Finite Group Databasebeta

← C2×#22599155 #32868053

Subgroups — C2×#22599155 #32868053

Order 18176.

2686 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986512C211yesmaximal, characteristic, complemented
2C2×#121×D71C211yesmaximal, characteristic, complemented
3#22599155C2116yesmaximal, direct product factor
4C2×#17986326C211yesmaximal, characteristic, complemented
5C2×#17986322C211yesmaximal, characteristic, complemented
6C2×#17986328C211yesmaximal, characteristic, complemented
7C2×#17986314C211yesmaximal, characteristic, complemented
8C2×#17986252C211yesmaximal, characteristic, complemented
9C2×#17986250C211yesmaximal, characteristic, complemented
10C2×#17986247C211yesmaximal, characteristic, complemented
11C2×#17986147C211yesmaximal, characteristic, complemented
12C2×#17986143C211yesmaximal, characteristic, complemented
13C2×#17986148C211yesmaximal, characteristic, complemented
14C2×#17986134C211yesmaximal, characteristic, complemented
15C2×#17985962C211yesmaximal, characteristic, complemented
16C2×#468×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic, complemented
18C22×D4×D71—21no—
19C22×D4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C22×#11765852C2211yescharacteristic, complemented
22C22×D568C2211yescharacteristic, complemented
23C22×#11765850C2211yescharacteristic, complemented
24C22×#11765849C2211yescharacteristic, complemented
25#17986512—24no—
26#17986512C2218yescomplemented
27C2×#14556113—21no—
28C2×#14556104C2211yescharacteristic
29C2×#14556103C2211yescharacteristic
30C2×#14556103C2211yescharacteristic
31C2×#14556102C2211yescharacteristic
32C2×#14556102C2211yescharacteristic, complemented
33C2×#14556101—21no—
34C2×#14556100—21no—
35C2×#14556099C2211yescharacteristic
36#121×D71—24no—
37#121×D71C2218yescomplemented
38C2×#14556098—21no—
39C2×#14556090—21no—
40C2×(C22⋊D71)⋊C4—21no—
41C2×#14556086C2211yescharacteristic, complemented
42C2×C4⋊C4×D71C2211yescharacteristic
43C2×C22⋊C4×D71—21no—
44#17986328C2218yescomplemented
45#17986326C2218yescomplemented
46#17986322C2218yescomplemented
47#17986314C2218yescomplemented
48#17986252C2218yescomplemented
49#17986250C2218yescomplemented
50#17986247C2218yescomplemented
51#17986148C2218yescomplemented
52#17986147C2218yescomplemented
53#17986143C2218yescomplemented
54#17986134C2218yescomplemented
55C2×#14556061C2211yescharacteristic, complemented
56C2×#14556060C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×#14556052C2211yescharacteristic, complemented
59C2×#14556050C2211yescharacteristic, complemented
60C2×#14556050C2211yescharacteristic, complemented
61C2×#14556049C2211yescharacteristic, complemented
62C2×#14556048C2211yescharacteristic, complemented
63C2×#14556048C2211yescharacteristic, complemented
64#17985962C2218yescomplemented
65C2×(C2×D71)⋊C8C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C71C2211yescharacteristic, complemented
