Finite Group Databasebeta

← #11860334

Subgroups — #11860334

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#239C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic
3D3×#893C211yesmaximal, characteristic, complemented
4#10592487C211yesmaximal, characteristic, complemented
5C3×#4817C211yesmaximal, characteristic, complemented
6C3×#4803C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590746C211yesmaximal, characteristic, complemented
11#10590740C211yesmaximal, characteristic, complemented
12#10590667C211yesmaximal, characteristic, complemented
13#10590580C211yesmaximal, characteristic, complemented
14#10590459C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#79773—31nomaximal
17#78866—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23#64102C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29#63939C418yescomplemented
30D3×(C2×D3)⋊C4—21no—
31#63904—21no—
32#63898—21no—
33#63898C2211yescharacteristic
34#63898C2211yescharacteristic, complemented
35#63894C2211yescharacteristic
36Dic3×D12—21no—
37Dic3×D12C2211yescharacteristic, complemented
38#63881—21no—
39C4×D3×Dic3—21no—
40C4×D3×Dic3C2211yescharacteristic
41#63841—21no—
42#63841C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3713C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#103C2211yescharacteristic, complemented
47#63648C2211yescharacteristic
48C8×C3⋊Dic3C2211yescharacteristic, complemented
49#63635C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#63553C2211yescharacteristic, complemented
62Dic3×#41—31no—
63C2×#949—31no—
64C2×#914—31no—
65C4×#239—31no—
66C4×D3×D4—31no—
67C2×#893—31no—
68C3×#440—31no—
69C3×#417—31no—
70Dic3×SD16—31no—
71#5131—31no—
72Dic3×M16—31no—
73#5026—31no—
74#5014—31no—
75#4964—31no—
76#4881—31no—
77#4872—31no—
78#4817—31no—
79#4817D311yescharacteristic, complemented
80#4803D311yescharacteristic, complemented
81#4788—31no—
82#4788—31no—
83#4788—31no—
84#4788—61no—
85#4785—31no—
86#4785—31no—
87#4770—31no—
88#4756—31no—
89#4756—31no—
90#4756—31no—
91#4711—31no—
92#4707—31no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C3×#239—22no—
98C3×#239C2×C414yescomplemented
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—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#3755C2×C414yescomplemented
119#3752—21no—
120C4⋊(C3⋊Dic3)—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#215C2×C414yescomplemented
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×ΓL(1,𝔽25)—22no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32D411yescharacteristic
143Dic32D411yescharacteristic
144#3714C2×C414yescomplemented
145#3713C2×C414yescomplemented
146#3711C2×C414yescomplemented
147C4×AGL(1,ℤ/8)—91noSylow
148C2×C3×#41—31no—
149C2×#239C2×D311yescharacteristic
150C2×D3×D4—31no—
151C22×D12—31no—
152C22×C4×D3—61no—
153C22×C4×D3—61no—
154C2×C3×SD16—31no—
155C2×C3×M16—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C2×C3×C4⋊C4—31no—
159#949—38no—
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—61no—
163Q8×Dic3C2×D311yescharacteristic, complemented
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167C2×#215C2×D311yescharacteristic
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—31no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213—31no—
176C4×#67—61no—
177C2×(C2×D3)⋊C4—61no—
178#926—31no—
179#926—61no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—61no—
182C2×#208—31no—
183#914—38no—
184C2×D24—31no—
185C2×ΓL(1,𝔽25)—31no—
186C2×ΓL(1,𝔽25)C2×D311yescharacteristic
187#893—31no—
188#893—31no—
189#893—31no—
190#893—31no—
191#893—31no—
192#893—61no—
193#893—61no—
194#893—61no—
195#893—61no—
196#893C2×D311yescharacteristic
197#892—31no—
198#892—61no—
199D3×C4⋊C4C2×D311yescharacteristic
200#67⋊C4—61no—
201D3×C22⋊C4—61no—
202C4×D12—31no—
203C4×D12—31no—
204C4×D12—61no—
205C42×D3—31no—
206C42×D3—61no—
207C3×#107—31no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic, complemented
211C3×#103C2×D311yescharacteristic, complemented
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#97—31no—
216#835C2×D311yescharacteristic, complemented
217#832—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821C2×D311yescharacteristic
224#821C2×D311yescharacteristic, complemented
225#817—31no—
226#815—31no—
227#815C2×D311yescharacteristic, complemented
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232C8×Dic3—61no—
233#809—31no—
234#809C2×D311yescharacteristic, complemented
235#808—31no—
236#808—31no—
237#808—31no—
238#808—61no—
239#807—31no—
240#807—31no—
241#807C2×D311yescharacteristic, complemented
242#803—31no—
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—24no—
248C2×D32—42no—
