Finite Group Databasebeta

← #11808707

Subgroups — #11808707

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63844C211yesmaximal, characteristic, complemented
2C2×#63836C211yesmaximal, characteristic
3#10592372C211yesmaximal, characteristic
4C3×#4659C211yesmaximal, characteristic, complemented
5C3×#4649C211yesmaximal, characteristic, complemented
6#10591354C211yesmaximal, characteristic, complemented
7#10591350C211yesmaximal, characteristic
8#10591347C212yesmaximal
9#10591339C212yesmaximal, complemented
10#10591242C212yesmaximal, complemented
11#10591233C212yesmaximal
12#78130—31nomaximal
13#73668—31nomaximal
14C22×#634C2211yescharacteristic
15C22×#624C2211yescharacteristic
16C2×#3752C2212yes—
17C2×#3752C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×Dic3⋊C4C2211yescharacteristic
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×#3724C2212yes—
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×#3722C2212yes—
28C2×#3722C2211yescharacteristic
29C2×Dic32C2212yes—
30C2×Dic32C2211yescharacteristic
31#63844—24no—
32#63836—24no—
33C32×#95C2211yescharacteristic
34#63658C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39C2×#892—31no—
40C2×#887—31no—
41C2×#872—31no—
42C2×C4×Dic6—31no—
43C3×#400—31no—
44C3×C4×C4⋊C4—31no—
45#4994—32no—
46#4993—31no—
47#4981—32no—
48#4979—31no—
49C4×(C2×D3)⋊C4—32no—
50C4×C4⋊Dic3—32no—
51#4677—31no—
52#4676—32no—
53#4673—31no—
54#4673—31no—
55#4673—61no—
56#4666—32no—
57#4659D311yescharacteristic, complemented
58#4657—32no—
59#4656—31no—
60#4649—32no—
61#4649D311yescharacteristic, complemented
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C2×#634—22no—
68C2×#634—24no—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C2×#624—22no—
76C2×#624—22no—
77C2×#624Q814yescomplemented
78#3752—22no—
79#3752—24no—
80C3×C4⋊Dic3—22no—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—24no—
83C3×C4×Dic3—24no—
84C3×C4×Dic3D414yes—
85#3724—24no—
86Dic3⋊Dic3—24no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—24no—
89#3722—22no—
90#3722—24no—
91Dic32—22no—
92Dic32—24no—
93#2396—91noSylow
94C22×C4×D3—31no—
95C22×C4×D3—31no—
96C22×Dic6—31no—
97C22×Dic6—31no—
98C22×Dic6—61no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C42—31no—
103C2×C3×C42—32no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—31no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—61no—
113C2×(C2×D3)⋊C4—62no—
114C2×C4⋊Dic3—32no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4C2×D312yes—
124C2×Dic3⋊C4C2×D311yescharacteristic
125C2×C4×Dic3—31no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3C2×D312yes—
130C2×C4×Dic3C2×D311yescharacteristic
131#892—64no—
132#887—64no—
133#872—64no—
134C4×Dic6—64no—
135C3×#95—21no—
136C3×#95—32no—
137C3×#95—31no—
138C3×#95—32no—
139C3×#95C2×D311yescharacteristic
140C3×#95C2×D311yescharacteristic
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—62no—
146C3⋊#95C2×D311yescharacteristic
147C3⋊#95C2×D312yes—
148C3⋊#95C2×D312yes—
149C23×C32C2411yescharacteristic
150C22×C3⋊D3—21no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3C2×Q812yes—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D412yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3#4114yes—
165#634—28no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×Q812yes—
179C2×C3×Dic3C2×Q812yes—
180C2×C3×Dic3#4114yes—
181C2×C3×Dic3#4112yes—
182#624—28no—
183C2×C4×Q8—91no—
184C2×#117—91no—
185#400—31no—
