Finite Group Databasebeta

← C2×#22598391 #32865503

Subgroups — C2×#22598391 #32865503

Order 18176.

2602 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986536C211yesmaximal, characteristic, complemented
2C2×C4×D4×D71C211yesmaximal, characteristic, complemented
3#22598391C2116yesmaximal, direct product factor
4C2×#17986333C211yesmaximal, characteristic, complemented
5C2×#17986319C211yesmaximal, characteristic, complemented
6C2×#17986298C211yesmaximal, characteristic, complemented
7C2×#17986297C211yesmaximal, characteristic, complemented
8C2×#17986217C211yesmaximal, characteristic, complemented
9C2×#17986216C211yesmaximal, characteristic, complemented
10C2×#17986148C211yesmaximal, characteristic, complemented
11C2×#17986134C211yesmaximal, characteristic
12C2×C4×#11765852C211yesmaximal, characteristic, complemented
13C2×C4×D568C211yesmaximal, characteristic, complemented
14C2×C4×#11765850C211yesmaximal, characteristic, complemented
15C2×#17986050C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C23×C4×D71—21no—
19C22×#11765852C2211yescharacteristic
20C22×D568C2211yescharacteristic
21C22×#11765850C2211yescharacteristic
22#17986536—24no—
23#17986536C2218yescomplemented
24C2×#14556123—21no—
25C2×#14556119C2211yescharacteristic, complemented
26C2×#14556117C2211yescharacteristic, complemented
27C2×#14556113—21no—
28C2×#14556104C2211yescharacteristic
29C2×#14556103C2211yescharacteristic
30C2×C4×D284—21no—
31C2×C4×D284C2211yescharacteristic
32C2×C4×D284C2211yescharacteristic, complemented
33C2×D4×Dic71C2211yescharacteristic
34C2×#14556090C2211yescharacteristic
35C2×C4×C22⋊D71—21no—
36C2×(C22⋊D71)⋊C4—21no—
37C4×D4×D71—24no—
38C4×D4×D71C2218yescomplemented
39C2×#14556085—21no—
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C22⋊C4×D71—21no—
42C2×C42×D71C2211yescharacteristic
43#17986333C2218yescomplemented
44#17986319C2218yescomplemented
45#17986298C2218yescomplemented
46#17986297C2218yescomplemented
47#17986217C2218yescomplemented
48#17986216C2218yescomplemented
49#17986148C2218yescomplemented
50#17986134C2218yes—
51C4×#11765852C2218yescomplemented
52C4×D568C2218yescomplemented
53C4×#11765850C2218yescomplemented
54#17986050C2218yescomplemented
55C2×#14556062C2211yescharacteristic, complemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59C2×Dic71⋊C8C2211yescharacteristic, complemented
60C2×#14556052C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic
62C2×#14556050C2211yescharacteristic, complemented
63C2×#14556049C2211yescharacteristic
64C2×#14556048C2211yescharacteristic
65C2×#14556048C2211yescharacteristic, complemented
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C4×C71⋊C8C2211yescharacteristic, complemented
69C22×SD16×C71C2211yescharacteristic
70C2×C4×Q8×C71C2211yescharacteristic, complemented
71C2×C4×D4×C71C2211yescharacteristic
72C4×SD16×C71C2218yescomplemented
