Finite Group Databasebeta

← #11859482

Subgroups — #11859482

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596019C211yesmaximal, characteristic
2C2×#63817C212yesmaximal, complemented
3C3×#5012C211yesmaximal, characteristic, complemented
4C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
5#10591153C212yesmaximal, complemented
6#10591148C212yesmaximal, complemented
7#10591051C212yesmaximal, complemented
8#10590340C211yesmaximal, characteristic, complemented
9#10590338C211yesmaximal, characteristic, complemented
10#10590327C211yesmaximal, characteristic, complemented
11C4×#3710C211yesmaximal, characteristic, complemented
12#79538—31nomaximal
13#79422—31nomaximal
14C2×#3828C2212yes—
15C32×C4×D4C2211yescharacteristic
16#64149C411yescharacteristic
17#64147C411yescharacteristic
18C4×#638C2212yes—
19#64104C411yescharacteristic
20#64097C411yescharacteristic
21#64094C412yes—
22#64093C412yes—
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C42×C3⋊D3C2211yescharacteristic
25C2×C3×#208C2212yes—
26C22×C3×C3⋊C8C2212yes—
27C2×#3712C2212yes—
28C2×#3712C2212yes—
29#63817—28no—
30C2×#3710C2211yescharacteristic
31C2×#3710C2212yes—
32C2×#3710C2211yescharacteristic
33C3×#830C2212yes—
34C3×#830C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38C3×C4×C3⋊C8C2211yescharacteristic
39#63572C2212yes—
40#63557C2212yes—
41#63557C2212yes—
42#63553C2211yescharacteristic
43#63553C2211yescharacteristic
44C2×#907—32no—
45C2×#901—32no—
46#5548—31no—
47#5548—31no—
48#5548—61no—
49C3×#436—31no—
50C3×C8×D4—31no—
51#5128—32no—
52C8×#67—32no—
53#5012D311yescharacteristic, complemented
54D4×C3⋊C8D311yescharacteristic, complemented
55#4838—31no—
56#4837—31no—
57#4837—31no—
58#4834—31no—
59#4729—32no—
60#4727—32no—
61#4727—32no—
62#67⋊C8—32no—
63#4688—31no—
64C8×D12—31no—
65C4×D3×C8—31no—
66C4×D3×C8—31no—
67C2×C32×D4C2×C411yescharacteristic
68C22×C32×C4C2312yes—
69C2×#638C2×C412yes—
70C2×#638C2×C412yes—
71C2×#638C2×C412yes—
72#3828—24no—
73#3828—24no—
74C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
75C2×C4⋊(C3⋊D3)C2×C412yes—
76C2×C4×C3⋊D3C2×C411yescharacteristic
77C2×C4×C3⋊D3C2×C411yescharacteristic
78C2×C4×C3⋊D3C2312yes—
79C2×C4×C3⋊D3C2311yescharacteristic
80C2×#634C2×C412yes—
81C32×C4⋊C4C2×C411yescharacteristic
82C32×C22⋊C4C2×C412yes—
83C32×C42C2311yescharacteristic
84#3757C2×C412yes—
85#3752C2×C412yes—
86#3752C2×C412yes—
87C4⋊(C3⋊Dic3)C2×C411yescharacteristic
88#3750C2×C412yes—
89C4×C3⋊Dic3C2×C411yescharacteristic
90C4×C3⋊Dic3C2×C411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C3×#208—24no—
93C2×C3×C3⋊C8—24no—
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100#3712—24no—
101#3712—24no—
102#3710—22no—
103#3710—24no—