70C22×M16×C71C2211yescharacteristic, complemented
71C2×C22⋊Q8×C71C2211yescharacteristic, complemented
72C2×#121×C71C2211yescharacteristic
73#468×C71C2218yescomplemented
74C2×#107×C71C2211yescharacteristic, complemented
75C2×#103×C71C2211yescharacteristic, complemented
76C2×#102×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C24×D71D411yescharacteristic
79C2×#11765866—22no—
80C2×#11765866—42no—
81C2×#11765866—42no—
82C2×#11765866C2314yescomplemented
83C22×D284—21no—
84C22×D284—21no—
85C22×D284—21no—
86C22×D284C2311yescharacteristic
87C22×D284C2311yescharacteristic
88C22×C22⋊D71—21no—
89C22×C22⋊D71—21no—
90C22×C22⋊D71—21no—
91C22×C22⋊D71—21no—
92C2×D4×D71—28no—
93C2×D4×D71—22no—
94C2×D4×D71—42no—
95C2×D4×D71—42no—
96C2×D4×D71—48no—
97C2×D4×D71C2314yes—
98C23×Dic71D411yescharacteristic
99C22×C4×D71—21no—
100C22×C4×D71—21no—
101C22×C4×D71—42no—
102C22×C4×D71—42no—
103C22×C4×D71D411yescharacteristic
104C22×C4×D71D414yes—
105C22×C4×D71D411yescharacteristic
106C22×C4×D71C2311yescharacteristic
107C22×C4×D71C2311yescharacteristic
108C22×C4×D71C2314yes—
109C2×#11765852—42no—
110C2×#11765852C2314yescomplemented
111C2×D568—42no—
112C2×D568C2314yescomplemented
113C2×#11765850—42no—
114C2×#11765850C2314yescomplemented
115C2×#11765849—42no—
116C2×#11765849C2314yescomplemented
117C22×C71⋊C8C2311yescharacteristic
118C22×C71⋊C8C2311yescharacteristic
119#14556113—28no—
120#14556104—22no—
121#14556104C2314yes—
122#14556103—22no—
123#14556103—22no—
124#14556103C2314yes—
125#14556103C2314yes—
126#14556102—22no—
127#14556102—22no—
128#14556102C2314yes—
129#14556102C2314yescomplemented
130#14556101—28no—
131#14556100—28no—
132#14556099—22no—
133#14556099C2314yes—
134#14556098—28no—
135#14556090—28no—
136(C22⋊D71)⋊C4—28no—
137#14556086—22no—
138#14556086C2314yescomplemented
139C2×C4⋊Dic71C2311yescharacteristic
140C2×C4⋊Dic71C2311yescharacteristic
141C2×Dic71⋊C4—21no—
142C2×Dic71⋊C4—21no—
143C4⋊C4×D71—22no—
144C4⋊C4×D71C2314yes—
145C2×C22⋊Dic71—21no—
146C2×(C2×D71)⋊C4—21no—
147C2×(C2×D71)⋊C4—21no—
148C2×(C2×D71)⋊C4—21no—
149C2×(C2×D71)⋊C4—21no—
150C2×(C2×D71)⋊C4—21no—
151C2×(C2×D71)⋊C4—21no—
152C22⋊C4×D71—28no—
153C2×C4×Dic71—21no—
154#14556061C2314yescomplemented
155#14556060C2314yescomplemented
156#14556059C2314yescomplemented
157#14556052C2314yescomplemented
158#14556050C2314yescomplemented
159#14556050C2314yescomplemented
160#14556049C2314yescomplemented
161#14556048C2314yescomplemented
162#14556048C2314yescomplemented
163(C2×D71)⋊C8C2314yes—
164(C2×D71)⋊C8C2314yes—
165(C2×D71)⋊C8C2314yescomplemented
166(C2×D71)⋊C8C2314yescomplemented
167C22×Q8×C71C2311yescharacteristic
168C22×D4×C71—21no—
169C22×D4×C71C2311yescharacteristic
170C23×C4×C71C2311yescharacteristic
171C2×SD16×C71—42no—
172C2×SD16×C71C2314yescomplemented
173C2×M16×C71—42no—
