Finite Group Databasebeta

← #11868824

Subgroups — #11868824

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63918C211yesmaximal, characteristic, complemented
2#10594954C211yesmaximal, characteristic
3#10592832C211yesmaximal, characteristic
4C3×#5121C211yesmaximal, characteristic, complemented
5C3×#5118C211yesmaximal, characteristic, complemented
6#10591131C211yesmaximal, characteristic, complemented
7#10591106C211yesmaximal, characteristic
8#10590805C212yesmaximal, complemented
9#10590802C212yesmaximal, complemented
10#10590764C212yesmaximal, complemented
11#10590759C212yesmaximal, complemented
12#79240—31nomaximal
13#79060—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×#627—21no—
16C2×C32×M16C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23#63952—21no—
24#63952—21no—
25#63918—21no—
26#63918—21no—
27#63918C2212yes—
28#63918C2212yes—
29#63894C2211yescharacteristic
30#63894C2211yescharacteristic
31C4×#624—21no—
32#63874—21no—
33#63844C2211yescharacteristic
34#63844C2211yescharacteristic
35#63648C2212yes—
36#63643C2212yes—
37C3×#818C2212yes—
38C3×#817C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×Dic3⋊C8C2212yes—
41#63575C2212yes—
42#63573C2212yes—
43#63567C2212yes—
44#63564C2212yes—
45#5522—31no—
46C2×#888—31no—
47C4×#235—31no—
48C2×#869—31no—
49C3×#428—31no—
50C3×#423—31no—
51#5133—31no—
52#5133—31no—
53#5133—31no—
54#5133—61no—
55#5121—31no—
56#5121D311yescharacteristic, complemented
57#5118D311yescharacteristic, complemented
58#4995—31no—
59#4966—31no—
60#4890—32no—
61#4875—32no—
62#4870—32no—
63#4854—32no—
64#4851—32no—
65#4850—32no—
66#4846—32no—
67#4842—32no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70C22×C3⋊Dic3—21no—
71#3828—22no—
72#3828Q814yescomplemented
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3—21no—
75C2×#634C2311yescharacteristic
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C2×#627—22no—
80C2×#627—22no—
81C2×#627—44no—
82C2×#624—21no—
83C2×#624—21no—
84C32×M16—22no—
85C2×C32×C8C2312yes—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C3×#217—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3—21no—
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×#208—22no—
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101#3724—21no—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104#3722—21no—
105#3722—21no—
106Dic32—21no—
107Dic32—21no—
108#3079—91noSylow
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C22×Dic6—61no—
113C22×Dic6—61no—
114C2×C3×M16—21no—
115C2×C3×M16—31no—
116C2×C3×M16C2×D311yescharacteristic
117C2×C3×M16C2×D311yescharacteristic
118C3×#117—31no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C42—31no—
121C4×#67—61no—
122C4×#67—61no—
123#926C2×D311yescharacteristic
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—61no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×Dic3⋊C4—61no—
130C2×C4×Dic3C2×D311yescharacteristic
131C2×#208C2×D311yescharacteristic
132#893—31no—
133#893—31no—
134#888—32no—
135#888—32no—
136#888—61no—
137#888—61no—
138#887—31no—
139#887—31no—
140#67⋊C4—61no—
141#67⋊C4—61no—
142C4×D12—31no—
143C4×D12—31no—
144#872—61no—
145#872—61no—
146C42×D3—61no—
147C42×D3—61no—
148#869—32no—
149#869—32no—
150#869—61no—
151#869—61no—
152C4×Dic6—31no—
153C4×Dic6—31no—
154C3×#107—32no—
155C3×#106—32no—
156C3×C4⋊C8—32no—
157C3×C4⋊C8—32no—
158#821—32no—
159#821—32no—
160#821—32no—
161#821—62no—
162#818—32no—
163#818C2×D312yes—
164#817—32no—
165#817C2×D312yes—
166#816—32no—
167#816—32no—
168#816—32no—
169#816—62no—
170Dic3⋊C8C2×D312yes—
171Dic3⋊C8C2×D312yes—
172#810—32no—
173#809—32no—
174#808—32no—
175#807—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×Q812yes—
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182#638—24no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—42no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)C2×Q812yescomplemented
188C4×C3⋊D3—24no—
189#634—21no—
190#634C2×Q812yescomplemented
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201#627—44no—