249C2×D32—42no—
250C32×Q8—21no—
251C32×Q8C22×C412yescomplemented
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)C22×C412yes—
260C4×C3⋊D3—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—24no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12C22×C412yes—
270C3×D12C22×C412yescomplemented
271C3×C4×D3—24no—
272C3×C4×D3—42no—
273C3×C4×D3—42no—
274C3×C4×D3C22×C412yes—
275C3×C4×D3#4112yes—
276#626—24no—
277#624—42no—
278D3×Dic3—22no—
279D3×Dic3—41no—
280D3×Dic3—42no—
281D3×Dic3—42no—
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—31no—
293#440—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296C4×D8—91no—
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—21no—
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—61no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322#239—22no—
323#239C4×D314yescomplemented
324D3×D4—34no—
325D3×D4—62no—
326C2×D12—21no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—34no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
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
351C3×SD16—34no—
352C3×M16—62no—
353C2×C3×C8—21no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#215—34no—
373#215—34no—
374#215—64no—
375#215C4×D314yescomplemented
376#213—34no—
377#213—34no—
378#213—34no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
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—21no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—121no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—21no—
399C4×Dic3—21no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—121no—
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
419D24—34no—
420ΓL(1,𝔽25)—22no—
421ΓL(1,𝔽25)—34no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—22no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3C4×D412yes—
435D32—48no—
436C32×C4—22no—
437C32×C4—41no—
438C32×C4C23×C411yescharacteristic
439C32×C4C2×#4111yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3C4×D412yes—
448C2×#41—31no—
449C22×D4—91no—
450C23×C4—181no—
451AGL(1,ℤ/8)—98no—
452C2×SD16—31no—
453C2×SD16—91no—
454C2×D8—91no—
455C2×D8—91no—
456C2×M16—31no—
457C2×M16—91no—
458C4×Q8—31no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—91no—
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#103D3211yescharacteristic, complemented
482#102—31no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#97—31no—
489#97—91no—
490C4×C8—91no—
491C4×C8—91no—
492C23×C3—31no—
493C23×C3—61no—
494C23×C3—61no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—64no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—64no—
501C22×D3—121no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3D3×D411yescharacteristic
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—22no—
510C3×Q8—41no—
511C3×Q8C2×C4×D312yescomplemented
512C3×Q8C2×C4×D312yescomplemented
513C3×D4—32no—
514C3×D4—32no—
515C3×D4—64no—
516C3×D4—61no—
517C3×D4—61no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—64no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—64no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—62no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C2×Dic3—122no—
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557D12—24no—
558D12—21no—
559D12—21no—
560D12—32no—
561D12—32no—
562D12—62no—
563D12—64no—
564D12—61no—
565D12—61no—
566D12—121no—
567D12C2×C4×D312yes—
568D12C2×C4×D312yescomplemented
569C4×D3—24no—
570C4×D3—42no—
571C4×D3—42no—
572C4×D3—62no—
573C4×D3—122no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—121no—
580C4×D3—122no—
581C4×D3—242no—
582C4×D3C2×C4×D312yes—
583C4×D3#23712yes—
584C3×C8—21no—
585C3×C8—21no—
586C3×C8—32no—
587C3×C8—41no—
588C3×C8—61no—
589C3⋊C8—21no—
590C3⋊C8—32no—
591C3⋊C8—32no—
592C3⋊C8—62no—
593C3⋊C8C2×C4×D312yescomplemented
594C2×C32C2×C4×D411yescharacteristic
595C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
596C2×C32#57511yescharacteristic
597C3⋊D3—42no—
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—42no—
601C24—181no—
602#41—34no—
603#41—62no—
604C2×Q8C2×D3211yescharacteristic
605C2×D4—31no—
606C2×D4—31no—
607C2×D4—61no—
608C2×D4—94no—
609C2×D4—91no—
610C2×D4—182no—
611C2×D4—181no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—364no—
624SD16—34no—
625SD16—94no—
626D8—94no—
627D8—94no—
628M16—62no—
629M16—94no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8C2×D3211yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4C2×D3211yescharacteristic
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—61no—
650C42—91no—
651C42—91no—
652C42—91no—
653C42—181no—
654C42—181no—
655C22×C3—21no—
656C22×C3—32no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—62no—
