Finite Group Databasebeta

← #11807201

Subgroups — #11807201

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63872C211yesmaximal, characteristic
2C4×#3750C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4C3×#4928C211yesmaximal, characteristic
5#10591357C211yesmaximal, characteristic
6#10591330C212yesmaximal
7#10591274C211yesmaximal, characteristic
8#10591274C211yesmaximal, characteristic
9#10591253C212yesmaximal
10#10591251C212yesmaximal
11Dic3×Dic3⋊C4C212yesmaximal
12#75988—31nomaximal
13#73660—31nomaximal
14C2×C32×C42C2211yescharacteristic
15C2×#3750C2211yescharacteristic
16C2×#3750C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30#63872C418yescomplemented
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#890—31no—
39C2×#890—31no—
40C3×#389—31no—
41C3×C4×C4⋊C4—31no—
42#4984—31no—
43#4976—32no—
44Dic3×C4⋊C4—31no—
45Dic3×C4⋊C4—31no—
46Dic3×C4⋊C4—31no—
47Dic3×C4⋊C4—31no—
48Dic3×C4⋊C4—32no—
49#4972—31no—
50C4×C4⋊Dic3D311yescharacteristic
51C4×Dic3⋊C4—31no—
52C4×Dic3⋊C4—31no—
53C4×Dic3⋊C4—32no—
54C4×Dic3⋊C4—61no—
55#4928—32no—
56#4928D311yescharacteristic
57#4655—32no—
58#4654—32no—
59#4653—32no—
60#4652—32no—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C32×C42—22no—
73#3750—22no—
74#3750—22no—
75C4×C3⋊Dic3—22no—
76C4×C3⋊Dic3C2×C414yes—
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2×C414yes—
79C3×C4⋊Dic3C2×C414yes—
80C3×C4⋊Dic3Q814yes—
81C3×Dic3⋊C4—24no—
82C3×C4×Dic3—42no—
83Dic3⋊Dic3—42no—
84Dic3⋊Dic3C2×C418yes—
85Dic3⋊Dic3C2×C418yes—
86Dic32—24no—
87Dic32—42no—
88#2370—91noSylow
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C42—21no—
95C2×C3×C42—32no—
96C2×C3×C42C2×D311yescharacteristic
97C2×C3×C42C2×D311yescharacteristic
98C2×C4⋊Dic3—32no—
99C2×C4⋊Dic3—32no—
100C2×C4⋊Dic3—32no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—31no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—61no—
113C2×Dic3⋊C4—61no—
114C2×Dic3⋊C4C2×D312yes—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—61no—
124C2×C4×Dic3—61no—
125C2×C4×Dic3C2×D312yes—
126#890—38no—
127#890—38no—
128C3×#95—32no—
129C3×#95—32no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—31no—
133C3⋊#95—31no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—61no—
141C3⋊#95—61no—
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D312yes—
144C23×C32C2411yescharacteristic
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4C22×C412yes—
151C2×C32×C4C2×Q812yes—
152C2×C32×C4#4112yes—
153C2×C32×C4#4112yes—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3⋊Dic3C22×C412yes—
165C2×C3⋊Dic3#4112yes—
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×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C22×C414yes—
176C2×C3×Dic3C22×C414yes—
177C2×C3×Dic3C2×Q814yes—
178C2×#125—91no—
179#389—31no—
180#389—92no—
181#389—91no—
182#387—92no—
183#387—92no—
184C4×C4⋊C4—31no—
185C4×C4⋊C4—92no—
186C4×C4⋊C4—91no—
187C4×C4⋊C4—91no—
188C4×C4⋊C4—91no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—32no—
195C22×C3×C4—32no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D312yes—
218C3×C4⋊C4—34no—
219C3×C4⋊C4—34no—
220C3×C4⋊C4—34no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—64no—
223C3×C42—22no—
224C3×C42—22no—
225C3×C42—42no—
226C3×C42—122no—
227C4⋊Dic3—22no—
228C4⋊Dic3—38no—
229C4⋊Dic3—38no—
230C4⋊Dic3—122no—
231C4⋊Dic3Dic614yes—
232C4⋊Dic3C4×D314yes—
233C4⋊Dic3C4×D314yes—
234Dic3⋊C4—24no—
235Dic3⋊C4—38no—
236Dic3⋊C4—38no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—64no—
240Dic3⋊C4—64no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—122no—
244C4×Dic3—34no—
245C4×Dic3—34no—
246C4×Dic3—42no—
247C4×Dic3—64no—
248C4×Dic3—64no—
249C4×Dic3—64no—
250C4×Dic3—62no—
251C4×Dic3—62no—
252C4×Dic3—122no—
253C4×Dic3—122no—
254C4×Dic3—122no—
255C22×C32C23×C411yescharacteristic
256C22×C32C22×Q811yescharacteristic
257C22×C32C2×#4111yescharacteristic
258C22×C32C2×#4111yescharacteristic
259C22×C32C2×#4111yescharacteristic
260C22×C32H(5,𝔽2)11yescharacteristic
261C22×C322−1+411yescharacteristic
262C32×C4—22no—
263C32×C4—41no—
264C32×C4C4×Q814yes—
265C3⋊Dic3—22no—
266C3⋊Dic3—22no—
267C3⋊Dic3—22no—
268C3⋊Dic3—41no—
269C3×Dic3—24no—
270C3×Dic3—24no—
271C3×Dic3—24no—
272C3×Dic3—42no—
273#125—98no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—32no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—92no—
280C2×C4⋊C4—92no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—92no—
284C2×C42—32no—
285C2×C42—91no—
286C2×C42—92no—
