Finite Group Databasebeta

← C2×#22600492 #32874134

Subgroups — C2×#22600492 #32874134

Order 18176.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986712C211yesmaximal, characteristic, complemented
2C2×#17986637C211yesmaximal, characteristic, complemented
3#22600492C2116yesmaximal, direct product factor
4C2×#17986360C211yesmaximal, characteristic, complemented
5C2×#17986339C211yesmaximal, characteristic, complemented
6C2×#17986323C211yesmaximal, characteristic, complemented
7C2×#17986277C211yesmaximal, characteristic, complemented
8C2×#17986248C211yesmaximal, characteristic, complemented
9C2×#17986235C211yesmaximal, characteristic, complemented
10C2×#17986217C211yesmaximal, characteristic, complemented
11C2×#17986144C211yesmaximal, characteristic, complemented
12C2×#17986134C211yesmaximal, characteristic, complemented
13C2×#17986108C211yesmaximal, characteristic, complemented
14C2×#17986070C211yesmaximal, characteristic, complemented
15C2×#17986002C211yesmaximal, characteristic, complemented
16C2×#416×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C22×#11765852C2211yescharacteristic, complemented
19C22×D568C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765848C2211yescharacteristic
22#17986712—24no—
23#17986712C2218yescomplemented
24#17986637—24no—
25#17986637C2218yescomplemented
26C2×#14556127C2211yescharacteristic, complemented
27C2×#14556117C2211yescharacteristic
28C2×#14556116—21no—
29C2×#14556114—21no—
30C2×#14556111—21no—
31C2×#14556104C2211yescharacteristic
32C2×#14556103C2211yescharacteristic
33C2×#14556102C2211yescharacteristic
34C2×#14556102C2211yescharacteristic, complemented
35C2×#14556101—21no—
36C2×#14556100—21no—
37C2×#14556096—21no—
38C2×D4×Dic71C2211yescharacteristic
39C2×#14556090C2211yescharacteristic, complemented
40C2×C4×C22⋊D71C2211yescharacteristic
41C2×#14556086C2211yescharacteristic
42C2×#14556085—21no—
43C22×(C2×D71)⋊C4—21no—
44#17986360C2218yescomplemented
45#17986339C2218yescomplemented
46#17986323C2218yescomplemented
47#17986277C2218yescomplemented
48#17986248C2218yescomplemented
49#17986235C2218yescomplemented
50#17986217C2218yescomplemented
51#17986144C2218yescomplemented
52#17986134C2218yescomplemented
53#17986108C2218yescomplemented
54#17986070C2218yescomplemented
55C2×#14556062C2211yescharacteristic, complemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59#17986002C2218yescomplemented
60C2×#14556052C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic
62C2×#14556050C2211yescharacteristic, complemented
63C2×#14556049C2211yescharacteristic
64C2×#14556048C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556038C2211yescharacteristic, complemented
69C22×#41×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic, complemented
71C2×#117×C71C2211yescharacteristic, complemented
72#416×C71C2218yescomplemented
