Finite Group Databasebeta

← #11802816

Subgroups — #11802816

Order 1152.

1141 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3⋊Dic3C211yesmaximal, characteristic
2#10592641C211yesmaximal, characteristic
3C3×#4943C211yesmaximal, characteristic
4C3×Dic3×C22⋊C4C211yesmaximal, characteristic
5#10591720C211yesmaximal, characteristic
6Dic3×#217C211yesmaximal, characteristic
7#10591696C211yesmaximal, characteristic
8#10591332C212yesmaximal, complemented
9#10591331C212yesmaximal, complemented
10#10591251C212yesmaximal, complemented
11#10591250C212yesmaximal, complemented
12#74054—31nomaximal
13#73445—31nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×#3750C2212yes—
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×C4×Dic3C2212yes—
23C2×#3724C2212yes—
24C2×Dic3⋊Dic3C418yescomplemented
25C2×Dic3⋊Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×Dic32C2212yes—
30#63658C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C22×C4⋊Dic3—31no—
39C22×Dic3⋊C4—31no—
40C3×#381—31no—
41C3×C4×C22⋊C4—31no—
42#5211—31no—
43C4×#217—31no—
44#4943—31no—
45#4943D311yescharacteristic
46#4942—31no—
47#4942—31no—
48#4942—31no—
49#4942—31no—
50#4942—61no—
51Dic3×C22⋊C4—31no—
52Dic3×C22⋊C4D311yescharacteristic
53#4933—32no—
54#4933—32no—
55#4654—32no—
56#4654—32no—
57#4653—32no—
58#4653—32no—
59#4652—32no—
60#4652—32no—
61C24×C32C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C3⋊Dic3—42no—
64C22×C3⋊Dic3C2×C414yes—
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3—22no—
69C22×C3×Dic3—22no—
70C22×C3×Dic3—42no—
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—
81#3750—42no—
82C3×#217—22no—
83C3×#217—22no—
84C3×C4×Dic3—42no—
85#3724—42no—
86Dic3⋊Dic3C2×C414yes—
87Dic3⋊Dic3C2×C414yes—
88Dic3⋊Dic3C2×C414yes—
89Dic3⋊Dic3C2×C414yes—
90Dic32—42no—
91#2313—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×C22⋊C4—21no—
100C2×C3×C22⋊C4—31no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4C2×D311yescharacteristic
103C2×C3×C22⋊C4C2×D311yescharacteristic
104C2×C3×C42—32no—
105C2×#217—31no—
106C2×#217—31no—
107C2×#217—61no—
108C2×#217C2×D311yescharacteristic
109C2×#217C2×D311yescharacteristic
110C2×C4⋊Dic3—38no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×Dic3⋊C4—38no—
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4—31no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—62no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3C2×D312yes—
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×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—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—44no—
160C2×C3⋊Dic3C22×C412yes—
161C2×C3⋊Dic3C22×C412yes—
162C2×C3×Dic3—28no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
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×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—44no—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C22×C4⋊C4—91no—
181#387—92no—
182#387—92no—
183#387—92no—
184#387—92no—
185#381—31no—
186#381—91no—
187#380—91no—
188#380—91no—
189C4×C22⋊C4—31no—
190C4×C22⋊C4—91no—
191C24×C3—21no—
192C24×C3C22×D311yescharacteristic
193C24×C3C22×D311yescharacteristic
194C22×C3×C4—22no—
195C22×C3×C4—34no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—34no—
201C22×C3×C4—32no—
202C22×C3×C4—32no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4—122no—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D312yes—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—34no—
215C22×Dic3—34no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—42no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—64no—
222C22×Dic3—62no—
223C22×Dic3—122no—
224C22×Dic3—122no—
225C22×Dic3—124no—
226C22×Dic3C4×D314yes—
227C22×Dic3C4×D314yes—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D311yescharacteristic
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D311yescharacteristic
234C3×C22⋊C4—22no—
235C3×C22⋊C4—22no—
236C3×C22⋊C4—42no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C42—122no—
240#217—22no—
241#217—22no—
242#217—62no—
243#217—62no—
244#217—122no—
245C4⋊Dic3—34no—
246C4⋊Dic3—34no—
247C4⋊Dic3—34no—
248C4⋊Dic3—34no—
249Dic3⋊C4—34no—
250Dic3⋊C4—34no—
251Dic3⋊C4—34no—
252Dic3⋊C4—34no—
253Dic3⋊C4—122no—
254Dic3⋊C4—122no—
255Dic3⋊C4—122no—
256Dic3⋊C4—122no—
257Dic3⋊C4—124no—
258C4×Dic3—42no—
259C4×Dic3—122no—
260C4×Dic3—122no—
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×C32H(5,𝔽2)12yes—
270C22×C322−1+412yes—
271C32×C4—42no—
272C3⋊Dic3—22no—
273C3⋊Dic3—22no—
274C3⋊Dic3—42no—