174C2×M16×C71C2314yescomplemented
175C22×C8×C71C2311yescharacteristic
176C22×C8×C71C2311yescharacteristic
177C22⋊Q8×C71—22no—
178C22⋊Q8×C71C2314yescomplemented
179#121×C71—22no—
180#121×C71C2314yes—
181C2×C4⋊C4×C71—21no—
182C2×C4⋊C4×C71C2311yescharacteristic
183C2×C4⋊C4×C71C2311yescharacteristic
184C2×C22⋊C4×C71—21no—
185C2×C22⋊C4×C71—21no—
186#107×C71C2314yescomplemented
187#103×C71C2314yescomplemented
188#102×C71C2314yescomplemented
189C23×D71—24no—
190C23×D71—21no—
191C23×D71—21no—
192C23×D71—24no—
193C23×D71—42no—
194C23×D71—42no—
195C23×D71—44no—
196C23×D71—44no—
197C23×D71—44no—
198C23×D71C2×D411yescharacteristic
199C23×D71C2×D411yescharacteristic
200C23×D71C2×D414yes—
201#11765866—44no—
202#11765866—44no—
203#11765866—48no—
204C2×D284—22no—
205C2×D284—22no—
206C2×D284—22no—
207C2×D284—22no—
208C2×D284—24no—
209C2×D284—24no—
210C2×D284—24no—
211C2×D284—21no—
212C2×D284—21no—
213C2×D284—44no—
214C2×D284—44no—
215C2×D284—44no—
216C2×D284C2412yes—
217C2×D284C2412yes—
218C2×C22⋊D71—24no—
219C2×C22⋊D71—24no—
220C2×C22⋊D71—24no—
221C2×C22⋊D71—24no—
222C2×C22⋊D71—44no—
223C2×C22⋊D71—44no—
224C2×C22⋊D71—44no—
225C2×C22⋊D71—44no—
226D4×D71—44no—
227D4×D71—44no—
228D4×D71—48no—
229D4×D71—432no—
230C22×Dic71—21no—
231C22×Dic71—21no—
232C22×Dic71—42no—
233C22×Dic71C2×D411yescharacteristic
234C22×Dic71C2×D411yescharacteristic
235C22×Dic71C2×D414yes—
236C2×C4×D71—22no—
237C2×C4×D71—22no—
238C2×C4×D71—22no—
239C2×C4×D71—22no—
240C2×C4×D71—24no—
241C2×C4×D71—24no—
242C2×C4×D71—48no—
243C2×C4×D71—44no—
244C2×C4×D71—44no—
245C2×C4×D71—42no—
246C2×C4×D71—42no—
247C2×C4×D71—44no—
248C2×C4×D71—44no—
249C2×C4×D71C2×D412yes—
250C2×C4×D71C2×D412yes—
251C2×C4×D71C2×D414yes—
252C2×C4×D71C2×D414yes—
253C2×C4×D71C2412yes—
254C2×C4×D71C2412yes—
255#11765852—44no—
256D568—44no—
257#11765850—44no—
258#11765849—44no—
259C2×C71⋊C8—22no—
260C2×C71⋊C8—22no—
261C2×C71⋊C8C2412yes—
262C2×C71⋊C8C2412yes—
263C4⋊Dic71—21no—
264C4⋊Dic71—21no—
265C4⋊Dic71C2412yes—
266C4⋊Dic71C2412yes—
267Dic71⋊C4—24no—
268Dic71⋊C4—24no—
269C22⋊Dic71—24no—
270(C2×D71)⋊C4—24no—
271(C2×D71)⋊C4—24no—
272(C2×D71)⋊C4—24no—
273(C2×D71)⋊C4—24no—
274(C2×D71)⋊C4—24no—
275(C2×D71)⋊C4—24no—
276C4×Dic71—24no—
277C24×C71—21no—
278C24×C71C2×D411yescharacteristic
279C2×Q8×C71—21no—
280C2×Q8×C71—22no—
281C2×Q8×C71—22no—
282C2×Q8×C71C2412yes—
283C2×D4×C71—24no—
284C2×D4×C71—21no—
285C2×D4×C71—22no—
286C2×D4×C71—22no—
287C2×D4×C71—44no—
288C2×D4×C71C2412yes—
289C22×C4×C71—22no—
290C22×C4×C71—22no—
291C22×C4×C71—21no—
292C22×C4×C71—21no—
293C22×C4×C71—21no—
294C22×C4×C71C2×D411yescharacteristic
295C22×C4×C71C2×D412yes—
296C22×C4×C71C2412yes—
297C22×C4×C71C2411yescharacteristic
298SD16×C71—44no—
299M16×C71—44no—
300C2×C8×C71—22no—
301C2×C8×C71—22no—
302C2×C8×C71C2412yes—
303C2×C8×C71C2412yes—
304C4⋊C4×C71—24no—
305C4⋊C4×C71—21no—
