Finite Group Databasebeta

← C2×#22599141 #32868038

Subgroups — C2×#22599141 #32868038

Order 18176.

2666 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D71C211yesmaximal, characteristic, complemented
2C2×#121×D71C211yesmaximal, characteristic
3#22599141C2116yesmaximal, direct product factor
4C2×#17986336C211yesmaximal, characteristic, complemented
5C2×#17986333C211yesmaximal, characteristic, complemented
6C2×#17986314C211yesmaximal, characteristic, complemented
7C2×#17986311C211yesmaximal, characteristic, complemented
8C2×#17986247C211yesmaximal, characteristic, complemented
9C2×#17986245C211yesmaximal, characteristic, complemented
10C2×#17986243C211yesmaximal, characteristic, complemented
11C2×#17986139C211yesmaximal, characteristic, complemented
12C2×#17986136C211yesmaximal, characteristic, complemented
13C2×#17986151C211yesmaximal, characteristic, complemented
14C2×#17986148C211yesmaximal, characteristic, complemented
15C2×#17985962C211yesmaximal, characteristic, complemented
16C2×#468×C71C211yesmaximal, characteristic, complemented
17C22×Q8×D71C2211yescharacteristic, complemented
18C22×D4×D71—21no—
19C22×D4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C22×#11765854C2211yescharacteristic, complemented
22C22×#11765853C2211yescharacteristic, complemented
23C22×#11765852C2211yescharacteristic, complemented
24C22×#11765849C2211yescharacteristic, complemented
25C2×#14556108C2211yescharacteristic
26C2×#14556107C2211yescharacteristic, complemented
27C2×#14556106—21no—
28C2×#14556105—21no—
29C2×#14556104C2211yescharacteristic
30C22⋊Q8×D71—24no—
31C22⋊Q8×D71C2218yescomplemented
32C2×#14556103C2211yescharacteristic
33C2×#14556102C2211yescharacteristic
34C2×#14556101—21no—
35C2×#14556100—21no—
36C2×#14556099C2211yescharacteristic
37#121×D71—24no—
38#121×D71C2218yes—
39C2×C4⋊C4×D71—21no—
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic, complemented
42C2×C22⋊C4×D71—21no—
43C2×C22⋊C4×D71—21no—
44#17986336C2218yescomplemented
45#17986333C2218yescomplemented
46#17986314C2218yescomplemented
47#17986311C2218yescomplemented
48#17986247C2218yescomplemented
49#17986245C2218yescomplemented
50#17986243C2218yescomplemented
51#17986151C2218yescomplemented
52#17986148C2218yescomplemented
53#17986139C2218yescomplemented
54#17986136C2218yescomplemented
55C2×#14556062C2211yescharacteristic, complemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556061C2211yescharacteristic, complemented
58C2×#14556053C2211yescharacteristic, complemented
59C2×#14556052C2211yescharacteristic, complemented
60C2×#14556051C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic, complemented
62C2×#14556049C2211yescharacteristic, 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
79C22×Dic142—21no—
80C22×Dic142C2311yescharacteristic
81C2×Q8×D71—22no—
82C2×Q8×D71—42no—
83C2×Q8×D71—42no—
84C2×Q8×D71C2314yescomplemented
85C22×D284—21no—
86C22×D284C2311yescharacteristic
87C22×C22⋊D71—21no—
