Finite Group Databasebeta

← C2×#22601299 #32877994

Subgroups — C2×#22601299 #32877994

Order 18176.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986708C211yesmaximal, characteristic, complemented
2C2×#17986706C211yesmaximal, characteristic, complemented
3#22601299C2116yesmaximal, direct product factor
4C2×#17986408C211yesmaximal, characteristic, complemented
5C2×#17986406C211yesmaximal, characteristic, complemented
6C2×#17986399C211yesmaximal, characteristic, complemented
7C2×#17986301C211yesmaximal, characteristic, complemented
8C2×#17986301C211yesmaximal, characteristic, complemented
9C2×#17986299C211yesmaximal, characteristic, complemented
10C2×#17986297C211yesmaximal, characteristic, complemented
11C2×#17986279C211yesmaximal, characteristic, complemented
12C2×#17986277C211yesmaximal, characteristic, complemented
13C2×#17986127C211yesmaximal, characteristic, complemented
14C2×#17986111C211yesmaximal, characteristic
15C2×D8×Dic71C211yesmaximal, characteristic
16C2×#442×C71C211yesmaximal, characteristic
17#17986708—24no—
18#17986708C2218yescomplemented
19#17986706—24no—
20#17986706C2218yescomplemented
21C2×#14556128C2211yescharacteristic
22C2×#14556127C2211yescharacteristic
23C2×#14556120C2211yescharacteristic
24C2×#14556119C2211yescharacteristic
25C2×#14556119C2211yescharacteristic
26C2×#14556119C2211yescharacteristic
27C2×#14556107—21no—
28C2×#14556107—21no—
29C2×#14556105—21no—
30C2×#14556105—21no—
31C2×#14556105—21no—
32C2×#14556105—21no—
33C2×C4×Dic142C2211yescharacteristic
34C2×D4×Dic71C2211yescharacteristic
35C2×D4×Dic71C2211yescharacteristic
36C2×D4×Dic71C2211yescharacteristic
37C2×D4×Dic71C2211yescharacteristic
38C22×C4⋊Dic71—21no—
39C22×Dic71⋊C4—21no—
40#17986408C2218yescomplemented
41#17986406C2218yescomplemented
42#17986399C2218yescomplemented
43#17986301C2218yescomplemented
44#17986301C2218yescomplemented
45#17986299C2218yescomplemented
46#17986297C2218yescomplemented
47#17986279C2218yescomplemented
48#17986277C2218yescomplemented
49#17986127C2218yescomplemented
50#17986111C2218yes—
51D8×Dic71C2218yes—
52C2×#14556062C2211yescharacteristic
53C2×#14556062C2211yescharacteristic
54C2×#14556061C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556060C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556059C2211yescharacteristic
60C2×C4⋊(C71⋊C8)C2211yescharacteristic
61C2×Dic71⋊C8C2211yescharacteristic
62C2×Dic71⋊C8C2211yescharacteristic
63C2×#14556049C2211yescharacteristic
64C2×#14556049C2211yescharacteristic
65C2×#14556049C2211yescharacteristic
66C2×#14556049C2211yescharacteristic
67C2×#14556038C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C22×D8×C71C2211yescharacteristic
70C2×C4×D4×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72#442×C71C2218yes—
73C2×#106×C71C2211yescharacteristic
74C2×#102×C71C2211yescharacteristic
75C2×#102×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142D411yescharacteristic
80C23×Dic71—21no—
81C23×Dic71—21no—
82C23×Dic71—21no—
83C23×Dic71—21no—
84C22×C71⋊C8C2311yescharacteristic
85C22×C71⋊C8C2311yescharacteristic
86#14556128—22no—
87#14556128C2314yes—
