Finite Group Databasebeta

← #10811069

Subgroups — #10811069

Order 768.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5768C211yesmaximal, characteristic
2#83793C211yesmaximal, characteristic, complemented
3C2×#5144C211yesmaximal, characteristic, complemented
4C2×#4823C211yesmaximal, characteristic, complemented
5#78663C211yesmaximal, characteristic, complemented
6C3×#1876C211yesmaximal, characteristic, complemented
7#72087C211yesmaximal, characteristic, complemented
8#70380C211yesmaximal, characteristic, complemented
9#70380C211yesmaximal, characteristic, complemented
10#70374C211yesmaximal, characteristic, complemented
11#69999C211yesmaximal, characteristic, complemented
12#68946C211yesmaximal, characteristic, complemented
13#68940C211yesmaximal, characteristic, complemented
14#68695C211yesmaximal, characteristic, complemented
15#68650C211yesmaximal, characteristic, complemented
16#22453—31nomaximal, Sylow
17C2×D3×#41C2211yescharacteristic
18C2×D3×#41C2211yescharacteristic
19C2×C3×#135C2211yescharacteristic
20C2×C3×#131C2211yescharacteristic, complemented
21C2×#950C2211yescharacteristic
22C2×#950C2211yescharacteristic
23C2×#948C2211yescharacteristic, complemented
24#5768—24no—
25#5768—24no—
26C2×#918C411yescharacteristic, complemented
27C2×#918C411yescharacteristic, complemented
28C2×#915C411yescharacteristic, complemented
29C2×#915C411yescharacteristic, complemented
30C2×#914C411yescharacteristic, complemented
31C2×#914C411yescharacteristic, complemented
32C2×#911C411yescharacteristic, complemented
33C2×#911C411yescharacteristic, complemented
34C2×#907C2211yescharacteristic, complemented
35C2×#904C2211yescharacteristic
36C2×#901C2211yescharacteristic, complemented
37C22×ΓL(1,𝔽25)C2211yescharacteristic
38C2×C3×#104C2211yescharacteristic, complemented
39C2×C3×#104C2211yescharacteristic, complemented
40C3×#408C2211yescharacteristic, complemented
41C2×#837C2211yescharacteristic, complemented
42C2×#837C2211yescharacteristic, complemented
43#5234C2211yescharacteristic, complemented
44#5144—24no—
45C2×#825C2211yescharacteristic, complemented
46C2×#825C2211yescharacteristic, complemented
47#5129—21no—
48#5129C2211yescharacteristic, complemented
49#5126—21no—
50#5126C2211yescharacteristic
51#5126C2211yescharacteristic
52C2×#822C2211yescharacteristic, complemented
53C2×#822C2211yescharacteristic, complemented
54#5110—21no—
55#5110C2211yescharacteristic, complemented
56C2×(C2×D3)⋊C8—21no—
57C2×(C2×D3)⋊C8C2211yescharacteristic
58C2×C8×Dic3C2211yescharacteristic, complemented
59C4×(C2×D3)⋊C4C2211yescharacteristic
60C2×#805C2211yescharacteristic, complemented
61C2×#805C2211yescharacteristic, complemented
62C2×#803C2211yescharacteristic, complemented
63#4823—24no—
64#4727—21no—
65#4727—21no—
66#4726—21no—
67D3×C22⋊C8—21no—
68C3×#341C2211yescharacteristic, complemented
69C3×#336C2211yescharacteristic, complemented
70#4552C2211yescharacteristic, complemented
71#4550C2211yescharacteristic, complemented
72C2×#575—31no—
73C2×#444—31no—
74C2×#443—31no—
75#2880—31no—