73C2×#106×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic
76C2×C4×C8×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C22×D284—21no—
79C22×D284C2311yescharacteristic
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C2×D4×D71—24no—
83C2×D4×D71—22no—
84C2×D4×D71—24no—
85C2×D4×D71C2314yes—
86C23×Dic71—21no—
87C22×C4×D71—21no—
88C22×C4×D71—21no—
89C22×C4×D71—28no—
90C22×C4×D71—21no—
91C22×C4×D71—21no—
92C22×C4×D71—48no—
93C22×C4×D71D411yescharacteristic
94C22×C4×D71D411yescharacteristic
95C22×C4×D71C2311yescharacteristic
96C2×#11765852—24no—
97C2×#11765852C2314yes—
98C2×D568—24no—
99C2×D568C2314yes—
100C2×#11765850—24no—
101C2×#11765850C2314yes—
102C22×C71⋊C8C2311yescharacteristic
103C22×C71⋊C8C2311yescharacteristic
104#14556123—28no—
105#14556119—22no—
106#14556119C2314yescomplemented
107#14556117—22no—
108#14556117C2314yescomplemented
109#14556113—28no—
110#14556104—22no—
111#14556104C2314yes—
112#14556103—22no—
113#14556103C2314yes—
114C4×D284—28no—
115C4×D284—22no—
116C4×D284—22no—
117C4×D284C2314yes—
118C4×D284C2314yescomplemented
119D4×Dic71—22no—
120D4×Dic71C2314yes—
121#14556090—22no—
122#14556090C2314yes—
123C4×C22⋊D71—28no—
124(C22⋊D71)⋊C4—28no—
125#14556085—28no—
126C2×C4⋊Dic71—21no—
127C2×C4⋊Dic71C2311yescharacteristic
128C2×C4⋊Dic71C2311yescharacteristic
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C4⋊C4×D71—22no—
133C4⋊C4×D71C2314yes—
134C2×C22⋊Dic71—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C22⋊C4×D71—28no—
143C2×C4×Dic71D411yescharacteristic
144C2×C4×Dic71D411yescharacteristic
145C2×C4×Dic71C2311yescharacteristic
146C42×D71D414yes—
147C42×D71C2314yes—
148#14556062C2314yescomplemented
149#14556061C2314yescomplemented
150#14556059C2314yescomplemented
151Dic71⋊C8C2314yescomplemented
152Dic71⋊C8C2314yescomplemented
153#14556052C2314yescomplemented
154#14556050C2314yes—
155#14556050C2314yescomplemented
156#14556049C2314yes—
157#14556048C2314yes—
158#14556048C2314yescomplemented
159(C2×D71)⋊C8C2314yes—
160(C2×D71)⋊C8C2314yes—
161C4×C71⋊C8C2314yescomplemented
162C22×Q8×C71C2311yescharacteristic
163C22×D4×C71C2311yescharacteristic
164C23×C4×C71—21no—
165C2×SD16×C71—24no—
166C2×SD16×C71C2314yes—
167C22×C8×C71C2311yescharacteristic
168C22×C8×C71C2311yescharacteristic
169C4×Q8×C71—22no—
170C4×Q8×C71C2314yescomplemented
171C4×D4×C71—22no—
172C4×D4×C71C2314yes—
173C2×C4⋊C4×C71—21no—
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C4⋊C4×C71C2311yescharacteristic
176C2×C22⋊C4×C71—21no—
177C2×C42×C71—21no—
178C2×C42×C71C2311yescharacteristic
179#106×C71C2314yescomplemented
180#103×C71C2314yescomplemented
181#102×C71C2314yes—
182C4×C8×C71C2314yescomplemented
183C23×D71—28no—
184C23×D71—21no—
185C23×D71—24no—
186C23×D71—21no—
187C23×D71—44no—
188C23×D71—44no—
189C23×D71C2×D411yescharacteristic
190C2×D284—21no—
191C2×D284—22no—
192C2×D284—22no—
193C2×D284—22no—
194C2×D284—24no—