88#14556127—22no—
89#14556127C2314yes—
90#14556120—22no—
91#14556120C2314yes—
92#14556119—22no—
93#14556119—22no—
94#14556119—22no—
95#14556119C2314yes—
96#14556119C2314yes—
97#14556119C2314yes—
98#14556107—28no—
99#14556107—28no—
100#14556105—28no—
101#14556105—28no—
102#14556105—28no—
103#14556105—28no—
104C4×Dic142D414yes—
105C4×Dic142C2314yes—
106D4×Dic71—22no—
107D4×Dic71—22no—
108D4×Dic71—22no—
109D4×Dic71—22no—
110D4×Dic71C2314yes—
111D4×Dic71C2314yes—
112D4×Dic71C2314yes—
113D4×Dic71C2314yes—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71—21no—
116C2×C4⋊Dic71—21no—
117C2×C4⋊Dic71—28no—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71D411yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—28no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4D411yescharacteristic
132C2×Dic71⋊C4D411yescharacteristic
133C2×C22⋊Dic71—21no—
134C2×C22⋊Dic71—21no—
135C2×C22⋊Dic71—21no—
136C2×C22⋊Dic71—21no—
137C2×C4×Dic71C2311yescharacteristic
138C2×C4×Dic71C2311yescharacteristic
139#14556062C2314yes—
140#14556062C2314yes—
141#14556061C2314yes—
142#14556061C2314yes—
143#14556061C2314yes—
144#14556060C2314yes—
145#14556060C2314yes—
146#14556059C2314yes—
147C4⋊(C71⋊C8)C2314yes—
148Dic71⋊C8C2314yes—
149Dic71⋊C8C2314yes—
150#14556049C2314yes—
151#14556049C2314yes—
152#14556049C2314yes—
153#14556049C2314yes—
154#14556038C2314yes—
155C8×Dic71C2314yes—
156C22×D4×C71C2311yescharacteristic
157C22×D4×C71C2311yescharacteristic
158C23×C4×C71—21no—
159C23×C4×C71—21no—
160C2×D8×C71Q818yescomplemented
161C2×D8×C71C2314yes—
162C22×C8×C71C2311yescharacteristic
163C22×C8×C71C2311yescharacteristic
164C4×D4×C71—22no—
165C4×D4×C71—22no—
166C4×D4×C71C2314yes—
167C4×D4×C71C2314yes—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C22⋊C4×C71—21no—
171C2×C22⋊C4×C71—21no—
172C2×C42×C71C2311yescharacteristic
173#106×C71C2314yes—
174#102×C71C2314yes—
175#102×C71C2314yes—
176#97×C71C2314yes—
177C2×Dic142—24no—
178C2×Dic142—24no—
179C2×Dic142—42no—
180C2×Dic142—82no—
181C2×Dic142—82no—
182C2×Dic142C2×D414yes—
183C22×Dic71—21no—
184C22×Dic71—21no—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C22×Dic71—24no—
188C22×Dic71—24no—
189C22×Dic71—24no—
190C22×Dic71—24no—
191C22×Dic71—44no—
192C22×Dic71—82no—
193C22×Dic71—82no—
194C22×Dic71—82no—
195C22×Dic71C2×D411yescharacteristic
196C22×Dic71C2×D411yescharacteristic
197C22×Dic71C2×D411yescharacteristic
198C22×Dic71C2×D411yescharacteristic
199C2×C71⋊C8—22no—
200C2×C71⋊C8—22no—
201C2×C71⋊C8C2412yes—
202C2×C71⋊C8C2412yes—
203C4⋊Dic71—24no—
204C4⋊Dic71—21no—
205C4⋊Dic71—21no—
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—24no—
209C4⋊Dic71—24no—
210C4⋊Dic71—24no—
211C4⋊Dic71C2×D414yes—
212C4⋊Dic71C2412yes—
213C4⋊Dic71C2412yes—
214C4⋊Dic71C2412yes—
215C4⋊Dic71C2412yes—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4C2×D414yes—
223Dic71⋊C4C2×D414yes—
224C22⋊Dic71—24no—
225C22⋊Dic71—24no—
226C22⋊Dic71—24no—
227C22⋊Dic71—24no—
228C4×Dic71C2×D412yes—
229C4×Dic71C2×D412yes—
230C4×Dic71C2412yes—
231C4×Dic71C2412yes—
232C24×C71—21no—
233C24×C71—21no—
234C2×D4×C71—21no—
235C2×D4×C71—21no—
