Finite Group Databasebeta

← #11859502

Subgroups — #11859502

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63804C212yesmaximal, complemented
2#10593972C211yesmaximal, characteristic
3#10592536C211yesmaximal, characteristic, complemented
4C3×#4838C211yesmaximal, characteristic, complemented
5C3×#4834C211yesmaximal, characteristic, complemented
6#10590959C212yesmaximal, complemented
7#10590735C212yesmaximal, complemented
8#10590717C212yesmaximal, complemented
9#10590337C211yesmaximal, characteristic, complemented
10C3⋊C8×D12C211yesmaximal, characteristic, complemented
11C4×#3710C211yesmaximal, characteristic, complemented
12#79538—31nomaximal
13#79422—31nomaximal
14C2×#3798C2212yes—
15C2×#3743C2212yes—
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×ΓL(1,𝔽25)C2212yes—
18C2×C3×D3×C8C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×C4×D12C2211yescharacteristic
21#63919C411yescharacteristic
22#63916C411yescharacteristic
23#63916C411yescharacteristic
24#63915C412yes—
25#63914C411yescharacteristic
26#63912C412yes—
27C4×#625C2212yes—
28C2×#3711C2212yes—
29C2×#3710C2211yescharacteristic
30C2×#3710C2211yescharacteristic
31C2×D3×C3⋊C8C2212yes—
32#63804—28no—
33C32×C4⋊C8C2211yescharacteristic
34#63641C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×(C2×D3)⋊C8C2212yes—
37C3×(C2×D3)⋊C8C2212yes—
38C3×C4×C3⋊C8C2211yescharacteristic
39C3×C4×C3⋊C8C2211yescharacteristic
40(C2×D3)⋊(C3⋊C8)C2212yes—
41(C2×D3)⋊(C3⋊C8)C2212yes—
42#63553C2211yescharacteristic
43#63553C2211yescharacteristic
44C2×#907—32no—
45C2×#901—32no—
46#5548—31no—
47#5548—31no—
48C3×#436—31no—
49C3×C8×D4—31no—
50#5128—32no—
51C8×#67—32no—
52#5012—31no—
53D4×C3⋊C8—31no—
54#4838D311yescharacteristic, complemented
55#4837—31no—
56#4837—31no—
57#4837—61no—
58#4834D311yescharacteristic, complemented
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×C4×C3⋊D3C2×C411yescharacteristic
68C2×C4×C3⋊D3C2×C411yescharacteristic
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×C3×D12C2×C411yescharacteristic
71C2×C3×D12C2×C411yescharacteristic
72C2×C3×C4×D3C2312yes—
73C2×C3×C4×D3C2312yes—
74C2×#627C2×C412yes—
75C2×#626C2×C412yes—
76C2×#626C2×C412yes—
77C2×#625C2×C412yes—
78C2×#625C2×C412yes—
79#3798—24no—
80#3798—24no—
81C2×C32×C8C2312yes—
82C32×C42C2311yescharacteristic
83C4×C3⋊Dic3C2×C411yescharacteristic
84C4×C3⋊Dic3C2×C411yescharacteristic
85C4×C3⋊Dic3C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2312yes—
87#3743—24no—
88C3×(C2×D3)⋊C4C2×C412yes—
89C3×(C2×D3)⋊C4C2×C412yes—
90C3×C4⋊Dic3C2×C411yescharacteristic
91C3×C4⋊Dic3C2×C411yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C3×ΓL(1,𝔽25)—24no—
97C3×D3×C8—24no—
98#3724C2×C412yes—
99(C2×D3)⋊Dic3C2×C412yes—
100(C2×D3)⋊Dic3C2×C412yes—
101#3711—24no—
102#3710—22no—
103#3710D414yescomplemented
104D3×C3⋊C8—24no—
105#2931—91noSylow
106C2×#235—32no—
107C2×#235—32no—
108C2×C3×M16—32no—
109C22×C3×C8—32no—
110C3×C4×D4—31no—
111C3×C4×D4—31no—
112#940—31no—
113#940—31no—
114#938—31no—
115#938—31no—
116C4×#67—32no—
117C4×#67—32no—
118C2×#208—32no—
119C22×C3⋊C8—32no—
120#907—68no—
121#901—68no—
122C2×ΓL(1,𝔽25)—32no—
123C2×ΓL(1,𝔽25)—32no—
124C2×ΓL(1,𝔽25)—32no—
125C2×ΓL(1,𝔽25)—62no—
