Finite Group Databasebeta

← #11861226

Subgroups — #11861226

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2C2×#63822C211yesmaximal, characteristic
3#10594776C211yesmaximal, characteristic, complemented
4C2×#63649C211yesmaximal, characteristic, complemented
5C3×#5139C211yesmaximal, characteristic, complemented
6#10591111C211yesmaximal, characteristic, complemented
7#10591057C211yesmaximal, characteristic, complemented
8#10590976C214yesmaximal, complemented
9#10590975C214yesmaximal, complemented
10#83812—31nomaximal
11#78990—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#907C2214yescomplemented
20C3×D3×M16—22no—
21C3×#901—22no—
22C2×#3718C411yescharacteristic, complemented
23C2×#3715C411yescharacteristic, complemented
24C2×#3715C411yescharacteristic, complemented
25#63822C412yescomplemented
26#63822C412yescomplemented
27#63822C2212yes—
28#63822C2212yes—
29C2×#3713C411yescharacteristic, complemented
30#63815—22no—
31#63814C2214yescomplemented
32D3×#208—22no—
33#63649C2212yescomplemented
34#63649C2212yescomplemented
35C3×#825C2214yescomplemented
36#63569C2214yescomplemented
37#63554C2212yescomplemented
38Dic3×C3⋊C8C2212yescomplemented
39C3×#568—31no—
40C2×#950—31no—
41C2×#950—31no—
42#5819—31no—
43#5745—31no—
44#5745D311yescharacteristic, complemented
45C3×#421—31no—
46#5236—31no—
47#5145—34no—
48#5144—34no—
49#5139D311yescharacteristic, complemented
50C2×#822—31no—
51C2×#822—31no—
52C2×#822—61no—
53#5122—31no—
54#5005—31no—
55#4997—31no—
56#4824—34no—
57#4823—34no—
58C22×C32×C4C2311yescharacteristic
59C2×C3×#67—21no—
60C2×C3×#67—21no—
61C3×#235—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235C2×C412yes—
66C3×#235C2×C412yes—
67C3×#235C2312yes—
68C3×#235C2312yes—
69C2×C3×D12C2×C411yescharacteristic
70C2×C3×D12C2×C411yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—21no—
73C2×C3×Dic6C2×C411yescharacteristic
74C2×C3×Dic6C2×C411yescharacteristic
75C32×M16—21no—
76C32×M16C2312yes—
77C2×C32×C8—21no—
78#3748—21no—
79#3748C2312yes—
80C2×C3⋊(C3⋊C8)—21no—
81C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
82C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
83C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
84C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×#217—21no—
88C3×C4⋊Dic3—21no—
89C3×C4×Dic3C2312yes—
90C3×#208D412yes—
91C3×#208D412yes—
92C2×C3×C3⋊C8C2312yes—
93C3×ΓL(1,𝔽25)—24no—
94C3×D3×C8—24no—
95#3718C2×C412yes—
96#3718C2×C412yes—
97#3715C2×C412yes—
98#3715C2×C412yes—
99#3715C2×C412yes—
100#3715C2×C412yes—
101#3713C2×C412yes—
102#3713C2×C412yes—
103#3711—24no—
104D3×C3⋊C8—24no—
105#2957—91noSylow
106C2×C3×#41—31no—
107C2×C3×#41—31no—
108C2×#235C2×D311yescharacteristic
109C2×#235C2×D311yescharacteristic
110C3×#131—34no—
111C3×#131—62no—
112C2×C3×M16—21no—
113C2×C3×M16—31no—
114C2×C3×M16—62no—
115C2×C3×M16C2×D311yescharacteristic
116C2×C3×M16C2×D311yescharacteristic
117C3×#117—31no—
118#950—32no—
119#950—32no—
120#950—32no—
121#950—32no—
122#950—32no—
123#950—32no—
124#950—32no—
125#950—32no—
126#948—34no—
127#948—62no—
128C2×#216—31no—
129C2×#216—31no—
130C2×#215—31no—
131C2×#215—31no—