306C4⋊C4×C71—21no—
307C4⋊C4×C71C2412yes—
308C4⋊C4×C71C2412yes—
309C22⋊C4×C71—24no—
310C22⋊C4×C71—24no—
311C23×C71—22no—
312C23×C71—22no—
313C23×C71—22no—
314C23×C71—22no—
315C23×C71—42no—
316C23×C71—42no—
317C23×C71—42no—
318C23×C71C22×D412yes—
319C23×C71C22×D411yescharacteristic
320C22×D71—22no—
321C22×D71—22no—
322C22×D71—22no—
323C22×D71—22no—
324C22×D71—22no—
325C22×D71—28no—
326C22×D71—22no—
327C22×D71—22no—
328C22×D71—44no—
329C22×D71—44no—
330C22×D71—416no—
331C22×D71—48no—
332C22×D71—48no—
333C22×D71—42no—
334C22×D71—42no—
335C22×D71—42no—
336C22×D71—42no—
337C22×D71—42no—
338C22×D71—42no—
339C22×D71—48no—
340C22×D71—816no—
341C22×D71AGL(1,ℤ/8)14yes—
342C22×D71C22×D412yes—
343C22×D71C22×D412yes—
344Q8×C71—22no—
345Q8×C71—22no—
346Q8×C71—42no—
347D4×C71—22no—
348D4×C71—22no—
349D4×C71—48no—
350D4×C71—42no—
351C2×C4×C71—22no—
352C2×C4×C71—24no—
353C2×C4×C71—22no—
354C2×C4×C71—22no—
355C2×C4×C71—22no—
356C2×C4×C71—22no—
357C2×C4×C71—22no—
358C2×C4×C71—42no—
359C2×C4×C71—42no—
360C2×C4×C71—42no—
361C2×C4×C71C22×D412yes—
362C2×C4×C71C22×D411yescharacteristic
363C2×C4×C71H(5,𝔽2)12yes—
364C2×C4×C71H(5,𝔽2)12yes—
365C2×C4×C71C2511yescharacteristic
366C22⋊D71—48no—
367C22⋊D71—48no—
368C22⋊D71—48no—
369C22⋊D71—48no—
370C2×Dic71—22no—
371C2×Dic71—22no—
372C2×Dic71—22no—
373C2×Dic71—22no—
374C2×Dic71—44no—
375C2×Dic71—42no—
376C2×Dic71—42no—
377C2×Dic71C22×D412yes—
378C2×Dic71C22×D412yes—
379D284—22no—
380D284—22no—
381D284—22no—
382D284—22no—
383D284—48no—
384D284—48no—
385D284—48no—
386D284—42no—
387D284—42no—
388C4×D71—24no—
389C4×D71—24no—
390C4×D71—22no—
391C4×D71—22no—
392C4×D71—22no—
393C4×D71—22no—
394C4×D71—44no—
395C4×D71—44no—
396C4×D71—48no—
397C4×D71—48no—
398C8×C71—22no—
399C8×C71—22no—
400C71⋊C8—22no—
401C71⋊C8—22no—
402C22×C71—22no—
403C22×C71—22no—
404C22×C71—22no—
405C22×C71—44no—
406C22×C71—42no—
407C22×C71—42no—
408C22×C71—42no—
409C22×C71—84no—
410C22×C71#53412yes—
411C22×C71C2×AGL(1,ℤ/8)12yes—
412C22×C71#57512yes—
413C22×C71C23×D411yescharacteristic
414C2×D71—22no—
415C2×D71—28no—
416C2×D71—22no—
417C2×D71—22no—
418C2×D71—22no—
419C2×D71—22no—
420C2×D71—416no—
421C2×D71—44no—
422C2×D71—42no—
423C2×D71—42no—
424C2×D71—42no—
425C2×D71—42no—
426C2×D71—42no—
427C2×D71—42no—
428C2×D71—816no—
429C2×D71—84no—
430C2×D71—84no—
431C2×D71C2×AGL(1,ℤ/8)14yes—
432C4×C71—22no—
433C4×C71—42no—
434C4×C71—42no—
435C4×C71—42no—
436C4×C71#53412yes—
437C4×C71C2×H(5,𝔽2)11yescharacteristic
438C4×C71C2×H(5,𝔽2)11yescharacteristic
439Dic71—22no—
440Dic71—22no—
441Dic71—42no—
442Dic71—42no—
443C2×#3194—711nomaximal, Sylow
444C2×C71—42no—
445C2×C71—82no—
446C2×C71#319414yescomplemented
447C2×C71C2×#53411yescharacteristic
448C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
449C2×C71C2×#57511yescharacteristic
450D71—24no—
451D71—42no—
452D71—82no—
453D71—82no—
