Finite Group Databasebeta

← #11807131

Subgroups — #11807131

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic
2C3×#4984C211yesmaximal, characteristic
3C3×Dic3×C4⋊C4C211yesmaximal, characteristic
4C4×#3724C211yesmaximal, characteristic
5#10591274C211yesmaximal, characteristic
6#10591273C212yesmaximal
7Dic3×C4⋊Dic3C211yesmaximal, characteristic
8#10591264C212yesmaximal
9#10591243C212yesmaximal
10#10591213C212yesmaximal
11#10591212C211yesmaximal, characteristic
12#75987—31nomaximal
13#73657—31nomaximal
14C22×#634C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19#64097C418yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2212yes—
26C2×#3724C2211yescharacteristic
27C2×#3724C2212yes—
28C2×#3724C2211yescharacteristic
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35#63579C2211yescharacteristic
36#63579C2212yes—
37#63579C2211yescharacteristic
38C2×#888—31no—
39C2×#888—31no—
40C2×#888—61no—
41C3×#389—31no—
42C3×C4×C4⋊C4—31no—
43#4984D311yescharacteristic
44#4976—32no—
45Dic3×C4⋊C4—31no—
46Dic3×C4⋊C4—31no—
47Dic3×C4⋊C4—31no—
48Dic3×C4⋊C4D311yescharacteristic
49#4973—32no—
50#4972—31no—
51C4×C4⋊Dic3—31no—
52C4×Dic3⋊C4—31no—
53C4×Dic3⋊C4—31no—
54C4×Dic3⋊C4—32no—
55#4929—32no—
56#4928—31no—
57#4649—32no—
58#4647—32no—
59#4646—32no—
60#4646—32no—
61C22×C32×C4C2312yes—
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C2×#634—42no—
67C2×#634—42no—
68C2×#634C2×C418yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C32×C4⋊C4C2×C414yes—
76C4⋊(C3⋊Dic3)C2×C414yes—
77#3750C2×C418yes—
78C4×C3⋊Dic3C2×C414yes—
79C3×C4⋊Dic3—22no—
80C3×C4⋊Dic3—42no—
81C3×C4⋊Dic3Q814yescomplemented
82C3×C4×Dic3—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3—42no—
85#3724—22no—
86#3724—42no—
87#3724Q814yescomplemented
88Dic32—24no—
89Dic32—42no—
90#2369—91noSylow
91C22×Dic6—32no—
92C22×Dic6—32no—
93C22×Dic6—62no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C42—31no—
101C2×C3×C42—31no—
102C2×C3×C42—32no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4⋊Dic3C2×D312yes—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—31no—
113C2×Dic3⋊C4—31no—
114C2×Dic3⋊C4—31no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—62no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—61no—
125C2×C4×Dic3C2×D311yescharacteristic
126C2×C4×Dic3C2×D311yescharacteristic
127C2×C4×Dic3C2×D312yes—
128#888—38no—
129#888—38no—
130#888—68no—
131C3×#95—32no—
132C3×#95—32no—
133C3⋊#95—31no—
134C3⋊#95—31no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—32no—
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4C22×C414yes—
149C2×C32×C4C22×C412yes—
150C2×C32×C4C2×Q812yes—
151C2×C32×C4#4112yes—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3C22×C412yes—
157C2×C3⋊Dic3C22×C414yes—
158C2×C3⋊Dic3C22×C412yes—
159C2×C3⋊Dic3C2×Q812yes—
160C2×C3⋊Dic3#4112yes—
161#634—48no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×Q814yes—
178C2×C3×Dic3C2×Q812yes—
179C2×C3×Dic3C2×Q812yes—
180C2×C4⋊Q8—91no—
181#391—92no—
182#391—92no—
183#389—31no—
184#389—92no—
185#389—91no—
186C4×C4⋊C4—31no—
187C4×C4⋊C4—92no—
188C4×C4⋊C4—91no—
189C4×C4⋊C4—91no—
190C4×C4⋊C4—91no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—31no—
194C22×C3×C4—32no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—32no—
198C22×C3×C4—31no—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—62no—
