Finite Group Databasebeta

← #11805373

Subgroups — #11805373

Order 1152.

1173 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×#64081C211yesmaximal, characteristic
2C3×#4937C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10591355C211yesmaximal, characteristic
5#10591266C212yesmaximal
6#10591264C212yesmaximal, complemented
7#10591260C211yesmaximal, characteristic
8#10591257C211yesmaximal, characteristic, complemented
9#10591243C212yesmaximal, complemented
10#10591229C211yesmaximal, characteristic, complemented
11#10591202C212yesmaximal
12#74263—31nomaximal
13#73635—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×#3752C2211yescharacteristic
17C2×#3752C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64081C418yescomplemented
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×#3724C2212yes—
25C2×#3724C2212yes—
26C2×#3722C2212yes—
27C2×#3722C2212yes—
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#872—31no—
39C2×#872—31no—
40C2×#872—61no—
41C3×#383—31no—
42C3×C4×C4⋊C4—31no—
43#4990—32no—
44#4976—32no—
45#4940—32no—
46#4937D311yescharacteristic, complemented
47C4×C4⋊Dic3D311yescharacteristic, complemented
48C4×Dic3⋊C4—32no—
49#4670—32no—
50#4669—32no—
51#4667—31no—
52#4667—31no—
53#4666—31no—
54#4666—31no—
55#4651—31no—
56#4651—31no—
57#4649—32no—
58#4649—31no—
59#4649—31no—
60#4647—32no—
61C23×C3⋊D3C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—24no—
69C2×C4×C3⋊D3C2×C414yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C32×C42C2×C414yes—
75#3752C2×C414yes—
76#3752C2×C414yes—
77#3750C2×C414yes—
78#3750C2×C414yes—
79C4×C3⋊Dic3C2×C414yes—
80C3×C4⋊Dic3—24no—
81C3×C4×Dic3—42no—
82#3724—24no—
83#3724—24no—
84#3722—24no—
85#3722—42no—
86Dic32—24no—
87Dic32—42no—
88#2347—91noSylow
89C22×C4×D3—31no—
90C22×C4×D3—31no—
91C22×C4×D3—61no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C42—21no—
94C2×C3×C42—32no—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C2×D311yescharacteristic
97C2×(C2×D3)⋊C4—31no—
98C2×(C2×D3)⋊C4—31no—
99C2×(C2×D3)⋊C4—31no—
100C2×(C2×D3)⋊C4—31no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3C2×D312yes—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—31no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—61no—
117C2×Dic3⋊C4—61no—
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×D312yes—
126#872—38no—
127#872—38no—
128#872—68no—
129C3×#95—32no—
130C3×#95—31no—
131C3×#95—31no—
132C3×#95—32no—
133C3×#95—31no—
134C3×#95—31no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95C2×D311yescharacteristic
140C3⋊#95C2×D311yescharacteristic
141C3⋊#95C2×D311yescharacteristic
142C3⋊#95C2×D311yescharacteristic
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3C22×C412yes—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4C22×C412yes—
156C2×C32×C4C22×C412yes—
157C2×C32×C4C22×C412yes—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3C22×C412yes—
162C2×C3⋊Dic3C22×C412yes—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3⋊Dic3#4114yes—
165C4×C3⋊D3—28no—
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×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3#4114yes—
178C2×#117—91no—
179#389—92no—
180#388—92no—
181#388—92no—
182#383—31no—
183#383—91no—
184#380—91no—
185C4×C4⋊C4—31no—
186C4×C4⋊C4—91no—
187C4×C4⋊C4—92no—
188C4×C22⋊C4—91no—
189C23×D3—31no—
190C23×D3—31no—
191C23×D3—61no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D312yes—
218C2×C4×D3—34no—
219C2×C4×D3—34no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—68no—
224C3×C4⋊C4—64no—
225C3×C42—24no—
226C3×C42—122no—
227C3×C42C4×D314yes—
228C3×C42C4×D314yes—
229(C2×D3)⋊C4—34no—
230(C2×D3)⋊C4—34no—
231(C2×D3)⋊C4—34no—
232(C2×D3)⋊C4—34no—
233(C2×D3)⋊C4—64no—
234(C2×D3)⋊C4—64no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—122no—
238(C2×D3)⋊C4—122no—
239C4⋊Dic3—24no—
240Dic3⋊C4—34no—
241Dic3⋊C4—34no—
242Dic3⋊C4—34no—
243Dic3⋊C4—34no—
244Dic3⋊C4—64no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247Dic3⋊C4—64no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250C4×Dic3—34no—
251C4×Dic3—34no—
252C4×Dic3—42no—
253C4×Dic3—64no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3—122no—
257C4×Dic3—122no—
258C22×C32C23×C411yescharacteristic
259C22×C32C2×#4112yes—
260C22×C32C2×#4112yes—
261C22×C32H(5,𝔽2)11yescharacteristic
262C22×C322−1+411yescharacteristic
263C2×C3⋊D3—22no—
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C32×C4—22no—
269C32×C4—22no—
270C32×C4—22no—
271C3⋊Dic3—22no—
272C3⋊Dic3—22no—
273C3⋊Dic3#11714yes—
274C3×Dic3—24no—
275C3×Dic3—42no—
276C3×Dic3—42no—
277C3×Dic3—42no—
278C23×C4—91no—
279#117—98no—
280C2×C4⋊C4—32no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—92no—
284C2×C4⋊C4—92no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4—91no—
287C2×C22⋊C4—92no—