76#2880—31no—
77#1975—31no—
78#1974—31no—
79#1876—31no—
80#1876—31no—
81#1876—31no—
82#1876D311yescharacteristic, complemented
83#1811—31no—
84#1789—31no—
85#1789—31no—
86#1753—31no—
87C2×C3×#41C2311yescharacteristic
88C2×C3×#41C2311yescharacteristic
89D3×#41—22no—
90D3×#41—22no—
91D3×#41—22no—
92D3×#41—22no—
93D3×#41—41no—
94D3×#41—41no—
95D3×#41—41no—
96D3×#41—41no—
97C2×#239C2×C411yescharacteristic
98C2×#239C2×C411yescharacteristic
99C2×D3×Q8C2×C411yescharacteristic
100C2×D3×Q8C2×C411yescharacteristic
101C2×#237—21no—
102C2×#237—21no—
103C2×#237C2×C411yescharacteristic
104C2×#237C2×C411yescharacteristic
105C2×D3×D4—21no—
106C2×D3×D4—21no—
107C2×D3×D4C2×C411yescharacteristic
108C2×D3×D4C2×C411yescharacteristic
109C2×#235—21no—
110C2×#235—21no—
111C2×#235C2311yescharacteristic
112C2×#235C2311yescharacteristic
113C22×C4×D3—21no—
114C22×C4×D3—21no—
115C22×C4×D3C2311yescharacteristic
116C3×#135—22no—
117C3×#135—22no—
118C2×C3×Q16C2×C411yescharacteristic
119C2×C3×SD16C2×C411yescharacteristic
120C2×C3×SD16C2×C411yescharacteristic
121C2×C3×D8C2×C411yescharacteristic
122C3×#131—22no—
123C3×#131—41no—
124C2×C3×M16—21no—
125C2×C3×M16C2311yescharacteristic
126C2×C3×M16C2311yescharacteristic
127C22×C3×C8—21no—
128C22×C3×C8C2311yescharacteristic
129C22×C3×C8C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131#950—22no—
132#950—22no—
133#950D414yes—
134#950D414yes—
135#948—22no—
136#948—41no—
137C2×#216C2×C411yescharacteristic
138C2×#216C2×C411yescharacteristic
139C2×#215C2×C411yescharacteristic
140C2×#215C2×C411yescharacteristic
141C2×#214C2×C411yescharacteristic
142C2×#214C2×C411yescharacteristic
143C2×#213C2×C411yescharacteristic
144C2×#213C2×C411yescharacteristic
145C2×(C2×D3)⋊C4—21no—
146C2×C4×Dic3C2311yescharacteristic
147C2×#208—21no—
148C2×#208C2311yescharacteristic
149C2×#208C2311yescharacteristic
150C22×C3⋊C8—21no—
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153#918—24no—
154#918—24no—
155#915—24no—
156#915—24no—
157#914—24no—
158#914—24no—
159#911—24no—
160#911—24no—
161#907—22no—
162#907—41no—
163C2×Dic12C2×C411yescharacteristic
164#904—22no—
165#904—22no—
166C2×D24C2×C411yescharacteristic
167C2×#204C2×C411yescharacteristic
168C2×#204C2×C411yescharacteristic
169#901—22no—
170#901—41no—
171C2×ΓL(1,𝔽25)—22no—
172C2×ΓL(1,𝔽25)—22no—
173C2×ΓL(1,𝔽25)—21no—
174C2×ΓL(1,𝔽25)—21no—
175C2×ΓL(1,𝔽25)C2×C411yescharacteristic
176C2×ΓL(1,𝔽25)C2×C411yescharacteristic
177C2×ΓL(1,𝔽25)C2×C411yescharacteristic
178C2×ΓL(1,𝔽25)C2×C411yescharacteristic
179C2×D3×C8—21no—
180C2×D3×C8—21no—
181C3×#104—22no—
182C3×#104—41no—
183C3×C22⋊C8—21no—
184C3×C22⋊C8—21no—
185#837—22no—
186#837—41no—
187C3⋊#95—21no—
188#830—21no—
189#830—21no—
190#825—22no—
191#825—41no—
192#822—22no—
193#822—22no—
194(C2×D3)⋊C8—21no—
195(C2×D3)⋊C8—21no—
196(C2×D3)⋊C8—21no—
197(C2×D3)⋊C8—21no—
198(C2×D3)⋊C8—21no—
199(C2×D3)⋊C8—21no—
200(C2×D3)⋊C8—21no—
201(C2×D3)⋊C8—21no—
202(C2×D3)⋊C8D411yescharacteristic
203(C2×D3)⋊C8D411yescharacteristic
204(C2×D3)⋊C8D411yescharacteristic
