712yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2283
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591248C2semidirect
9. #10591245C2semidirect
10. Dic3×Dic3⋊C4C2semidirect
11. #10591239C2semidirect
24. C2×Dic32C4semidirect
484. C32#2283semidirect
559. C3#73437semidirect
560. C3#73863semidirect

Maximal subgroups

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

subgroupindex
C22×Dic322
#105926422
C3×#49422
C3×Dic3×C22⋊C42
#105917162
Dic3×#2172
#105916972
#105912482
#105912452
Dic3×Dic3⋊C42
#105912392
#738633
#734373