454C2×#525—711no—
455C22×#121—711no—
456#3194—7116no—
457C2×#482—711no—
458C2×#482—711no—
459C2×#483—711no—
460C2×#480—711no—
461C2×#469—711no—
462C2×#469—711no—
463C2×#468—711no—
464C2×#468D7111yescharacteristic, complemented
465C2×#449—711no—
466C2×#449—711no—
467C2×#450—711no—
468C2×#447—711no—
469C2×#407—711no—
470C71C2×#319411yescharacteristic, complemented, Sylow
471C22×#41—711no—
472C23×D4—711no—
473C23×D4—1421no—
474C24×C4—711no—
475C22×SD16—711no—
476C22×SD16C2×D7111yescharacteristic, complemented
477C22×D8—711no—
478C22×D8—711no—
479C22×M16—711no—
480C22×M16C2×D7111yescharacteristic, complemented
481#525—718no—
482#525—1424no—
483C2×#123—1421no—
484C2×C22⋊Q8—711no—
485C2×C22⋊Q8C2×D7111yescharacteristic, complemented
486C2×#121—711no—
487C2×#121—711no—
488C2×#121—711no—
489C2×#121—718no—
490C2×#121—711no—
491C2×#121—711no—
492C2×#121—1421no—
493C2×#121—1424no—
494C2×#121—1421no—
495C2×#121C2×D7111yescharacteristic
496C2×#120—1421no—
497C2×C4×D4—1421no—
498C2×C4×D4—1421no—
499C2×#117—711no—
500C22×C4⋊C4—711no—
501C22×C22⋊C4—1421no—
502#483—718no—
503#482—718no—
504#482—718no—
505#480—718no—
506#469—718no—
507#469—718no—
508#468—718no—
509#468C2×D7118yescomplemented
510#450—718no—
511#449—718no—
512#449—718no—
513#447—718no—
514C2×#107—711no—
515C2×#107C2×D7111yescharacteristic, complemented
516C2×#106—711no—
517C2×#106—711no—
518C2×#103—711no—
519C2×#103C2×D7111yescharacteristic, complemented
520C2×#102—711no—
521C2×#102—711no—
522C2×#102—711no—
523C2×#102—711no—
524C2×#102—711no—
525C2×#102C2×D7111yescharacteristic, complemented
526#407—718no—
527C2×C22⋊C8—711no—
528C2×C22⋊C8—711no—
529C2×C22⋊C8—711no—
530C2×C22⋊C8—711no—
531C25—711no—
532C25—1421no—
533C2×#41—2842no—
534C2×#41—2842no—
535C2×#41—714no—
536C2×#41—1422no—
537C22×Q8C22×D7111yescharacteristic
538C22×D4—21no—
539C22×D4—2848no—
540C22×D4—2842no—
541C22×D4—2842no—
542C22×D4—714no—
543C22×D4—711no—
544C22×D4—711no—
545C22×D4—1421no—
546C22×D4—1421no—
547C22×D4—1421no—
548C22×D4—1422no—
549C22×D4—1421no—
550C22×D4—1428no—
551C22×D4—1421no—
552C22×D4—1421no—
553C22×D4—1421no—
554C22×D4C22×D7111yescharacteristic
555C23×C4—2842no—
556C23×C4—2842no—
557C23×C4—711no—
558C23×C4—711no—
559C23×C4—711no—
560C23×C4—714no—
561C23×C4—714no—
562C23×C4—711no—
563C23×C4—711no—
564C23×C4—1421no—
565C23×C4—1421no—
566C23×C4C22×D7111yescharacteristic
567C2×SD16—42no—
568C2×SD16—2842no—
569C2×SD16—714no—
570C2×SD16C22×D7114yescomplemented
571C2×D8—2842no—
572C2×D8—2842no—
573C2×D8—714no—
574C2×D8—714no—
575C2×M16—42no—
576C2×M16—2842no—
577C2×M16—714no—
578C2×M16C22×D7114yescomplemented
579C22×C8—711no—
580C22×C8—711no—
581C22×C8C22×D7111yescharacteristic
582C22×C8C22×D7111yescharacteristic
583#123—1428no—
584C22⋊Q8—22no—
585C22⋊Q8—714no—
586C22⋊Q8—1422no—
587C22⋊Q8C22×D7114yescomplemented
588#121—22no—
589#121—714no—
