Finite Group Databasebeta

← C2×#22600961 #32876197

Subgroups — C2×#22600961 #32876197

Order 18176.

1930 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986713C211yesmaximal, characteristic
2C2×#17986707C211yesmaximal, characteristic, complemented
3#22600961C2116yesmaximal, direct product factor
4C2×#17986403C211yesmaximal, characteristic, complemented
5C2×#17986338C211yesmaximal, characteristic, complemented
6C2×#17986337C211yesmaximal, characteristic, complemented
7C2×#17986311C211yesmaximal, characteristic, complemented
8C2×#17986310C211yesmaximal, characteristic, complemented
9C2×#17986292C211yesmaximal, characteristic, complemented
10C2×#17986287C211yesmaximal, characteristic, complemented
11C2×#17986242C211yesmaximal, characteristic, complemented
12C2×SD16×Dic71C211yesmaximal, characteristic, complemented
13C2×#17986075C211yesmaximal, characteristic, complemented
14C2×#17986041C211yesmaximal, characteristic, complemented
15C2×#17986040C211yesmaximal, characteristic, complemented
16C2×#468×C71C211yesmaximal, characteristic, complemented
17C22×#11765848C2211yescharacteristic
18#17986713—24no—
19#17986713C2218yes—
20#17986707—24no—
21#17986707C2218yescomplemented
22C2×#14556127C2211yescharacteristic
23C2×#14556127C2211yescharacteristic
24C2×#14556118—21no—
25C2×#14556115—21no—
26C2×#14556114—21no—
27C2×#14556108—21no—
28C2×#14556105—21no—
29C2×#14556104C2211yescharacteristic
30C2×#14556100—21no—
31C2×#14556099C2211yescharacteristic
32C2×Q8×Dic71C2211yescharacteristic
33C2×D4×Dic71C2211yescharacteristic
34C2×C4×C22⋊D71C2211yescharacteristic
35C2×(C22⋊D71)⋊C4—21no—
36C2×#14556087C2211yescharacteristic
37C2×#14556086C2211yescharacteristic
38C2×#14556084—21no—
39C22×C4⋊Dic71C2211yescharacteristic
40C2×C4⋊C4×D71C2211yescharacteristic
41#17986403C2218yescomplemented
42#17986338C2218yescomplemented
43#17986337C2218yescomplemented
44#17986311C2218yescomplemented
45#17986310C2218yescomplemented
46#17986292C2218yescomplemented
47#17986287C2218yescomplemented
48#17986242C2218yescomplemented
49SD16×Dic71C2218yescomplemented
50#17986075C2218yescomplemented
51#17986041C2218yescomplemented
52#17986040C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556059C2211yescharacteristic
61C2×Dic71⋊C8C2211yescharacteristic
62C2×#14556052C2211yescharacteristic
63C2×#14556052C2211yescharacteristic
64C2×#14556049C2211yescharacteristic
65C2×#14556049C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C22×SD16×C71C2211yescharacteristic
70C22×M16×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×#121×C71C2211yescharacteristic
73#468×C71C2218yescomplemented
74C2×#107×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×C22⋊D71—21no—
80C22×C22⋊D71D411yescharacteristic
81C23×Dic71—21no—
82C23×Dic71—21no—
83C22×C4×D71—21no—
84C22×C4×D71C2311yescharacteristic
85C2×#11765848—24no—
86C2×#11765848C2314yes—
87C22×C71⋊C8C2311yescharacteristic
88C22×C71⋊C8C2311yescharacteristic
89#14556127—22no—
90#14556127—22no—
91#14556127C2314yes—
92#14556127C2314yes—
93#14556118—28no—
94#14556115—28no—
95#14556114—28no—
96#14556108—28no—
97#14556105—28no—
98#14556104—22no—
99#14556104C2314yes—
100#14556100—28no—
101#14556099—22no—
102#14556099C2314yes—
103Q8×Dic71—22no—
104Q8×Dic71C2314yes—
105D4×Dic71—22no—