288C2×C22⋊C4—92no—
289C2×C42—32no—
290C2×C42—91no—
291C2×C42—92no—
292C2×C42—92no—
293C2×C42D3211yescharacteristic
294#95—31no—
295#95—31no—
296#95—31no—
297#95—31no—
298#95—32no—
299#95—32no—
300#95—92no—
301#95—92no—
302C23×C3—21no—
303C23×C3C23×D311yescharacteristic
304C23×C3C23×D311yescharacteristic
305C22×D3—32no—
306C22×D3—32no—
307C22×D3—62no—
308C22×D3—64no—
309C22×D3—62no—
310C22×D3—61no—
311C22×D3—61no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—61no—
316C22×D3—61no—
317C22×D3—121no—
318C22×D3—122no—
319C22×D3—121no—
320C2×C3×C4—24no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—34no—
333C2×C3×C4—41no—
334C2×C3×C4—42no—
335C2×C3×C4—41no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
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×C4C2×C4×D312yes—
348C2×C3×C4C2×C4×D312yes—
349C2×C3×C4C2×C4×D312yes—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4C2×C4×D312yes—
353C2×Dic3—22no—
354C2×Dic3—22no—
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—22no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—62no—
373C2×Dic3—64no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—62no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—121no—
383C2×Dic3—122no—
384C2×Dic3—121no—
385C2×Dic3#23514yes—
386C4×D3—68no—
387C4×D3—68no—
388C4×D3—616no—
389C2×C32C2×#11711yescharacteristic
390C2×C32C4×#4111yescharacteristic
391C2×C32#52011yescharacteristic
392C2×C32#55312yes—
393C2×C32#55612yes—
394C3⋊D3—42no—
395C24—91no—
396C22×C4—32no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—32no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—94no—
404C22×C4—184no—
405C22×C4C2×D3211yescharacteristic
406C22×C4C2×D3211yescharacteristic
407C22×C4C2×D3211yescharacteristic
408C4⋊C4—64no—
409C4⋊C4—94no—
410C4⋊C4—94no—
411C4⋊C4—184no—
412C4⋊C4—184no—
413C22⋊C4—94no—
414C22⋊C4—94no—
415C22⋊C4—184no—
416C22⋊C4—362no—
417C42—94no—
418C42—122no—
419C42—184no—
420C42—362no—
421C42#62414yes—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3C22×C4×D311yescharacteristic
428C22×C3C22×C4×D311yescharacteristic
429C22×C3C2×#23512yes—
430C22×C3#100411yescharacteristic
431C22×C3#100711yescharacteristic
432C22×C3D3×#4112yes—
433C22×C3D3×#4112yes—
434C22×C3D3×#4112yes—
435C22×C3#100911yescharacteristic
436C22×C3#101011yescharacteristic
437C2×D3—64no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—62no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C3×C4—24no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—42no—
460C3×C4—42no—
461C3×C4—64no—
462C3×C4—122no—
463C3×C4—122no—
464C3×C4—122no—
465Dic3—24no—
466Dic3—34no—
467Dic3—34no—
468Dic3—42no—
469Dic3—42no—
470Dic3—42no—
471Dic3—64no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—122no—
477Dic3—122no—
478C32#234711yescharacteristic, complemented, Sylow
479C23—92no—
480C23—181no—
481C23—182no—
482C23—182no—
483C23—181no—
484C23C22×D3211yescharacteristic
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—34no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—94no—
502C2×C4—92no—
503C2×C4—92no—
504C2×C4—92no—
505C2×C4—188no—
506C2×C4—181no—
507C2×C4—182no—
508C2×C4—181no—
509C2×C4C2×#62412yes—
510C2×C4C2×#62412yes—
511C2×C4C2×#62412yes—
512C2×C3—22no—
513C2×C3—21no—
514C2×C3—22no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3C4×#23511yescharacteristic
518C2×C3#550411yescharacteristic
519C2×C3D3×#11711yescharacteristic
520C2×C3D3×#11711yescharacteristic
521C2×C3#552211yescharacteristic
522C2×C3#552311yescharacteristic
523C2×C3#554012yes—
524C2×C3#556812yes—
525C2×C3#570212yes—
526C2×C3#570912yes—
527D3—124no—
528D3—122no—
529D3—122no—
530C22—182no—
531C22—182no—
532C22—182no—
533C22—362no—
534C22—362no—
535C22#6429711yescharacteristic
536C22D3×#23512yes—
537C22#6430612yes—
538C22#6430711yescharacteristic
539C22C22×#62411yescharacteristic
540C4—22no—
541C4—22no—
542C4—22no—
543C4—64no—
544C4—94no—
545C4—122no—
546C4—122no—
547C4—122no—
548C4—182no—
549C4—182no—
550C3—21no—
551C3#7363511yescharacteristic, complemented
552C3#7426311yescharacteristic, complemented
553C2—362no—
554C2#1059392412yes—
555C2#1059394012yes—
556C2#1059495411yescharacteristic
557C2#1059496911yescharacteristic
558C2#1059499011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2347
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4937C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
6. #10591264C2semidirect
8. #10591257C2semidirect
9. #10591243C2semidirect
10. #10591229C2semidirect
21. #64081C4semidirect
46. #4937D3semidirect
47. C4×C4⋊Dic3D3semidirect
478. C32#2347semidirect
551. C3#73635semidirect
552. C3#74263semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×#49372
C3×C4×C4⋊Dic32
#105913552
#105912662
#105912642
#105912602
#105912572
#105912432
#105912292
#105912022
#742633
#736353