590#121—714no—
591#121—714no—
592#121—714no—
593#121—714no—
594#121—1428no—
595#121—1422no—
596#121—1422no—
597#121—1422no—
598#121—1428no—
599#121—1422no—
600#121—1422no—
601#121C22×D7114yes—
602#120—1428no—
603C4×D4—1428no—
604C4×D4—1428no—
605#117—714no—
606#117—1422no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—711no—
609C2×C4⋊C4—711no—
610C2×C4⋊C4—714no—
611C2×C4⋊C4—1422no—
612C2×C4⋊C4—1421no—
613C2×C4⋊C4—1421no—
614C2×C4⋊C4C22×D7111yescharacteristic
615C2×C4⋊C4C22×D7111yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—1428no—
619C2×C22⋊C4—1421no—
620C2×C22⋊C4—1421no—
621C2×C22⋊C4—1421no—
622C2×C22⋊C4—1421no—
623C2×C22⋊C4—1421no—
624C2×C22⋊C4—1421no—
625C2×C22⋊C4—1421no—
626C2×C42—1421no—
627#107—714no—
628#107C22×D7114yescomplemented
629#106—714no—
630#106—714no—
631#103—714no—
632#103C22×D7114yescomplemented
633#102—714no—
634#102—714no—
635#102—714no—
636#102—714no—
637#102—714no—
638#102C22×D7114yescomplemented
639C22⋊C8—714no—
640C22⋊C8—714no—
641C22⋊C8—714no—
642C22⋊C8—714no—
643C24—21no—
644C24—2842no—
645C24—2842no—
646C24—2844no—
647C24—2844no—
648C24—2844no—
649C24—714no—
650C24—711no—
651C24—711no—
652C24—1424no—
653C24—1424no—
654C24—1421no—
655C24—1421no—
656C24D4×D7111yescharacteristic
657#41—2848no—
658#41—2844no—
659#41—2844no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8C23×D7112yes—
664C2×D4—24no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—44no—
669C2×D4—2844no—
670C2×D4—2844no—
671C2×D4—2844no—
672C2×D4—28432no—
673C2×D4—2844no—
674C2×D4—2844no—
675C2×D4—2844no—
676C2×D4—2844no—
677C2×D4—2844no—
678C2×D4—2848no—
679C2×D4—2844no—
680C2×D4—712no—
681C2×D4—712no—
682C2×D4—1424no—
683C2×D4—1424no—
684C2×D4—1424no—
685C2×D4—1424no—
686C2×D4—1424no—
687C2×D4—1424no—
688C2×D4—1424no—
689C2×D4—1421no—
690C2×D4—1421no—
691C2×D4—1422no—
692C2×D4—1422no—
693C2×D4—1422no—
694C2×D4—1422no—
695C2×D4C23×D7112yes—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—2842no—
702C22×C4—2842no—
703C22×C4—2844no—
704C22×C4—2844no—
705C22×C4—2848no—
706C22×C4—2844no—
707C22×C4—2844no—
708C22×C4—2842no—
709C22×C4—714no—
710C22×C4—714no—
711C22×C4—714no—
712C22×C4—711no—
713C22×C4—711no—
714C22×C4—712no—
715C22×C4—712no—
716C22×C4—712no—
717C22×C4—712no—
718C22×C4—1424no—
719C22×C4—1424no—
720C22×C4—1421no—
721C22×C4—1421no—
722C22×C4—1422no—
723C22×C4—1422no—
724C22×C4—1422no—
725C22×C4—1422no—
726C22×C4D4×D7112yes—
727C22×C4D4×D7111yescharacteristic
728C22×C4C23×D7112yes—
729C22×C4C23×D7111yescharacteristic
730SD16—44no—
731SD16—2844no—
732D8—2844no—
733D8—2844no—
734M16—44no—
735M16—2844no—
736C2×C8—22no—
737C2×C8—22no—
738C2×C8—712no—
739C2×C8—712no—
740C2×C8—1422no—
741C2×C8—1422no—
742C2×C8C23×D7112yes—
743C2×C8C23×D7112yes—
744C4⋊C4—24no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—712no—
748C4⋊C4—712no—
749C4⋊C4—1424no—