106D4×Dic71C2314yes—
107C4×C22⋊D71D414yes—
108C4×C22⋊D71C2314yes—
109(C22⋊D71)⋊C4—28no—
110#14556087—22no—
111#14556087C2314yes—
112#14556086—22no—
113#14556086C2314yes—
114#14556084—28no—
115C2×C4⋊Dic71—21no—
116C2×C4⋊Dic71—22no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71C2314yes—
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×Dic71⋊C4—21no—
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4D411yescharacteristic
128C4⋊C4×D71—22no—
129C4⋊C4×D71C2314yes—
130C2×C22⋊Dic71—21no—
131C2×C22⋊Dic71—21no—
132C2×C22⋊Dic71—21no—
133C2×C22⋊Dic71D411yescharacteristic
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4D411yescharacteristic
137C2×C4×Dic71—21no—
138C2×C4×Dic71—21no—
139C2×C4×Dic71—21no—
140C2×C4×Dic71C2311yescharacteristic
141#14556062C2314yes—
142#14556062C2314yes—
143#14556061C2314yes—
144#14556061C2314yes—
145#14556061C2314yes—
146#14556060C2314yes—
147#14556060C2314yes—
148#14556059C2314yes—
149Dic71⋊C8C2314yes—
150#14556052C2314yes—
151#14556052C2314yes—
152#14556049C2314yes—
153#14556049C2314yes—
154C22⋊(C71⋊C8)C2314yes—
155(C2×D71)⋊C8C2314yes—
156C8×Dic71C2314yes—
157C22×Q8×C71C2311yescharacteristic
158C22×D4×C71—21no—
159C22×D4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C2×SD16×C71—24no—
162C2×SD16×C71C2314yes—
163C2×M16×C71—24no—
164C2×M16×C71C2314yes—
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22⋊Q8×C71—22no—
168C22⋊Q8×C71C2314yes—
169#121×C71—22no—
170#121×C71C2314yes—
171C2×C4⋊C4×C71—21no—
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176#107×C71C2314yes—
177#103×C71C2314yes—
178#102×C71C2314yes—
179C23×D71C2×D411yescharacteristic
180C2×Dic142—24no—
181C2×Dic142—24no—
182C2×Dic142—82no—
183C2×Dic142—82no—
184C2×C22⋊D71—24no—
185C2×C22⋊D71—24no—
186C2×C22⋊D71—82no—
187C2×C22⋊D71C2×D414yes—
188C22×Dic71—21no—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C22×Dic71—24no—
193C22×Dic71—24no—
194C22×Dic71—44no—
195C22×Dic71—82no—
196C22×Dic71C2×D411yescharacteristic
197C22×Dic71C2×D411yescharacteristic
198C22×Dic71C2×D411yescharacteristic
199C2×C4×D71—22no—
200C2×C4×D71—22no—
201C2×C4×D71—24no—
202C2×C4×D71—82no—
203C2×C4×D71C2×D412yes—
204C2×C4×D71C2412yes—
205#11765848—28no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—22no—
208C2×C71⋊C8C2412yes—
209C2×C71⋊C8C2412yes—
210C4⋊Dic71—21no—
211C4⋊Dic71—21no—
212C4⋊Dic71—24no—
213C4⋊Dic71—21no—
214C4⋊Dic71—21no—
215C4⋊Dic71—24no—
216C4⋊Dic71C2412yes—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4C2×D414yes—
225C22⋊Dic71—24no—
226C22⋊Dic71—24no—
227C22⋊Dic71—24no—
228C22⋊Dic71C2×D414yes—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4C2×D414yes—
232C4×Dic71—24no—
233C4×Dic71—24no—
234C4×Dic71—24no—
235C4×Dic71C2×D412yes—
236C4×Dic71C2412yes—
237C24×C71—21no—
238C24×C71C2×D411yescharacteristic
239C2×Q8×C71—21no—
240C2×Q8×C71—22no—
241C2×Q8×C71—22no—
242C2×Q8×C71C2412yes—
243C2×D4×C71—24no—
244C2×D4×C71—21no—
245C2×D4×C71—22no—
246C2×D4×C71—22no—
247C2×D4×C71—82no—
248C2×D4×C71C2412yes—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D412yes—
256C22×C4×C71C2412yes—
257C22×C4×C71C2411yescharacteristic
258SD16×C71—28no—
259M16×C71—28no—
260C2×C8×C71—22no—
261C2×C8×C71#4114yes—
262C2×C8×C71C2412yes—
263C2×C8×C71C2412yes—
264C4⋊C4×C71—24no—
265C4⋊C4×C71—21no—