88C22×C22⋊D71—21no—
89C22×C22⋊D71—21no—
90C2×D4×D71—28no—
91C2×D4×D71—22no—
92C2×D4×D71—42no—
93C2×D4×D71—42no—
94C2×D4×D71—48no—
95C2×D4×D71C2314yes—
96C23×Dic71D411yescharacteristic
97C22×C4×D71—21no—
98C22×C4×D71—21no—
99C22×C4×D71—21no—
100C22×C4×D71—42no—
101C22×C4×D71—42no—
102C22×C4×D71D411yescharacteristic
103C22×C4×D71D411yescharacteristic
104C22×C4×D71D414yes—
105C22×C4×D71C2311yescharacteristic
106C22×C4×D71C2311yescharacteristic
107C22×C4×D71C2314yes—
108C2×#11765854—42no—
109C2×#11765854C2314yescomplemented
110C2×#11765853—42no—
111C2×#11765853C2314yescomplemented
112C2×#11765852—42no—
113C2×#11765852C2314yescomplemented
114C2×#11765849—42no—
115C2×#11765849C2314yescomplemented
116C22×C71⋊C8C2311yescharacteristic
117C22×C71⋊C8C2311yescharacteristic
118#14556108—22no—
119#14556108C2314yes—
120#14556107—22no—
121#14556107C2314yescomplemented
122#14556106—28no—
123#14556105—28no—
124#14556104—22no—
125#14556104C2314yes—
126#14556103—22no—
127#14556103C2314yes—
128#14556102—22no—
129#14556102C2314yes—
130#14556101—28no—
131#14556100—28no—
132#14556099—22no—
133#14556099C2314yes—
134C2×C4⋊Dic71—21no—
135C2×C4⋊Dic71C2311yescharacteristic
136C2×C4⋊Dic71C2311yescharacteristic
137C2×Dic71⋊C4—21no—
138C2×Dic71⋊C4—21no—
139C2×Dic71⋊C4—21no—
140C2×Dic71⋊C4—21no—
141C4⋊C4×D71—28no—
142C4⋊C4×D71—22no—
143C4⋊C4×D71—22no—
144C4⋊C4×D71C2314yes—
145C4⋊C4×D71C2314yescomplemented
146C2×C22⋊Dic71—21no—
147C2×C22⋊Dic71—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—
153C22⋊C4×D71—28no—
154#14556062C2314yescomplemented
155#14556061C2314yescomplemented
156#14556061C2314yescomplemented
157#14556053C2314yescomplemented
158#14556052C2314yescomplemented
159#14556051C2314yescomplemented
160#14556050C2314yescomplemented
161#14556049C2314yescomplemented
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—24no—
191C23×D71—21no—
192C23×D71—24no—
193C23×D71—42no—
194C23×D71—44no—
195C23×D71—44no—
196C23×D71—44no—
197C23×D71C2×D414yes—
198C23×D71C2×D411yescharacteristic
199C23×D71C2×D411yescharacteristic
200C2×Dic142—22no—
201C2×Dic142—22no—
202C2×Dic142—21no—
203C2×Dic142—24no—
204C2×Dic142—44no—
205C2×Dic142C2412yes—
206Q8×D71—44no—
207Q8×D71—44no—
208Q8×D71—48no—
209C2×D284—22no—
210C2×D284—22no—
211C2×D284—24no—
212C2×D284—21no—
213C2×D284—44no—
214C2×D284C2412yes—
215C2×C22⋊D71—24no—
216C2×C22⋊D71—24no—
217C2×C22⋊D71—24no—
218C2×C22⋊D71—44no—
219C2×C22⋊D71—44no—
220C2×C22⋊D71—44no—
221D4×D71—44no—
222D4×D71—44no—
223D4×D71—48no—
224D4×D71—432no—
225C22×Dic71—21no—
226C22×Dic71—21no—
227C22×Dic71—21no—
228C22×Dic71—42no—
229C22×Dic71C2×D411yescharacteristic
230C22×Dic71C2×D411yescharacteristic
231C22×Dic71C2×D414yes—
232C2×C4×D71—22no—
233C2×C4×D71—22no—
234C2×C4×D71—22no—
235C2×C4×D71—22no—
236C2×C4×D71—24no—
237C2×C4×D71—24no—
238C2×C4×D71—24no—
239C2×C4×D71—48no—
240C2×C4×D71—44no—
241C2×C4×D71—44no—
242C2×C4×D71—42no—
243C2×C4×D71—42no—
244C2×C4×D71—44no—
245C2×C4×D71—44no—
