Finite Group Databasebeta

← #11860330

Subgroups — #11860330

Order 1152.

1162 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#237C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic
3D3×#893C211yesmaximal, characteristic, complemented
4#10592484C211yesmaximal, characteristic, complemented
5C3×#4771C211yesmaximal, characteristic, complemented
6C3×#4756C211yesmaximal, characteristic, complemented
7#10591436C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590792C211yesmaximal, characteristic, complemented
11#10590743C211yesmaximal, characteristic, complemented
12Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
13#10590580C211yesmaximal, characteristic, complemented
14#10590484C211yesmaximal, characteristic, complemented
15#10590475C211yesmaximal, characteristic, complemented
16C4×#911—31nomaximal
17#78866—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21D4×C3⋊Dic3C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23#64102C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31#63955—21no—
32C2×Dic32—21no—
33#63925C418yescomplemented
34D3×(C2×D3)⋊C4—21no—
35#63904—21no—
36#63898C2211yescharacteristic
37#63894C2211yescharacteristic
38#63881—21no—
39C4×D3×Dic3C2211yescharacteristic
40#63843C2211yescharacteristic, complemented
41Dic3×Dic6C2211yescharacteristic, complemented
42#63841C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#102C2211yescharacteristic, complemented
47#63648C2211yescharacteristic
48#63642C2211yescharacteristic, complemented
49#63635C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic
52C3×#816C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62Dic3×#41—31no—
63C2×#949—31no—
64C2×#911—31no—
65C4×D3×D4—31no—
66C4×#237—31no—
67C2×#893—31no—
68C3×C4×D8—31no—
69C3×#417—31no—
70#5152—31no—
71#5131—31no—
72Dic3×M16—31no—
73C4×#214—31no—
74C4×#213—31no—
75#4964—31no—
76#4889—31no—
77#4881—31no—
78#4817—31no—
79#4817—31no—
80#4788—31no—
81#4788—31no—
82#4785—31no—
83#4785—31no—
84#4785—31no—
85#4785—61no—
86#4771D311yescharacteristic, complemented
87#4770—31no—
88#4757—31no—
89#4756—31no—
90#4756D311yescharacteristic, complemented
91C4×#204—31no—
92C4×ΓL(1,𝔽25)—31no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#237—22no—
102C3×#237C2×C414yescomplemented
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3D411yescharacteristic
112C2×D3×Dic3D411yescharacteristic
113D3×D12—22no—
114D3×D12C2×C414yescomplemented
115C4×D32—44no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3757—21no—
119#3753C2×C414yescomplemented
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#217—21no—
125C3×#213C2×C414yescomplemented
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×ΓL(1,𝔽25)—22no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32D411yescharacteristic
143Dic32D411yescharacteristic
144#3717C2×C414yescomplemented
145#3715C2×C414yescomplemented
146#3711C2×C414yescomplemented
147C4×AGL(1,ℤ/8)—91noSylow
148C2×C3×#41—31no—
149C2×#237C2×D311yescharacteristic
150C2×D3×D4—31no—
151C22×D12—31no—
152C22×C4×D3—61no—
153C22×C4×D3—61no—
154C2×C3×D8—31no—
155C2×C3×M16—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C2×C3×C4⋊C4—31no—
159#949—38no—
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162C2×#215—31no—
163C2×#215—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—61no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170D4×Dic3C2×D311yescharacteristic, complemented
171C2×#214—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—61no—
175C2×#213C2×D311yescharacteristic
176C4×#67—61no—
177C4×#67—61no—
178C2×(C2×D3)⋊C4—61no—
179#926—31no—
180#926—61no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—61no—
183C2×C4×Dic3—61no—
184C2×#208—31no—
185#911—38no—
186C2×#204—31no—
187C2×ΓL(1,𝔽25)—31no—
188C2×ΓL(1,𝔽25)C2×D311yescharacteristic
189#893—31no—
190#893—31no—
191#893—31no—
192#893—31no—
193#893—61no—