266C4⋊C4×C71—21no—
267C4⋊C4×C71C2412yes—
268C4⋊C4×C71C2412yes—
269C22⋊C4×C71—24no—
270C22⋊C4×C71—24no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—42no—
276C23×C71—42no—
277C23×C71—42no—
278C23×C71C22×D412yes—
279C23×C71C22×D411yescharacteristic
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71C22×D412yes—
284Q8×C71—22no—
285Q8×C71—22no—
286Q8×C71—42no—
287D4×C71—22no—
288D4×C71—22no—
289D4×C71—42no—
290D4×C71—84no—
291C2×C4×C71—22no—
292C2×C4×C71—24no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—42no—
299C2×C4×C71—42no—
300C2×C4×C71—42no—
301C2×C4×C71C22×D412yes—
302C2×C4×C71C22×D411yescharacteristic
303C2×C4×C71C2×#4112yes—
304C2×C4×C712−1+412yes—
305C2×C4×C71C2511yescharacteristic
306C22⋊D71—28no—
307C22⋊D71—84no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—42no—
315C2×Dic71—42no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—48no—
319C2×Dic71—84no—
320C2×Dic71#13714yes—
321C2×Dic71C22×D412yes—
322C2×Dic71C22×D412yes—
323C2×Dic71C22×D412yes—
324C4×D71—24no—
325C4×D71—22no—
326C4×D71—22no—
327C4×D71—84no—
328Dic142—84no—
329Dic142—84no—
330C8×C71—22no—
331C8×C71C2×#4114yes—
332C71⋊C8—22no—
333C71⋊C8—22no—
334C22×C71—22no—
335C22×C71—22no—
336C22×C71—22no—
337C22×C71—44no—
338C22×C71—42no—
339C22×C71—42no—
340C22×C71—42no—
341C22×C71—84no—
342C22×C71#54712yes—
343C22×C71C2×#13712yes—
344C22×C71#57612yes—
345C22×C71C23×D411yescharacteristic
346C2×D71—22no—
347C2×D71—22no—
348C2×D71—22no—
349C2×D71—44no—
350C4×C71—22no—
351C4×C71—42no—
352C4×C71—42no—
353C4×C71—42no—
354C4×C71#54712yes—
355C4×C71C22×#4111yescharacteristic
356C4×C71C2×2−1+411yescharacteristic
357Dic71—22no—
358Dic71—22no—
359Dic71—42no—
360Dic71—42no—
361Dic71—42no—
362Dic71—42no—
363Dic71C2×#13714yes—
364C2×#3357—711nomaximal, Sylow
365C2×C71—42no—
366C2×C71—82no—
367C2×C71#335714yescomplemented
368C2×C71C2×#54711yescharacteristic
369C2×C71C22×#13711yescharacteristic
370C2×C71C2×#57611yescharacteristic
371D71—42no—
372C2×#555—711no—
373C2×#554—711no—
374#3357—7116no—
375C2×#500—711no—
376C2×#485—711no—
377C2×#485—711no—
378C2×#480—711no—
379C2×#480—711no—
380C2×#477—711no—
381C2×#476—711no—
382C2×#468—711no—
383C2×#468D7111yescharacteristic, complemented
384C2×C4×SD16—711no—
385C2×#436—711no—
386C2×#428—711no—
387C2×#428—711no—
388C71C2×#335711yescharacteristic, complemented, Sylow
389C22×SD16C2×D7111yescharacteristic
390C22×M16—711no—
391C22×M16C2×D7111yescharacteristic
392#555—718no—
393#555—1424no—
394#554—718no—
395#554—1424no—
396C2×C4⋊Q8—711no—
397C2×C4⋊Q8—711no—
398C2×#125—1421no—
399C2×#124—1421no—
400C2×#124—1421no—
401C2×C22⋊Q8—711no—
402C2×C22⋊Q8—1421no—
403C2×C22⋊Q8—1421no—
404C2×C22⋊Q8C2×D7111yescharacteristic
405C2×#121—711no—
406C2×#121—1421no—
407C2×#121C2×D7111yescharacteristic
408C2×C4×Q8—711no—
409C2×C4×D4—711no—
410C2×C4×D4—711no—
411C2×C4×D4—1421no—
412C2×#117—711no—
413C2×#117—711no—
414C2×#117—1421no—
415C22×C4⋊C4—711no—
416C22×C4⋊C4—711no—
417#500—718no—
418#485—718no—
419#485—718no—
420#480—718no—
421#480—718no—
422#477—718no—
423#476—718no—
424#468—718no—
425#468C2×D7118yescomplemented
426C4×SD16—718no—
427#436—718no—
428#428—718no—
429#428—718no—
430C2×#107—711no—
431C2×#107—711no—
432C2×#107—711no—
433C2×#107—711no—
434C2×#107—711no—
435C2×#107C2×D7111yescharacteristic