246C2×C4×D71—44no—
247C2×C4×D71C2×D412yes—
248C2×C4×D71C2×D412yes—
249C2×C4×D71C2×D414yes—
250C2×C4×D71C2×D414yes—
251C2×C4×D71C2412yes—
252C2×C4×D71C2412yes—
253#11765854—44no—
254#11765853—44no—
255#11765852—44no—
256#11765849—44no—
257C2×C71⋊C8—22no—
258C2×C71⋊C8—22no—
259C2×C71⋊C8C2412yes—
260C2×C71⋊C8C2412yes—
261C4⋊Dic71—21no—
262C4⋊Dic71—21no—
263C4⋊Dic71—24no—
264C4⋊Dic71C2412yes—
265C4⋊Dic71C2412yes—
266Dic71⋊C4—24no—
267Dic71⋊C4—24no—
268Dic71⋊C4—24no—
269Dic71⋊C4—24no—
270C22⋊Dic71—24no—
271C22⋊Dic71—24no—
272(C2×D71)⋊C4—24no—
273(C2×D71)⋊C4—24no—
274(C2×D71)⋊C4—24no—
275(C2×D71)⋊C4—24no—
276C24×C71—21no—
277C24×C71C2×D411yescharacteristic
278C2×Q8×C71—21no—
279C2×Q8×C71—22no—
280C2×Q8×C71—22no—
281C2×Q8×C71C2412yes—
282C2×D4×C71—24no—
283C2×D4×C71—21no—
284C2×D4×C71—22no—
285C2×D4×C71—22no—
286C2×D4×C71—44no—
287C2×D4×C71C2412yes—
288C22×C4×C71—22no—
289C22×C4×C71—22no—
290C22×C4×C71—21no—
291C22×C4×C71—21no—
292C22×C4×C71—21no—
293C22×C4×C71C2×D411yescharacteristic
294C22×C4×C71C2×D412yes—
295C22×C4×C71C2412yes—
296C22×C4×C71C2411yescharacteristic
297SD16×C71—44no—
298M16×C71—44no—
299C2×C8×C71—22no—
300C2×C8×C71—22no—
301C2×C8×C71C2412yes—
302C2×C8×C71C2412yes—
303C4⋊C4×C71—24no—
304C4⋊C4×C71—21no—
305C4⋊C4×C71—21no—
306C4⋊C4×C71C2412yes—
307C4⋊C4×C71C2412yes—
308C22⋊C4×C71—24no—
309C22⋊C4×C71—24no—
310C23×C71—22no—
311C23×C71—22no—
312C23×C71—22no—
313C23×C71—22no—
314C23×C71—42no—
315C23×C71—42no—
316C23×C71—42no—
317C23×C71C22×D412yes—
318C23×C71C22×D411yescharacteristic
319C22×D71—22no—
320C22×D71—22no—
321C22×D71—22no—
322C22×D71—22no—
323C22×D71—28no—
324C22×D71—28no—
325C22×D71—22no—
326C22×D71—44no—
327C22×D71—416no—
328C22×D71—48no—
329C22×D71—48no—
330C22×D71—42no—
331C22×D71—42no—
332C22×D71—42no—
333C22×D71—48no—
334C22×D71—816no—
335C22×D71AGL(1,ℤ/8)14yes—
336C22×D71#13714yes—
337C22×D71C22×D412yes—
338C22×D71C22×D412yes—
339Q8×C71—22no—
340Q8×C71—22no—
341Q8×C71—42no—
342D4×C71—22no—
343D4×C71—22no—
344D4×C71—48no—
345D4×C71—42no—
346C2×C4×C71—22no—
347C2×C4×C71—24no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—42no—
354C2×C4×C71—42no—
355C2×C4×C71—42no—
356C2×C4×C71C22×D412yes—
357C2×C4×C71C22×D411yescharacteristic
358C2×C4×C71H(5,𝔽2)12yes—
359C2×C4×C71H(5,𝔽2)12yes—
360C2×C4×C71C2511yescharacteristic
361C22⋊D71—48no—
362C22⋊D71—48no—
363C22⋊D71—48no—
364C2×Dic71—22no—
365C2×Dic71—22no—
366C2×Dic71—22no—
367C2×Dic71—22no—
368C2×Dic71—22no—
369C2×Dic71—44no—
370C2×Dic71—42no—
371C2×Dic71—42no—
372C2×Dic71—42no—
373C2×Dic71C22×D412yes—
374C2×Dic71C22×D412yes—
375D284—22no—
376D284—22no—
377D284—48no—
378D284—42no—
379C4×D71—24no—
380C4×D71—24no—
381C4×D71—22no—
382C4×D71—22no—
383C4×D71—22no—
384C4×D71—22no—
385C4×D71—44no—
386C4×D71—44no—
387C4×D71—48no—
388C4×D71—48no—
389C4×D71—48no—
390Dic142—22no—
391Dic142—22no—
392Dic142—48no—
393Dic142—42no—
394C8×C71—22no—
395C8×C71—22no—
396C71⋊C8—22no—
397C71⋊C8—22no—
398C22×C71—22no—
399C22×C71—22no—
