Finite Group Databasebeta

← #11865767

Subgroups — #11865767

Order 1152.

1052 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63806C212yesmaximal, complemented
2C4×#3799C211yesmaximal, characteristic, complemented
3#10593897C211yesmaximal, characteristic, complemented
4#10592540C211yesmaximal, characteristic, complemented
5C3×#4848C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
7#10590954C212yesmaximal, complemented
8#10590860C212yesmaximal, complemented
9#10590859C212yesmaximal, complemented
10#10590385C211yesmaximal, characteristic, complemented
11#10590355C211yesmaximal, characteristic, complemented
12#80382—31nomaximal
13#79021—31nomaximal
14C2×#3799C2211yescharacteristic
15C2×#3795C2212yes—
16C2×#3744C2212yes—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18#64078C2211yescharacteristic
19C2×C3×#204C2212yes—
20C2×C3×D3×C8C2212yes—
21C3×#874C2211yescharacteristic
22C3×C42×D3C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63908—21no—
25#63908—21no—
26#63904—21no—
27C4×#626—21no—
28#63894C2211yescharacteristic
29Dic3×D12—21no—
30Dic3×D12—21no—
31C4×#624—21no—
32#63860C2212yes—
33Dic3×Dic6C2211yescharacteristic
34#63841C2211yescharacteristic
35#63836—21no—
36C2×#3719C2212yes—
37C2×#3714C2212yes—
38#63806—28no—
39C32×C4⋊C8C2211yescharacteristic
40#63643C2212yes—
41C3×#821C2212yes—
42C3×Dic3⋊C8C2212yes—
43C3×C4⋊(C3⋊C8)C2211yescharacteristic
44#63567C2212yes—
45#63563C2212yes—
46C2×#916—32no—
47C2×#904—32no—
48#5716—31no—
49C4×#239—31no—
50#5477—31no—
51C4×#235—31no—
52C3×#460—31no—
53C2×C3×C4⋊C8—31no—
54#5166—32no—
55#5113—32no—
56#5072—31no—
57#5031—31no—
58#4849—31no—
59#4848D311yescharacteristic, complemented
60#4845—32no—
61#4844—32no—
62#4843—31no—
63#4841—31no—
64#4841—31no—
65#4841—61no—
66D3×C4⋊C8D311yescharacteristic, complemented
67#4787—32no—
68#4772—32no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×#634C2312yes—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3C2311yescharacteristic
78C2×C3×Dic6C2311yescharacteristic
79C2×#626—21no—
80C2×#625—22no—
81C2×#624—21no—
82C2×#624—21no—
83C2×D3×Dic3—22no—
84#3799—22no—
85#3799D414yescomplemented
86#3795—24no—
87#3795—24no—
88C2×C32×C8C2312yes—
89C32×C42C2311yescharacteristic
90#3752—21no—
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)—21no—
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94#3744—24no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102C3×#204—24no—
103C3×D3×C8—24no—
104Dic3⋊Dic3—21no—
105#3722—21no—
106(C2×D3)⋊Dic3—21no—
107(C2×D3)⋊Dic3—22no—
108(C2×D3)⋊Dic3—22no—
109Dic32—21no—
110Dic32—21no—
111#3719—24no—
112#3714—24no—
113#3035—91noSylow
114C2×#239—31no—
115C2×#237—32no—
116C2×#235—32no—
117C2×#235—31no—
118C2×C3×SD16—32no—
119C22×C3×C8—32no—
120C3×#127—31no—
121C3×C4×Q8—31no—
122C2×C3×C42—31no—
123Q8×Dic3—31no—
124C2×#216—32no—
125#938—61no—
126#938—61no—
127#936—32no—
128D4×Dic3—61no—
129D4×Dic3—61no—
130C2×#213—32no—
131#930—61no—
132#930—61no—
133C4×#67—61no—
134C4×#67—61no—
135#926—31no—
136#916—68no—
137C2×Dic12—32no—
138#904—68no—
139C2×D24—32no—
140C2×#204—32no—
141C2×#204—32no—
142C2×#204—62no—
143C2×#204C2×D312yes—
144C2×D3×C8C2×D312yes—
145#893—31no—
146#893—61no—
147#892—31no—