104#3710D414yescomplemented
105#2931—91noSylow
106C2×#235—32no—
107C2×#235—32no—
108C2×#235—62no—
109C2×C3×M16—32no—
110C22×C3×C8—32no—
111C3×C4×D4—21no—
112C3×C4×D4C2×D311yescharacteristic
113C3×C4×D4C2×D311yescharacteristic
114#940—31no—
115#940—31no—
116#940—61no—
117#938—31no—
118#938—31no—
119#938—61no—
120C4×#67—32no—
121C4×#67—32no—
122C4×#67—62no—
123C2×#208C2×D312yes—
124C22×C3⋊C8C2×D312yes—
125#907—68no—
126#901—68no—
127C2×ΓL(1,𝔽25)—32no—
128C2×ΓL(1,𝔽25)—32no—
129C2×ΓL(1,𝔽25)—32no—
130C2×ΓL(1,𝔽25)—32no—
131C2×D3×C8—31no—
132C2×D3×C8—31no—
133C2×D3×C8—31no—
134C2×D3×C8—31no—
135C2×D3×C8—32no—
136C2×D3×C8—32no—
137#895—31no—
138#895—31no—
139#895—61no—
140#888—31no—
141#888—31no—
142#888—61no—
143#885—32no—
144#885—32no—
145#885—62no—
146#884—32no—
147#884—32no—
148#884—62no—
149C4×D12—31no—
150C4×D12—31no—
151C4×D12—61no—
152C42×D3—31no—
153C42×D3—31no—
154C42×D3—61no—
155C3×C4⋊C8—31no—
156C3×C4⋊C8—31no—
157C3×C22⋊C8—32no—
158C3×C22⋊C8—32no—
159C3×C4×C8—31no—
160C3×C4×C8—31no—
161#830C2×D312yes—
162#830C2×D312yes—
163(C2×D3)⋊C8—32no—
164(C2×D3)⋊C8—32no—
165(C2×D3)⋊C8—32no—
166(C2×D3)⋊C8—32no—
167Dic3⋊C8—32no—
168Dic3⋊C8—32no—
169C8×Dic3—31no—
170C8×Dic3—31no—
171C8×Dic3—31no—
172C8×Dic3—31no—
173C4⋊(C3⋊C8)C2×D311yescharacteristic
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C4×C3⋊C8C2×D311yescharacteristic
176C4×C3⋊C8C2×D311yescharacteristic
177C23×C32C22×C412yes—
178C22×C3⋊D3C22×C412yes—
179C22×C3⋊D3C22×C411yescharacteristic
180C32×D4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4C22×C411yescharacteristic
184C2×C32×C4C22×C412yes—
185C2×C32×C4C22×C411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187#638—24no—
188#638—24no—
189#638—24no—
190C2×C3⋊Dic3C22×C411yescharacteristic
191C2×C3⋊Dic3C22×C412yes—
192C2×C3⋊Dic3C22×C411yescharacteristic
193C2×C3⋊Dic3C22×C411yescharacteristic
194C4⋊(C3⋊D3)—24no—
195C4⋊(C3⋊D3)—22no—
196C4×C3⋊D3—22no—
197C4×C3⋊D3—22no—
198C4×C3⋊D3—22no—
199C4×C3⋊D3—22no—
200C4×C3⋊D3C2×D412yes—
201C4×C3⋊D3#4112yes—
202#634—24no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C3×C3⋊C8—21no—
206C3×C3⋊C8—21no—
207C3×C3⋊C8C2×D412yes—
208C3×C3⋊C8C2×D412yes—
209C2×#131—92no—
210#532—91no—
211#436—31no—
212#436—91no—
213#436—92no—
214C8×D4—31no—
215C8×D4—91no—
216C8×D4—92no—
217#423—91no—
218#408—92no—
219C2×C4×C8—91no—
220C2×C3×D4—21no—
221C2×C3×D4C4×D311yescharacteristic
222C2×C3×D4C4×D311yescharacteristic
223C22×C3×C4—22no—
224C22×C3×C4C22×D312yes—
225C22×C3×C4C22×D312yes—
226C2×#67—32no—
227C2×#67—32no—
228C2×#67—32no—
229C2×#67—32no—
230C2×#67—32no—
231C2×#67—32no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—62no—
235#235—64no—
236#235—64no—
237#235—64no—
238#235—64no—