436C2×#106—711no—
437C2×#106—711no—
438C2×#106—711no—
439C2×C4⋊C8—711no—
440C2×#103—711no—
441C2×#103—711no—
442C2×#103C2×D7111yescharacteristic
443C2×#102—711no—
444C2×#102—711no—
445C2×#102C2×D7111yescharacteristic
446C2×C22⋊C8—711no—
447C2×C22⋊C8—711no—
448C2×C4×C8—711no—
449C22×Q8—1421no—
450C22×Q8—1421no—
451C22×Q8C22×D7111yescharacteristic
452C22×D4—21no—
453C22×D4—711no—
454C22×D4—1421no—
455C22×D4C22×D7111yescharacteristic
456C23×C4—711no—
457C23×C4—1421no—
458C23×C4—1421no—
459C23×C4—1421no—
460C23×C4C22×D7111yescharacteristic
461C2×SD16—24no—
462C2×SD16C22×D7114yes—
463C2×M16—24no—
464C2×M16—714no—
465C2×M16—1424no—
466C2×M16C22×D7114yes—
467C22×C8—711no—
468C22×C8—711no—
469C22×C8C22×D7111yescharacteristic
470C22×C8C22×D7111yescharacteristic
471C4⋊Q8—714no—
472C4⋊Q8—714no—
473C4⋊Q8—1422no—
474C4⋊Q8—1422no—
475#125—1428no—
476#124—1428no—
477#124—1428no—
478C22⋊Q8—22no—
479C22⋊Q8—714no—
480C22⋊Q8—1428no—
481C22⋊Q8—1428no—
482C22⋊Q8—1422no—
483C22⋊Q8C22×D7114yes—
484#121—22no—
485#121—714no—
486#121—1422no—
487#121—1428no—
488#121C22×D7114yes—
489C4×Q8—714no—
490C4×Q8—1422no—
491C4×D4—714no—
492C4×D4—714no—
493C4×D4—714no—
494C4×D4—1422no—
495C4×D4—1428no—
496#117—714no—
497#117—714no—
498#117—1428no—
499#117—1422no—
500#117—1422no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—711no—
503C2×C4⋊C4—711no—
504C2×C4⋊C4—711no—
505C2×C4⋊C4—714no—
506C2×C4⋊C4—711no—
507C2×C4⋊C4—711no—
508C2×C4⋊C4—714no—
509C2×C4⋊C4—1422no—
510C2×C4⋊C4—1421no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1422no—
517C2×C4⋊C4C22×D7111yescharacteristic
518C2×C4⋊C4C22×D7111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—711no—
522C2×C22⋊C4—711no—
523C2×C22⋊C4—1421no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C42—711no—
529C2×C42—1421no—
530C2×C42—1421no—
531C2×C42—1421no—
532#107—714no—
533#107—714no—
534#107—714no—
535#107—714no—
536#107—714no—
537#107C22×D7114yes—
538#106—714no—
539#106—714no—
540#106—714no—
541C4⋊C8—714no—
542#103—714no—
543#103—714no—
544#103C22×D7114yes—
545#102—714no—
546#102—714no—
547#102C22×D7114yes—
548C22⋊C8—714no—
549C22⋊C8—714no—
550C4×C8—714no—
551C24—21no—
552C24—711no—
553C24D4×D7111yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—5682no—
558C2×Q8—5682no—
559C2×Q8—1424no—
560C2×Q8—1424no—
561C2×Q8C23×D7112yes—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—82no—
567C2×D4—5682no—
568C2×D4—714no—
569C2×D4—1424no—
570C2×D4—1424no—
571C2×D4C23×D7112yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—2844no—
578C22×C4—5682no—
579C22×C4—5682no—
580C22×C4—711no—
581C22×C4—711no—
582C22×C4—711no—
583C22×C4—712no—
584C22×C4—712no—
585C22×C4—1424no—
586C22×C4—1424no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1421no—
590C22×C4—1421no—
591C22×C4—1424no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4D4×D7112yes—
595C22×C4D4×D7111yescharacteristic
596C22×C4C23×D7112yes—
597C22×C4C23×D7111yescharacteristic
598SD16—28no—
599M16—28no—
600M16—1428no—
601C2×C8—22no—
602C2×C8—712no—
603C2×C8—712no—
604C2×C8—1422no—
605C2×C8—1422no—
606C2×C8#1176586414yes—
607C2×C8C23×D7112yes—
608C2×C8C23×D7112yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—714no—
613C4⋊C4—712no—
614C4⋊C4—712no—
615C4⋊C4—712no—
616C4⋊C4—712no—