194#893—61no—
195#893—61no—
196#893C2×D311yescharacteristic
197#892—31no—
198D3×C4⋊C4C2×D311yescharacteristic
199#887—31no—
200#67⋊C4—61no—
201#67⋊C4—61no—
202D3×C22⋊C4—61no—
203#877—61no—
204C4×D12—31no—
205C42×D3—31no—
206C4×Dic6—31no—
207C3×#107—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#102—21no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102C2×D311yescharacteristic, complemented
214C3×#102C2×D311yescharacteristic, complemented
215C3×C4×C8—31no—
216#832—31no—
217#832C2×D311yescharacteristic, complemented
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821C2×D311yescharacteristic
224#817—31no—
225#816C2×D311yescharacteristic, complemented
226#815—31no—
227#815—31no—
228#815—31no—
229#815—31no—
230#815—61no—
231C8×Dic3—31no—
232C8×Dic3C2×D311yescharacteristic, complemented
233#810C2×D311yescharacteristic, complemented
234#809—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238#808—61no—
239#807—31no—
240#807—31no—
241#807C2×D311yescharacteristic, complemented
242C4×C3⋊C8—31no—
243C23×C32—21no—
244C22×C3⋊D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—24no—
248C2×D32—42no—
249C2×D32—42no—
250C32×D4—21no—
251C32×D4C22×C412yescomplemented
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—42no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)C22×C412yes—
260C4×C3⋊D3—42no—
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—24no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—42no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12C22×C412yes—
272C3×C4×D3—42no—
273C3×C4×D3—42no—
274C3×C4×D3C22×C412yes—
275C3×C4×D3#4112yes—
276C3×Dic6—21no—
277C3×Dic6C22×C412yescomplemented
278#626—24no—
279#624—42no—
280D3×Dic3—22no—
281D3×Dic3—41no—
282D3×Dic3—42no—
283C32×C8—21no—
284C3⋊(C3⋊C8)C22×C412yescomplemented
285C3×C3⋊C8—21no—
286C3×C3⋊C8C22×C412yescomplemented
287C2×AGL(1,ℤ/8)—91no—
288C4×#41—91no—
289C2×C4×D4—91no—
290#442—91no—
291#442—91no—
292#440—91no—
293#440—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296C4×D8—31no—
297C4×D8—91no—
298#428—91no—
299#418—91no—
300#417—31no—
301C4×M16—91no—
302C23×D3—61no—
303C23×D3—61no—
304C3×#41—34no—
305C3×#41—62no—
306C2×C3×Q8—31no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C2×#67—21no—
318C2×#67—61no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—121no—
327#237—22no—
328#237C4×D314yescomplemented
329D3×D4—34no—
330D3×D4—62no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—34no—
334C2×D12—61no—
335C2×D12—62no—
336C2×D12—61no—
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—121no—
348C2×C4×D3—124no—
349C2×C4×D3—124no—
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6C22×D311yescharacteristic
352C3×D8—34no—
353C3×M16—62no—
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368#217—21no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—121no—
374#215—34no—
375#215—34no—
376#214—34no—
377#213—34no—
378#213—34no—
379#213—64no—
380#213C4×D314yescomplemented
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—121no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3C22×D311yescharacteristic
413#208—34no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419#204—34no—
420ΓL(1,𝔽25)—22no—
421ΓL(1,𝔽25)—34no—
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32C22×D411yescharacteristic
426C2×C3⋊D3—22no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—22no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3C4×D412yes—
435D32—48no—
436C32×C4—41no—
437C32×C4C23×C411yescharacteristic
438C32×C4C2×#4111yescharacteristic
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3×Dic3—22no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3C4×D412yes—
447C3×Dic3AGL(1,ℤ/8)12yescomplemented
448C2×#41—31no—
449C22×D4—91no—
450C23×C4—181no—
451AGL(1,ℤ/8)—98no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×D8—31no—
455C2×D8—91no—
456C2×M16—31no—