236C2×D4×C71—22no—
237C2×D4×C71—22no—
238C2×D4×C71C2×Q814yes—
239C2×D4×C71C2×Q814yes—
240C2×D4×C71C2412yes—
241C2×D4×C71C2412yes—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—24no—
245C22×C4×C71—24no—
246C22×C4×C71—44no—
247C22×C4×C71—82no—
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2411yescharacteristic
251D8×C71C2×Q8116yescomplemented
252C2×C8×C71—22no—
253C2×C8×C71C2×Q814yes—
254C2×C8×C71C2412yes—
255C2×C8×C71C2412yes—
256C4⋊C4×C71—21no—
257C4⋊C4×C71—21no—
258C4⋊C4×C71C2412yes—
259C4⋊C4×C71C2412yes—
260C22⋊C4×C71—24no—
261C22⋊C4×C71—24no—
262C42×C71C2×D412yes—
263C42×C71C2412yes—
264C23×C71—24no—
265C23×C71—24no—
266C23×C71—22no—
267C23×C71—22no—
268C23×C71—42no—
269C23×C71—42no—
270C23×C71—42no—
271C23×C71—42no—
272C23×C71C22×D411yescharacteristic
273D4×C71—24no—
274D4×C71—24no—
275D4×C71—22no—
276D4×C71—22no—
277D4×C71C22×Q814yes—
278D4×C71C22×Q814yes—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—48no—
284C2×C4×C71—42no—
285C2×C4×C71—42no—
286C2×C4×C71—84no—
287C2×C4×C71C22×D412yes—
288C2×C4×C71C22×D412yes—
289C2×C4×C71C22×D411yescharacteristic
290C2×C4×C71C22×Q812yes—
291C2×C4×C712−1+412yes—
292C2×C4×C71C2511yescharacteristic
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—48no—
302C2×Dic71—42no—
303C2×Dic71—42no—
304C2×Dic71—42no—
305C2×Dic71—42no—
306C2×Dic71—84no—
307C2×Dic71—84no—
308C2×Dic71—84no—
309C2×Dic71C22×D412yes—
310C2×Dic71C22×D412yes—
311C2×Dic71C22×D412yes—
312C2×Dic71C22×D412yes—
313Dic142—44no—
314Dic142—84no—
315Dic142—84no—
316C8×C71—22no—
317C8×C71C22×Q814yes—
318C71⋊C8—22no—
319C71⋊C8—22no—
320C22×C71—24no—
321C22×C71—24no—
322C22×C71—48no—
323C22×C71—48no—
324C22×C71—42no—
325C22×C71—42no—
326C22×C71—42no—
327C22×C71—42no—
328C22×C71D4×Q812yes—
329C22×C71#57512yes—
330C22×C71#57612yes—
331C22×C71C23×D411yescharacteristic
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—42no—
335C4×C71—42no—
336C4×C71D4×Q812yes—
337C4×C71C23×Q811yescharacteristic
338C4×C71C2×2−1+411yescharacteristic
339Dic71—22no—
340Dic71—22no—
341Dic71—22no—
342Dic71—22no—
343Dic71—42no—
344Dic71—42no—
345Dic71—42no—
346Dic71—42no—
347C2×#3389—711nomaximal, Sylow
348C2×C71—44no—
349C2×C71—44no—
350C2×C71#338914yescomplemented
351C2×C71C2×D4×Q811yescharacteristic
352C2×C71C2×#57511yescharacteristic
353C2×C71C2×#57611yescharacteristic
354C2×#554—711no—
355C2×#554—711no—
356#3389—7116no—
357C2×#501—711no—
358C2×#501—711no—
359C2×#499—711no—
360C2×#478—711no—
361C2×#478—711no—
362C2×#478—711no—
363C2×#478—711no—
364C2×#474—711no—
365C2×#474—711no—
366C2×#446—711no—
367C2×#442—711no—
368C2×#442D7111yescharacteristic
369C2×C4×D8—711no—
370C71C2×#338911yescharacteristic, complemented, Sylow
371C22×D8C2×D7111yescharacteristic
372#554—718no—
373#554—718no—
374#554—1424no—
375#554—1424no—
376C2×C4⋊Q8—711no—
377C2×C4⋊Q8—711no—
378C2×#125—711no—
379C2×#125—711no—
380C2×#125—711no—
381C2×#125—711no—
382C2×C22⋊Q8—1421no—
383C2×C22⋊Q8—1421no—
384C2×C22⋊Q8—1421no—
385C2×C22⋊Q8—1421no—
386C2×C22⋊Q8—1421no—
387C2×C22⋊Q8—1421no—
388C2×C4×Q8—711no—
389C2×C4×D4—711no—
390C2×C4×D4—711no—
391C2×C4×D4—711no—