205(C2×D3)⋊C8D411yescharacteristic
206C8×Dic3—22no—
207#805—22no—
208#805—41no—
209#803—22no—
210C22×#41—31no—
211C22×#41—31no—
212#575—64no—
213#575—64no—
214C2×#137—31no—
215C2×#137—31no—
216C2×#137—31no—
217C2×#137—31no—
218C2×AGL(1,ℤ/8)—31no—
219C2×AGL(1,ℤ/8)—31no—
220C2×AGL(1,ℤ/8)—31no—
221C2×AGL(1,ℤ/8)—31no—
222C2×#135—31no—
223C2×#135—31no—
224C2×#135—31no—
225C2×#135C2×D311yescharacteristic
226C2×#131—31no—
227C2×#131—31no—
228C2×#131—31no—
229C2×#131C2×D311yescharacteristic, complemented
230C22×M16—31no—
231#444—64no—
232#443—64no—
233C2×#108—31no—
234C2×#108—31no—
235C2×#104—31no—
236C2×#104—31no—
237C2×#104—31no—
238C2×#104—31no—
239C2×#104—31no—
240C2×#104—31no—
241C2×#104C2×D311yescharacteristic, complemented
242C2×#104C2×D311yescharacteristic, complemented
243#408—31no—
244#408—31no—
245#408—31no—
246#408—61no—
247#408—61no—
248#408—61no—
249#408—61no—
250#408C2×D311yescharacteristic, complemented
251#407—31no—
252#407—31no—
253#407—61no—
254#407—61no—
255C2×C22⋊C8—31no—
256C2×C22⋊C8—61no—
257C2×C22⋊C8—61no—
258C2×#97—31no—
259C2×C4×C8—31no—
260C4×C22⋊C4—31no—
261#341—31no—
262#341C2×D311yescharacteristic, complemented
263#336—31no—
264#336C2×D311yescharacteristic, complemented
265C23×D3—21no—
266C23×D3—21no—
267C23×D3#4111yescharacteristic
268C3×#41—21no—
269C3×#41—21no—
270C3×#41—21no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41C2×D412yes—
275C3×#41C2×D412yes—
276C2×C3×Q8C22×C411yescharacteristic
277C2×C3×Q8C22×C411yescharacteristic
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4C22×C411yescharacteristic
281C2×C3×D4C22×C411yescharacteristic
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4C2411yescharacteristic
286C2×#67—21no—
287C2×#67—21no—
288C2×#67—21no—
289C2×#67—21no—
290C2×#67—21no—
291C2×#67—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3#4111yescharacteristic
296#239—22no—
297#239—22no—
298#239—41no—
299#239—41no—
300D3×Q8—22no—
301D3×Q8—22no—
302D3×Q8—41no—
303D3×Q8—41no—
304#237—22no—
305#237—22no—
306#237—41no—
307#237—41no—
308#237—42no—
309#237—42no—
310#237—42no—
311#237—42no—
312D3×D4—22no—
313D3×D4—22no—
314D3×D4—41no—
315D3×D4—41no—
316D3×D4—42no—
317D3×D4—42no—
318D3×D4—42no—
319D3×D4—42no—
320#235—21no—
321#235—21no—
322#235—21no—
323#235—21no—
324#235—21no—
325#235—21no—
326#235—42no—
327#235—42no—
328#235—42no—
329#235—42no—
330#235C2×D412yes—
331#235C2×D412yes—
332C2×D12—21no—
333C2×D12—21no—
334C2×D12C22×C411yescharacteristic
335C2×D12C22×C411yescharacteristic
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3—21no—
346C2×C4×D3—42no—
347C2×C4×D3—42no—
348C2×C4×D3—42no—
349C2×C4×D3—42no—
350C2×C4×D3C22×C411yescharacteristic
351C2×C4×D3C22×C411yescharacteristic
352C2×C4×D3C2×D411yescharacteristic
353C2×C4×D3C2×D411yescharacteristic
354C2×Dic6—21no—
355C2×Dic6—21no—
356C2×Dic6C22×C411yescharacteristic
357C2×Dic6C22×C411yescharacteristic
358C3×Q16—22no—
359C3×SD16—22no—
360C3×SD16—22no—
361C3×D8—22no—
362C3×M16—21no—
363C3×M16—21no—
364C3×M16—21no—
365C3×M16—21no—
366C3×M16—42no—
367C2×C3×C8—21no—