195C2×D284—21no—
196C2×D284—44no—
197C2×D284#4114yes—
198C2×D284C2412yes—
199C2×D284C2412yes—
200C2×C22⋊D71—28no—
201C2×C22⋊D71—24no—
202D4×D71—216no—
203D4×D71—28no—
204D4×D71—28no—
205C22×Dic71—21no—
206C22×Dic71—21no—
207C22×Dic71—24no—
208C22×Dic71—44no—
209C22×Dic71C2×D411yescharacteristic
210C22×Dic71C2×D411yescharacteristic
211C22×Dic71C2×D411yescharacteristic
212C2×C4×D71—24no—
213C2×C4×D71—24no—
214C2×C4×D71—22no—
215C2×C4×D71—22no—
216C2×C4×D71—24no—
217C2×C4×D71—24no—
218C2×C4×D71—24no—
219C2×C4×D71—24no—
220C2×C4×D71—432no—
221C2×C4×D71—44no—
222C2×C4×D71—44no—
223C2×C4×D71—44no—
224C2×C4×D71—44no—
225C2×C4×D71C2×D414yes—
226C2×C4×D71C2×D414yes—
227C2×C4×D71C2×D412yes—
228C2×C4×D71C2412yes—
229#11765852—28no—
230D568—28no—
231#11765850—28no—
232C2×C71⋊C8—22no—
233C2×C71⋊C8—22no—
234C2×C71⋊C8C2412yes—
235C2×C71⋊C8C2412yes—
236C4⋊Dic71—21no—
237C4⋊Dic71—21no—
238C4⋊Dic71—24no—
239C4⋊Dic71C2412yes—
240C4⋊Dic71C2412yes—
241Dic71⋊C4—24no—
242Dic71⋊C4—24no—
243Dic71⋊C4—24no—
244C22⋊Dic71—24no—
245(C2×D71)⋊C4—24no—
246(C2×D71)⋊C4—24no—
247(C2×D71)⋊C4—24no—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—24no—
252C4×Dic71C2×D412yes—
253C4×Dic71C2×D414yes—
254C4×Dic71C2×D414yes—
255C4×Dic71C2412yes—
256C24×C71—21no—
257C2×Q8×C71—21no—
258C2×Q8×C71—22no—
259C2×Q8×C71—22no—
260C2×Q8×C71C2412yes—
261C2×D4×C71—21no—
262C2×D4×C71—22no—
263C2×D4×C71#4114yes—
264C2×D4×C71C2412yes—
265C22×C4×C71—21no—
266C22×C4×C71—21no—
267C22×C4×C71—21no—
268C22×C4×C71—24no—
269C22×C4×C71—44no—
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2411yescharacteristic
273SD16×C71—28no—
274C2×C8×C71—22no—
275C2×C8×C71—22no—
276C2×C8×C71C2412yes—
277C2×C8×C71C2412yes—
278C4⋊C4×C71—24no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71C2412yes—
282C4⋊C4×C71C2412yes—
283C22⋊C4×C71—24no—
284C42×C71—24no—
285C42×C71C2×D412yes—
286C42×C71C2412yes—
287C23×C71—24no—
288C23×C71—22no—
289C23×C71—42no—
290C23×C71—42no—
291C23×C71C22×D411yescharacteristic
292C22×D71—22no—
293C22×D71—22no—
294C22×D71—216no—
295C22×D71—24no—
296C22×D71—22no—
297C22×D71—22no—
298C22×D71—48no—
299C22×D71—432no—
300C22×D71—42no—
301C22×D71—42no—
302C22×D71—48no—
303C22×D71—42no—
304C22×D71—42no—
305C22×D71—42no—
306C22×D71#13514yes—
307C22×D71C22×D412yes—
308Q8×C71—22no—
309Q8×C71—22no—
310Q8×C71—42no—
311D4×C71—24no—
312D4×C71—22no—
313D4×C71C2×#4114yes—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—42no—
319C2×C4×C71—42no—
320C2×C4×C71—42no—
321C2×C4×C71—48no—
322C2×C4×C71AGL(1,ℤ/8)14yes—
323C2×C4×C71C22×D412yes—
324C2×C4×C71C22×D411yescharacteristic
325C2×C4×C71C22×D412yes—
326C2×C4×C71C2×#4112yes—
327C2×C4×C71C2×#4112yes—
328C2×C4×C71C2511yescharacteristic
329C22⋊D71—216no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—48no—
336C2×Dic71—42no—
337C2×Dic71—42no—
338C2×Dic71C22×D412yes—
339C2×Dic71C22×D412yes—