132C2×#214—31no—
133C2×#214—31no—
134C2×#213—31no—
135C2×#213—31no—
136#926C2×D311yescharacteristic
137C2×#208—31no—
138C2×#208—31no—
139C2×#208—61no—
140C2×#208—62no—
141C2×#208C2×D311yescharacteristic
142C22×C3⋊C8—31no—
143C22×C3⋊C8—31no—
144C22×C3⋊C8—61no—
145#907—62no—
146#907C2×D314yescomplemented
147D3×M16—22no—
148D3×M16—62no—
149#901—22no—
150#901—34no—
151C3×#104—34no—
152#837—34no—
153#825C2×D314yescomplemented
154#822—32no—
155#822—32no—
156#822—32no—
157#822—32no—
158#822—62no—
159#822—62no—
160#815—32no—
161C8×Dic3—32no—
162#805—34no—
163#803—32no—
164C4×C3⋊C8—32no—
165C23×C32#4111yescharacteristic
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C2×C32×C4C22×C411yescharacteristic
169C2×C32×C4C22×C411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4#4111yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C3×#67—22no—
175C3×#67—22no—
176C3×#67—22no—
177C3×#67—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C3×D12—21no—
182C3×D12—21no—
183C3×D12C22×C412yes—
184C3×D12C22×C412yes—
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×C4×D3—22no—
189C3×Dic6—21no—
190C3×Dic6—21no—
191C3×Dic6C22×C412yes—
192C3×Dic6C22×C412yes—
193C32×C8—22no—
194C3⋊(C3⋊C8)—22no—
195C3⋊(C3⋊C8)C22×C411yescharacteristic
196C3⋊(C3⋊C8)C22×C411yescharacteristic
197C3⋊(C3⋊C8)C22×C411yescharacteristic
198C3⋊(C3⋊C8)C22×C411yescharacteristic
199C3×C3⋊C8C2×D414yes—
200C2×#135—91no—
201#568—31no—
202#568—91no—
203#444—94no—
204#443—94no—
205C2×#108—91no—
206#421—31no—
207#421—91no—
208#405—91no—
209C3×#41—32no—
210C3×#41—32no—
211C3×#41—32no—
212C3×#41—32no—
213C3×#41—61no—
214C3×#41—61no—
215C3×#41—61no—
216C3×#41—61no—
217C2×C3×Q8—31no—
218C2×C3×Q8—31no—
219C2×C3×D4—31no—
220C2×C3×D4—31no—
221C2×C3×D4—61no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—21no—
229C2×#67—21no—
230#235—21no—
231#235—21no—
232#235—21no—
233#235—21no—
234#235C4×D312yes—
235#235C4×D312yes—
236#235C22×D312yes—
237#235C22×D312yes—
238C2×D12C4×D311yescharacteristic
239C2×D12C4×D311yescharacteristic
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×Dic6C4×D311yescharacteristic
243C2×Dic6C4×D311yescharacteristic
244C3×M16—21no—
245C3×M16—21no—
246C3×M16—22no—
247C3×M16—32no—
248C3×M16—32no—
249C3×M16—41no—
250C3×M16—64no—
251C3×M16C22×D312yes—
252C3×M16C22×D312yes—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—32no—
256C2×C3×C8—41no—
257C2×C3×C8—64no—
258C3×C4⋊C4—61no—
259C3×C22⋊C4—61no—
260C3×C42—32no—
261#217—21no—
262#216—32no—
263#216—32no—
264#216—32no—
265#216—32no—
266#215—32no—
267#215—32no—
268#215—32no—
269#215—32no—
270#214—32no—
271#214—32no—
272#214—32no—
273#214—32no—
274#213—32no—
275#213—32no—
276#213—32no—
277#213—32no—
278C4⋊Dic3—21no—
279C4×Dic3C22×D312yes—
280#208—32no—
281#208—32no—
282#208—62no—
283#208—61no—
284#208—61no—
285#208—64no—
286#208—121no—
287#208#6712yes—
288#208#6712yes—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—31no—
296C2×C3⋊C8—31no—
297C2×C3⋊C8—31no—
298C2×C3⋊C8—31no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—31no—
301C2×C3⋊C8—61no—
302C2×C3⋊C8—61no—
303C2×C3⋊C8—61no—