239#235—124no—
240#235—124no—
241C2×D12—31no—
242C2×D12—31no—
243C2×D12—32no—
244C2×D12—32no—
245C2×D12—61no—
246C2×D12—62no—
247C2×C4×D3—31no—
248C2×C4×D3—31no—
249C2×C4×D3—31no—
250C2×C4×D3—31no—
251C2×C4×D3—31no—
252C2×C4×D3—31no—
253C2×C4×D3—32no—
254C2×C4×D3—32no—
255C2×C4×D3—61no—
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×C4×D3—62no—
259C2×Dic6—32no—
260C2×Dic6—32no—
261C2×Dic6—62no—
262C3×M16—64no—
263C2×C3×C8—31no—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C2×C3×C8—32no—
268C2×C3×C8—32no—
269C2×C3×C8—64no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4C4×D311yescharacteristic
272C3×C4⋊C4C4×D311yescharacteristic
273C3×C22⋊C4—22no—
274C3×C22⋊C4C4×D312yes—
275C3×C22⋊C4C4×D312yes—
276C3×C42—21no—
277C3×C42C22×D311yescharacteristic
278C3×C42C22×D311yescharacteristic
279#217—32no—
280#217—32no—
281#217—62no—
282(C2×D3)⋊C4—32no—
283(C2×D3)⋊C4—32no—
284(C2×D3)⋊C4—32no—
285(C2×D3)⋊C4—32no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—62no—
288C4⋊Dic3—31no—
289C4⋊Dic3—31no—
290C4⋊Dic3—61no—
291Dic3⋊C4—32no—
292Dic3⋊C4—32no—
293Dic3⋊C4—62no—
294C4×Dic3—31no—
295C4×Dic3—31no—
296C4×Dic3—31no—
297C4×Dic3—31no—
298C4×Dic3—31no—
299C4×Dic3—31no—
300C4×Dic3—61no—
301C4×Dic3—61no—
302C4×Dic3—61no—
303#208—24no—
304C2×C3⋊C8—24no—
305C2×C3⋊C8C22×D311yescharacteristic
306C2×C3⋊C8C22×D311yescharacteristic
307C2×C3⋊C8C22×D312yes—
308C2×C3⋊C8C22×D312yes—
309C2×C3⋊C8C22×D311yescharacteristic
310C2×C3⋊C8C22×D311yescharacteristic
311ΓL(1,𝔽25)—64no—
312ΓL(1,𝔽25)—64no—
313ΓL(1,𝔽25)—64no—
314ΓL(1,𝔽25)—64no—
315D3×C8—34no—
316D3×C8—34no—
317D3×C8—64no—
318D3×C8—62no—
319D3×C8—62no—
320D3×C8—64no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32C23×C411yescharacteristic
325C2×C3⋊D3—21no—
326C2×C3⋊D3—21no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3—22no—
330C2×C3⋊D3C4×D412yes—
331C32×C4—22no—
332C32×C4—21no—
333C32×C4#13112yescomplemented
334C32×C4C22×D411yescharacteristic
335C32×C4C2×#4111yescharacteristic
336C3⋊Dic3—22no—
337C3⋊Dic3—21no—
338C3⋊Dic3C4×D412yes—
339C3⋊Dic3#13112yescomplemented
340C2×#41—92no—
341#131—188no—
342C2×M16—32no—
343C2×M16—92no—
344C2×M16—92no—
345C22×C8—32no—
346C22×C8—91no—
347C22×C8—92no—
348C22×C8—91no—
349C4⋊Q8—91no—
350#127—91no—
351#124—92no—
352#121—91no—
353#121—91no—
354#121—92no—
355C4×D4—92no—
356C4×D4—91no—
357C4×D4D3211yescharacteristic
358C2×C42—91no—
359C4⋊C8—31no—
360C4⋊C8—31no—
361C4⋊C8—92no—
362C22⋊C8—32no—
363C22⋊C8—32no—
364C22⋊C8—92no—
365C22⋊C8—92no—
366C4×C8—31no—
367C4×C8—31no—
368C4×C8—91no—
369C4×C8—91no—
370C23×C3—22no—
371C23×C3C2×C4×D312yes—
372C23×C3C2×C4×D312yes—
373C22×D3—31no—
374C22×D3—31no—
375C22×D3—32no—
376C22×D3—32no—
377C22×D3—61no—