126C2×ΓL(1,𝔽25)C2×D312yes—
127C2×D3×C8—31no—
128C2×D3×C8—31no—
129C2×D3×C8—32no—
130C2×D3×C8—31no—
131C2×D3×C8—31no—
132C2×D3×C8C2×D312yes—
133#895—31no—
134#895—31no—
135#888—31no—
136#888—31no—
137#885—32no—
138#885—32no—
139#884—32no—
140#884—32no—
141C4×D12C2×D311yescharacteristic
142C4×D12C2×D311yescharacteristic
143C42×D3—31no—
144C42×D3—31no—
145C42×D3—61no—
146C3×C4⋊C8—21no—
147C3×C4⋊C8C2×D311yescharacteristic
148C3×C4⋊C8C2×D311yescharacteristic
149C3×C22⋊C8—32no—
150C3×C22⋊C8—32no—
151C3×C4×C8—31no—
152C3×C4×C8—31no—
153#830—32no—
154#830—32no—
155(C2×D3)⋊C8—32no—
156(C2×D3)⋊C8—32no—
157(C2×D3)⋊C8C2×D312yes—
158(C2×D3)⋊C8C2×D312yes—
159Dic3⋊C8—32no—
160Dic3⋊C8—32no—
161Dic3⋊C8—62no—
162C8×Dic3—31no—
163C8×Dic3—31no—
164C8×Dic3—31no—
165C8×Dic3—31no—
166C4⋊(C3⋊C8)—31no—
167C4⋊(C3⋊C8)—31no—
168C4⋊(C3⋊C8)—61no—
169C4×C3⋊C8C2×D311yescharacteristic
170C4×C3⋊C8C2×D311yescharacteristic
171C22×C3⋊D3C22×C411yescharacteristic
172C22×C3×D3C22×C412yes—
173C22×C3×D3C22×C412yes—
174C2×C32×C4C22×C411yescharacteristic
175C2×C32×C4C22×C411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3C22×C411yescharacteristic
178C2×C3⋊Dic3C22×C411yescharacteristic
179C2×C3⋊Dic3C22×C411yescharacteristic
180C4×C3⋊D3—22no—
181C4×C3⋊D3—22no—
182C4×C3⋊D3C2×D412yes—
183C4×C3⋊D3#4112yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C22×C412yes—
186C3×D12—22no—
187C3×D12—22no—
188C3×C4×D3—22no—
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192#627—24no—
193#626—24no—
194#626—24no—
195#625—24no—
196#625—24no—
197C32×C8—22no—
198C3⋊(C3⋊C8)—22no—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8C2×D412yes—
202C3×C3⋊C8C2×D412yes—
203C2×#131—92no—
204#532—91no—
205#436—31no—
206#436—91no—
207#436—92no—
208C8×D4—31no—
209C8×D4—91no—
210C8×D4—92no—
211#423—91no—
212#408—92no—
213C2×C4×C8—91no—
214C2×C3×D4—31no—
215C2×C3×D4—31no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C2×#67—32no—
219C2×#67—32no—
220C2×#67—32no—
221C2×#67—32no—
222C2×#67—32no—
223C2×#67—32no—
224#235—64no—
225#235—64no—
226#235—64no—
227#235—64no—
228C2×D12—32no—
229C2×D12—32no—
230C2×D12C4×D311yescharacteristic
231C2×D12C4×D311yescharacteristic
232C2×C4×D3—31no—
233C2×C4×D3—31no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—31no—
237C2×C4×D3—31no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—61no—
241C2×C4×D3C22×D312yes—
242C2×C4×D3C22×D312yes—
243C2×Dic6—32no—
244C2×Dic6—32no—
245C3×M16—64no—
246C2×C3×C8—22no—
247C2×C3×C8—31no—
248C2×C3×C8—31no—
249C2×C3×C8—31no—
250C2×C3×C8—31no—
251C2×C3×C8—64no—
252C2×C3×C8C22×D312yes—
253C2×C3×C8C22×D312yes—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—31no—
256C3×C22⋊C4—32no—
257C3×C22⋊C4—32no—
258C3×C42—21no—
259C3×C42C22×D311yescharacteristic
260C3×C42C22×D311yescharacteristic
261#217—32no—
262#217—32no—
263(C2×D3)⋊C4—32no—
264(C2×D3)⋊C4—32no—
265(C2×D3)⋊C4C4×D312yes—
266(C2×D3)⋊C4C4×D312yes—
267C4⋊Dic3C4×D311yescharacteristic
268C4⋊Dic3C4×D311yescharacteristic
269Dic3⋊C4—32no—
270Dic3⋊C4—32no—
271C4×Dic3—31no—
272C4×Dic3—31no—
273C4×Dic3—31no—
274C4×Dic3—31no—
275C4×Dic3—31no—
276C4×Dic3—31no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C4×Dic3—61no—