340C2×Dic71C22×D412yes—
341D284—24no—
342D284—22no—
343D284—22no—
344D284—22no—
345D284—48no—
346D284—42no—
347D284C2×#4114yes—
348C4×D71—28no—
349C4×D71—24no—
350C4×D71—28no—
351C4×D71—22no—
352C4×D71—22no—
353C4×D71—48no—
354C4×D71—48no—
355C4×D71—48no—
356C4×D71—48no—
357C8×C71—22no—
358C8×C71—22no—
359C71⋊C8—22no—
360C71⋊C8—22no—
361C22×C71—24no—
362C22×C71—48no—
363C22×C71—42no—
364C22×C71—42no—
365C22×C71#52512yes—
366C22×C71C2×#13512yes—
367C22×C71C2×AGL(1,ℤ/8)12yes—
368C22×C71C23×D411yescharacteristic
369C2×D71—28no—
370C2×D71—22no—
371C2×D71—22no—
372C2×D71—24no—
373C2×D71—432no—
374C2×D71—48no—
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—42no—
378C2×D71—42no—
379C2×D71—42no—
380C2×D71—84no—
381C2×D71C2×#13514yes—
382C4×C71—22no—
383C4×C71—42no—
384C4×C71—42no—
385C4×C71—42no—
386C4×C71#52512yes—
387C4×C71C2×AGL(1,ℤ/8)14yes—
388C4×C71C22×#4111yescharacteristic
389C4×C71C22×#4111yescharacteristic
390Dic71—22no—
391Dic71—22no—
392Dic71—22no—
393Dic71—42no—
394Dic71—42no—
395C2×#3105—711nomaximal, Sylow
396C2×C71—44no—
397C2×C71#310514yescomplemented
398C2×C71C2×#52511yescharacteristic
399C2×C71C22×#13511yescharacteristic
400C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
401D71—24no—
402D71—44no—
403D71—82no—
404C2×#529—711no—
405C22×C4×D4—711no—
406#3105—7116no—
407C2×#484—711no—
408C2×#481—711no—
409C2×#478—711no—
410C2×#478—711no—
411C2×#463—711no—
412C2×#463—711no—
413C2×#450—711no—
414C2×#447—711no—
415C2×C4×SD16—711no—
416C2×C4×SD16D7111yescharacteristic, complemented
417C2×C4×D8—711no—
418C2×C4×D8—711no—
419C2×#431—711no—
420C71C2×#310511yescharacteristic, complemented, Sylow
421C23×D4—711no—
422C24×C4—1421no—
423C22×SD16—711no—
424C22×SD16C2×D7111yescharacteristic
425C22×D8—711no—
426C22×D8—711no—
427#529—718no—
428#529—1424no—
429C2×#126—1421no—
430C2×#125—711no—
431C2×#124—711no—
432C2×#123—1421no—
433C2×C22⋊Q8—711no—
434C2×#121—711no—
435C2×C4×Q8C2×D7111yescharacteristic, complemented
436C2×C4×D4—711no—
437C2×C4×D4—718no—
438C2×C4×D4—711no—
439C2×C4×D4—711no—
440C2×C4×D4—711no—
441C2×C4×D4—1421no—
442C2×C4×D4—1421no—
443C2×C4×D4—1424no—
444C2×C4×D4—1421no—
445C2×C4×D4C2×D7111yescharacteristic
446C2×#117—1421no—
447C22×C4⋊C4—711no—
448C22×C22⋊C4—1421no—
449C22×C42—711no—
450#484—718no—
451#481—718no—
452#478—718no—
453#478—718no—
454#463—718no—
455#463—718no—
456#450—718no—
457#447—718no—
458C4×SD16—718no—
459C4×SD16C2×D7118yescomplemented
460C4×D8—718no—
461C4×D8—718no—
462#431—718no—
463C2×#107—711no—
464C2×#107—711no—
465C2×#106—711no—
466C2×#106C2×D7111yescharacteristic, complemented
467C2×C4⋊C8—711no—
468C2×C4⋊C8—711no—
469C2×#103—711no—
470C2×#103C2×D7111yescharacteristic, complemented
471C2×#102—711no—
472C2×#102—711no—
473C2×#102—711no—
474C2×#102—711no—
475C2×#102—711no—
476C2×#102C2×D7111yescharacteristic
477C2×C22⋊C8—711no—
478C2×C22⋊C8—711no—
479C2×C4×C8—711no—