148#892—61no—
149#875—32no—
150#874C2×D311yescharacteristic
151C4×D12—31no—
152C4×D12—31no—
153C4×D12—31no—
154C4×D12—61no—
155C4×D12—61no—
156C4×D12—61no—
157C4×D12—61no—
158#872—61no—
159C42×D3—61no—
160C42×D3—61no—
161C42×D3C2×D311yescharacteristic
162#869—31no—
163#869—31no—
164#869—61no—
165C4×Dic6—31no—
166C4×Dic6C2×D311yescharacteristic
167C3×C4⋊C8—21no—
168C3×C4⋊C8—32no—
169C3×C4⋊C8—31no—
170C3×C4⋊C8C2×D311yescharacteristic
171C3×C4⋊C8C2×D311yescharacteristic
172C3×#102—32no—
173#832—32no—
174#821—32no—
175#821C2×D312yes—
176#816—32no—
177#816—32no—
178#816—32no—
179#816—62no—
180Dic3⋊C8C2×D312yes—
181#810—32no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C22×C3⋊D3—21no—
184C22×C3×D3—22no—
185C22×C3×D3C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—22no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)C2×D412yes—
193C4×C3⋊D3—42no—
194#634—22no—
195#634—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C3×D12—22no—
202C3×D12—22no—
203C3×D12—42no—
204C3×D12—42no—
205C3×C4×D3—22no—
206C3×C4×D3—41no—
207C3×C4×D3C2×D412yes—
208C3×C4×D3#4112yes—
209C3×Dic6—21no—
210C3×Dic6C2×D412yes—
211#626—24no—
212#625—44no—
213#624—24no—
214#624—42no—
215D3×Dic3—44no—
216C32×C8—22no—
217C3×C3⋊C8—22no—
218C2×#135—92no—
219#532—91no—
220C4×#41—91no—
221#464—92no—
222#463—92no—
223#462—91no—
224#461—91no—
225#460—31no—
226#459—91no—
227C2×C4⋊C8—31no—
228#416—92no—
229C2×C3×Q8—31no—
230C2×C3×D4—32no—
231C2×C3×D4—61no—
232C2×C3×D4—61no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C2×#67—61no—
237C2×#67—62no—
238C2×#67—62no—
239C22×Dic3—62no—
240#239—34no—
241#239—62no—
242#237—64no—
243#237—64no—
244#235—34no—
245#235—62no—
246#235—64no—
247#235—64no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12C22×D312yes—
255C2×C4×D3—61no—
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×C4×D3—62no—
259C2×C4×D3—61no—
260C2×C4×D3—61no—
261C2×C4×D3—61no—
262C2×C4×D3—121no—
263C2×C4×D3D1211yescharacteristic
264C2×C4×D3D1211yescharacteristic
265C2×C4×D3C22×D311yescharacteristic
266C2×Dic6—32no—
267C2×Dic6—32no—
268C2×Dic6—62no—
269C2×Dic6C22×D311yescharacteristic
270C3×SD16—64no—
271C2×C3×C8—22no—
272C2×C3×C8—32no—
273C2×C3×C8—64no—
274C2×C3×C8C22×D312yes—
275C2×C3×C8C22×D312yes—
276C3×C4⋊C4—31no—
277C3×C4⋊C4—61no—
278C3×C42—21no—
279C3×C42—31no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—61no—
283C3×C42C22×D311yescharacteristic
284C3×C42C22×D311yescharacteristic
285#217—61no—
286#217—62no—
287#217—62no—
288#216—64no—
289#213—64no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—121no—
298C4⋊Dic3—31no—
299C4⋊Dic3—31no—
300C4⋊Dic3—61no—
301C4⋊Dic3—61no—
302C4⋊Dic3—61no—
303C4⋊Dic3—61no—
304C4⋊Dic3—61no—
305C4⋊Dic3—61no—
306C4⋊Dic3—121no—
307C4⋊Dic3—121no—
308C4⋊Dic3C22×D311yescharacteristic
309Dic3⋊C4—21no—
310Dic3⋊C4—61no—
311C4×Dic3—21no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C4×Dic3D1211yescharacteristic
317C4×Dic3D1211yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C2×C3⋊C8C22×D312yes—
320Dic12—64no—
321D24—64no—
322#204—24no—
323#204—64no—
324#204—64no—
325#204—124no—
326D3×C8—24no—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—22no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3×D3—21no—