617C4⋊C4—1424no—
618C4⋊C4—1424no—
619C4⋊C4—1424no—
620C4⋊C4—1424no—
621C4⋊C4—1424no—
622C4⋊C4—1421no—
623C4⋊C4—1424no—
624C4⋊C4—1421no—
625C4⋊C4—1421no—
626C4⋊C4—1421no—
627C4⋊C4C23×D7112yes—
628C4⋊C4C23×D7112yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—714no—
632C22⋊C4—714no—
633C22⋊C4—1424no—
634C22⋊C4—1424no—
635C22⋊C4—1424no—
636C22⋊C4—1424no—
637C22⋊C4—1424no—
638C42—712no—
639C42—712no—
640C42—1424no—
641C42—1424no—
642C42—1424no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—712no—
651C23—1422no—
652C23—1422no—
653C23—1422no—
654C23C2×D4×D7112yes—
655C23C2×D4×D7111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—5684no—
660Q8—5684no—
661D4—22no—
662D4—22no—
663D4—42no—
664D4—84no—
665D4—5684no—
666D4—1428no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—2842no—
678C2×C4—2842no—
679C2×C4—2842no—
680C2×C4—2842no—
681C2×C4—2848no—
682C2×C4—5684no—
683C2×C4—5684no—
684C2×C4—712no—
685C2×C4—714no—
686C2×C4—712no—
687C2×C4—712no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1424no—
697C2×C4C2×D4×D7112yes—
698C2×C4C2×D4×D7111yescharacteristic
699C2×C4C2×#1176586412yes—
700C2×C4#1455617512yes—
701C2×C4C24×D7111yescharacteristic
702C8—22no—
703C8—1422no—
704C8—1422no—
705C8C2×#1176586414yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—2844no—
715C22—1422no—
716C22—1422no—
717C22—1422no—
718C22#1798664912yes—
719C22#137×D7112yes—
720C22#1798680312yes—
721C22C22×D4×D7111yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—2842no—
727C4—2842no—
728C4—2842no—
729C4—2842no—
730C4—714no—
731C4—1422no—
732C4—1422no—
733C4#1798664912yes—
734C4C22×#1176586411yescharacteristic
735C4C2×#1455617511yescharacteristic
736C2—42no—
737C2—82no—
738C2—2842no—
739C2#2260096114yesdirect product factor
740C2C2×#1798664911yescharacteristic
741C2C2×#137×D7111yescharacteristic
742C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#468×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986713C2
hypercenterC2×#468D71
hypocenterC71C2×#3357
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#17986707C2semidirect
3. #22600961C2direct (N × H)
4. C2×#17986403C2semidirect
5. C2×#17986338C2semidirect
6. C2×#17986337C2semidirect
7. C2×#17986311C2semidirect
8. C2×#17986310C2semidirect
9. C2×#17986292C2semidirect
10. C2×#17986287C2semidirect
11. C2×#17986242C2semidirect
12. C2×SD16×Dic71C2semidirect
13. C2×#17986075C2semidirect
14. C2×#17986041C2semidirect
15. C2×#17986040C2semidirect
16. C2×#468×C71C2semidirect
21. #17986707C22semidirect
41. #17986403C22semidirect
42. #17986338C22semidirect
43. #17986337C22semidirect
44. #17986311C22semidirect
45. #17986310C22semidirect
46. #17986292C22semidirect
47. #17986287C22semidirect
48. #17986242C22semidirect
49. SD16×Dic71C22semidirect
50. #17986075C22semidirect
51. #17986041C22semidirect
52. #17986040C22semidirect
73. #468×C71C22semidirect
367. C2×C71#3357semidirect
383. C2×#468D71semidirect
388. C71C2×#3357semidirect
425. #468C2×D71semidirect
739. C2#22600961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867132
C2×#179867072
#226009612
C2×#179864032
C2×#179863382
C2×#179863372
C2×#179863112
C2×#179863102
C2×#179862922
C2×#179862872
C2×#179862422
C2×SD16×Dic712
C2×#179860752
C2×#179860412
C2×#179860402
C2×#468×C712
C2×#335771