480C2×C4×C8C2×D7111yescharacteristic, complemented
481C25—1421no—
482C22×Q8C22×D7111yescharacteristic
483C22×D4—714no—
484C22×D4—711no—
485C22×D4—711no—
486C22×D4—1421no—
487C22×D4—1422no—
488C22×D4—1421no—
489C22×D4—1424no—
490C22×D4—1424no—
491C22×D4C22×D7111yescharacteristic
492C23×C4—21no—
493C23×C4—2848no—
494C23×C4—711no—
495C23×C4—711no—
496C23×C4—711no—
497C23×C4—1421no—
498C23×C4—1428no—
499C23×C4—1421no—
500C23×C4—1421no—
501C23×C4—1421no—
502C23×C4—1421no—
503C2×SD16—24no—
504C2×SD16—714no—
505C2×SD16—1424no—
506C2×SD16C22×D7114yes—
507C2×D8—714no—
508C2×D8—714no—
509C2×D8—1424no—
510C2×D8—1424no—
511C22×C8—711no—
512C22×C8—711no—
513C22×C8C22×D7111yescharacteristic
514C22×C8C22×D7111yescharacteristic
515#126—1428no—
516#125—714no—
517#125—1422no—
518#124—714no—
519#124—1422no—
520#123—1428no—
521C22⋊Q8—714no—
522C22⋊Q8—1422no—
523#121—714no—
524#121—1422no—
525C4×Q8—22no—
526C4×Q8C22×D7114yescomplemented
527C4×D4—22no—
528C4×D4—714no—
529C4×D4—714no—
530C4×D4—714no—
531C4×D4—714no—
532C4×D4—1428no—
533C4×D4—1428no—
534C4×D4—1422no—
535C4×D4—1428no—
536C4×D4—1422no—
537C4×D4—1422no—
538C4×D4—1422no—
539C4×D4C22×D7114yes—
540#117—1428no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—711no—
543C2×C4⋊C4—711no—
544C2×C4⋊C4—714no—
545C2×C4⋊C4—1422no—
546C2×C4⋊C4—1421no—
547C2×C4⋊C4—1421no—
548C2×C4⋊C4—1421no—
549C2×C4⋊C4—1421no—
550C2×C4⋊C4C22×D7111yescharacteristic
551C2×C4⋊C4C22×D7111yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—1428no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4—1421no—
556C2×C22⋊C4—1421no—
557C2×C22⋊C4—1421no—
558C2×C22⋊C4—1421no—
559C2×C22⋊C4—1421no—
560C2×C22⋊C4—1421no—
561C2×C22⋊C4—1421no—
562C2×C42—21no—
563C2×C42—711no—
564C2×C42—711no—
565C2×C42—711no—
566C2×C42—714no—
567C2×C42—714no—
568C2×C42C22×D7111yescharacteristic
569#107—714no—
570#107—714no—
571#106—714no—
572#106C22×D7114yescomplemented
573C4⋊C8—714no—
574C4⋊C8—714no—
575#103—714no—
576#103C22×D7114yescomplemented
577#102—714no—
578#102—714no—
579#102—714no—
580#102—714no—
581#102—714no—
582#102C22×D7114yes—
583C22⋊C8—714no—
584C22⋊C8—714no—
585C4×C8—714no—
586C4×C8C22×D7114yescomplemented
587C24—21no—
588C24—2844no—
589C24—2844no—
590C24—711no—
591C24—1424no—
592C24—1428no—
593C24—1421no—
594C24—1421no—
595C2×Q8—21no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8C23×D7112yes—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—2844no—
602C2×D4—714no—
603C2×D4—712no—
604C2×D4—712no—
605C2×D4—1424no—
606C2×D4—1424no—
607C2×D4—1428no—
608C2×D4—14216no—
609C2×D4—1428no—
610C2×D4—1428no—
611C2×D4—1421no—
612C2×D4—1421no—
613C2×D4—1422no—
614C2×D4—1422no—
615C2×D4—1422no—
616C2×D4#1176586514yes—
617C2×D4C23×D7112yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—44no—
623C22×C4—2844no—
624C22×C4—2844no—
625C22×C4—28432no—
626C22×C4—2844no—
627C22×C4—2844no—
628C22×C4—2844no—