73C2×#103×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C24×D71—21no—
78C22×Dic142—21no—
79C22×D284—21no—
80C22×D284C2311yescharacteristic
81C22×D284C2311yescharacteristic
82C22×C22⋊D71—21no—
83C22×C22⋊D71—21no—
84C22×C22⋊D71—21no—
85C22×C22⋊D71D411yescharacteristic
86C2×D4×D71—22no—
87C2×D4×D71—24no—
88C2×D4×D71—42no—
89C2×D4×D71C2314yes—
90C23×Dic71—21no—
91C22×C4×D71—21no—
92C22×C4×D71C2311yescharacteristic
93C2×#11765852—42no—
94C2×#11765852C2314yescomplemented
95C2×D568—42no—
96C2×D568C2314yes—
97C2×#11765850—24no—
98C2×#11765850C2314yes—
99C2×#11765848—42no—
100C2×#11765848C2314yes—
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103#14556127—22no—
104#14556127C2314yescomplemented
105#14556117—22no—
106#14556117C2314yes—
107#14556116—28no—
108#14556114—28no—
109#14556111—28no—
110#14556104—22no—
111#14556104C2314yes—
112#14556103—22no—
113#14556103C2314yes—
114#14556102—22no—
115#14556102—22no—
116#14556102C2314yes—
117#14556102C2314yescomplemented
118#14556101—28no—
119#14556100—28no—
120#14556096—28no—
121D4×Dic71—22no—
122D4×Dic71C2314yes—
123#14556090—22no—
124#14556090C2314yescomplemented
125C4×C22⋊D71D414yes—
126C4×C22⋊D71C2314yes—
127#14556086—22no—
128#14556086C2314yes—
129#14556085—28no—
130C2×C4⋊Dic71C2311yescharacteristic
131C2×C4⋊Dic71C2311yescharacteristic
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4D411yescharacteristic
135C2×C22⋊Dic71—21no—
136C2×C22⋊Dic71D411yescharacteristic
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—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—28no—
144C2×(C2×D71)⋊C4—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4D411yescharacteristic
147C2×C4×Dic71—21no—
148C2×C4×Dic71C2311yescharacteristic
149#14556062C2314yescomplemented
150#14556061C2314yescomplemented
151#14556059C2314yescomplemented
152Dic71⋊C8C2314yescomplemented
153#14556052C2314yescomplemented
154#14556050C2314yes—
155#14556050C2314yescomplemented
156#14556049C2314yes—
157#14556048C2314yes—
158#14556048C2314yes—
159C22⋊(C71⋊C8)C2314yescomplemented
160(C2×D71)⋊C8C2314yes—
161#14556038C2314yescomplemented
162C2×#41×C71—22no—
163C2×#41×C71—24no—
164C2×#41×C71—42no—
165C2×#41×C71C2314yes—
166C22×Q8×C71C2311yescharacteristic
167C22×D4×C71—21no—
168C22×D4×C71C2311yescharacteristic
169C23×C4×C71—21no—
170C23×C4×C71C2311yescharacteristic
171C22×C8×C71—42no—
172C22×C8×C71C2311yescharacteristic
173C22×C8×C71C2311yescharacteristic
174C22×C8×C71C2314yescomplemented
175#117×C71—22no—
176#117×C71C2314yescomplemented
177C2×C4⋊C4×C71C2311yescharacteristic
178C2×C4⋊C4×C71C2311yescharacteristic
179C2×C22⋊C4×C71—21no—
180C2×C42×C71—21no—
181#103×C71C2314yescomplemented
182#103×C71C2314yescomplemented
183#102×C71C2314yes—
184#102×C71C2314yes—
185C23×D71—21no—
186C23×D71—21no—
187C23×D71—24no—
188C23×D71—44no—
189C23×D71—44no—
190C23×D71—82no—
191C23×D71C2×D411yescharacteristic
192C2×Dic142—24no—