202#627—44no—
203#624—42no—
204#624—42no—
205C32×C8—22no—
206C3×C3⋊C8—22no—
207C2×C4⋊Q8—91no—
208C4×#41—91no—
209#477—92no—
210#476—92no—
211#475—92no—
212#474—92no—
213#428—31no—
214#428—91no—
215#423—31no—
216#417—91no—
217#417—91no—
218C22×C3×C4—21no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C2×#67—61no—
225C2×#67—61no—
226C2×#67—121no—
227C22×Dic3—21no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—121no—
231C22×Dic3D1211yescharacteristic
232C22×Dic3D1211yescharacteristic
233#235—34no—
234#235—34no—
235#235—64no—
236#235—62no—
237#235—62no—
238#235—122no—
239C2×D12—31no—
240C2×D12—31no—
241C2×D12—61no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—121no—
249C2×Dic6—31no—
250C2×Dic6—31no—
251C2×Dic6—61no—
252C2×Dic6—62no—
253C2×Dic6—62no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C2×Dic6—124no—
257C2×Dic6—124no—
258C3×M16—22no—
259C3×M16—22no—
260C3×M16—42no—
261C3×M16—62no—
262C2×C3×C8—22no—
263C2×C3×C8—32no—
264C2×C3×C8C22×D312yes—
265C2×C3×C8C22×D312yes—
266C3×C4⋊C4—31no—
267C3×C4⋊C4—31no—
268C3×C4⋊C4—32no—
269C3×C4⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42—61no—
276#217—21no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281C4⋊Dic3—21no—
282C4⋊Dic3—32no—
283C4⋊Dic3—32no—
284C4⋊Dic3—62no—
285C4⋊Dic3—62no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3—121no—
290C4⋊Dic3C22×D312yes—
291C4⋊Dic3C22×D311yescharacteristic
292C4⋊Dic3C22×D311yescharacteristic
293Dic3⋊C4—61no—
294Dic3⋊C4—61no—
295Dic3⋊C4—61no—
296Dic3⋊C4—61no—
297Dic3⋊C4—62no—
298Dic3⋊C4—62no—
299C4×Dic3—21no—
300C4×Dic3—61no—
301C4×Dic3—61no—
302C4×Dic3—61no—
303C4×Dic3—61no—
304C4×Dic3D1211yescharacteristic
305C4×Dic3D1211yescharacteristic
306C4×Dic3C22×D311yescharacteristic
307C4×Dic3C22×D311yescharacteristic
308#208—22no—
309C2×C3⋊C8C22×D312yes—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32C22⋊Q812yes—
313C22×C32C22×D411yescharacteristic
314C2×C3⋊D3—22no—
315C2×C3⋊D3—41no—
316C2×C3⋊D3—41no—
317C32×C4C22⋊Q812yes—
318C32×C4C22×Q811yescharacteristic
319C32×C4C2×#4111yescharacteristic
320C3⋊Dic3—22no—
321C3⋊Dic3—42no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3—41no—
327C3×Dic3AGL(1,ℤ/8)12yes—
328C3×Dic3#13712yes—
329C2×#41—91no—
330C22×Q8—181no—
331C2×M16—31no—
332C2×M16D3211yescharacteristic
333C4⋊Q8—92no—
334C4⋊Q8—92no—
335C4⋊Q8—181no—
336C4⋊Q8—181no—
337C4×Q8—91no—
338C4×Q8—91no—
339C4×D4—91no—
340C4×D4—91no—
341C4×D4—181no—
342C4×D4—181no—
343#117—31no—
344#117—181no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—91no—
347C2×C4⋊C4—181no—
348C2×C42—31no—
349C2×C42—181no—
350#107—32no—
351#107—92no—
352#106—32no—
353#106—92no—
354C4⋊C8—32no—
355C4⋊C8—32no—
356#103—92no—
357#103—92no—
358#102—92no—
359#102—92no—
360C23×C3—21no—
361C23×C3C2×D1211yescharacteristic
362C23×C3D3×D411yescharacteristic
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—121no—
366C2×C3×C4—21no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—31no—
371C2×C3×C4—31no—
372C2×C3×C4—31no—
373C2×C3×C4—31no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—62no—
379C2×C3×C4—122no—
380C2×C3×C4C2×D1211yescharacteristic
381C2×C3×C4#23512yes—
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4#23712yes—
384C2×C3×C4D3×Q812yes—
385C2×C3×C4D3×Q812yes—
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388#67—64no—
389#67—64no—
390#67—124no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—42no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—121no—
402C2×Dic3—122no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—242no—
406C2×Dic3C2×D1211yescharacteristic
407C2×Dic3C2×D1211yescharacteristic
408C2×Dic3C2×D1211yescharacteristic
409C2×Dic3C2×D1211yescharacteristic
410D12—32no—
411D12—32no—
412D12—62no—
413D12—61no—
414D12—61no—
415D12—121no—
416C4×D3—64no—
417C4×D3—64no—
418C4×D3—124no—
419C4×D3—122no—
420C4×D3—122no—
421C4×D3—122no—
422C4×D3—122no—
423Dic6—32no—
424Dic6—32no—
425Dic6—62no—
426Dic6—61no—
427Dic6—61no—
428Dic6—121no—