660C22×C3—62no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C2×D3×D411yescharacteristic
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—122no—
678C2×D3—128no—
679C2×D3—128no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3#67⋊C412yes—
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—32no—
692C3×C4—42no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—81no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C22×C4×D311yescharacteristic
701C3×C4C22×C4×D311yescharacteristic
702C3×C4C2×#23711yescharacteristic
703C3×C4D3×#4111yescharacteristic
704Dic3—21no—
705Dic3—21no—
706Dic3—32no—
707Dic3—32no—
708Dic3—41no—
709Dic3—41no—
710Dic3—62no—
711Dic3—61no—
712Dic3—61no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—241no—
717Dic3#67⋊C412yes—
718C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
719C23—31no—
720C23—61no—
721C23—61no—
722C23—184no—
723C23—181no—
724C23—362no—
725C23—362no—
726Q8—21no—
727Q8C4×D3212yescomplemented
728D4—32no—
729D4—32no—
730D4—64no—
731D4—61no—
732D4—61no—
733D4—92no—
734D4—184no—
735D4—181no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—31no—
739C2×C4—32no—
740C2×C4—32no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—64no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—91no—
747C2×C4—91no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—182no—
751C2×C4—181no—
752C2×C4—362no—
753C2×C4—362no—
754C2×C4—361no—
755C2×C4—362no—
756C2×C4—362no—
757C2×C4—362no—
758C2×C4C22×D3211yescharacteristic
759C8—21no—
760C8—32no—
761C8—61no—
762C8—92no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—62no—
767C2×C3—122no—
768C2×C3—122no—
769C2×C3C2×#67⋊C411yescharacteristic
770C2×C3C4×D3×D411yescharacteristic
771C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
772C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
773C2×C3#577711yescharacteristic
774C2×C3#577711yescharacteristic
775D3—22no—
776D3—42no—
777D3—42no—
778D3—122no—
779D3—122no—
780D3—242no—
781C22—32no—
782C22—61no—
783C22—61no—
784C22—62no—
785C22—62no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—182no—
791C22—368no—
792C22—361no—
793C22—361no—
794C22D32×D411yescharacteristic
795C4—22no—
796C4—32no—
797C4—41no—
798C4—61no—
799C4—61no—
800C4—92no—
801C4—121no—
802C4—121no—
803C4—181no—
804C4—361no—
805C4C2×C4×D3211yescharacteristic
806C4D3×#23711yescharacteristic
807C3—21no—
808C3#7886611yescharacteristic, complemented
809C3#7977311yescharacteristic, complemented
810C2—62no—
811C2—122no—
812C2—122no—
813C2—362no—
814C2D3×#67⋊C411yescharacteristic
815C2#1059474011yescharacteristic
816C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63939C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. Dic3×#239C2semidirect
3. D3×#893C2semidirect
4. #10592487C2semidirect
5. C3×#4817C2semidirect
6. C3×#4803C2semidirect
7. #10591571C2semidirect
8. #10591540C2semidirect
9. #10590939C2semidirect
10. #10590746C2semidirect
11. #10590740C2semidirect
12. #10590667C2semidirect
13. #10590580C2semidirect
14. #10590459C2semidirect
15. #10590455C2semidirect
21. Q8×C3⋊Dic3C22semidirect
24. C3×Q8×Dic3C22semidirect
29. #63939C4semidirect
34. #63898C22semidirect
37. Dic3×D12C22semidirect
46. C32×#103C22semidirect
48. C8×C3⋊Dic3C22semidirect
49. #63635C22semidirect
50. C3×#835C22semidirect
52. C3×#821C22semidirect
53. C3×#815C22semidirect
54. C3×#809C22semidirect
55. C3×#807C22semidirect
56. #63576C22semidirect
57. #63573C22semidirect
60. #63554C22semidirect
61. #63553C22semidirect
79. #4817D3semidirect
80. #4803D3semidirect
98. C3×#239C2×C4semidirect
114. D3×D12C2×C4semidirect
118. #3755C2×C4semidirect
125. C3×#215C2×C4semidirect
144. #3714C2×C4semidirect
145. #3713C2×C4semidirect
146. #3711C2×C4semidirect
163. Q8×Dic3C2×D3semidirect
210. C3×#103C2×D3semidirect
211. C3×#103C2×D3semidirect
216. #835C2×D3semidirect
224. #821C2×D3semidirect
227. #815C2×D3semidirect
234. #809C2×D3semidirect
241. #807C2×D3semidirect
251. C32×Q8C22×C4semidirect
270. C3×D12C22×C4semidirect
284. C3⋊(C3⋊C8)C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
323. #239C4×D3semidirect
375. #215C4×D3semidirect
442. C3⋊Dic3AGL(1,ℤ/8)semidirect
481. #103D32semidirect
511. C3×Q8C2×C4×D3semidirect
512. C3×Q8C2×C4×D3semidirect
568. D12C2×C4×D3semidirect
593. C3⋊C8C2×C4×D3semidirect
718. C32C4×AGL(1,ℤ/8)semidirect
727. Q8C4×D32semidirect
808. C3#78866semidirect
809. C3#79773semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2392
C2×#639392
D3×#8932
#105924872
C3×#48172
C3×#48032
#105915712
#105915402
#105909392
#105907462
#105907402
#105906672
#105905802
#105904592
#105904552
#797733
#788663