304C2×C3⋊C8—61no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8—61no—
307C2×C3⋊C8—61no—
308C2×C3⋊C8—61no—
309C2×C3⋊C8—64no—
310C2×C3⋊C8—121no—
311C2×C3⋊C8C22×D312yes—
312ΓL(1,𝔽25)—24no—
313ΓL(1,𝔽25)—64no—
314D3×C8—24no—
315D3×C8—64no—
316C22×C32—41no—
317C22×C32C4×D411yescharacteristic
318C22×C32C4×D411yescharacteristic
319C22×C32C2×#4111yescharacteristic
320C2×C3×D3—22no—
321C2×C3×D3—22no—
322C2×C3×D3—81no—
323C2×C3×D3—81no—
324C32×C4C4×D411yescharacteristic
325C32×C4C4×D411yescharacteristic
326C32×C4C23×C411yescharacteristic
327C32×C4C22×D411yescharacteristic
328C3×Dic3—22no—
329C3×Dic3—22no—
330C3×Dic3—42no—
331C2×#41—31no—
332C2×#41—31no—
333#135—92no—
334#135—92no—
335#135—92no—
336#135—92no—
337C2×Q16—91no—
338C2×SD16—91no—
339C2×SD16—91no—
340C2×D8—91no—
341#131—34no—
342#131—62no—
343#131—94no—
344#131—182no—
345C2×M16—31no—
346C2×M16—62no—
347C2×M16—91no—
348C2×M16—182no—
349C2×M16D3211yescharacteristic
350C22×C8—91no—
351#117—31no—
352#108—92no—
353#108—92no—
354#104—34no—
355#104—94no—
356#97—92no—
357C4×C8—92no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3—61no—
361C23×C3#23511yescharacteristic
362C23×C3#23711yescharacteristic
363C22×D3—21no—
364C22×D3—21no—
365C3×Q8—32no—
366C3×Q8—32no—
367C3×Q8—61no—
368C3×Q8—61no—
369C3×D4—32no—
370C3×D4—32no—
371C3×D4—62no—
372C3×D4—62no—
373C3×D4—62no—
374C3×D4—62no—
375C3×D4—61no—
376C3×D4—61no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4C2×C4×D311yescharacteristic
391C2×C3×C4C2×C4×D311yescharacteristic
392C2×C3×C4C2×C4×D311yescharacteristic
393C2×C3×C4C2×C4×D311yescharacteristic
394C2×C3×C4#23511yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4#23711yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—22no—
403#67—22no—
404#67—22no—
405#67—22no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409D12—21no—
410D12—21no—
411D12C2×C4×D312yes—
412D12C2×C4×D312yes—
413C4×D3—22no—
414C4×D3—22no—
415C4×D3—22no—
416C4×D3—22no—
417Dic6—21no—
418Dic6—21no—
419Dic6C2×C4×D312yes—
420Dic6C2×C4×D312yes—
421C3×C8—22no—
422C3×C8—22no—
423C3×C8—34no—
424C3×C8—42no—
425C3⋊C8—31no—
426C3⋊C8—31no—
427C3⋊C8—31no—
428C3⋊C8—31no—
429C3⋊C8—31no—
430C3⋊C8—31no—
431C3⋊C8—31no—
432C3⋊C8—31no—
433C3⋊C8—61no—
434C3⋊C8—61no—
435C3⋊C8—61no—
436C3⋊C8—61no—
437C3⋊C8—62no—
438C3⋊C8—62no—
439C3⋊C8—122no—
440C3⋊C8C2×#6714yes—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32—21no—
444C2×C32C2×C4×D411yescharacteristic
445C3×D3—42no—
446C3×D3—42no—
447#41—32no—
448#41—32no—
449#41—32no—
450#41—32no—
451#41—61no—
452#41—61no—
453#41—61no—
454#41—61no—
455C2×Q8—31no—
456C2×Q8—31no—
457C2×D4—31no—
458C2×D4—31no—
459C2×D4—61no—
460C2×D4—61no—
461C22×C4—61no—
462C22×C4—61no—
463C22×C4C2×D3211yescharacteristic
464Q16—92no—
465Q16—92no—
466SD16—92no—
467SD16—92no—
468SD16—92no—
469SD16—92no—
470D8—92no—
471D8—92no—
472M16—21no—
473M16—32no—
474M16—32no—
475M16—64no—
476M16—92no—
477M16—184no—
478M16—181no—
479M16C2×D3212yes—
480C2×C8—21no—
481C2×C8—32no—
482C2×C8—64no—
483C2×C8—91no—
484C2×C8—91no—
485C2×C8—91no—
486C2×C8—91no—
487C2×C8—91no—
488C2×C8—91no—
489C2×C8—184no—
490C2×C8—181no—
491C4⋊C4—61no—
492C22⋊C4—61no—