193C2×Dic142—82no—
194C2×D284—22no—
195C2×D284—22no—
196C2×D284—22no—
197C2×D284—22no—
198C2×D284—21no—
199C2×D284—21no—
200C2×D284—24no—
201C2×D284—82no—
202C2×D284C2412yes—
203C2×D284C2412yes—
204C2×C22⋊D71—24no—
205C2×C22⋊D71—24no—
206C2×C22⋊D71—24no—
207C2×C22⋊D71—42no—
208C2×C22⋊D71—44no—
209C2×C22⋊D71—82no—
210C2×C22⋊D71—82no—
211C2×C22⋊D71C2×D414yes—
212D4×D71—28no—
213D4×D71—44no—
214D4×D71—48no—
215C22×Dic71—21no—
216C22×Dic71—21no—
217C22×Dic71—24no—
218C22×Dic71—82no—
219C22×Dic71C2×D411yescharacteristic
220C22×Dic71C2×D411yescharacteristic
221C22×Dic71C2×D411yescharacteristic
222C2×C4×D71—22no—
223C2×C4×D71—22no—
224C2×C4×D71—24no—
225C2×C4×D71—44no—
226C2×C4×D71C2×D412yes—
227C2×C4×D71C2412yes—
228#11765852—44no—
229D568—44no—
230#11765850—28no—
231#11765848—44no—
232C2×C71⋊C8—22no—
233C2×C71⋊C8—22no—
234C2×C71⋊C8C2412yes—
235C2×C71⋊C8C2412yes—
236C4⋊Dic71—21no—
237C4⋊Dic71—21no—
238C4⋊Dic71C2412yes—
239C4⋊Dic71C2412yes—
240Dic71⋊C4—24no—
241Dic71⋊C4—24no—
242Dic71⋊C4C2×D414yes—
243C22⋊Dic71—24no—
244C22⋊Dic71C2×D414yes—
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—
252(C2×D71)⋊C4—24no—
253(C2×D71)⋊C4C2×D414yes—
254C4×Dic71—24no—
255C4×Dic71C2×D412yes—
256C4×Dic71C2412yes—
257C24×C71—21no—
258C24×C71C2×D411yescharacteristic
259#41×C71—28no—
260#41×C71—44no—
261#41×C71—48no—
262C2×Q8×C71—21no—
263C2×Q8×C71—22no—
264C2×Q8×C71—22no—
265C2×Q8×C71C2412yes—
266C2×D4×C71—24no—
267C2×D4×C71—21no—
268C2×D4×C71—22no—
269C2×D4×C71—44no—
270C2×D4×C71#4114yes—
271C2×D4×C71C2412yes—
272C22×C4×C71—22no—
273C22×C4×C71—22no—
274C22×C4×C71—21no—
275C22×C4×C71—21no—
276C22×C4×C71—21no—
277C22×C4×C71—24no—
278C22×C4×C71—44no—
279C22×C4×C71C2×D411yescharacteristic
280C22×C4×C71C2×D412yes—
281C22×C4×C71C2412yes—
282C22×C4×C71C2411yescharacteristic
283C2×C8×C71—22no—
284C2×C8×C71—22no—
285C2×C8×C71—44no—
286C2×C8×C71C2412yes—
287C2×C8×C71C2412yes—
288C4⋊C4×C71—21no—
289C4⋊C4×C71—21no—
290C4⋊C4×C71C2412yes—
291C4⋊C4×C71C2412yes—
292C22⋊C4×C71—24no—
293C42×C71—24no—
294C23×C71—22no—
295C23×C71—24no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—42no—
300C23×C71—42no—
301C23×C71C22×D412yes—
302C23×C71C22×D411yescharacteristic
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—48no—
309C22×D71—48no—
310C22×D71—42no—
311C22×D71—42no—
312C22×D71—42no—
313C22×D71—42no—
314C22×D71—42no—
315C22×D71—42no—
316C22×D71—84no—
317C22×D71—816no—
318C22×D71C22×D412yes—
319Q8×C71—22no—
320Q8×C71—22no—
321Q8×C71—42no—
322D4×C71—24no—
323D4×C71—22no—
324D4×C71—48no—
325D4×C71C2×#4114yes—
326C2×C4×C71—22no—
327C2×C4×C71—24no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—48no—
334C2×C4×C71—42no—
335C2×C4×C71—42no—
336C2×C4×C71—42no—
337C2×C4×C71C22×D412yes—
338C2×C4×C71C22×D411yescharacteristic
339C2×C4×C71C2×#4112yes—
340C2×C4×C71H(5,𝔽2)12yes—
341C2×C4×C71C2511yescharacteristic
342C22⋊D71—44no—
343C22⋊D71—48no—