400C22×C71—22no—
401C22×C71—44no—
402C22×C71—42no—
403C22×C71—42no—
404C22×C71—42no—
405C22×C71—84no—
406C22×C71#53412yes—
407C22×C71C2×AGL(1,ℤ/8)12yes—
408C22×C71C2×#13712yes—
409C22×C71C23×D411yescharacteristic
410C2×D71—22no—
411C2×D71—22no—
412C2×D71—28no—
413C2×D71—28no—
414C2×D71—22no—
415C2×D71—22no—
416C2×D71—416no—
417C2×D71—42no—
418C2×D71—42no—
419C2×D71—42no—
420C2×D71—816no—
421C2×D71—84no—
422C2×D71C2×AGL(1,ℤ/8)14yes—
423C2×D71C2×#13714yes—
424C4×C71—22no—
425C4×C71—42no—
426C4×C71—42no—
427C4×C71—42no—
428C4×C71#53412yes—
429C4×C71C2×H(5,𝔽2)11yescharacteristic
430C4×C71C2×H(5,𝔽2)11yescharacteristic
431Dic71—22no—
432Dic71—22no—
433Dic71—42no—
434Dic71—42no—
435Dic71—42no—
436C2×#3193—711nomaximal, Sylow
437C2×C71—42no—
438C2×C71—82no—
439C2×C71#319314yescomplemented
440C2×C71C2×#53411yescharacteristic
441C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
442C2×C71C22×#13711yescharacteristic
443D71—24no—
444D71—24no—
445D71—82no—
446C22×C22⋊Q8—711no—
447C22×#121—711no—
448#3193—7116no—
449C2×#484—711no—
450C2×#484—711no—
451C2×#480—711no—
452C2×#480—711no—
453C2×#468—711no—
454C2×#468—711no—
455C2×#468—711no—
456C2×#468D7111yescharacteristic, complemented
457C2×#448—711no—
458C2×#448—711no—
459C2×#450—711no—
460C2×#450—711no—
461C2×#407—711no—
462C71C2×#319311yescharacteristic, complemented, Sylow
463C23×Q8—711no—
464C23×D4—711no—
465C23×D4—1421no—
466C24×C4—711no—
467C22×SD16—711no—
468C22×SD16—711no—
469C22×SD16—711no—
470C22×SD16C2×D7111yescharacteristic, complemented
471C22×M16—711no—
472C22×M16C2×D7111yescharacteristic, complemented
473C2×C22⋊Q8—711no—
474C2×C22⋊Q8—711no—
475C2×C22⋊Q8—718no—
476C2×C22⋊Q8—711no—
477C2×C22⋊Q8—1421no—
478C2×C22⋊Q8—1421no—
479C2×C22⋊Q8—1424no—
480C2×C22⋊Q8C2×D7111yescharacteristic, complemented
481C2×#121—711no—
482C2×#121—711no—
483C2×#121—718no—
484C2×#121—711no—
485C2×#121—1421no—
486C2×#121—1424no—
487C2×#121—1421no—
488C2×#121C2×D7111yescharacteristic
489C22×C4⋊C4—711no—
490C22×C4⋊C4—711no—
491C22×C4⋊C4—1421no—
492C22×C22⋊C4—1421no—
493C22×C22⋊C4—1421no—
494#484—718no—
495#484—718no—
496#480—718no—
497#480—718no—
498#468—718no—
499#468—718no—
500#468—718no—
501#468C2×D7118yescomplemented
502#450—718no—
503#450—718no—
504#448—718no—
505#448—718no—
506C2×#107—711no—
507C2×#107—711no—
508C2×#107—711no—
509C2×#107C2×D7111yescharacteristic, complemented
510C2×#103—711no—
511C2×#103—711no—
512C2×#103—711no—
513C2×#103C2×D7111yescharacteristic, complemented
514C2×#102—711no—
515C2×#102—711no—
516C2×#102—711no—
517C2×#102C2×D7111yescharacteristic, complemented
518#407—718no—
519C2×C22⋊C8—711no—
520C2×C22⋊C8—711no—
521C2×C22⋊C8—711no—
522C2×C22⋊C8—711no—
523C25—711no—
524C25—1421no—
525C22×Q8—2842no—
526C22×Q8—2842no—
527C22×Q8—714no—
528C22×Q8—711no—
529C22×Q8—1421no—
530C22×Q8—1422no—
531C22×Q8C22×D7111yescharacteristic
532C22×D4—21no—
533C22×D4—2848no—
534C22×D4—2842no—
535C22×D4—2842no—
536C22×D4—714no—
537C22×D4—711no—