750C4⋊C4—1424no—
751C4⋊C4—1421no—
752C4⋊C4—1421no—
753C4⋊C4C23×D7112yes—
754C4⋊C4C23×D7112yes—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—1424no—
758C22⋊C4—1424no—
759C22⋊C4—1424no—
760C22⋊C4—1424no—
761C22⋊C4—1424no—
762C22⋊C4—1424no—
763C22⋊C4—1424no—
764C42—1424no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—2844no—
773C23—2844no—
774C23—28416no—
775C23—2848no—
776C23—2848no—
777C23—2848no—
778C23—2842no—
779C23—2842no—
780C23—2842no—
781C23—2842no—
782C23—2842no—
783C23—2842no—
784C23—56816no—
785C23—712no—
786C23—714no—
787C23—712no—
788C23—1428no—
789C23—1422no—
790C23—1422no—
791C23—1422no—
792C23—1422no—
793C23—1422no—
794C23—1422no—
795C23—1422no—
796C23C2×D4×D7112yes—
797C23C2×D4×D7111yescharacteristic
798Q8—22no—
799Q8—22no—
800Q8—42no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—42no—
805D4—2848no—
806D4—2848no—
807D4—2848no—
808D4—2848no—
809D4—2848no—
810D4—2848no—
811D4—2848no—
812D4—2842no—
813D4—2842no—
814D4—1422no—
815D4—1422no—
816D4—1422no—
817D4—1422no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—2844no—
829C2×C4—2844no—
830C2×C4—2848no—
831C2×C4—2848no—
832C2×C4—2842no—
833C2×C4—2842no—
834C2×C4—2844no—
835C2×C4—712no—
836C2×C4—712no—
837C2×C4—1422no—
838C2×C4—1422no—
839C2×C4—1422no—
840C2×C4—1422no—
841C2×C4—1422no—
842C2×C4—1422no—
843C2×C4—1422no—
844C2×C4—1422no—
845C2×C4—1424no—
846C2×C4—1424no—
847C2×C4C2×D4×D7112yes—
848C2×C4C2×D4×D7111yescharacteristic
849C2×C4#1455617312yes—
850C2×C4#1455617412yes—
851C2×C4C24×D7111yescharacteristic
852C8—22no—
853C8—22no—
854C8—1422no—
855C8—1422no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—84no—
864C22—28416no—
865C22—2844no—
866C22—2842no—
867C22—2842no—
868C22—2842no—
869C22—2842no—
870C22—2842no—
871C22—2842no—
872C22—56816no—
873C22—5684no—
874C22—5684no—
875C22—714no—
876C22—1422no—
877C22—1422no—
878C22—1422no—
879C22—1422no—
880C22—1422no—
881C22—1428no—
882C22#1798655712yes—
883C22AGL(1,ℤ/8)×D7112yes—
884C22#1798679812yes—
885C22C22×D4×D7111yescharacteristic
886C4—22no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—2842no—
891C4—2842no—
892C4—1422no—
893C4—1422no—
894C4#1798655712yes—
895C4C2×#1455617311yescharacteristic
896C4C2×#1455617411yescharacteristic
897C2—42no—
898C2—82no—
899C2—2842no—
900C2—5682no—
901C2—5682no—
902C2—1424no—
903C2#2259915514yesdirect product factor
904C2C2×#1798655711yescharacteristic
905C2C2×AGL(1,ℤ/8)×D7111yescharacteristic
906C2C2×#1798679811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#468×C71C2
socleC23×C71C22×D4
hypercenterC2×#468D71
hypocenterC71C2×#3194
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
1. C2×#17986512C2semidirect
2. C2×#121×D71C2semidirect
3. #22599155C2direct (N × H)
4. C2×#17986326C2semidirect
5. C2×#17986322C2semidirect
6. C2×#17986328C2semidirect
7. C2×#17986314C2semidirect