212C22×Dic3C22×D311yescharacteristic
213C22×Dic3C22×D312yes—
214C22×Dic3C22×D311yescharacteristic
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D311yescharacteristic
217C22×Dic3C22×D311yescharacteristic
218C2×Dic6—38no—
219C2×Dic6—38no—
220C2×Dic6—68no—
221C2×Dic6—122no—
222C2×Dic6—122no—
223C2×Dic6—122no—
224C2×Dic6—122no—
225C2×Dic6—124no—
226C2×Dic6—124no—
227C3×C4⋊C4—24no—
228C3×C4⋊C4—34no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—122no—
231C3×C4⋊C4C4×D314yes—
232C3×C4⋊C4C4×D314yes—
233C3×C42—62no—
234C3×C42—62no—
235C3×C42—122no—
236C4⋊Dic3—22no—
237C4⋊Dic3—34no—
238C4⋊Dic3—34no—
239C4⋊Dic3—42no—
240C4⋊Dic3—64no—
241C4⋊Dic3Dic614yescomplemented
242Dic3⋊C4—38no—
243Dic3⋊C4—38no—
244Dic3⋊C4—34no—
245Dic3⋊C4—34no—
246Dic3⋊C4—68no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—122no—
250Dic3⋊C4—122no—
251C4×Dic3—22no—
252C4×Dic3—22no—
253C4×Dic3—34no—
254C4×Dic3—34no—
255C4×Dic3—42no—
256C4×Dic3—64no—
257C4×Dic3—64no—
258C4×Dic3—64no—
259C4×Dic3—122no—
260C4×Dic3—122no—
261C22×C32C23×C411yescharacteristic
262C22×C32C22×Q811yescharacteristic
263C22×C32C22×Q811yescharacteristic
264C22×C32C2×#4111yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C22×C32H(5,𝔽2)11yescharacteristic
267C22×C32H(5,𝔽2)11yescharacteristic
268C32×C4—24no—
269C32×C4C4×Q814yes—
270C3⋊Dic3—22no—
271C3⋊Dic3—24no—
272C3⋊Dic3C4×Q814yes—
273C3×Dic3—22no—
274C3×Dic3—22no—
275C3×Dic3—24no—
276C3×Dic3—41no—
277C3×Dic3—42no—
278C3×Dic3—41no—
279C22×Q8—92no—
280C4⋊Q8—98no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—31no—
283C2×C4⋊C4—32no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—92no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—92no—
289C2×C4⋊C4D3211yescharacteristic
290C2×C42—31no—
291C2×C42—31no—
292C2×C42—32no—
293C2×C42—91no—
294C2×C42—92no—
295C2×C42—92no—
296#95—32no—
297#95—32no—
298#95—92no—
299#95—92no—
300#95—91no—
301#95—92no—
302#95—91no—
303C23×C3—21no—
304C23×C3C23×D311yescharacteristic
305C23×C3C23×D311yescharacteristic
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—34no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—62no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—62no—
333C2×C3×C4—61no—
334C2×C3×C4C2×Dic612yes—
335C2×C3×C4C2×C4×D314yes—
336C2×C3×C4C2×C4×D314yes—
337C2×C3×C4C2×C4×D312yes—
338C2×C3×C4C2×C4×D312yes—
339C2×C3×C4#23512yes—
340C2×C3×C4#23712yes—
341C2×C3×C4D3×Q812yes—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—21no—
353C2×Dic3—22no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—34no—
366C2×Dic3—34no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3C2×Dic614yes—
385C2×Dic3D3×Q812yes—
386C2×Dic3D3×Q812yes—
387Dic6—128no—
388Dic6—128no—
389Dic6—1216no—
390C2×C32C2×C4×Q811yescharacteristic
391C2×C32C2×C4×Q811yescharacteristic
392C2×C32#51811yescharacteristic
393C2×C32#55411yescharacteristic
394C2×C32#55411yescharacteristic
395C2×C32#55511yescharacteristic
396C2×C32Q8211yescharacteristic
397C2×Q8—98no—
398C2×Q8—362no—
399C2×Q8—362no—
400C22×C4—31no—
401C22×C4—32no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—32no—
405C22×C4—31no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—92no—
409C22×C4C2×D3212yes—
410C22×C4C2×D3211yescharacteristic
411C4⋊C4—34no—
412C4⋊C4—62no—
413C4⋊C4—94no—
414C4⋊C4—98no—