538C22×D4—1421no—
539C22×D4—1422no—
540C22×D4—1421no—
541C22×D4—1428no—
542C22×D4—1421no—
543C22×D4—1421no—
544C22×D4C22×D7111yescharacteristic
545C23×C4—2842no—
546C23×C4—2842no—
547C23×C4—711no—
548C23×C4—711no—
549C23×C4—711no—
550C23×C4—714no—
551C23×C4—714no—
552C23×C4—711no—
553C23×C4—711no—
554C23×C4—1421no—
555C23×C4—1421no—
556C23×C4—1421no—
557C23×C4C22×D7111yescharacteristic
558C2×SD16—42no—
559C2×SD16—2842no—
560C2×SD16—2842no—
561C2×SD16—2842no—
562C2×SD16—714no—
563C2×SD16—714no—
564C2×SD16—714no—
565C2×SD16C22×D7114yescomplemented
566C2×M16—42no—
567C2×M16—2842no—
568C2×M16—714no—
569C2×M16C22×D7114yescomplemented
570C22×C8—711no—
571C22×C8—711no—
572C22×C8C22×D7111yescharacteristic
573C22×C8C22×D7111yescharacteristic
574C22⋊Q8—22no—
575C22⋊Q8—714no—
576C22⋊Q8—714no—
577C22⋊Q8—714no—
578C22⋊Q8—1428no—
579C22⋊Q8—1428no—
580C22⋊Q8—1422no—
581C22⋊Q8—1422no—
582C22⋊Q8—1422no—
583C22⋊Q8C22×D7114yescomplemented
584#121—22no—
585#121—714no—
586#121—714no—
587#121—714no—
588#121—1428no—
589#121—1422no—
590#121—1422no—
591#121—1428no—
592#121—1422no—
593#121C22×D7114yes—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—711no—
596C2×C4⋊C4—711no—
597C2×C4⋊C4—714no—
598C2×C4⋊C4—714no—
599C2×C4⋊C4—1422no—
600C2×C4⋊C4—1422no—
601C2×C4⋊C4—1428no—
602C2×C4⋊C4—1421no—
603C2×C4⋊C4—1421no—
604C2×C4⋊C4—1421no—
605C2×C4⋊C4—1421no—
606C2×C4⋊C4—1421no—
607C2×C4⋊C4C22×D7111yescharacteristic
608C2×C4⋊C4C22×D7111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—1428no—
612C2×C22⋊C4—1428no—
613C2×C22⋊C4—1421no—
614C2×C22⋊C4—1421no—
615C2×C22⋊C4—1421no—
616C2×C22⋊C4—1421no—
617C2×C22⋊C4—1421no—
618C2×C22⋊C4—1421no—
619#107—714no—
620#107—714no—
621#107—714no—
622#107C22×D7114yescomplemented
623#103—714no—
624#103—714no—
625#103—714no—
626#103C22×D7114yescomplemented
627#102—714no—
628#102—714no—
629#102—714no—
630#102C22×D7114yescomplemented
631C22⋊C8—714no—
632C22⋊C8—714no—
633C22⋊C8—714no—
634C22⋊C8—714no—
635C24—21no—
636C24—2842no—
637C24—2844no—
638C24—2844no—
639C24—2844no—
640C24—714no—
641C24—711no—
642C24—711no—
643C24—1424no—
644C24—1424no—
645C24—1424no—
646C24—1421no—
647C24D4×D7111yescharacteristic
648C2×Q8—21no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—2844no—
652C2×Q8—2844no—
653C2×Q8—2844no—
654C2×Q8—2848no—
655C2×Q8—712no—
656C2×Q8—1424no—
657C2×Q8—1422no—
658C2×Q8—1422no—
659C2×Q8—1421no—
660C2×Q8C23×D7112yes—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—44no—
666C2×D4—2844no—
667C2×D4—28432no—
668C2×D4—2844no—
669C2×D4—2844no—
670C2×D4—2844no—
671C2×D4—2844no—
672C2×D4—2848no—
673C2×D4—2844no—
674C2×D4—712no—
675C2×D4—1424no—
676C2×D4—1424no—
677C2×D4—1424no—
678C2×D4—1424no—
679C2×D4—1421no—
680C2×D4—1422no—
681C2×D4—1422no—
682C2×D4C23×D7112yes—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—2842no—
689C22×C4—2842no—
690C22×C4—2844no—
691C22×C4—2844no—
692C22×C4—2848no—
693C22×C4—2844no—
694C22×C4—2844no—
695C22×C4—2844no—