8. C2×#17986252C2semidirect
9. C2×#17986250C2semidirect
10. C2×#17986247C2semidirect
11. C2×#17986147C2semidirect
12. C2×#17986143C2semidirect
13. C2×#17986148C2semidirect
14. C2×#17986134C2semidirect
15. C2×#17985962C2semidirect
16. C2×#468×C71C2semidirect
17. C22×#11765866C22semidirect
21. C22×#11765852C22semidirect
22. C22×D568C22semidirect
23. C22×#11765850C22semidirect
24. C22×#11765849C22semidirect
26. #17986512C22semidirect
32. C2×#14556102C22semidirect
37. #121×D71C22semidirect
41. C2×#14556086C22semidirect
44. #17986328C22semidirect
45. #17986326C22semidirect
46. #17986322C22semidirect
47. #17986314C22semidirect
48. #17986252C22semidirect
49. #17986250C22semidirect
50. #17986247C22semidirect
51. #17986148C22semidirect
52. #17986147C22semidirect
53. #17986143C22semidirect
54. #17986134C22semidirect
55. C2×#14556061C22semidirect
56. C2×#14556060C22semidirect
57. C2×#14556059C22semidirect
58. C2×#14556052C22semidirect
59. C2×#14556050C22semidirect
60. C2×#14556050C22semidirect
61. C2×#14556049C22semidirect
62. C2×#14556048C22semidirect
63. C2×#14556048C22semidirect
64. #17985962C22semidirect
67. C2×(C2×D71)⋊C8C22semidirect
68. C2×(C2×D71)⋊C8C22semidirect
69. C22×SD16×C71C22semidirect
70. C22×M16×C71C22semidirect
71. C2×C22⋊Q8×C71C22semidirect
73. #468×C71C22semidirect
74. C2×#107×C71C22semidirect
75. C2×#103×C71C22semidirect
76. C2×#102×C71C22semidirect
82. C2×#11765866C23semidirect
110. C2×#11765852C23semidirect
112. C2×D568C23semidirect
114. C2×#11765850C23semidirect
116. C2×#11765849C23semidirect
129. #14556102C23semidirect
138. #14556086C23semidirect
154. #14556061C23semidirect
155. #14556060C23semidirect
156. #14556059C23semidirect
157. #14556052C23semidirect
158. #14556050C23semidirect
159. #14556050C23semidirect
160. #14556049C23semidirect
161. #14556048C23semidirect
162. #14556048C23semidirect
165. (C2×D71)⋊C8C23semidirect
166. (C2×D71)⋊C8C23semidirect
172. C2×SD16×C71C23semidirect
174. C2×M16×C71C23semidirect
178. C22⋊Q8×C71C23semidirect
186. #107×C71C23semidirect
187. #103×C71C23semidirect
188. #102×C71C23semidirect
446. C2×C71#3194semidirect
464. C2×#468D71semidirect
470. C71C2×#3194semidirect
476. C22×SD16C2×D71semidirect
480. C22×M16C2×D71semidirect
485. C2×C22⋊Q8C2×D71semidirect
509. #468C2×D71semidirect
515. C2×#107C2×D71semidirect
519. C2×#103C2×D71semidirect
525. C2×#102C2×D71semidirect
570. C2×SD16C22×D71semidirect
578. C2×M16C22×D71semidirect
587. C22⋊Q8C22×D71semidirect
628. #107C22×D71semidirect
632. #103C22×D71semidirect
638. #102C22×D71semidirect
903. C2#22599155direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865122
C2×#121×D712
#225991552
C2×#179863262
C2×#179863222
C2×#179863282
C2×#179863142
C2×#179862522
C2×#179862502
C2×#179862472
C2×#179861472
C2×#179861432
C2×#179861482
C2×#179861342
C2×#179859622
C2×#468×C712
C2×#319471