275C3×Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—22no—
279C3×Dic3—42no—
280C3×Dic3—42no—
281C23×C4—31no—
282C23×C4—31no—
283C23×C4—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—98no—
289C2×C4⋊C4—92no—
290C2×C4⋊C4—92no—
291C2×C22⋊C4—31no—
292C2×C22⋊C4—31no—
293C2×C22⋊C4—91no—
294C2×C22⋊C4D3211yescharacteristic
295C2×C42—32no—
296C2×C42—92no—
297#95—32no—
298#95—32no—
299#95—32no—
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#23712yes—
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—32no—
332C2×C3×C4—32no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—68no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
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—124no—
350C2×Dic3—28no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—44no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—64no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—122no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—124no—
386C2×Dic3—124no—
387C2×Dic3—128no—
388C2×Dic3C2×C4×D312yes—
389C2×Dic3C2×C4×D312yes—
390C2×Dic3C2×C4×D312yes—
391C2×Dic3C2×C4×D312yes—
392C2×C32—24no—
393C2×C32C2×#11711yescharacteristic
394C2×C32#51811yescharacteristic
395C2×C32#51911yescharacteristic
396C2×C32#53912yes—
397C2×C32#53912yes—
398C24C2×D3211yescharacteristic
399C22×C4—31no—
400C22×C4—31no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—34no—
404C22×C4—34no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—62no—
408C22×C4—62no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—94no—
412C22×C4—92no—
413C22×C4—122no—
414C22×C4—362no—
415C22×C4C2×D3212yes—
416C4⋊C4—94no—
417C4⋊C4—94no—
418C4⋊C4—94no—
419C4⋊C4—94no—
420C4⋊C4—362no—
421C4⋊C4—362no—
422C22⋊C4—22no—
423C22⋊C4—62no—
424C22⋊C4—62no—
425C22⋊C4—182no—
426C42—122no—
427C42—362no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—24no—
442C22×C3—42no—
443C22×C3—44no—
444C22×C3—44no—
445C22×C3—42no—
446C22×C3#87214yes—
447C22×C3#87714yes—
448C22×C3C22×C4×D311yescharacteristic
449C22×C3C22×C4×D311yescharacteristic
450C22×C3C2×#23511yescharacteristic
451C22×C3C2×#23511yescharacteristic
452C22×C3C2×#23711yescharacteristic
453C22×C3C2×#23711yescharacteristic
454C22×C3#100412yes—
455C22×C3#100912yes—
456C22×C3#101012yes—
457C22×C3#101012yes—
458C3×C4—42no—
459C3×C4—42no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—62no—
463C3×C4—62no—
464C3×C4—82no—
465C3×C4—122no—
466C3×C4—122no—
467Dic3—22no—
468Dic3—22no—
469Dic3—22no—
470Dic3—22no—
471Dic3—42no—
472Dic3—42no—
473Dic3—64no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—62no—
478Dic3—122no—
479Dic3—122no—
480Dic3—122no—
481Dic3—242no—
482C32#231311yescharacteristic, complemented, Sylow
483C23—22no—
484C23—22no—
485C23#379512yes—
486C23C4×D3212yes—
487C23#380412yes—
488C23C22×D3211yescharacteristic
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—68no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—124no—
512C2×C4—182no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—364no—
518C2×C3—24no—
519C2×C3—24no—
520C2×C3—21no—
521C2×C3—22no—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—44no—
526C2×C3C2×#87211yescharacteristic
527C2×C3C2×#87711yescharacteristic
528C2×C3#548611yescharacteristic
529C2×C3#551611yescharacteristic
530C2×C3#551611yescharacteristic
531C2×C3#552111yescharacteristic
532C2×C3#556412yes—
533C2×C3#556412yes—
534C2×C3#566512yes—
535C2×C3#566512yes—
536C22—24no—
537C22—24no—
538C22—22no—
539C22—22no—
540C22#6387714yes—
541C22C2×#379511yescharacteristic
542C22C2×C4×D3211yescharacteristic
543C22#6430912yes—
544C22#6431412yes—
545C22C2×#380411yescharacteristic
546C4—42no—
547C4—62no—
548C4—62no—
549C4—62no—
550C4—62no—
551C4—122no—
552C4—122no—
553C4—182no—
554C4—182no—
555C4—362no—
556C3—21no—
557C3#7344511yescharacteristic, complemented
558C3#7405411yescharacteristic, complemented
559C2—24no—
560C2#1059417712yes—
561C2#1059418211yescharacteristic
562C2#1059424511yescharacteristic
563C2C2×#6387711yescharacteristic
564C2#1059512712yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2313
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591332C2semidirect
9. #10591331C2semidirect
10. #10591251C2semidirect
11. #10591250C2semidirect
24. C2×Dic3⋊Dic3C4semidirect
482. C32#2313semidirect
557. C3#73445semidirect
558. C3#74054semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3⋊Dic32
#105926412
C3×#49432
C3×Dic3×C22⋊C42
#105917202
Dic3×#2172
#105916962
#105913322
#105913312
#105912512
#105912502
#740543
#734453