332C2×C3×D3—21no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3#12112yes—
337C32×C4—21no—
338C32×C4#13512yescomplemented
339C32×C4C22×D411yescharacteristic
340C32×C4C2×#4111yescharacteristic
341C3⋊Dic3—42no—
342C3⋊Dic3—41no—
343C3×Dic3—22no—
344C3×Dic3—21no—
345C3×Dic3—21no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—92no—
349C2×#41—91no—
350#135—188no—
351C2×Q16—92no—
352C2×SD16—32no—
353C2×SD16—92no—
354C2×D8—92no—
355C22×C8—32no—
356C4⋊Q8—91no—
357#127—31no—
358#124—92no—
359#121—181no—
360#121—181no—
361C4×Q8—31no—
362C4×Q8—91no—
363C4×D4—91no—
364C4×D4—91no—
365C4×D4—181no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4—181no—
369#117—91no—
370#117—181no—
371C2×C42—31no—
372C2×C42—181no—
373C4⋊C8—32no—
374C4⋊C8—31no—
375C4⋊C8D3211yescharacteristic
376#103—92no—
377#103—92no—
378#102—32no—
379#102—92no—
380C23×C3—31no—
381C23×C3—62no—
382C22×D3—22no—
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—121no—
386C22×D3C2×D1211yescharacteristic
387C3×Q8—32no—
388C3×Q8—61no—
389C3×D4—62no—
390C3×D4—62no—
391C3×D4—122no—
392C3×D4—122no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—31no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—31no—
400C2×C3×C4—31no—
401C2×C3×C4—61no—
402C2×C3×C4—62no—
403C2×C3×C4—61no—
404C2×C3×C4—121no—
405C2×C3×C4C2×D1211yescharacteristic
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—64no—
412#67—124no—
413#67—124no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—61no—
417C2×Dic3—62no—
418C2×Dic3—61no—
419C2×Dic3—62no—
420C2×Dic3—121no—
421C2×Dic3—122no—
422C2×Dic3—124no—
423C2×Dic3C2×D1211yescharacteristic
424C2×Dic3C2×D1211yescharacteristic
425C2×Dic3C2×D1211yescharacteristic
426D12—22no—
427D12—22no—
428D12—32no—
429D12—32no—
430D12—42no—
431D12—42no—
432D12—62no—
433D12—64no—
434D12—61no—
435D12—61no—
436D12—121no—
437C4×D3—22no—
438C4×D3—41no—
439C4×D3—64no—
440C4×D3—64no—
441C4×D3—122no—
442C4×D3—122no—
443C4×D3—124no—
444C4×D3—122no—
445C4×D3—122no—
446C4×D3—242no—
447C4×D3D3×D412yes—
448C4×D3#23912yes—
449Dic6—21no—
450Dic6—62no—
451Dic6—62no—
452Dic6—62no—
453Dic6—62no—
454Dic6—122no—
455Dic6—122no—
456Dic6D3×D412yes—
457C3×C8—22no—
458C3×C8—22no—
459C3×C8—42no—
460C3×C8—62no—
461C3⋊C8—22no—
462C2×C32C2×#12111yescharacteristic
463C2×C32C2×#13511yescharacteristic
464C2×C32#57511yescharacteristic
465C3⋊D3—42no—
466C3×D3—22no—
467C3×D3—82no—
468#41—94no—
469#41—182no—
470#41—184no—
471#41—184no—
472C2×Q8—31no—
473C2×Q8—92no—
474C2×D4—32no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—91no—
478C2×D4—181no—
479C2×D4—182no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—181no—
484C22×C4—181no—
485C22×C4—182no—
486C22×C4—181no—
487Q16—184no—
488SD16—64no—
489SD16—184no—
490D8—184no—
491C2×C8—32no—
492C2×C8—64no—
493C2×C8C2×D3212yes—
494C4⋊C4—31no—
495C4⋊C4—61no—
496C4⋊C4—91no—
497C4⋊C4—181no—
498C4⋊C4—181no—
499C4⋊C4—181no—
500C22⋊C4—181no—
501C22⋊C4—182no—
502C22⋊C4—182no—
503C22⋊C4—181no—
504C22⋊C4—181no—
505C42—31no—
506C42—31no—
507C42—31no—
508C42—61no—
509C42—181no—
510C42—181no—
511C42C2×D3211yescharacteristic
512C22×C3—21no—
513C22×C3—32no—
514C22×C3—61no—
515C22×C3—61no—
516C22×C3—122no—