457C2×M16—91no—
458C4×Q8—91no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—181no—
467C4×D4—181no—
468C4×D4—181no—
469C4×D4—181no—
470#117—91no—
471#117—181no—
472C2×C4⋊C4—31no—
473C2×C22⋊C4—181no—
474C2×C42—91no—
475C2×C42—181no—
476#107—31no—
477#107—91no—
478#106—91no—
479#106—91no—
480#103—31no—
481#103—31no—
482#102—31no—
483#102—31no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102D3211yescharacteristic, complemented
488#97—91no—
489#97—91no—
490C4×C8—31no—
491C4×C8—91no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—41no—
496C23×C3—61no—
497C22×D3—21no—
498C22×D3—64no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—64no—
502C22×D3—121no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3D3×D411yescharacteristic
508C3×Q8—32no—
509C3×Q8—61no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—32no—
514C3×D4—41no—
515C3×D4—64no—
516C3×D4—61no—
517C3×D4C2×C4×D312yescomplemented
518C3×D4C2×C4×D312yescomplemented
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—31no—
527C2×C3×C4—41no—
528C2×C3×C4—64no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—24no—
538#67—64no—
539C2×Dic3—21no—
540C2×Dic3—24no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—42no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—62no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3—122no—
556C2×Dic3—122no—
557C2×Dic3—122no—
558C2×Dic3—242no—
559C2×Dic3D3×D411yescharacteristic
560C2×Dic3D3×D411yescharacteristic
561C2×Dic3D3×D411yescharacteristic
562D12—21no—
563D12—32no—
564D12—32no—
565D12—62no—
566D12—64no—
567D12—61no—
568D12—61no—
569D12—121no—
570D12C2×C4×D312yes—
571C4×D3—42no—
572C4×D3—42no—
573C4×D3—62no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—121no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—242no—
581C4×D3C2×C4×D312yes—
582C4×D3#23712yes—
583Dic6—21no—
584Dic6C2×C4×D312yescomplemented
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—32no—
588C3×C8—41no—
589C3×C8—61no—
590C3⋊C8—21no—
591C3⋊C8—32no—
592C3⋊C8—32no—
593C3⋊C8—62no—
594C3⋊C8C2×C4×D312yescomplemented
595C2×C32—42no—
596C2×C32C2×C4×D411yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57511yescharacteristic
599C3⋊D3—42no—
600C3×D3—22no—
601C3×D3—42no—
602C24—181no—
603#41—34no—
604#41—62no—
605C2×Q8—31no—
606C2×D4—31no—
607C2×D4—61no—
608C2×D4—94no—
609C2×D4—91no—
610C2×D4—182no—
611C2×D4—181no—
612C2×D4C2×D3211yescharacteristic
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—91no—
619C22×C4—91no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—364no—
625SD16—94no—
626SD16—94no—
627D8—34no—
628D8—94no—
629M16—62no—
630M16—94no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8—91no—
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4C2×D3211yescharacteristic
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C42—31no—
650C42—91no—
651C42—91no—
652C42—91no—
653C42—181no—
654C42—181no—
655C42—181no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—21no—
659C22×C3—32no—
660C22×C3—42no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—62no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3C2×D3×D411yescharacteristic
673C22×C3C2×D3×D411yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—22no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—122no—
682C2×D3—128no—
683C2×D3—128no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—241no—
689C2×D3—241no—
690C2×D3#67⋊C412yes—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—32no—
694C3×C4—32no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—61no—
698C3×C4—62no—
699C3×C4—81no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4C22×C4×D311yescharacteristic
703C3×C4C22×C4×D311yescharacteristic
704C3×C4C2×#23711yescharacteristic
705C3×C4D3×#4111yescharacteristic
706Dic3—22no—
707Dic3—21no—
708Dic3—41no—
709Dic3—41no—
710Dic3—61no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—241no—