378C22×D3—62no—
379C3×D4—22no—
380C3×D4—22no—
381C3×D4—42no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4C2×C4×D311yescharacteristic
393C2×C3×C4C2×C4×D311yescharacteristic
394C2×C3×C4C2×C4×D312yes—
395C2×C3×C4C2×C4×D312yes—
396C2×C3×C4C2×C4×D311yescharacteristic
397C2×C3×C4C2×C4×D311yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400#67—64no—
401#67—64no—
402#67—64no—
403#67—64no—
404#67—64no—
405#67—64no—
406#67—124no—
407#67—124no—
408#67—124no—
409C2×Dic3—31no—
410C2×Dic3—31no—
411C2×Dic3—31no—
412C2×Dic3—31no—
413C2×Dic3—31no—
414C2×Dic3—31no—
415C2×Dic3—32no—
416C2×Dic3—32no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—62no—
421D12—64no—
422D12—64no—
423D12—62no—
424D12—62no—
425D12—122no—
426D12—124no—
427C4×D3—32no—
428C4×D3—32no—
429C4×D3—32no—
430C4×D3—32no—
431C4×D3—62no—
432C4×D3—62no—
433C4×D3—62no—
434C4×D3—62no—
435C4×D3—62no—
436C4×D3—62no—
437C4×D3—62no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—122no—
442C4×D3—122no—
443C4×D3—122no—
444C4×D3—122no—
445Dic6—64no—
446Dic6—64no—
447Dic6—124no—
448C3×C8—32no—
449C3×C8—32no—
450C3×C8—62no—
451C3×C8—62no—
452C3×C8—61no—
453C3×C8—61no—
454C3⋊C8—22no—
455C3⋊C8—22no—
456C3⋊C8—21no—
457C3⋊C8—21no—
458C3⋊C8D3×D412yes—
459C3⋊C8D3×D412yes—
460C2×C32—42no—
461C2×C32C2×C4×D411yescharacteristic
462C2×C32C2×#13111yescharacteristic
463C2×C32C2×#13111yescharacteristic
464C3⋊D3—22no—
465C3⋊D3—42no—
466#41—184no—
467#41—184no—
468C2×Q8—92no—
469C2×D4—92no—
470C2×D4—92no—
471C2×D4—92no—
472C2×D4—91no—
473C2×D4—92no—
474C2×D4#62411yescharacteristic
475C22×C4—91no—
476C22×C4—92no—
477C22×C4—91no—
478C22×C4—91no—
479C22×C4C2×D3212yes—
480M16—64no—
481M16—184no—
482M16—184no—
483C2×C8—31no—
484C2×C8—31no—
485C2×C8—31no—
486C2×C8—31no—
487C2×C8—32no—
488C2×C8—32no—
489C2×C8—64no—
490C2×C8—94no—
491C2×C8—184no—
492C2×C8—182no—
493C4⋊C4—92no—
494C4⋊C4—91no—
495C4⋊C4#62411yescharacteristic
496C22⋊C4—92no—
497C22⋊C4—92no—
498C22⋊C4—92no—
499C22⋊C4#62412yes—
500C42—91no—
501C42—91no—
502C42—91no—
503C42C2×D3211yescharacteristic
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—21no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3C22×C4×D311yescharacteristic
515C22×C3C22×C4×D311yescharacteristic
516C2×D3—32no—
517C2×D3—32no—
518C2×D3—62no—
519C2×D3—61no—
520C2×D3—61no—
521C2×D3—61no—
522C2×D3—61no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—62no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—62no—
529C2×D3—121no—
530C2×D3—121no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—22no—
537C3×C4—22no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—42no—
542C3×C4—41no—
543C3×C4#90112yescomplemented
544C3×C4#90712yescomplemented