629C22×C4—711no—
630C22×C4—711no—
631C22×C4—711no—
632C22×C4—714no—
633C22×C4—712no—
634C22×C4—714no—
635C22×C4—712no—
636C22×C4—1424no—
637C22×C4—1424no—
638C22×C4—1424no—
639C22×C4—1424no—
640C22×C4—1421no—
641C22×C4—1421no—
642C22×C4—1424no—
643C22×C4—1424no—
644C22×C4—1422no—
645C22×C4—1422no—
646C22×C4—1424no—
647C22×C4D4×D7111yescharacteristic
648C22×C4D4×D7111yescharacteristic
649C22×C4C23×D7111yescharacteristic
650SD16—28no—
651SD16—1428no—
652D8—1428no—
653D8—1428no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—712no—
657C2×C8—712no—
658C2×C8—1422no—
659C2×C8—1422no—
660C2×C8C23×D7112yes—
661C2×C8C23×D7112yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—712no—
666C4⋊C4—712no—
667C4⋊C4—1424no—
668C4⋊C4—1424no—
669C4⋊C4—1424no—
670C4⋊C4—1424no—
671C4⋊C4—1421no—
672C4⋊C4—1421no—
673C4⋊C4C23×D7112yes—
674C4⋊C4C23×D7112yes—
675C22⋊C4—24no—
676C22⋊C4—1424no—
677C22⋊C4—1424no—
678C22⋊C4—1424no—
679C22⋊C4—1424no—
680C22⋊C4—1424no—
681C22⋊C4—1424no—
682C22⋊C4—1424no—
683C22⋊C4—1424no—
684C42—24no—
685C42—714no—
686C42—712no—
687C42—714no—
688C42—712no—
689C42D4×D7112yes—
690C42C23×D7112yes—
691C23—22no—
692C23—24no—
693C23—42no—
694C23—42no—
695C23—2848no—
696C23—2848no—
697C23—28432no—
698C23—2842no—
699C23—2842no—
700C23—2842no—
701C23—2842no—
702C23—2842no—
703C23—712no—
704C23—714no—
705C23—14216no—
706C23—1422no—
707C23—1422no—
708C23—1424no—
709C23—1422no—
710C23—1422no—
711C23C2×D4×D7111yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—42no—
715D4—22no—
716D4—24no—
717D4—2848no—
718D4—2842no—
719D4—714no—
720D4—14216no—
721D4—1422no—
722D4—1422no—
723D4—1422no—
724D4—1424no—
725D4C2×#1176586514yes—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—48no—
734C2×C4—2848no—
735C2×C4—2848no—
736C2×C4—2842no—
737C2×C4—2842no—
738C2×C4—2848no—
739C2×C4—2848no—
740C2×C4—2848no—
741C2×C4—712no—
742C2×C4—712no—
743C2×C4—712no—
744C2×C4—1428no—
745C2×C4—1422no—
746C2×C4—1422no—
747C2×C4—1422no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4—1424no—
753C2×C4—1428no—
754C2×C4#1455615514yes—
755C2×C4C2×D4×D7112yes—
756C2×C4C2×D4×D7111yescharacteristic
757C2×C4C2×D4×D7112yes—
758C2×C4#41×D7112yes—
759C2×C4C2×#1176586512yes—
760C2×C4C24×D7111yescharacteristic
761C8—22no—
762C8—22no—
763C8—1422no—
764C8—1422no—
765C22—24no—
766C22—42no—
767C22—42no—
768C22—48no—
769C22—28432no—
770C22—2842no—
771C22—2842no—
772C22—2848no—
773C22—2842no—
774C22—2842no—
775C22—2842no—
776C22—5684no—
777C22—714no—
778C22—1424no—
779C22—1422no—
780C22—1422no—
781C22—1428no—
782C22#1798650812yes—
783C22#135×D7112yes—
784C22C2×#1455615512yes—
785C22C22×D4×D7111yescharacteristic
786C4—22no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—2842no—
791C4—2842no—
792C4—1422no—
793C4—1422no—
794C4—1422no—
795C4#1798650812yes—
796C4C2×#1455615514yes—
797C4C2×#41×D7111yescharacteristic
798C4C22×#1176586511yescharacteristic