368C2×C3×C8—21no—
369C2×C3×C8—21no—
370C2×C3×C8—21no—
371C2×C3×C8—21no—
372C2×C3×C8—21no—
373C2×C3×C8—42no—
374C2×C3×C8C22×C411yescharacteristic
375C2×C3×C8C22×C411yescharacteristic
376C2×C3×C8C2×D411yescharacteristic
377C2×C3×C8C2×D411yescharacteristic
378C3×C42—21no—
379C3×C42—21no—
380#216—22no—
381#216C22⋊C414yescomplemented
382#215—22no—
383#215C22⋊C414yescomplemented
384#214—22no—
385#214C22⋊C414yescomplemented
386#213—22no—
387#213C22⋊C414yescomplemented
388(C2×D3)⋊C4—42no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391#208—21no—
392#208—21no—
393#208—21no—
394#208—21no—
395#208—42no—
396C2×C3⋊C8—21no—
397C2×C3⋊C8—21no—
398C2×C3⋊C8—21no—
399C2×C3⋊C8—21no—
400C2×C3⋊C8—42no—
401C2×C3⋊C8C22×C411yescharacteristic
402C2×C3⋊C8C22×C411yescharacteristic
403C2×C3⋊C8C2×D411yescharacteristic
404C2×C3⋊C8C2×D411yescharacteristic
405C2×C3⋊C8C2×D412yes—
406C2×C3⋊C8C2×D412yes—
407Dic12—22no—
408D24—22no—
409#204—22no—
410#204—22no—
411ΓL(1,𝔽25)—22no—
412ΓL(1,𝔽25)—22no—
413ΓL(1,𝔽25)—22no—
414ΓL(1,𝔽25)—22no—
415ΓL(1,𝔽25)—42no—
416ΓL(1,𝔽25)—42no—
417D3×C8—42no—
418D3×C8—42no—
419C2×#41—31no—
420C2×#41—31no—
421C2×#41—31no—
422C2×#41—31no—
423C2×#41—31no—
424C2×#41—31no—
425C2×#41—61no—
426C2×#41—61no—
427C2×#41—61no—
428C2×#41—61no—
429C2×#41—62no—
430C2×#41—62no—
431C2×#41—62no—
432C2×#41—62no—
433C2×#41—121no—
434C2×#41—121no—
435C2×#41—121no—
436C2×#41—121no—
437C2×#41C22×D311yescharacteristic
438C2×#41C22×D311yescharacteristic
439C22×Q8—31no—
440C22×Q8—31no—
441C22×D4—31no—
442C22×D4—31no—
443C22×D4—61no—
444C22×D4—61no—
445C23×C4—31no—
446C23×C4—61no—
447C23×C4—61no—
448#137—64no—
449#137—64no—
450#137—64no—
451#137—64no—
452AGL(1,ℤ/8)—64no—
453AGL(1,ℤ/8)—64no—
454AGL(1,ℤ/8)—64no—
455AGL(1,ℤ/8)—64no—
456#135—22no—
457#135—22no—
458#135—34no—
459#135—34no—
460#135—62no—
461#135—62no—
462#135—62no—
463#135—62no—
464C2×Q16—31no—
465C2×Q16—31no—
466C2×Q16—31no—
467C2×Q16C4×D311yescharacteristic
468C2×SD16—31no—
469C2×SD16—31no—
470C2×SD16—31no—
471C2×SD16—31no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16C4×D311yescharacteristic
475C2×SD16C4×D311yescharacteristic
476C2×D8—31no—
477C2×D8—31no—
478C2×D8—31no—
479C2×D8C4×D311yescharacteristic
480#131—22no—
481#131—41no—
482#131—62no—
483#131—62no—
484#131—62no—
485#131—121no—
486#131—121no—
487#131—121no—
488C2×M16—21no—
489C2×M16—31no—
490C2×M16—31no—
491C2×M16—31no—
492C2×M16—31no—
493C2×M16—31no—
494C2×M16—31no—
495C2×M16—62no—
496C2×M16—62no—
497C2×M16—61no—
498C2×M16—61no—
499C2×M16—61no—
500C2×M16C22×D311yescharacteristic
501C2×M16C22×D311yescharacteristic
502C22×C8—21no—
503C22×C8—31no—
504C22×C8—31no—
505C22×C8—61no—
506C22×C8—61no—
507C22×C8—61no—
508C22×C8C22×D311yescharacteristic
509C22×C8C22×D311yescharacteristic
510C2×C22⋊C4—61no—
511C2×C42—31no—
512C2×C42C22×D311yescharacteristic
513#108—62no—
514#108—62no—
515#104—22no—
516#104—41no—
517#104—62no—
518#104—62no—
519#104—62no—
520#104—121no—
521#104—121no—
522#104—121no—
523C22⋊C8—21no—
524C22⋊C8—21no—
525C22⋊C8—31no—
526C22⋊C8—31no—