517C22×C3—122no—
518C22×C3—122no—
519C22×C3C22×D1211yescharacteristic
520C22×C3C2×D3×D411yescharacteristic
521C2×D3—21no—
522C2×D3—21no—
523C2×D3—42no—
524C2×D3—42no—
525C2×D3—42no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—122no—
529C2×D3—121no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—241no—
534C2×D3—241no—
535C2×D3#89512yes—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—22no—
540C3×C4—21no—
541C3×C4—32no—
542C3×C4—41no—
543C3×C4—61no—
544C3×C4—62no—
545C3×C4—61no—
546C3×C4—121no—
547C3×C4#90412yescomplemented
548C3×C4#91612yescomplemented
549C3×C4C2×D3×D411yescharacteristic
550C3×C4C2×D3×D411yescharacteristic
551C3×C4C2×#23911yescharacteristic
552C3×C4D3×#4111yescharacteristic
553Dic3—21no—
554Dic3—21no—
555Dic3—22no—
556Dic3—41no—
557Dic3—121no—
558Dic3—121no—
559Dic3—122no—
560Dic3—122no—
561Dic3—242no—
562Dic3—241no—
563Dic3#89512yes—
564C32#303511yescharacteristic, complemented, Sylow
565C23—31no—
566C23—62no—
567C23—181no—
568Q8—32no—
569Q8—61no—
570Q8—182no—
571Q8—182no—
572D4—62no—
573D4—62no—
574D4—92no—
575D4—122no—
576D4—122no—
577D4—184no—
578D4—181no—
579D4—364no—
580C2×C4—31no—
581C2×C4—32no—
582C2×C4—32no—
583C2×C4—31no—
584C2×C4—31no—
585C2×C4—61no—
586C2×C4—62no—
587C2×C4—61no—
588C2×C4—121no—
589C2×C4—184no—
590C2×C4—181no—
591C2×C4—182no—
592C2×C4—364no—
593C2×C4—362no—
594C2×C4—362no—
595C2×C4D3×D1211yescharacteristic
596C2×C4D3×D1211yescharacteristic
597C2×C4C22×D3211yescharacteristic
598C8—22no—
599C8—62no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—62no—
604C2×C3—242no—
605C2×C3C2×#89511yescharacteristic
606C2×C3D3×#12111yescharacteristic
607C2×C3C2×#90411yescharacteristic
608C2×C3#574811yescharacteristic
609C2×C3C2×#91611yescharacteristic
610C2×C3#577311yescharacteristic
611D3—22no—
612D3—82no—
613D3—122no—
614D3—122no—
615D3—242no—
616C22—32no—
617C22—61no—
618C22—61no—
619C22—122no—
620C22—122no—
621C22—122no—
622C22—182no—
623C22—361no—
624C22—361no—
625C22C2×D3×D1211yescharacteristic
626C4—21no—
627C4—32no—
628C4—62no—
629C4—61no—
630C4—61no—
631C4—121no—
632C4—362no—
633C4—361no—
634C4#6380612yescomplemented
635C4D32×D411yescharacteristic
636C4D3×#23911yescharacteristic
637C3—21no—
638C3#7902111yescharacteristic, complemented
639C3#8038211yescharacteristic, complemented
640C2—62no—
641C2—242no—
642C2—362no—
643C2D3×#89511yescharacteristic
644C2C2×#6380611yescharacteristic
645C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63806C2semidirect
2. C4×#3799C2semidirect
3. #10593897C2semidirect
4. #10592540C2semidirect
5. C3×#4848C2semidirect
6. C3×D3×C4⋊C8C2semidirect
7. #10590954C2semidirect
8. #10590860C2semidirect
9. #10590859C2semidirect
10. #10590385C2semidirect
11. #10590355C2semidirect
59. #4848D3semidirect
66. D3×C4⋊C8D3semidirect
85. #3799D4semidirect
338. C32×C4#135semidirect
547. C3×C4#904semidirect
548. C3×C4#916semidirect
564. C32#3035semidirect
634. C4#63806semidirect
638. C3#79021semidirect
639. C3#80382semidirect

Maximal subgroups

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

subgroupindex
C2×#638062
C4×#37992
#105938972
#105925402
C3×#48482
C3×D3×C4⋊C82
#105909542
#105908602
#105908592
#105903852
#105903552
#803823
#790213