696C22×C4—2842no—
697C22×C4—714no—
698C22×C4—714no—
699C22×C4—714no—
700C22×C4—711no—
701C22×C4—711no—
702C22×C4—712no—
703C22×C4—712no—
704C22×C4—712no—
705C22×C4—712no—
706C22×C4—1424no—
707C22×C4—1424no—
708C22×C4—1424no—
709C22×C4—1421no—
710C22×C4—1421no—
711C22×C4—1421no—
712C22×C4—1422no—
713C22×C4—1422no—
714C22×C4—1422no—
715C22×C4—1422no—
716C22×C4D4×D7112yes—
717C22×C4D4×D7111yescharacteristic
718C22×C4C23×D7112yes—
719C22×C4C23×D7111yescharacteristic
720SD16—44no—
721SD16—2844no—
722SD16—2844no—
723SD16—2844no—
724M16—44no—
725M16—2844no—
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—712no—
729C2×C8—712no—
730C2×C8—1422no—
731C2×C8—1422no—
732C2×C8C23×D7112yes—
733C2×C8C23×D7112yes—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—712no—
738C4⋊C4—712no—
739C4⋊C4—1424no—
740C4⋊C4—1424no—
741C4⋊C4—1424no—
742C4⋊C4—1424no—
743C4⋊C4—1424no—
744C4⋊C4—1421no—
745C4⋊C4—1421no—
746C4⋊C4C23×D7112yes—
747C4⋊C4C23×D7112yes—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—1424no—
751C22⋊C4—1424no—
752C22⋊C4—1424no—
753C22⋊C4—1424no—
754C22⋊C4—1424no—
755C22⋊C4—1424no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—2844no—
764C23—28416no—
765C23—2848no—
766C23—2848no—
767C23—2848no—
768C23—2842no—
769C23—2842no—
770C23—2842no—
771C23—56816no—
772C23—712no—
773C23—712no—
774C23—714no—
775C23—714no—
776C23—1428no—
777C23—1428no—
778C23—1422no—
779C23—1422no—
780C23—1422no—
781C23—1422no—
782C23—1422no—
783C23C2×D4×D7112yes—
784C23C2×D4×D7111yescharacteristic
785Q8—22no—
786Q8—22no—
787Q8—42no—
788Q8—2848no—
789Q8—2842no—
790Q8—1422no—
791Q8—1422no—
792D4—22no—
793D4—22no—
794D4—48no—
795D4—42no—
796D4—2848no—
797D4—2848no—
798D4—2848no—
799D4—2848no—
800D4—2842no—
801D4—1422no—
802D4—1422no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—2844no—
814C2×C4—2844no—
815C2×C4—2848no—
816C2×C4—2848no—
817C2×C4—2848no—
818C2×C4—2842no—
819C2×C4—2842no—
820C2×C4—2842no—
821C2×C4—2844no—
822C2×C4—712no—
823C2×C4—712no—
824C2×C4—1422no—
825C2×C4—1422no—
826C2×C4—1422no—
827C2×C4—1422no—
828C2×C4—1422no—
829C2×C4—1422no—
830C2×C4—1422no—
831C2×C4—1422no—
832C2×C4—1422no—
833C2×C4—1424no—
834C2×C4—1424no—
835C2×C4C2×D4×D7112yes—
836C2×C4C2×D4×D7111yescharacteristic
837C2×C4#1455617312yes—
838C2×C4#1455617412yes—
839C2×C4C24×D7111yescharacteristic
840C8—22no—
841C8—22no—
842C8—1422no—
843C8—1422no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—44no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—28416no—
853C22—2842no—
854C22—2842no—
855C22—2842no—
856C22—56816no—
857C22—5684no—
858C22—714no—
859C22—714no—
860C22—1422no—
861C22—1422no—
862C22—1422no—
863C22—1422no—
864C22—1428no—
865C22—1428no—
866C22#1798655712yes—
867C22AGL(1,ℤ/8)×D7112yes—
868C22#137×D7112yes—
869C22C22×D4×D7111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—2842no—
875C4—2842no—
876C4—2842no—
877C4—1422no—
878C4—1422no—
879C4#1798655712yes—
880C4C2×#1455617311yescharacteristic