280#208—64no—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8—64no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D311yescharacteristic
288C2×C3⋊C8C22×D311yescharacteristic
289ΓL(1,𝔽25)—24no—
290ΓL(1,𝔽25)—64no—
291ΓL(1,𝔽25)—64no—
292ΓL(1,𝔽25)—64no—
293ΓL(1,𝔽25)—124no—
294D3×C8—24no—
295D3×C8—34no—
296D3×C8—34no—
297D3×C8—62no—
298D3×C8—62no—
299D3×C8—64no—
300C22×C32C23×C411yescharacteristic
301C2×C3⋊D3—21no—
302C2×C3⋊D3—21no—
303C2×C3⋊D3C4×D412yes—
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C2×C3×D3—22no—
308C2×C3×D3—22no—
309C2×C3×D3—22no—
310C32×C4—21no—
311C32×C4#13112yescomplemented
312C32×C4C22×D411yescharacteristic
313C32×C4C2×#4111yescharacteristic
314C3⋊Dic3—21no—
315C3⋊Dic3C4×D412yes—
316C3⋊Dic3#13112yescomplemented
317C3×Dic3—22no—
318C3×Dic3—22no—
319C2×#41—92no—
320#131—188no—
321C2×M16—32no—
322C2×M16—92no—
323C2×M16—92no—
324C22×C8—32no—
325C22×C8—91no—
326C22×C8—91no—
327C22×C8—92no—
328C4⋊Q8—91no—
329#127—91no—
330#124—92no—
331#121—92no—
332#121—91no—
333#121—91no—
334C4×D4—31no—
335C4×D4—31no—
336C4×D4—92no—
337C2×C42—91no—
338C4⋊C8—92no—
339C4⋊C8—91no—
340C4⋊C8D3211yescharacteristic
341C22⋊C8—32no—
342C22⋊C8—32no—
343C22⋊C8—92no—
344C22⋊C8—92no—
345C4×C8—31no—
346C4×C8—31no—
347C4×C8—91no—
348C4×C8—91no—
349C23×C3—32no—
350C23×C3—32no—
351C22×D3—31no—
352C22×D3—31no—
353C22×D3—61no—
354C22×D3C2×C4×D312yes—
355C22×D3C2×C4×D312yes—
356C3×D4—62no—
357C3×D4—62no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4C2×C4×D311yescharacteristic
368C2×C3×C4C2×C4×D311yescharacteristic
369C2×C3×C4C2×C4×D311yescharacteristic
370C2×C3×C4C2×C4×D311yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—64no—
374#67—64no—
375#67—64no—
376#67—64no—
377#67—64no—
378#67—64no—
379C2×Dic3—31no—
380C2×Dic3—31no—
381C2×Dic3—31no—
382C2×Dic3—31no—
383C2×Dic3—31no—
384C2×Dic3—31no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3C2×C4×D312yes—
389C2×Dic3C2×C4×D312yes—
390D12—22no—
391D12—22no—
392D12—64no—
393D12—64no—
394C4×D3—22no—
395C4×D3—22no—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—32no—
399C4×D3—32no—
400C4×D3—32no—
401C4×D3—32no—
402C4×D3—62no—
403C4×D3—62no—
404C4×D3—62no—
405C4×D3—62no—
406C4×D3—62no—
407C4×D3—62no—
408C4×D3—122no—
409C4×D3—122no—
410Dic6—64no—
411Dic6—64no—
412C3×C8—22no—
413C3×C8—22no—
414C3×C8—32no—
415C3×C8—32no—
416C3×C8—42no—
417C3×C8—61no—
418C3×C8—61no—
419C3⋊C8—21no—
420C3⋊C8—21no—
421C3⋊C8—62no—
422C3⋊C8—62no—
423C3⋊C8—122no—
424C3⋊C8D3×D412yes—
425C3⋊C8D3×D412yes—
426C2×C32C2×C4×D411yescharacteristic
427C2×C32C2×#13111yescharacteristic
428C2×C32C2×#13111yescharacteristic
429C3⋊D3—22no—
430C3×D3—42no—
431C3×D3—42no—
432#41—184no—
433#41—184no—
434C2×Q8—92no—
435C2×D4—31no—
436C2×D4—31no—
437C2×D4—92no—
438C2×D4—92no—
439C2×D4—92no—
440C2×D4—92no—
441C22×C4—32no—
442C22×C4—32no—
443C22×C4—91no—
444C22×C4—91no—
445C22×C4—91no—
446M16—64no—
447M16—184no—
448M16—184no—
449C2×C8—31no—
450C2×C8—31no—
451C2×C8—31no—
452C2×C8—31no—
453C2×C8—64no—
454C2×C8—94no—
455C2×C8—92no—
456C2×C8—184no—
457C2×C8—182no—
458C2×C8C2×D3212yes—
459C4⋊C4—31no—
460C4⋊C4—31no—
461C4⋊C4—92no—
462C22⋊C4—32no—
463C22⋊C4—32no—
464C22⋊C4—92no—
465C22⋊C4—92no—