344C22⋊D71—84no—
345C22⋊D71—84no—
346C2×Dic71—22no—
347C2×Dic71—22no—
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—42no—
352C2×Dic71—42no—
353C2×Dic71—84no—
354C2×Dic71C22×D412yes—
355C2×Dic71C22×D412yes—
356C2×Dic71C22×D412yes—
357D284—22no—
358D284—22no—
359D284—22no—
360D284—22no—
361D284—42no—
362D284—42no—
363D284—84no—
364C4×D71—24no—
365C4×D71—22no—
366C4×D71—22no—
367C4×D71—48no—
368Dic142—84no—
369C8×C71—22no—
370C8×C71—22no—
371C71⋊C8—22no—
372C71⋊C8—22no—
373C22×C71—24no—
374C22×C71—22no—
375C22×C71—22no—
376C22×C71—22no—
377C22×C71—48no—
378C22×C71—44no—
379C22×C71—42no—
380C22×C71—42no—
381C22×C71#54612yes—
382C22×C71#57512yes—
383C22×C71#57612yes—
384C22×C71C23×D411yescharacteristic
385C2×D71—22no—
386C2×D71—22no—
387C2×D71—22no—
388C2×D71—44no—
389C2×D71—42no—
390C2×D71—42no—
391C2×D71—42no—
392C2×D71—42no—
393C2×D71—42no—
394C2×D71—42no—
395C2×D71—816no—
396C2×D71—84no—
397C2×D71—84no—
398C4×C71—22no—
399C4×C71—42no—
400C4×C71—42no—
401C4×C71—42no—
402C4×C71#54612yes—
403C4×C71C22×#4111yescharacteristic
404C4×C71C2×H(5,𝔽2)11yescharacteristic
405Dic71—22no—
406Dic71—22no—
407Dic71—22no—
408Dic71—42no—
409Dic71—42no—
410C2×#3319—711nomaximal, Sylow
411C2×C71—44no—
412C2×C71—42no—
413C2×C71#331914yescomplemented
414C2×C71C2×#54611yescharacteristic
415C2×C71C2×#57511yescharacteristic
416C2×C71C2×#57611yescharacteristic
417D71—42no—
418D71—82no—
419D71—82no—
420C2×#555—711no—
421C2×#546—711no—
422#3319—7116no—
423C2×#489—711no—
424C2×#485—711no—
425C2×#482—711no—
426C2×#474—711no—
427C2×#468—711no—
428C2×#466—711no—
429C2×#463—711no—
430C2×#449—711no—
431C2×#447—711no—
432C2×#442—711no—
433C2×#435—711no—
434C2×#418—711no—
435C2×#416D7111yescharacteristic, complemented
436C71C2×#331911yescharacteristic, complemented, Sylow
437C22×#41C2×D7111yescharacteristic
438C23×D4—711no—
439C22×SD16—711no—
440C22×D8—711no—
441C22×D8—711no—
442C22×M16—711no—
443C23×C8C2×D7111yescharacteristic, complemented
444#555—718no—
445#555—1424no—
446#546—718no—
447#546—1424no—
448C2×C4⋊Q8—711no—
449C2×#124—711no—
450C2×#124—1421no—
451C2×#124—1421no—
452C2×#123—1421no—
453C2×C22⋊Q8—711no—
454C2×#121—711no—
455C2×#121—711no—
456C2×#121—711no—
457C2×#121—1421no—
458C2×#121—1421no—
459C2×#120—1421no—
460C2×C4×D4—711no—
461C2×C4×D4—711no—
462C2×C4×D4—711no—
463C2×#117—711no—
464C2×#117—1421no—
465C2×#117C2×D7111yescharacteristic, complemented
466C22×C22⋊C4—1421no—
467#489—718no—
468#485—718no—
469#482—718no—
470#474—718no—
471#468—718no—
472#466—718no—
473#463—718no—
474#449—718no—
475#447—718no—
476#442—718no—
477#435—718no—
478C2×#107—711no—
479C2×#107—711no—
480C2×#106—711no—
481C2×C4⋊C8—711no—
482#418—718no—
483#416C2×D7118yescomplemented
484C2×#103—711no—
485C2×#103C2×D7111yescharacteristic, complemented
486C2×#103C2×D7111yescharacteristic, complemented
487C2×#102—711no—
488C2×#102—711no—
489C2×#102—711no—