186#399—91no—
187#398—92no—
188#396—92no—
189#395—91no—
190#393—91no—
191C4×C4⋊C4—31no—
192C4×C4⋊C4—92no—
193C4×C22⋊C4—92no—
194C23×D3—31no—
195C23×D3—31no—
196C23×D3—61no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—32no—
202C22×C3×C4—31no—
203C22×C3×C4—32no—
204C22×C3×C4—31no—
205C22×C3×C4C22×D312yes—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×Dic3—32no—
210C22×Dic3—32no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—62no—
214C22×Dic3—61no—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D311yescharacteristic
217C22×Dic3C22×D311yescharacteristic
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D311yescharacteristic
220C22×Dic3C22×D311yescharacteristic
221C2×C4×D3—34no—
222C2×C4×D3—34no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×Dic6—64no—
228C2×Dic6—64no—
229C2×Dic6—62no—
230C2×Dic6—62no—
231C2×Dic6—124no—
232C2×Dic6—122no—
233C3×C4⋊C4—64no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C42—34no—
237C3×C42—64no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—124no—
247(C2×D3)⋊C4—122no—
248C4⋊Dic3—22no—
249C4⋊Dic3—64no—
250C4⋊Dic3—64no—
251C4⋊Dic3—62no—
252Dic3⋊C4—22no—
253Dic3⋊C4—24no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—62no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259C4×Dic3—24no—
260C4×Dic3—64no—
261C4×Dic3—62no—
262C4×Dic3—64no—
263C4×Dic3—62no—
264C4×Dic3D1214yes—
265C22×C32C22×D411yescharacteristic
266C22×C32C22×Q811yescharacteristic
267C22×C32C2×#4112yes—
268C22×C32C2×#4111yescharacteristic
269C22×C32C2×#4112yes—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—24no—
272C2×C3⋊D3—41no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—41no—
275C32×C4—22no—
276C32×C4—42no—
277C3⋊Dic3—24no—
278C3⋊Dic3—41no—
279C3×Dic3—22no—
280C3×Dic3—24no—
281C3×Dic3—22no—
282C3×Dic3—41no—
283C3×Dic3—42no—
284C3×Dic3C22⋊Q814yes—
285C22×Q8—91no—
286C23×C4—91no—
287C4×Q8—184no—
288#117—184no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—92no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—91no—
299C2×C22⋊C4—92no—
300C2×C42—31no—
301C2×C42—32no—
302C2×C42—91no—
303C2×C42—92no—
304#95—32no—
305#95—31no—
306#95—32no—
307#95—92no—
308#95—92no—
309#95D3211yescharacteristic
310C23×C3—21no—
311C23×C3C23×D311yescharacteristic
312C23×C3C23×D311yescharacteristic
313C22×D3—32no—
314C22×D3—32no—
315C22×D3—62no—
316C22×D3—61no—
317C22×D3—62no—
318C22×D3—61no—
319C22×D3—61no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—61no—
324C22×D3—121no—
325C22×D3—122no—
326C22×D3—122no—
327C22×D3—121no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—34no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4C2×D1212yes—
358C2×C3×C4D3×D412yes—
359C2×Dic3—22no—
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—61no—
377C2×Dic3—62no—
378C2×Dic3—61no—
379C2×Dic3—62no—
380C2×Dic3—122no—
381C2×Dic3—122no—
382C2×Dic3—121no—
383C2×Dic3—122no—
384C2×Dic3C2×D1212yes—
385C2×Dic3C2×D1212yes—
386C2×Dic3#23514yes—
387C2×Dic3#23712yes—
388C2×Dic3D3×Q812yes—
389C2×Dic3D3×Q812yes—
390C4×D3—68no—
391C4×D3—68no—
392Dic6—68no—
393Dic6—68no—
394Dic6—128no—
395C2×C32C2×C22⋊Q811yescharacteristic
396C2×C32#52511yescharacteristic
397C2×C32#52912yes—
398C2×C32#53211yescharacteristic
399C2×C32#53312yes—
400C3⋊D3—42no—
401C24—91no—
402C2×Q8—184no—
403C2×Q8—182no—
404C22×C4—31no—
405C22×C4—31no—
406C22×C4—32no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—32no—
410C22×C4—94no—