527C22⋊C8—31no—
528C22⋊C8—31no—
529C22⋊C8—61no—
530C22⋊C8—61no—
531C22⋊C8—61no—
532C22⋊C8—61no—
533C22⋊C8—61no—
534C22⋊C8—61no—
535C22⋊C8—61no—
536C22⋊C8—61no—
537C22⋊C8—61no—
538C22⋊C8—61no—
539#97—62no—
540C4×C8—62no—
541#95—61no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3C2×#4111yescharacteristic
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—42no—
555C22×D3—81no—
556C22×D3—81no—
557C22×D3C4×D411yescharacteristic
558C22×D3C4×D411yescharacteristic
559C3×Q8—21no—
560C3×Q8—21no—
561C3×Q8—21no—
562C3×Q8C2×C22⋊C412yes—
563C3×D4—22no—
564C3×D4—22no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—41no—
569C3×D4—41no—
570C3×D4C2×C22⋊C412yes—
571C2×C3×C4—21no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—21no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4C23×C411yescharacteristic
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4C22×D411yescharacteristic
584C2×C3×C4H(5,𝔽2)11yescharacteristic
585C2×C3×C4H(5,𝔽2)11yescharacteristic
586#67—22no—
587#67—22no—
588#67—42no—
589#67—42no—
590#67—42no—
591#67—42no—
592#67—41no—
593#67—41no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—22no—
598C2×Dic3—21no—
599C2×Dic3—42no—
600C2×Dic3—42no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3C4×D411yescharacteristic
604C2×Dic3C4×D411yescharacteristic
605D12—21no—
606D12—21no—
607D12—21no—
608D12—42no—
609D12—42no—
610D12C2×C22⋊C412yes—
611C4×D3—21no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—21no—
615C4×D3—22no—
616C4×D3—22no—
617C4×D3—21no—
618C4×D3—21no—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—42no—
622C4×D3—42no—
623C4×D3—42no—
624C4×D3—42no—
625C4×D3—41no—
626C4×D3—41no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630Dic6—42no—
631Dic6—42no—
632Dic6C2×C22⋊C412yes—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—21no—
637C3×C8—41no—
638C3×C8—41no—
639C3⋊C8—21no—
640C3⋊C8—21no—
641C3⋊C8—41no—
642C3⋊C8—41no—
643C3⋊C8C2×C22⋊C412yes—
644C3⋊C8C2×C22⋊C412yes—
645C24—31no—
646C24—61no—
647C24—61no—
648#41—21no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—32no—
655#41—32no—
656#41—61no—
657#41—61no—
658#41—62no—
659#41—62no—
660#41—62no—
661#41—62no—
662#41—61no—
663#41—61no—
664#41—61no—
665#41—61no—
666#41—122no—
667#41—122no—
668#41—122no—
669#41—122no—
670#41—121no—
671#41—121no—
672#41—122no—
673#41—122no—
674#41—122no—
675#41—122no—
676#41—121no—
677#41—121no—
678#41D3×D412yes—
679#41D3×D412yes—
680C2×Q8—31no—
681C2×Q8—31no—
682C2×Q8—61no—
683C2×Q8—61no—
684C2×Q8—62no—
685C2×Q8—62no—
686C2×Q8—121no—
687C2×Q8—121no—
688C2×Q8C2×C4×D311yescharacteristic
689C2×Q8C2×C4×D311yescharacteristic
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—31no—
693C2×D4—31no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—61no—
698C2×D4—62no—
699C2×D4—61no—
700C2×D4—62no—
701C2×D4—61no—
702C2×D4—61no—
703C2×D4—61no—
704C2×D4—121no—
705C2×D4—121no—
706C2×D4—122no—
707C2×D4—122no—
708C2×D4—122no—
709C2×D4—122no—
710C2×D4C2×C4×D311yescharacteristic
