Finite Group Databasebeta

← #11860284

Subgroups — #11860284

Order 1152.

1156 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
1D3×D4×Dic3C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic
3#10594358C211yesmaximal, characteristic, complemented
4#10592456C211yesmaximal, characteristic, complemented
5C3×#4770C211yesmaximal, characteristic, complemented
6C3×#4756C211yesmaximal, characteristic, complemented
7#10591436C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590744C211yesmaximal, characteristic, complemented
10#10590741C211yesmaximal, characteristic, complemented
11#10590670C211yesmaximal, characteristic, complemented
12Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
13#10590461C211yesmaximal, characteristic, complemented
14#10590452C211yesmaximal, characteristic, complemented
15#10590436C211yesmaximal, characteristic, complemented
16C4×#911—31nomaximal
17#78914—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×D3×Dic3—21no—
20C2×#3795C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23#64096C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27C3×#893C2211yescharacteristic, complemented
28C3×#892C2211yescharacteristic
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31D3×#217—21no—
32#63932C418yescomplemented
33#63902—21no—
34#63898C2211yescharacteristic
35#63898C2211yescharacteristic, complemented
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63879—21no—
39#63877—21no—
40C4×D3×Dic3—21no—
41C4×D3×Dic3C2211yescharacteristic
42#63844C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C2×#3713C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63643C2211yescharacteristic, complemented
48#63642C2211yescharacteristic, complemented
49#63634C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55C3×#807C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×D4×Dic3—31no—
63C2×#932—31no—
64C2×#911—31no—
65C4×D3×D4—31no—
66C4×#237—31no—
67#5522—31no—
68C3×C4×D8—31no—
69C3×#418—31no—
70#5152—31no—
71#5133—31no—
72Dic3×M16—31no—
73C4×#214—31no—
74C4×#213—31no—
75#4995—31no—
76#4889—31no—
77#4881—31no—
78#4785—31no—
79#4785—31no—
80#4785—31no—
81#4771—31no—
82#4770D311yescharacteristic, complemented
83#4758—31no—
84#4758—31no—
85#4757—31no—
86#4757—31no—
87#4757—31no—
88#4757—61no—
89#4756—31no—
90#4756D311yescharacteristic, complemented
91C4×#204—31no—
92C4×ΓL(1,𝔽25)—31no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4C2×C414yescomplemented
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—44no—
112C2×D3×Dic3D411yescharacteristic
113C2×D3×Dic3D411yescharacteristic
114#3795—22no—
115#3795C2×C414yescomplemented
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3757—21no—
119#3754C2×C414yescomplemented
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#213C2×C414yescomplemented
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×ΓL(1,𝔽25)—22no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32D411yescharacteristic
143Dic32D411yescharacteristic
144#3716C2×C414yescomplemented
145#3713C2×C414yescomplemented
146#3711C2×C414yescomplemented
147C4×AGL(1,ℤ/8)—91noSylow
148C22×C3×D4—31no—
149C23×Dic3—61no—
150C2×#237—31no—
151C2×D3×D4C2×D311yescharacteristic
152C2×#235—31no—
153C22×C4×D3—61no—
154C2×C3×D8—31no—
155C2×C3×M16—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×#117—31no—
159C2×#217—61no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3C2×D311yescharacteristic
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—61no—
173#932—38no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213C2×D311yescharacteristic
177C4×#67—61no—
178C4×#67—61no—
179C2×C4⋊Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—61no—
182C2×#208—31no—
183#911—38no—
184C2×#204—31no—
185C2×ΓL(1,𝔽25)—31no—
186C2×ΓL(1,𝔽25)C2×D311yescharacteristic
187#893—31no—
188#893—31no—
189#893C2×D311yescharacteristic, complemented
190#892C2×D311yescharacteristic
191D3×C4⋊C4—31no—
192#887—31no—
193#887—31no—
194#887—31no—
195#887—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#67⋊C4—61no—
199#67⋊C4—61no—
200D3×C22⋊C4—61no—
201#877—61no—
202C4×D12—31no—
203#872—61no—
204C42×D3—31no—
205C42×D3—61no—
206C4×Dic6—31no—
207C3×#107—31no—
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102C2×D311yescharacteristic
214C3×#102C2×D311yescharacteristic
215C3×C4×C8—31no—
216#832—31no—
217#832C2×D311yescharacteristic
218#821—31no—
219#821C2×D311yescharacteristic
220#821C2×D311yescharacteristic, complemented
221#817—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#815—31no—
227#815—31no—
228#815—31no—
229#815—31no—
230#815—61no—
231C8×Dic3—31no—