881C4C2×#1455617411yescharacteristic
882C2—42no—
883C2—82no—
884C2—5682no—
885C2—1424no—
886C2—1424no—
887C2#2259914114yesdirect product factor
888C2C2×#1798655711yescharacteristic
889C2C2×AGL(1,ℤ/8)×D7111yescharacteristic
890C2C2×#137×D7111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#468×C71C2
socleC23×C71C22×D4
prime radicalC2×#121×D71C2
hypercenterC2×#468D71
hypocenterC71C2×#3193
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×C22⋊Q8×D71C2semidirect
3. #22599141C2direct (N × H)
4. C2×#17986336C2semidirect
5. C2×#17986333C2semidirect
6. C2×#17986314C2semidirect
7. C2×#17986311C2semidirect
8. C2×#17986247C2semidirect
9. C2×#17986245C2semidirect
10. C2×#17986243C2semidirect
11. C2×#17986139C2semidirect
12. C2×#17986136C2semidirect
13. C2×#17986151C2semidirect
14. C2×#17986148C2semidirect
15. C2×#17985962C2semidirect
16. C2×#468×C71C2semidirect
17. C22×Q8×D71C22semidirect
21. C22×#11765854C22semidirect
22. C22×#11765853C22semidirect
23. C22×#11765852C22semidirect
24. C22×#11765849C22semidirect
26. C2×#14556107C22semidirect
31. C22⋊Q8×D71C22semidirect
41. C2×C4⋊C4×D71C22semidirect
44. #17986336C22semidirect
45. #17986333C22semidirect
46. #17986314C22semidirect
47. #17986311C22semidirect
48. #17986247C22semidirect
49. #17986245C22semidirect
50. #17986243C22semidirect
51. #17986151C22semidirect
52. #17986148C22semidirect
53. #17986139C22semidirect
54. #17986136C22semidirect
55. C2×#14556062C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556061C22semidirect
58. C2×#14556053C22semidirect
59. C2×#14556052C22semidirect
60. C2×#14556051C22semidirect
61. C2×#14556050C22semidirect
62. C2×#14556049C22semidirect
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
84. C2×Q8×D71C23semidirect
109. C2×#11765854C23semidirect
111. C2×#11765853C23semidirect
113. C2×#11765852C23semidirect
115. C2×#11765849C23semidirect
121. #14556107C23semidirect
145. C4⋊C4×D71C23semidirect
154. #14556062C23semidirect
155. #14556061C23semidirect
156. #14556061C23semidirect
157. #14556053C23semidirect
158. #14556052C23semidirect
159. #14556051C23semidirect
160. #14556050C23semidirect
161. #14556049C23semidirect
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
439. C2×C71#3193semidirect
456. C2×#468D71semidirect
462. C71C2×#3193semidirect
470. C22×SD16C2×D71semidirect
472. C22×M16C2×D71semidirect
480. C2×C22⋊Q8C2×D71semidirect
501. #468C2×D71semidirect
509. C2×#107C2×D71semidirect
513. C2×#103C2×D71semidirect
517. C2×#102C2×D71semidirect
565. C2×SD16C22×D71semidirect
569. C2×M16C22×D71semidirect
583. C22⋊Q8C22×D71semidirect
622. #107C22×D71semidirect
626. #103C22×D71semidirect
630. #102C22×D71semidirect
887. C2#22599141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D712
C2×#121×D712
#225991412
C2×#179863362
C2×#179863332
C2×#179863142
C2×#179863112
C2×#179862472
C2×#179862452
C2×#179862432
C2×#179861392
C2×#179861362
C2×#179861512
C2×#179861482
C2×#179859622
C2×#468×C712
C2×#319371