415C4⋊C4—94no—
416C4⋊C4—122no—
417C4⋊C4—182no—
418C4⋊C4—362no—
419C4⋊C4#62414yes—
420C42—62no—
421C42—62no—
422C42—94no—
423C42—122no—
424C42—184no—
425C42—362no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3C22×Dic611yescharacteristic
434C22×C3C22×C4×D311yescharacteristic
435C22×C3C22×C4×D311yescharacteristic
436C22×C3C2×#23511yescharacteristic
437C22×C3C2×#23711yescharacteristic
438C22×C3#100411yescharacteristic
439C22×C3#100411yescharacteristic
440C22×C3C2×D3×Q811yescharacteristic
441C22×C3C2×D3×Q811yescharacteristic
442C22×C3C2×D3×Q811yescharacteristic
443C22×C3D3×#4111yescharacteristic
444C22×C3D3×#4111yescharacteristic
445C22×C3#100911yescharacteristic
446C22×C3#100911yescharacteristic
447C3×C4—24no—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—44no—
451C3×C4—62no—
452C3×C4—64no—
453C3×C4—62no—
454C3×C4—121no—
455C3×C4—122no—
456C3×C4—121no—
457C3×C4C4×Dic614yes—
458C3×C4#88714yes—
459Dic3—22no—
460Dic3—22no—
461Dic3—24no—
462Dic3—34no—
463Dic3—34no—
464Dic3—41no—
465Dic3—41no—
466Dic3—42no—
467Dic3—64no—
468Dic3—64no—
469Dic3—62no—
470Dic3—62no—
471Dic3—64no—
472Dic3—64no—
473Dic3—124no—
474C32#236911yescharacteristic, complemented, Sylow
475C23C22×D3211yescharacteristic
476Q8—368no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—34no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—62no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—61no—
494C2×C4—62no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—92no—
498C2×C4—92no—
499C2×C4—92no—
500C2×C4—92no—
501C2×C4—94no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4D3×Dic612yes—
507C2×C4#379512yes—
508C2×C4C2×#62414yes—
509C2×C4C2×#62412yes—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3C2×C4×Dic611yescharacteristic
518C2×C3C2×#88711yescharacteristic
519C2×C3#551111yescharacteristic
520C2×C3#553211yescharacteristic
521C2×C3#553911yescharacteristic
522C2×C3#554511yescharacteristic
523C2×C3#554511yescharacteristic
524C2×C3Q8×Dic611yescharacteristic
525C2×C3C4×D3×Q811yescharacteristic
526C2×C3C4×D3×Q811yescharacteristic
527C2×C3#561611yescharacteristic
528C2×C3#563511yescharacteristic
529C2×C3#569011yescharacteristic
530C2×C3#572211yescharacteristic
531C22C2×D3×Dic611yescharacteristic
532C22C2×#379511yescharacteristic
533C22#6431411yescharacteristic
534C22#6431411yescharacteristic
535C22D32×Q811yescharacteristic
536C22#6431911yescharacteristic
537C22C22×#62411yescharacteristic
538C4—24no—
539C4—64no—
540C4—62no—
541C4—62no—
542C4—94no—
543C4—121no—
544C4—121no—
545C4—122no—
546C4—182no—
547C4—184no—
548C4#6384414yes—
549C3—21no—
550C3#7365711yescharacteristic, complemented
551C3#7598711yescharacteristic, complemented
552C2#1059431211yescharacteristic
553C2#1059448511yescharacteristic
554C2#1059448611yescharacteristic
555C2#1059453211yescharacteristic
556C2C2×#6384411yescharacteristic
557C2#1059522311yescharacteristic
558C2Q8×#62411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
19. #64097C4semidirect
81. C3×C4⋊Dic3Q8semidirect
87. #3724Q8semidirect
241. C4⋊Dic3Dic6semidirect
474. C32#2369semidirect
550. C3#73657semidirect
551. C3#75987semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
C3×#49842
C3×Dic3×C4⋊C42
C4×#37242
#105912742
#105912732
Dic3×C4⋊Dic32
#105912642
#105912432
#105912132
#105912122
#759873
#736573