232C8×Dic3C2×D311yescharacteristic, complemented
233#810—31no—
234#809C2×D311yescharacteristic
235#808—31no—
236#808—31no—
237#808—31no—
238#807—31no—
239#807—31no—
240#807—61no—
241#807C2×D311yescharacteristic, complemented
242C4×C3⋊C8—31no—
243C23×C32—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—24no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4C22×C412yes—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—42no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259#634—21no—
260#634C22×C412yescomplemented
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×D12C22×C412yes—
271C3×D12C22×C412yescomplemented
272C3×C4×D3—42no—
273C3×C4×D3C22×C412yes—
274C3×C4×D3#4112yes—
275#625—24no—
276D3×Dic3—24no—
277D3×Dic3—22no—
278D3×Dic3—41no—
279D3×Dic3—42no—
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—91no—
293#440—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296C4×D8—31no—
297C4×D8—91no—
298#428—91no—
299#418—31no—
300#417—91no—
301C4×M16—91no—
302C24×C3—61no—
303C23×D3—21no—
304C2×C3×D4—21no—
305C2×C3×D4—34no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C2×#67—21no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—21no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—121no—
329C22×Dic3—124no—
330#237—34no—
331#237—62no—
332D3×D4—22no—
333D3×D4C4×D314yescomplemented
334#235—34no—
335#235—62no—
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—124no—
347C2×C4×D3C22×D311yescharacteristic
348C2×Dic6—31no—
349C2×Dic6—31no—
350C2×Dic6—61no—
351C3×D8—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⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—61no—
368#217—21no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—121no—
375#214—34no—
376#214—34no—
377#214—34no—
378#214—64no—
379#213—34no—
380#213—34no—
381#213C4×D314yescomplemented
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
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
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—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—48no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3C4×D412yes—
436C32×C4—41no—
437C32×C4C23×C411yescharacteristic
438C32×C4C2×#4111yescharacteristic
439C3⋊Dic3—22no—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3C4×D412yes—
447C3×Dic3AGL(1,ℤ/8)12yescomplemented
448C2×#41—91no—
449C22×D4—31no—
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—31no—
471#117—181no—
472C2×C4⋊C4—91no—
473C2×C22⋊C4—181no—
474C2×C42—91no—
475C2×C42—181no—
476#107—31no—
477#107—91no—
478#106—91no—
479#106—91no—
480#103—91no—
481#103—91no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—31no—
486#102—91no—
487#102D3211yescharacteristic
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—64no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—24no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3D3×D411yescharacteristic
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—22no—
510C3×D4—32no—
511C3×D4—32no—
512C3×D4—41no—
513C3×D4—64no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4C2×C4×D312yes—
517C3×D4C2×C4×D312yes—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—24no—
534#67—64no—
535#67—64no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—42no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—64no—
548C2×Dic3—62no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—122no—
555C2×Dic3—122no—
556C2×Dic3—122no—
557C2×Dic3—122no—
558C2×Dic3—122no—
559C2×Dic3—122no—
560C2×Dic3—242no—
561C2×Dic3D3×D411yescharacteristic
562C2×Dic3D3×D411yescharacteristic
563C2×Dic3D3×D411yescharacteristic
564D12—21no—
565D12—21no—
566D12C2×C4×D312yes—
567D12C2×C4×D312yescomplemented
568C4×D3—42no—
569C4×D3—62no—
570C4×D3—64no—
571C4×D3—121no—
572C4×D3—122no—
573C4×D3—122no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3C2×C4×D312yes—
577C4×D3#23712yes—
578Dic6—32no—
579Dic6—32no—
580Dic6—62no—
581Dic6—61no—
582Dic6—61no—
583Dic6—121no—
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×C32—42no—
595C2×C32C2×C4×D411yescharacteristic
596C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
597C2×C32#57511yescharacteristic
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—42no—
601C24—61no—
602#41—94no—
603#41—182no—
604C2×Q8—91no—
605C2×D4—34no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—62no—
609C2×D4—61no—
610C2×D4—181no—
611C2×D4C2×D3211yescharacteristic
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—364no—
624SD16—94no—
625SD16—94no—
626D8—34no—
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—91no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4C2×D3211yescharacteristic