490C2×#102—711no—
491C2×#102—711no—
492C2×#102C2×D7111yescharacteristic
493C2×#102C2×D7111yescharacteristic
494C2×C22⋊C8—711no—
495C2×C22⋊C8—711no—
496C2×#97—711no—
497C25—1421no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D7114yes—
502C22×Q8—1421no—
503C22×Q8C22×D7111yescharacteristic
504C22×D4—21no—
505C22×D4—2842no—
506C22×D4—711no—
507C22×D4—714no—
508C22×D4—711no—
509C22×D4—711no—
510C22×D4—1421no—
511C22×D4—1422no—
512C22×D4—1421no—
513C22×D4—1424no—
514C22×D4—1421no—
515C22×D4—1421no—
516C22×D4C22×D7111yescharacteristic
517C23×C4—21no—
518C23×C4—711no—
519C23×C4—1421no—
520C23×C4—1421no—
521C23×C4C22×D7111yescharacteristic
522C2×SD16—2842no—
523C2×SD16—714no—
524C2×D8—2842no—
525C2×D8—714no—
526C2×D8—714no—
527C2×D8—1424no—
528C2×M16—2842no—
529C2×M16—714no—
530C22×C8—42no—
531C22×C8—711no—
532C22×C8—711no—
533C22×C8C22×D7111yescharacteristic
534C22×C8C22×D7111yescharacteristic
535C22×C8C22×D7114yescomplemented
536C4⋊Q8—714no—
537C4⋊Q8—1422no—
538#124—714no—
539#124—1428no—
540#124—1422no—
541#124—1428no—
542#123—1428no—
543C22⋊Q8—714no—
544C22⋊Q8—1422no—
545#121—714no—
546#121—714no—
547#121—714no—
548#121—1428no—
549#121—1428no—
550#121—1422no—
551#121—1422no—
552#121—1422no—
553#120—1428no—
554C4×D4—714no—
555C4×D4—714no—
556C4×D4—714no—
557C4×D4—714no—
558C4×D4—1422no—
559C4×D4—1422no—
560#117—22no—
561#117—714no—
562#117—1428no—
563#117—1422no—
564#117C22×D7114yescomplemented
565C2×C4⋊C4—711no—
566C2×C4⋊C4—711no—
567C2×C4⋊C4—711no—
568C2×C4⋊C4—1421no—
569C2×C4⋊C4—1421no—
570C2×C4⋊C4C22×D7111yescharacteristic
571C2×C4⋊C4C22×D7111yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—711no—
574C2×C22⋊C4—711no—
575C2×C22⋊C4—1428no—
576C2×C22⋊C4—1421no—
577C2×C22⋊C4—1421no—
578C2×C22⋊C4—1421no—
579C2×C22⋊C4—1421no—
580C2×C22⋊C4—1421no—
581C2×C22⋊C4—1421no—
582C2×C22⋊C4—1421no—
583C2×C22⋊C4—1421no—
584C2×C22⋊C4—1421no—
585C2×C42—21no—
586C2×C42—711no—
587C2×C42—1421no—
588#107—714no—
589#107—714no—
590#106—714no—
591C4⋊C8—714no—
592#103—714no—
593#103C22×D7114yescomplemented
594#103C22×D7114yescomplemented
595#102—714no—
596#102—714no—
597#102—714no—
598#102—714no—
599#102—714no—
600#102C22×D7114yes—
601#102C22×D7114yes—
602C22⋊C8—714no—
603C22⋊C8—714no—
604#97—714no—
605C24—21no—
606C24—2844no—
607C24—2844no—
608C24—5682no—
609C24—711no—
610C24—1424no—
611C24—1421no—
612C24—1421no—
613C24D4×D7111yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—5682no—
621C2×Q8—1424no—
622C2×Q8C23×D7112yes—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—2848no—
628C2×D4—2844no—
629C2×D4—2844no—
630C2×D4—2842no—
631C2×D4—5682no—
632C2×D4—5682no—
633C2×D4—5682no—
634C2×D4—714no—
635C2×D4—712no—
636C2×D4—712no—
637C2×D4—1424no—
638C2×D4—1424no—
639C2×D4—1428no—
640C2×D4—1424no—
641C2×D4—1424no—
642C2×D4—1421no—
643C2×D4—1421no—
644C2×D4—1422no—
645C2×D4—1422no—
646C2×D4—1422no—