493C42—32no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—42no—
500C22×C3—62no—
501C22×C3—62no—
502C22×C3—241no—
503C22×C3—241no—
504C22×C3#67⋊C411yescharacteristic
505C22×C3#67⋊C411yescharacteristic
506C22×C3C4×#6711yescharacteristic
507C22×C3C4×#6711yescharacteristic
508C22×C3C2×#23511yescharacteristic
509C22×C3C2×#23711yescharacteristic
510C2×D3—22no—
511C2×D3—22no—
512C2×D3—81no—
513C2×D3—81no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—62no—
519C3×C4—62no—
520C3×C4—122no—
521C3×C4#67⋊C411yescharacteristic
522C3×C4#67⋊C411yescharacteristic
523C3×C4C4×#6711yescharacteristic
524C3×C4C4×#6711yescharacteristic
525C3×C4C22×C4×D311yescharacteristic
526C3×C4C22×C4×D311yescharacteristic
527C3×C4C2×D3×D411yescharacteristic
528C3×C4C22×#6711yescharacteristic
529Dic3—22no—
530Dic3—22no—
531Dic3—42no—
532C32#295711yescharacteristic, complemented, Sylow
533C23—61no—
534C23—61no—
535C23#379511yescharacteristic
536Q8—32no—
537Q8—32no—
538Q8—61no—
539Q8—61no—
540D4—32no—
541D4—32no—
542D4—62no—
543D4—62no—
544D4—62no—
545D4—62no—
546D4—61no—
547D4—61no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4#379511yescharacteristic
556C2×C4C4×D3211yescharacteristic
557C2×C4C4×D3211yescharacteristic
558C2×C4D3×#6711yescharacteristic
559C2×C4D3×#6711yescharacteristic
560C2×C4C22×D3211yescharacteristic
561C8—22no—
562C8—34no—
563C8—91no—
564C8—91no—
565C8—91no—
566C8—91no—
567C8—182no—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—41no—
577C2×C3—41no—
578C2×C3—122no—
579C2×C3—122no—
580C2×C3C2×#67⋊C411yescharacteristic
581C2×C3C2×C4×#6711yescharacteristic
582D3—42no—
583D3—42no—
584C22—41no—
585C22—62no—
586C22—62no—
587C22—241no—
588C22—241no—
589C22#6387911yescharacteristic
590C22#6387911yescharacteristic
591C22C2×#379511yescharacteristic
592C4—62no—
593C4—62no—
594C4—122no—
595C4#6387911yescharacteristic
596C4#6387911yescharacteristic
597C4C2×C4×D3211yescharacteristic
598C4C2×D3×#6711yescharacteristic
599C3—21no—
600C3#7899011yescharacteristic, complemented
601C3#8381211yescharacteristic, complemented
602C2—21no—
603C2—21no—
604C2—21no—
605C2—122no—
606C2—122no—
607C2C2×#6387911yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×C4×D4
prime radicalC2×#63822C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5745C2semidirect
3. #10594776C2semidirect
4. C2×#63649C2semidirect
5. C3×#5139C2semidirect
6. #10591111C2semidirect
7. #10591057C2semidirect
8. #10590976C2semidirect
9. #10590975C2semidirect
19. C3×#907C22semidirect
22. C2×#3718C4semidirect
23. C2×#3715C4semidirect
24. C2×#3715C4semidirect
25. #63822C4semidirect
26. #63822C4semidirect
29. C2×#3713C4semidirect
31. #63814C22semidirect
33. #63649C22semidirect
34. #63649C22semidirect
35. C3×#825C22semidirect
36. #63569C22semidirect
37. #63554C22semidirect
38. Dic3×C3⋊C8C22semidirect
44. #5745D3semidirect
49. #5139D3semidirect
146. #907C2×D3semidirect
153. #825C2×D3semidirect
532. C32#2957semidirect
600. C3#78990semidirect
601. C3#83812semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
C2×#638222
#105947762
C2×#636492
C3×#51392
#105911112
#105910572
#105909762
#105909752
#838123
#789903