466C42—91no—
467C42—91no—
468C42—91no—
469C42C2×D3211yescharacteristic
470C22×C3—21no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3C22×C4×D311yescharacteristic
478C22×C3C22×C4×D311yescharacteristic
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—32no—
486C2×D3—32no—
487C2×D3—62no—
488C2×D3—61no—
489C2×D3—61no—
490C2×D3—61no—
491C2×D3—61no—
492C2×D3—121no—
493C2×D3—121no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—22no—
498C3×C4—21no—
499C3×C4—41no—
500C3×C4—62no—
501C3×C4—62no—
502C3×C4#90112yescomplemented
503C3×C4#90712yescomplemented
504C3×C4C2×D3×D411yescharacteristic
505C3×C4C2×D3×D411yescharacteristic
506C3×C4D3×#4111yescharacteristic
507C3×C4D3×#4111yescharacteristic
508Dic3—22no—
509Dic3—22no—
510Dic3—32no—
511Dic3—32no—
512Dic3—32no—
513Dic3—32no—
514Dic3—62no—
515Dic3—62no—
516Dic3—61no—
517Dic3—61no—
518Dic3—121no—
519C32#293111yescharacteristic, complemented, Sylow
520C23—32no—
521C23—32no—
522C23—91no—
523Q8—184no—
524D4—62no—
525D4—62no—
526D4—184no—
527D4—184no—
528D4—184no—
529D4—184no—
530C2×C4—32no—
531C2×C4—32no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—91no—
537C2×C4—91no—
538C2×C4—92no—
539C2×C4—92no—
540C2×C4—91no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4C4×D3211yescharacteristic
544C2×C4C4×D3211yescharacteristic
545C2×C4C22×D3211yescharacteristic
546C8—22no—
547C8—32no—
548C8—32no—
549C8—61no—
550C8—61no—
551C8—182no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—122no—
556C2×C3—122no—
557C2×C3C4×D3×D411yescharacteristic
558C2×C3C4×D3×D411yescharacteristic
559C2×C3C2×#90111yescharacteristic
560C2×C3C2×#90711yescharacteristic
561C2×C3D3×#13111yescharacteristic
562C2×C3D3×#13111yescharacteristic
563D3—42no—
564D3—42no—
565D3—62no—
566D3—62no—
567D3—122no—
568C22—62no—
569C22—62no—
570C22—62no—
571C22—62no—
572C22—62no—
573C22—62no—
574C22—92no—
575C22—181no—
576C22—181no—
577C22C2×C4×D3211yescharacteristic
578C4—21no—
579C4—62no—
580C4—62no—
581C4—92no—
582C4—92no—
583C4—181no—
584C4#6380412yescomplemented
585C4D32×D411yescharacteristic
586C4#6431911yescharacteristic
587C3—21no—
588C3#7942211yescharacteristic, complemented
589C3#7953811yescharacteristic, complemented
590C2—122no—
591C2—122no—
592C2—182no—
593C2#1059460511yescharacteristic
594C2C2×#6380411yescharacteristic
595C2#1059470711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radical#10593972C2
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63804C2semidirect
3. #10592536C2semidirect
4. C3×#4838C2semidirect
5. C3×#4834C2semidirect
6. #10590959C2semidirect
7. #10590735C2semidirect
8. #10590717C2semidirect
9. #10590337C2semidirect
10. C3⋊C8×D12C2semidirect
11. C4×#3710C2semidirect
54. #4838D3semidirect
58. #4834D3semidirect
103. #3710D4semidirect
311. C32×C4#131semidirect
316. C3⋊Dic3#131semidirect
502. C3×C4#901semidirect
503. C3×C4#907semidirect
519. C32#2931semidirect
584. C4#63804semidirect
588. C3#79422semidirect
589. C3#79538semidirect

Maximal subgroups

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

subgroupindex
C2×#638042
#105939722
#105925362
C3×#48382
C3×#48342
#105909592
#105907352
#105907172
#105903372
C3⋊C8×D122
C4×#37102
#795383
#794223