647C2×D4—1422no—
648C2×D4#1176586514yes—
649C2×D4C23×D7112yes—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—2844no—
658C22×C4—5682no—
659C22×C4—711no—
660C22×C4—711no—
661C22×C4—711no—
662C22×C4—712no—
663C22×C4—712no—
664C22×C4—1424no—
665C22×C4—1421no—
666C22×C4—1421no—
667C22×C4—1424no—
668C22×C4—1422no—
669C22×C4—1422no—
670C22×C4D4×D7112yes—
671C22×C4D4×D7111yescharacteristic
672C22×C4C23×D7112yes—
673C22×C4C23×D7111yescharacteristic
674SD16—2844no—
675D8—2844no—
676D8—1428no—
677M16—2844no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—44no—
681C2×C8—712no—
682C2×C8—712no—
683C2×C8—1422no—
684C2×C8—1422no—
685C2×C8C23×D7112yes—
686C2×C8C23×D7112yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—714no—
690C4⋊C4—712no—
691C4⋊C4—712no—
692C4⋊C4—1424no—
693C4⋊C4—1424no—
694C4⋊C4—1421no—
695C4⋊C4—1421no—
696C4⋊C4C23×D7112yes—
697C4⋊C4C23×D7112yes—
698C22⋊C4—24no—
699C22⋊C4—714no—
700C22⋊C4—714no—
701C22⋊C4—1424no—
702C22⋊C4—1424no—
703C22⋊C4—1424no—
704C22⋊C4—1424no—
705C22⋊C4—1424no—
706C22⋊C4—1424no—
707C22⋊C4—1424no—
708C22⋊C4—1424no—
709C22⋊C4—1424no—
710C42—24no—
711C42—712no—
712C42—712no—
713C42—1424no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—2848no—
722C23—2848no—
723C23—2842no—
724C23—2842no—
725C23—2842no—
726C23—2842no—
727C23—2842no—
728C23—2842no—
729C23—56816no—
730C23—5684no—
731C23—712no—
732C23—1422no—
733C23—1422no—
734C23—1422no—
735C23—1422no—
736C23—1422no—
737C23C2×D4×D7112yes—
738C23C2×D4×D7111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742Q8—5684no—
743D4—22no—
744D4—24no—
745D4—48no—
746D4—2848no—
747D4—2844no—
748D4—2842no—
749D4—2842no—
750D4—5684no—
751D4—5684no—
752D4—5684no—
753D4—1422no—
754D4—1422no—
755D4—1422no—
756D4—1422no—
757D4C2×#1176586514yes—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—48no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—2848no—
770C2×C4—2842no—
771C2×C4—2842no—
772C2×C4—5684no—
773C2×C4—712no—
774C2×C4—712no—
775C2×C4—712no—
776C2×C4—1422no—
777C2×C4—1422no—
778C2×C4—1422no—
779C2×C4—1422no—
780C2×C4—1422no—
781C2×C4—1422no—
782C2×C4—1422no—
783C2×C4—1424no—
784C2×C4C2×D4×D7112yes—
785C2×C4C2×D4×D7111yescharacteristic
786C2×C4C2×#1176586512yes—
787C2×C4#1455617312yes—
788C2×C4C24×D7111yescharacteristic
789C8—22no—
790C8—22no—
791C8—1422no—
792C8—1422no—
793C22—22no—
794C22—24no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—48no—
799C22—42no—
800C22—42no—
801C22—2844no—
802C22—2842no—
803C22—2842no—
804C22—2842no—
805C22—2842no—
806C22—2842no—
807C22—2842no—
808C22—56816no—
809C22—5684no—
810C22—5684no—
811C22—1422no—
812C22—1422no—
813C22—1422no—
814C22#1798663912yes—
815C22#1798679612yes—
816C22#1798680112yes—
817C22C22×D4×D7111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—2842no—
823C4—2842no—
824C4—1422no—
825C4—1422no—
826C4—1422no—
827C4#1798663912yes—
828C4C22×#1176586511yescharacteristic