711C2×D4C2×C4×D311yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—122no—
734C22×C4—122no—
735C22×C4—122no—
736C22×C4—122no—
737C22×C4C23×D311yescharacteristic
738Q16—22no—
739Q16—34no—
740Q16—62no—
741Q16—62no—
742SD16—22no—
743SD16—22no—
744SD16—34no—
745SD16—34no—
746SD16—62no—
747SD16—62no—
748SD16—62no—
749SD16—62no—
750D8—22no—
751D8—34no—
752D8—62no—
753D8—62no—
754M16—21no—
755M16—21no—
756M16—21no—
757M16—21no—
758M16—42no—
759M16—62no—
760M16—62no—
761M16—62no—
762M16—62no—
763M16—61no—
764M16—61no—
765M16—61no—
766M16—61no—
767M16—122no—
768M16—122no—
769M16—122no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—31no—
777C2×C8—31no—
778C2×C8—32no—
779C2×C8—32no—
780C2×C8—31no—
781C2×C8—31no—
782C2×C8—42no—
783C2×C8—61no—
784C2×C8—61no—
785C2×C8—61no—
786C2×C8—61no—
787C2×C8—122no—
788C2×C8—122no—
789C2×C8—122no—
790C2×C8C2×C4×D311yescharacteristic
791C2×C8C2×C4×D311yescharacteristic
792C2×C8D3×D411yescharacteristic
793C2×C8D3×D411yescharacteristic
794C22⋊C4—122no—
795C42—21no—
796C42—21no—
797C42—61no—
798C42—61no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—22no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3C2×C4×D411yescharacteristic
808C22×C3#54611yescharacteristic
809C22×C3#54611yescharacteristic
810C2×D3—21no—
811C2×D3—21no—
812C2×D3—22no—
813C2×D3—21no—
814C2×D3—21no—
815C2×D3—21no—
816C2×D3—21no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—81no—
823C2×D3—81no—
824C2×D3—84no—
825C2×D3—84no—
826C3×C4—22no—
827C3×C4—41no—
828C3×C4—81no—
829C3×C4C22×C22⋊C411yescharacteristic
830C3×C4#51811yescharacteristic
831C3×C4D4211yescharacteristic
832C3×C4D4211yescharacteristic
833Dic3—22no—
834Dic3—21no—
835Dic3—21no—
836Dic3—42no—
837Dic3—41no—
838C23—21no—
839C23—21no—
840C23—31no—
841C23—31no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—121no—
847C23—121no—
848C23—122no—
849C23—122no—
850C23—122no—
851C23—122no—
852C23—241no—
853C23—241no—
854C23D3×#4111yescharacteristic
855Q8—21no—
856Q8—21no—
857Q8—21no—
858Q8—32no—
859Q8—61no—
860Q8—61no—
861Q8—61no—
862Q8—122no—
863Q8—122no—
864Q8D3×C22⋊C412yes—
865D4—22no—
866D4—22no—
867D4—21no—
868D4—21no—
869D4—21no—
870D4—32no—
871D4—41no—
872D4—41no—
873D4—62no—
874D4—62no—
875D4—61no—
876D4—61no—
877D4—61no—
878D4—122no—
879D4—122no—
880D4—122no—
881D4—122no—
882D4—122no—
883D4—122no—
884D4—121no—
885D4—121no—
886D4D3×C22⋊C412yes—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—31no—
892C2×C4—31no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—62no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—62no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—62no—
912C2×C4—61no—
913C2×C4—122no—
914C2×C4—122no—
915C2×C4—122no—
916C2×C4—122no—
917C2×C4—122no—
918C2×C4—122no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4C22×C4×D311yescharacteristic
924C2×C4C2×D3×D411yescharacteristic
925C2×C4C2×D3×D411yescharacteristic
926C2×C4C2×D3×D411yescharacteristic
927C2×C4#100411yescharacteristic
928C2×C4#100911yescharacteristic
929C8—21no—
930C8—21no—
931C8—21no—
932C8—21no—
933C8—32no—