287C2×C42—91no—
288C2×C42—92no—
289C2×C42D3211yescharacteristic
290#95—32no—
291#95—32no—
292#95—92no—
293#95—92no—
294#95—92no—
295#95—91no—
296#95—91no—
297C23×C3—21no—
298C23×C3C23×D311yescharacteristic
299C23×C3C23×D311yescharacteristic
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—34no—
316C2×C3×C4—34no—
317C2×C3×C4—34no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4C2×Dic612yes—
332C2×C3×C4C2×C4×D312yes—
333C2×C3×C4C2×C4×D312yes—
334C2×C3×C4#23512yes—
335C2×C3×C4#23712yes—
336C2×C3×C4#23712yes—
337C2×C3×C4D3×Q812yes—
338C2×C3×C4#23912yes—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—32no—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—62no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3C2×Dic614yes—
385C2×Dic3C2×C4×D314yes—
386C2×Dic3C2×C4×D314yes—
387C2×C32C2×C4×Q811yescharacteristic
388C2×C32C4×#4111yescharacteristic
389C2×C32#52011yescharacteristic
390C2×C32#55211yescharacteristic
391C2×C32#55311yescharacteristic
392C2×C32#55411yescharacteristic
393C2×C32#55711yescharacteristic
394C22×C4—32no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—32no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4C2×D3211yescharacteristic
403C22×C4C2×D3211yescharacteristic
404C22×C4C2×D3211yescharacteristic
405C4⋊C4—34no—
406C4⋊C4—34no—
407C4⋊C4—34no—
408C4⋊C4—64no—
409C4⋊C4—62no—
410C4⋊C4—98no—
411C4⋊C4—98no—
412C4⋊C4—182no—
413C4⋊C4—182no—
414C4⋊C4—362no—
415C42—22no—
416C42—94no—
417C42—122no—
418C42—184no—
419C42—182no—
420C42—362no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3C22×Dic611yescharacteristic
429C22×C3C22×C4×D311yescharacteristic
430C22×C3C22×C4×D311yescharacteristic
431C22×C3C2×#23511yescharacteristic
432C22×C3C2×#23711yescharacteristic
433C22×C3C2×#23711yescharacteristic
434C22×C3#100411yescharacteristic
435C22×C3C2×D3×Q811yescharacteristic
436C22×C3C2×#23911yescharacteristic
437C22×C3#100711yescharacteristic
438C22×C3D3×#4111yescharacteristic
439C22×C3D3×#4111yescharacteristic
440C22×C3#100911yescharacteristic
441C22×C3#101011yescharacteristic
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—24no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—64no—
450C3×C4—64no—
451C3×C4—64no—
452C3×C4—122no—
453C3×C4C4×Dic614yes—
454C3×C4#88714yes—
455Dic3—24no—
456Dic3—24no—
457Dic3—24no—
458Dic3—42no—
459Dic3—64no—
460Dic3—62no—
461Dic3—62no—
462Dic3—62no—
463Dic3—62no—
464Dic3—62no—
465Dic3—62no—
466Dic3—122no—
467Dic3—122no—
468Dic3—122no—
469Dic3—121no—
470Dic3—121no—
471C32#237011yescharacteristic, complemented, Sylow
472C23C22×D3211yescharacteristic
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—34no—
479C2×C4—34no—
480C2×C4—34no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4D3×Dic612yes—
503C2×C4#379612yes—
504C2×C4C4×D3212yes—
505C2×C4#380412yes—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3C2×C4×Dic611yescharacteristic
514C2×C3C2×#88711yescharacteristic
515C2×C3#551411yescharacteristic
516C2×C3#552911yescharacteristic
517C2×C3C4×#23711yescharacteristic
518C2×C3#553911yescharacteristic
519C2×C3#554611yescharacteristic
520C2×C3#557011yescharacteristic
521C2×C3C4×#23911yescharacteristic
522C2×C3#557411yescharacteristic
523C2×C3#561811yescharacteristic
524C2×C3#563911yescharacteristic
525C2×C3#569011yescharacteristic
526C2×C3#572111yescharacteristic
527C22C2×D3×Dic611yescharacteristic
528C22C2×#379611yescharacteristic
529C22#6429711yescharacteristic
530C22C2×C4×D3211yescharacteristic
531C22#6430611yescharacteristic
532C22#6430711yescharacteristic
533C22C2×#380411yescharacteristic
534C4—22no—
535C4—41no—
536C4—64no—
537C4—64no—
538C4—64no—
539C4—122no—
540C4—182no—
541C4—182no—
542C4—182no—
543C4—361no—
544C4#6383714yes—
545C3—21no—
546C3#7366011yescharacteristic, complemented
547C3#7598811yescharacteristic, complemented
548C2#1059386111yescharacteristic
549C2C4×#379611yescharacteristic
550C2#1059388911yescharacteristic
551C2#1059394111yescharacteristic
552C2C2×#6383711yescharacteristic
553C2#1059497011yescharacteristic
554C2#1059498911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2370
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
30. #63872C4semidirect
471. C32#2370semidirect
546. C3#73660semidirect
547. C3#75988semidirect

Maximal subgroups

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

subgroupindex
C2×#638722
C4×#37502
C3×C4×C4⋊Dic32
C3×#49282
#105913572
#105913302
#105912742
#105912532
#105912512
Dic3×Dic3⋊C42
#759883
#736603