799C2—44no—
800C2—2844no—
801C2—5682no—
802C2—1424no—
803C2#2259839114yesdirect product factor
804C2C2×#1798650811yescharacteristic
805C2C2×#135×D7111yescharacteristic
806C2C22×#1455615511yescharacteristic
subgroupG/H
centerC22×C4D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×C4×SD16×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986134C2
hypercenterC2×C4×SD16D71
hypocenterC71C2×#3105
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#17986536C2semidirect
2. C2×C4×D4×D71C2semidirect
3. #22598391C2direct (N × H)
4. C2×#17986333C2semidirect
5. C2×#17986319C2semidirect
6. C2×#17986298C2semidirect
7. C2×#17986297C2semidirect
8. C2×#17986217C2semidirect
9. C2×#17986216C2semidirect
10. C2×#17986148C2semidirect
12. C2×C4×#11765852C2semidirect
13. C2×C4×D568C2semidirect
14. C2×C4×#11765850C2semidirect
15. C2×#17986050C2semidirect
16. C2×C4×SD16×C71C2semidirect
23. #17986536C22semidirect
25. C2×#14556119C22semidirect
26. C2×#14556117C22semidirect
32. C2×C4×D284C22semidirect
38. C4×D4×D71C22semidirect
43. #17986333C22semidirect
44. #17986319C22semidirect
45. #17986298C22semidirect
46. #17986297C22semidirect
47. #17986217C22semidirect
48. #17986216C22semidirect
49. #17986148C22semidirect
51. C4×#11765852C22semidirect
52. C4×D568C22semidirect
53. C4×#11765850C22semidirect
54. #17986050C22semidirect
55. C2×#14556062C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556059C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. C2×Dic71⋊C8C22semidirect
60. C2×#14556052C22semidirect
62. C2×#14556050C22semidirect
65. C2×#14556048C22semidirect
68. C2×C4×C71⋊C8C22semidirect
70. C2×C4×Q8×C71C22semidirect
72. C4×SD16×C71C22semidirect
73. C2×#106×C71C22semidirect
74. C2×#103×C71C22semidirect
76. C2×C4×C8×C71C22semidirect
106. #14556119C23semidirect
108. #14556117C23semidirect
118. C4×D284C23semidirect
148. #14556062C23semidirect
149. #14556061C23semidirect
150. #14556059C23semidirect
151. Dic71⋊C8C23semidirect
152. Dic71⋊C8C23semidirect
153. #14556052C23semidirect
155. #14556050C23semidirect
158. #14556048C23semidirect
161. C4×C71⋊C8C23semidirect
170. C4×Q8×C71C23semidirect
179. #106×C71C23semidirect
180. #103×C71C23semidirect
182. C4×C8×C71C23semidirect
397. C2×C71#3105semidirect
416. C2×C4×SD16D71semidirect
420. C71C2×#3105semidirect
435. C2×C4×Q8C2×D71semidirect
459. C4×SD16C2×D71semidirect
466. C2×#106C2×D71semidirect
470. C2×#103C2×D71semidirect
480. C2×C4×C8C2×D71semidirect
526. C4×Q8C22×D71semidirect
572. #106C22×D71semidirect
576. #103C22×D71semidirect
586. C4×C8C22×D71semidirect
803. C2#22598391direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865362
C2×C4×D4×D712
#225983912
C2×#179863332
C2×#179863192
C2×#179862982
C2×#179862972
C2×#179862172
C2×#179862162
C2×#179861482
C2×#179861342
C2×C4×#117658522
C2×C4×D5682
C2×C4×#117658502
C2×#179860502
C2×C4×SD16×C712
C2×#310571