934C8—32no—
935C8—41no—
936C8—41no—
937C8—61no—
938C8—61no—
939C8—121no—
940C8—121no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—42no—
944C2×C3—81no—
945C2×C3D4×C22⋊C411yescharacteristic
946C2×C3#295511yescharacteristic
947C2×C3#295611yescharacteristic
948D3—41no—
949D3—41no—
950D3—42no—
951D3—81no—
952C22—21no—
953C22—21no—
954C22—22no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—61no—
961C22—61no—
962C22—61no—
963C22—61no—
964C22—61no—
965C22—61no—
966C22—62no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—121no—
972C22—241no—
973C22—241no—
974C22—244no—
975C22—244no—
976C22C4×D3×D411yescharacteristic
977C22#561011yescharacteristic
978C22#565411yescharacteristic
979C4—22no—
980C4—41no—
981C4—61no—
982C4—61no—
983C4—62no—
984C4—81no—
985C4—122no—
986C4—121no—
987C4C2×D3×C22⋊C411yescharacteristic
988C4#554511yescharacteristic
989C4#559011yescharacteristic
990C4#560911yescharacteristic
991C3#2245311yescharacteristic, complemented, Sylow
992C2—21no—
993C2—21no—
994C2—42no—
995C2—81no—
996C2—121no—
997C2—121no—
998C2—122no—
999C2—241no—
1000C2#7487811yescharacteristic
1001C2#7988811yescharacteristic
1002C2#7989811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1876C2
socleC22×C3C2×C4×D4
prime radicalC2×#5768C2
cosocleC22×C3×C4C24
hypercenter#1876D3
hypocenterC3#22453
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. #83793C2semidirect
3. C2×#5144C2semidirect
4. C2×#4823C2semidirect
5. #78663C2semidirect
6. C3×#1876C2semidirect
7. #72087C2semidirect
8. #70380C2semidirect
9. #70380C2semidirect
10. #70374C2semidirect
11. #69999C2semidirect
12. #68946C2semidirect
13. #68940C2semidirect
14. #68695C2semidirect
15. #68650C2semidirect
20. C2×C3×#131C22semidirect
23. C2×#948C22semidirect
26. C2×#918C4semidirect
27. C2×#918C4semidirect
28. C2×#915C4semidirect
29. C2×#915C4semidirect
30. C2×#914C4semidirect
31. C2×#914C4semidirect
32. C2×#911C4semidirect
33. C2×#911C4semidirect
34. C2×#907C22semidirect
36. C2×#901C22semidirect
38. C2×C3×#104C22semidirect
39. C2×C3×#104C22semidirect
40. C3×#408C22semidirect
41. C2×#837C22semidirect
42. C2×#837C22semidirect
43. #5234C22semidirect
45. C2×#825C22semidirect
46. C2×#825C22semidirect
48. #5129C22semidirect
52. C2×#822C22semidirect
53. C2×#822C22semidirect
55. #5110C22semidirect
58. C2×C8×Dic3C22semidirect
60. C2×#805C22semidirect
61. C2×#805C22semidirect
62. C2×#803C22semidirect
68. C3×#341C22semidirect
69. C3×#336C22semidirect
70. #4552C22semidirect
71. #4550C22semidirect
82. #1876D3semidirect
229. C2×#131C2×D3semidirect
241. C2×#104C2×D3semidirect
242. C2×#104C2×D3semidirect
250. #408C2×D3semidirect
262. #341C2×D3semidirect
264. #336C2×D3semidirect
381. #216C22⋊C4semidirect
383. #215C22⋊C4semidirect
385. #214C22⋊C4semidirect
387. #213C22⋊C4semidirect
991. C3#22453semidirect

Maximal subgroups

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

subgroupindex
C2×#57682
#837932
C2×#51442
C2×#48232
#786632
C3×#18762
#720872
#703802
#703742
#699992
#689462
#689402
#686952
#686502
#224533