719Dic3#67⋊C412yes—
720Dic3#91112yescomplemented
721C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
722C23—21no—
723C23—31no—
724C23—61no—
725C23—184no—
726C23—181no—
727C23—362no—
728C23—362no—
729Q8—32no—
730Q8—61no—
731D4—21no—
732D4—32no—
733D4—64no—
734D4—61no—
735D4—92no—
736D4—184no—
737D4—181no—
738D4C4×D3212yescomplemented
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—32no—
743C2×C4—32no—
744C2×C4—31no—
745C2×C4—64no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—91no—
750C2×C4—91no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—182no—
755C2×C4—181no—
756C2×C4—362no—
757C2×C4—362no—
758C2×C4—361no—
759C2×C4—362no—
760C2×C4—362no—
761C2×C4C22×D3211yescharacteristic
762C8—21no—
763C8—32no—
764C8—61no—
765C8—92no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—42no—
771C2×C3—62no—
772C2×C3—82no—
773C2×C3—122no—
774C2×C3C2×#67⋊C411yescharacteristic
775C2×C3C4×D3×D411yescharacteristic
776C2×C3C2×#91111yescharacteristic
777C2×C3#576811yescharacteristic
778C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
779C2×C3#577711yescharacteristic
780D3—22no—
781D3—42no—
782D3—122no—
783D3—122no—
784D3—242no—
785C22—22no—
786C22—32no—
787C22—41no—
788C22—41no—
789C22—61no—
790C22—61no—
791C22—62no—
792C22—121no—
793C22—121no—
794C22—182no—
795C22—368no—
796C22—361no—
797C22—361no—
798C22D32×D411yescharacteristic
799C4—32no—
800C4—32no—
801C4—41no—
802C4—61no—
803C4—62no—
804C4—121no—
805C4—121no—
806C4—181no—
807C4—181no—
808C4—361no—
809C4C2×C4×D3211yescharacteristic
810C4D3×#23711yescharacteristic
811C3—21no—
812C3#7886611yescharacteristic, complemented
813C3C4×#91111yescharacteristic, complemented
814C2—42no—
815C2—62no—
816C2—122no—
817C2—362no—
818C2D3×#67⋊C411yescharacteristic
819C2D3×#91111yescharacteristic
820C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63925C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. Dic3×#237C2semidirect
3. D3×#893C2semidirect
4. #10592484C2semidirect
5. C3×#4771C2semidirect
6. C3×#4756C2semidirect
7. #10591436C2semidirect
8. #10591400C2semidirect
9. #10590939C2semidirect
10. #10590792C2semidirect
11. #10590743C2semidirect
12. Dic3×ΓL(1,𝔽25)C2semidirect
13. #10590580C2semidirect
14. #10590484C2semidirect
15. #10590475C2semidirect
21. D4×C3⋊Dic3C22semidirect
24. C3×D4×Dic3C22semidirect
33. #63925C4semidirect
40. #63843C22semidirect
41. Dic3×Dic6C22semidirect
46. C32×#102C22semidirect
48. #63642C22semidirect
49. #63635C22semidirect
50. C3×#832C22semidirect
52. C3×#816C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#810C22semidirect
55. C3×#807C22semidirect
56. #63576C22semidirect
57. #63573C22semidirect
60. #63555C22semidirect
61. Dic3×C3⋊C8C22semidirect
86. #4771D3semidirect
90. #4756D3semidirect
102. C3×#237C2×C4semidirect
114. D3×D12C2×C4semidirect
119. #3753C2×C4semidirect
125. C3×#213C2×C4semidirect
144. #3717C2×C4semidirect
145. #3715C2×C4semidirect
146. #3711C2×C4semidirect
170. D4×Dic3C2×D3semidirect
213. C3×#102C2×D3semidirect
214. C3×#102C2×D3semidirect
217. #832C2×D3semidirect
225. #816C2×D3semidirect
232. C8×Dic3C2×D3semidirect
233. #810C2×D3semidirect
241. #807C2×D3semidirect
251. C32×D4C22×C4semidirect
277. C3×Dic6C22×C4semidirect
284. C3⋊(C3⋊C8)C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
328. #237C4×D3semidirect
380. #213C4×D3semidirect
447. C3×Dic3AGL(1,ℤ/8)semidirect
487. #102D32semidirect
517. C3×D4C2×C4×D3semidirect
518. C3×D4C2×C4×D3semidirect
584. Dic6C2×C4×D3semidirect
594. C3⋊C8C2×C4×D3semidirect
720. Dic3#911semidirect
721. C32C4×AGL(1,ℤ/8)semidirect
738. D4C4×D32semidirect
812. C3#78866semidirect
813. C3C4×#911semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2372
C2×#639252
D3×#8932
#105924842
C3×#47712
C3×#47562
#105914362
#105914002
#105909392
#105907922
#105907432
Dic3×ΓL(1,𝔽25)2
#105905802
#105904842
#105904752
C4×#9113
#788663