829C4C2×#1455617311yescharacteristic
830C2—42no—
831C2—44no—
832C2—2842no—
833C2—5682no—
834C2—5682no—
835C2#2260049214yesdirect product factor
836C2C2×#1798663911yescharacteristic
837C2C2×#1798679611yescharacteristic
838C2C2×#1798680111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#416×C71C2
socleC23×C71C22×D4
hypercenterC2×#416D71
hypocenterC71C2×#3319
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#17986712C2semidirect
2. C2×#17986637C2semidirect
3. #22600492C2direct (N × H)
4. C2×#17986360C2semidirect
5. C2×#17986339C2semidirect
6. C2×#17986323C2semidirect
7. C2×#17986277C2semidirect
8. C2×#17986248C2semidirect
9. C2×#17986235C2semidirect
10. C2×#17986217C2semidirect
11. C2×#17986144C2semidirect
12. C2×#17986134C2semidirect
13. C2×#17986108C2semidirect
14. C2×#17986070C2semidirect
15. C2×#17986002C2semidirect
16. C2×#416×C71C2semidirect
18. C22×#11765852C22semidirect
23. #17986712C22semidirect
25. #17986637C22semidirect
26. C2×#14556127C22semidirect
34. C2×#14556102C22semidirect
39. C2×#14556090C22semidirect
44. #17986360C22semidirect
45. #17986339C22semidirect
46. #17986323C22semidirect
47. #17986277C22semidirect
48. #17986248C22semidirect
49. #17986235C22semidirect
50. #17986217C22semidirect
51. #17986144C22semidirect
52. #17986134C22semidirect
53. #17986108C22semidirect
54. #17986070C22semidirect
55. C2×#14556062C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556059C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. #17986002C22semidirect
60. C2×#14556052C22semidirect
62. C2×#14556050C22semidirect
66. C2×C22⋊(C71⋊C8)C22semidirect
68. C2×#14556038C22semidirect
70. C23×C8×C71C22semidirect
71. C2×#117×C71C22semidirect
72. #416×C71C22semidirect
73. C2×#103×C71C22semidirect
74. C2×#103×C71C22semidirect
94. C2×#11765852C23semidirect
104. #14556127C23semidirect
117. #14556102C23semidirect
124. #14556090C23semidirect
149. #14556062C23semidirect
150. #14556061C23semidirect
151. #14556059C23semidirect
152. Dic71⋊C8C23semidirect
153. #14556052C23semidirect
155. #14556050C23semidirect
159. C22⋊(C71⋊C8)C23semidirect
161. #14556038C23semidirect
174. C22×C8×C71C23semidirect
176. #117×C71C23semidirect
181. #103×C71C23semidirect
182. #103×C71C23semidirect
413. C2×C71#3319semidirect
435. C2×#416D71semidirect
436. C71C2×#3319semidirect
443. C23×C8C2×D71semidirect
465. C2×#117C2×D71semidirect
483. #416C2×D71semidirect
485. C2×#103C2×D71semidirect
486. C2×#103C2×D71semidirect
535. C22×C8C22×D71semidirect
564. #117C22×D71semidirect
593. #103C22×D71semidirect
594. #103C22×D71semidirect
835. C2#22600492direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867122
C2×#179866372
#226004922
C2×#179863602
C2×#179863392
C2×#179863232
C2×#179862772
C2×#179862482
C2×#179862352
C2×#179862172
C2×#179861442
C2×#179861342
C2×#179861082
C2×#179860702
C2×#179860022
C2×#416×C712
C2×#331971