411C22×C4—92no—
412C22×C4—91no—
413C22×C4—182no—
414C22×C4—182no—
415C22×C4C2×D3212yes—
416C22×C4C2×D3211yescharacteristic
417C4⋊C4—64no—
418C4⋊C4—62no—
419C4⋊C4—62no—
420C4⋊C4—182no—
421C4⋊C4—184no—
422C4⋊C4—184no—
423C4⋊C4—184no—
424C22⋊C4—184no—
425C22⋊C4—182no—
426C22⋊C4—184no—
427C22⋊C4—182no—
428C42—34no—
429C42—64no—
430C42—182no—
431C42—184no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3C22×D1211yescharacteristic
438C22×C3C2×#23512yes—
439C22×C3C2×D3×D411yescharacteristic
440C22×C3C2×#23711yescharacteristic
441C22×C3C2×D3×Q811yescharacteristic
442C22×C3C2×D3×Q811yescharacteristic
443C22×C3D3×#4112yes—
444C22×C3D3×#4111yescharacteristic
445C22×C3D3×#4112yes—
446C22×C3D3×#4112yes—
447C2×D3—64no—
448C2×D3—62no—
449C2×D3—64no—
450C2×D3—62no—
451C2×D3—122no—
452C2×D3—124no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—122no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—122no—
459C2×D3—241no—
460C2×D3—242no—
461C2×D3—241no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—34no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—62no—
469C3×C4—64no—
470C3×C4—62no—
471C3×C4—82no—
472C3×C4—122no—
473C3×C4—121no—
474Dic3—22no—
475Dic3—24no—
476Dic3—22no—
477Dic3—41no—
478Dic3—42no—
479Dic3—64no—
480Dic3—64no—
481Dic3—124no—
482Dic3—121no—
483Dic3—121no—
484Dic3—241no—
485Dic3#89714yes—
486C32#239611yescharacteristic, complemented, Sylow
487C23—92no—
488C23—181no—
489C23—182no—
490C23—181no—
491C23—182no—
492C23C22×D3211yescharacteristic
493Q8—188no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—32no—
501C2×C4—32no—
502C2×C4—34no—
503C2×C4—32no—
504C2×C4—61no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—61no—
508C2×C4—62no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—94no—
515C2×C4—188no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—181no—
519C2×C4—182no—
520C2×C4D3×D1212yes—
521C2×C3—21no—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3—22no—
525C2×C3—21no—
526C2×C3#547711yescharacteristic
527C2×C3C2×#89711yescharacteristic
528C2×C3#552411yescharacteristic
529C2×C3#553812yes—
530C2×C3#557812yes—
531C2×C3D3×C22⋊Q811yescharacteristic
532C2×C3#565611yescharacteristic
533C2×C3#566811yescharacteristic
534C2×C3#568812yes—
535C2×C3#570612yes—
536D3—122no—
537D3—122no—
538D3—242no—
539C22—182no—
540C22—184no—
541C22—361no—
542C22—362no—
543C22—361no—
544C22C2×D3×D1211yescharacteristic
545C22D3×#23512yes—
546C22D3×#23711yescharacteristic
547C22#6431212yes—
548C22D32×Q811yescharacteristic
549C4—22no—
550C4—34no—
551C4—42no—
552C4—64no—
553C4—62no—
554C4—62no—
555C4—121no—
556C4—122no—
557C4—184no—
558C4—361no—
559C3—21no—
560C3#7366811yescharacteristic, complemented
561C3#7813011yescharacteristic, complemented
562C2—362no—
563C2#1059396911yescharacteristic
564C2#1059407911yescharacteristic
565C2#1059408912yes—
566C2#1059439812yes—
567C2D3×#89711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63844C2semidirect
4. C3×#4659C2semidirect
5. C3×#4649C2semidirect
6. #10591354C2semidirect
9. #10591339C2semidirect
10. #10591242C2semidirect
57. #4659D3semidirect
61. #4649D3semidirect
77. C2×#624Q8semidirect
486. C32#2396semidirect
560. C3#73668semidirect
561. C3#78130semidirect

Maximal subgroups

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

subgroupindex
C2×#638442
C2×#638362
#105923722
C3×#46592
C3×#46492
#105913542
#105913502
#105913472
#105913392
#105912422
#105912332
#781303
#736683