429Dic6—124no—
430Dic6—124no—
431Dic6—124no—
432Dic6—124no—
433C3×C8—22no—
434C3×C8—22no—
435C3×C8—42no—
436C3×C8—62no—
437C3⋊C8—22no—
438C2×C32—22no—
439C2×C32C2×C22⋊Q811yescharacteristic
440C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
441C2×C32C2×#13711yescharacteristic
442C3⋊D3—42no—
443#41—94no—
444#41—182no—
445C2×Q8—91no—
446C2×Q8—182no—
447C2×Q8—182no—
448C2×Q8—364no—
449C2×D4—91no—
450C2×D4—181no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—61no—
454C22×C4—181no—
455C22×C4—181no—
456C22×C4—181no—
457C22×C4—181no—
458C22×C4C2×D3211yescharacteristic
459M16—22no—
460M16—62no—
461C2×C8—32no—
462C2×C8C2×D3212yes—
463C4⋊C4—32no—
464C4⋊C4—31no—
465C4⋊C4—31no—
466C4⋊C4—61no—
467C4⋊C4—92no—
468C4⋊C4—182no—
469C4⋊C4—182no—
470C4⋊C4—181no—
471C4⋊C4—181no—
472C4⋊C4—181no—
473C22⋊C4—61no—
474C22⋊C4—181no—
475C22⋊C4—181no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—31no—
480C42—61no—
481C42—181no—
482C42—181no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—22no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3#89612yes—
492C22×C3#89712yes—
493C22×C3C22×D1211yescharacteristic
494C22×C3C2×D3×D411yescharacteristic
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—122no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—241no—
503C2×D3—241no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—32no—
508C3×C4—32no—
509C3×C4—61no—
510C3×C4—61no—
511C3×C4—122no—
512C3×C4—121no—
513C3×C4—121no—
514C3×C4#89612yes—
515C3×C4#89712yes—
516C3×C4C2×#23511yescharacteristic
517C3×C4C2×#23711yescharacteristic
518C3×C4C2×D3×Q811yescharacteristic
519C3×C4C2×D3×Q811yescharacteristic
520Dic3—21no—
521Dic3—21no—
522Dic3—42no—
523Dic3—41no—
524Dic3—41no—
525Dic3—62no—
526Dic3—62no—
527Dic3—122no—
528Dic3—122no—
529Dic3—122no—
530Dic3—242no—
531Dic3#90812yes—
532Dic3#90912yes—
533C32#307911yescharacteristic, complemented, Sylow
534C23—181no—
535C23D3×D1211yescharacteristic
536Q8—92no—
537Q8—181no—
538Q8—364no—
539Q8—364no—
540D4—92no—
541D4—184no—
542D4—181no—
543C2×C4—31no—
544C2×C4—31no—
545C2×C4—31no—
546C2×C4—31no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—122no—
553C2×C4—181no—
554C2×C4—184no—
555C2×C4—182no—
556C2×C4—362no—
557C2×C4—362no—
558C2×C4—362no—
559C2×C4#379712yes—
560C2×C4D3×D1211yescharacteristic
561C2×C4#380412yes—
562C2×C4C22×D3211yescharacteristic
563C8—22no—
564C8—62no—
565C2×C3—22no—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—42no—
571C2×C3C2×#89611yescharacteristic
572C2×C3C2×#89711yescharacteristic
573C2×C3C2×#90811yescharacteristic
574C2×C3C2×#90911yescharacteristic
575C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
576C2×C3D3×#13711yescharacteristic
577D3—122no—
578D3—122no—
579D3—242no—
580C22—21no—
581C22—21no—
582C22—182no—
583C22—361no—
584C22—361no—
585C22#6389512yes—
586C22C2×D3×D1211yescharacteristic
587C4—32no—
588C4—32no—
589C4—61no—
590C4—61no—
591C4—122no—
592C4—121no—
593C4—121no—
594C4—182no—
595C4—362no—
596C4#6389512yes—
597C4C2×#379711yescharacteristic
598C4C2×#380411yescharacteristic
599C3—21no—
600C3#7906011yescharacteristic, complemented
601C3#7924011yescharacteristic, complemented
602C2—22no—
603C2—362no—
604C2D3×#90811yescharacteristic
605C2D3×#90911yescharacteristic
606C2C2×#6389511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenterC2×M16D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#63918C2semidirect
4. C3×#5121C2semidirect
5. C3×#5118C2semidirect
6. #10591131C2semidirect
8. #10590805C2semidirect
9. #10590802C2semidirect
10. #10590764C2semidirect
11. #10590759C2semidirect
56. #5121D3semidirect
57. #5118D3semidirect
72. #3828Q8semidirect
187. C4⋊(C3⋊D3)C2×Q8semidirect
190. #634C2×Q8semidirect
533. C32#3079semidirect
600. C3#79060semidirect
601. C3#79240semidirect

Maximal subgroups

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

subgroupindex
C2×#639182
#105949542
#105928322
C3×#51212
C3×#51182
#105911312
#105911062
#105908052
#105908022
#105907642
#105907592
#792403
#790603