545C3×C4C2×D3×D411yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547C3×C4D3×#4111yescharacteristic
548C3×C4D3×#4111yescharacteristic
549Dic3—32no—
550Dic3—32no—
551Dic3—32no—
552Dic3—32no—
553Dic3—62no—
554Dic3—62no—
555Dic3—61no—
556Dic3—61no—
557Dic3—62no—
558Dic3—62no—
559Dic3—122no—
560Dic3—121no—
561C32#293111yescharacteristic, complemented, Sylow
562C23—91no—
563C23—92no—
564C23C2×#62412yes—
565Q8—184no—
566D4—22no—
567D4—184no—
568D4—184no—
569D4—184no—
570D4—184no—
571D4—182no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—91no—
575C2×C4—91no—
576C2×C4—92no—
577C2×C4—92no—
578C2×C4—91no—
579C2×C4—92no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4—182no—
583C2×C4—182no—
584C2×C4C2×#62411yescharacteristic
585C2×C4C2×#62412yes—
586C2×C4C2×#62411yescharacteristic
587C2×C4C22×D3211yescharacteristic
588C8—32no—
589C8—32no—
590C8—62no—
591C8—62no—
592C8—61no—
593C8—61no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—42no—
598C2×C3—42no—
599C2×C3—82no—
600C2×C3C4×D3×D411yescharacteristic
601C2×C3C4×D3×D411yescharacteristic
602C2×C3C2×#90111yescharacteristic
603C2×C3C2×#90711yescharacteristic
604C2×C3D3×#13111yescharacteristic
605C2×C3D3×#13111yescharacteristic
606D3—62no—
607D3—62no—
608D3—122no—
609D3—122no—
610D3—122no—
611D3—242no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—92no—
616C22—181no—
617C22—181no—
618C22—182no—
619C22—182no—
620C22—182no—
621C22C22×#62411yescharacteristic
622C4—22no—
623C4—21no—
624C4—92no—
625C4—92no—
626C4—182no—
627C4—181no—
628C4#6381712yescomplemented
629C4D32×D411yescharacteristic
630C4#6431211yescharacteristic
631C3—21no—
632C3#7942211yescharacteristic, complemented
633C3#7953811yescharacteristic, complemented
634C2—42no—
635C2—182no—
636C2—362no—
637C2C2×#6381711yescharacteristic
638C2D4×#62411yescharacteristic
639C2#1059544211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C22
prime radical#10596019C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C3×#5012C2semidirect
4. C3×D4×C3⋊C8C2semidirect
5. #10591153C2semidirect
6. #10591148C2semidirect
7. #10591051C2semidirect
8. #10590340C2semidirect
9. #10590338C2semidirect
10. #10590327C2semidirect
11. C4×#3710C2semidirect
53. #5012D3semidirect
54. D4×C3⋊C8D3semidirect
104. #3710D4semidirect
333. C32×C4#131semidirect
339. C3⋊Dic3#131semidirect
543. C3×C4#901semidirect
544. C3×C4#907semidirect
561. C32#2931semidirect
628. C4#63817semidirect
632. C3#79422semidirect
633. C3#79538semidirect

Maximal subgroups

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

subgroupindex
#105960192
C2×#638172
C3×#50122
C3×D4×C3⋊C82
#105911532
#105911482
#105910512
#105903402
#105903382
#105903272
C4×#37102
#795383
#794223