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
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—22no—
656C22×C3—22no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—42no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—128no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3C2×D3×D411yescharacteristic
676C22×C3C2×D3×D411yescharacteristic
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—48no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3#67⋊C412yes—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—32no—
690C3×C4—32no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—81no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4C22×C4×D311yescharacteristic
698C3×C4C22×C4×D311yescharacteristic
699C3×C4C2×#23711yescharacteristic
700C3×C4D3×#4111yescharacteristic
701Dic3—21no—
702Dic3—41no—
703Dic3—41no—
704Dic3—62no—
705Dic3—61no—
706Dic3—61no—
707Dic3—61no—
708Dic3—61no—
709Dic3—62no—
710Dic3—122no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716Dic3#67⋊C412yes—
717Dic3#91112yescomplemented
718C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—64no—
722C23—61no—
723C23—61no—
724C23—122no—
725C23—122no—
726Q8—92no—
727Q8—181no—
728D4—21no—
729D4—32no—
730D4—32no—
731D4—64no—
732D4—61no—
733D4—61no—
734D4—184no—
735D4C4×D3212yes—
736C2×C4—21no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—32no—
740C2×C4—32no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—91no—
745C2×C4—91no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—182no—
749C2×C4—184no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—362no—
753C2×C4—361no—
754C2×C4—362no—
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—42no—
767C2×C3—42no—
768C2×C3—62no—
769C2×C3—82no—
770C2×C3—122no—
771C2×C3—122no—
772C2×C3C2×#67⋊C411yescharacteristic
773C2×C3C4×D3×D411yescharacteristic
774C2×C3C2×#91111yescharacteristic
775C2×C3#576811yescharacteristic
776C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
777C2×C3#577311yescharacteristic
778D3—22no—
779D3—42no—
780D3—42no—
781C22—22no—
782C22—32no—
783C22—41no—
784C22—41no—
785C22—61no—
786C22—61no—
787C22—62no—
788C22—62no—
789C22—128no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22D32×D411yescharacteristic
795C4—32no—
796C4—32no—
797C4—41no—
798C4—61no—
799C4—121no—
800C4—121no—
801C4—181no—
802C4—181no—
803C4—182no—
804C4—361no—
805C4C2×C4×D3211yescharacteristic
806C4D3×#23711yescharacteristic
807C3—21no—
808C3#7891411yescharacteristic, complemented
809C3C4×#91111yescharacteristic, complemented
810C2—42no—
811C2—62no—
812C2—122no—
813C2—122no—
814C2D3×#67⋊C411yescharacteristic
815C2D3×#91111yescharacteristic
816C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63932C2
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. D3×D4×Dic3C2semidirect
3. #10594358C2semidirect
4. #10592456C2semidirect
5. C3×#4770C2semidirect
6. C3×#4756C2semidirect
7. #10591436C2semidirect
8. #10591401C2semidirect
9. #10590744C2semidirect
10. #10590741C2semidirect
11. #10590670C2semidirect
12. Dic3×ΓL(1,𝔽25)C2semidirect
13. #10590461C2semidirect
14. #10590452C2semidirect
15. #10590436C2semidirect
23. #64096C22semidirect
27. C3×#893C22semidirect
32. #63932C4semidirect
35. #63898C22semidirect
42. #63844C22semidirect
47. #63643C22semidirect
48. #63642C22semidirect
49. #63634C22semidirect
52. C3×#821C22semidirect
53. C3×C8×Dic3C22semidirect
55. C3×#807C22semidirect
56. #63574C22semidirect
57. #63573C22semidirect
58. #63567C22semidirect
59. #63563C22semidirect
60. #63555C22semidirect
61. Dic3×C3⋊C8C22semidirect
82. #4770D3semidirect
90. #4756D3semidirect
100. C3×D3×D4C2×C4semidirect
115. #3795C2×C4semidirect
119. #3754C2×C4semidirect
126. C3×#213C2×C4semidirect
144. #3716C2×C4semidirect
145. #3713C2×C4semidirect
146. #3711C2×C4semidirect
189. #893C2×D3semidirect
220. #821C2×D3semidirect
232. C8×Dic3C2×D3semidirect
241. #807C2×D3semidirect
260. #634C22×C4semidirect
271. C3×D12C22×C4semidirect
284. C3⋊(C3⋊C8)C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
333. D3×D4C4×D3semidirect
381. #213C4×D3semidirect
447. C3×Dic3AGL(1,ℤ/8)semidirect
567. D12C2×C4×D3semidirect
593. C3⋊C8C2×C4×D3semidirect
717. Dic3#911semidirect
718. C32C4×AGL(1,ℤ/8)semidirect
808. C3#78914semidirect
809. C3C4×#911semidirect

Maximal subgroups

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

subgroupindex
D3×D4×Dic32
C2×#639322
#105943582
#105924562
C3×#47702
C3×#47562
#105914362
#105914012
#105907442
#105907412
#105906702
Dic3×ΓL(1,𝔽25)2
#105904612
#105904522
#105904362
C4×#9113
#789143