392C2×C4×D4—711no—
393C2×C4×D4C2×D7111yescharacteristic
394C2×C4×D4C2×D7111yescharacteristic
395C22×C4⋊C4—1421no—
396C22×C4⋊C4—1421no—
397#501—718no—
398#501—718no—
399#499—718no—
400#478—718no—
401#478—718no—
402#478—718no—
403#478—718no—
404#474—718no—
405#474—718no—
406#446—718no—
407#442—718no—
408#442C2×D7118yes—
409C4×D8—718no—
410C2×#107—711no—
411C2×#107—711no—
412C2×#107—711no—
413C2×#107—711no—
414C2×#107—711no—
415C2×#106—711no—
416C2×#106—711no—
417C2×#106—711no—
418C2×#106C2×D7111yescharacteristic
419C2×C4⋊C8—711no—
420C2×C4⋊C8—711no—
421C2×C4⋊C8—711no—
422C2×#102—711no—
423C2×#102—711no—
424C2×#102—711no—
425C2×#102—711no—
426C2×#102C2×D7111yescharacteristic
427C2×#102C2×D7111yescharacteristic
428C2×#97—711no—
429C2×#97C2×D7111yescharacteristic
430C2×C4×C8—711no—
431C22×Q8—711no—
432C22×Q8—1421no—
433C22×Q8—1421no—
434C22×D4C22×D7111yescharacteristic
435C22×D4C22×D7111yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—1421no—
439C23×C4—1421no—
440C23×C4—1421no—
441C23×C4—1421no—
442C2×D8Dic14218yescomplemented
443C2×D8C22×D7114yes—
444C22×C8—711no—
445C22×C8—711no—
446C22×C8C22×D7111yescharacteristic
447C22×C8C22×D7111yescharacteristic
448C4⋊Q8—714no—
449C4⋊Q8—714no—
450C4⋊Q8—1422no—
451C4⋊Q8—1422no—
452#125—714no—
453#125—714no—
454#125—714no—
455#125—714no—
456#125—1422no—
457#125—1422no—
458#125—1422no—
459#125—1422no—
460C22⋊Q8—1428no—
461C22⋊Q8—1428no—
462C22⋊Q8—1428no—
463C22⋊Q8—1428no—
464C22⋊Q8—1428no—
465C22⋊Q8—1428no—
466C4×Q8—714no—
467C4×Q8—714no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—714no—
471C4×D4—714no—
472C4×D4—714no—
473C4×D4—714no—
474C4×D4—1422no—
475C4×D4—1422no—
476C4×D4—1422no—
477C4×D4—1422no—
478C4×D4C22×D7114yes—
479C4×D4C22×D7114yes—
480C2×C4⋊C4—711no—
481C2×C4⋊C4—711no—
482C2×C4⋊C4—711no—
483C2×C4⋊C4—711no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—1428no—
488C2×C4⋊C4—1428no—
489C2×C4⋊C4—1421no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4—1421no—
492C2×C4⋊C4—1421no—
493C2×C4⋊C4—1421no—
494C2×C4⋊C4—1421no—
495C2×C4⋊C4—1421no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4—1421no—
498C2×C4⋊C4—1421no—
499C2×C4⋊C4C22×D7111yescharacteristic
500C2×C4⋊C4C22×D7111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—1421no—
504C2×C22⋊C4—1421no—
505C2×C22⋊C4—1421no—
506C2×C22⋊C4—1421no—
507C2×C42—711no—
508C2×C42—711no—
509C2×C42C22×D7111yescharacteristic
510#107—714no—
511#107—714no—
512#107—714no—
513#107—714no—
514#107—714no—
515#106—714no—
516#106—714no—
517#106—714no—
518#106C22×D7114yes—
519C4⋊C8—714no—
520C4⋊C8—714no—
521C4⋊C8—714no—
522#102—714no—
523#102—714no—
524#102—714no—
525#102—714no—
526#102C22×D7114yes—
527#102C22×D7114yes—
528#97—714no—
529#97C22×D7114yes—
530C4×C8—714no—
531C24—21no—
532C24—21no—
533C2×Q8—2842no—
534C2×Q8—5682no—
535C2×Q8—5682no—
536C2×Q8—714no—
537C2×Q8—1424no—
538C2×Q8—1424no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4C2×Dic14214yes—
544C2×D4C2×Dic14214yes—
545C2×D4C23×D7112yes—
546C2×D4C23×D7112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—44no—
552C22×C4—82no—
553C22×C4—2844no—
554C22×C4—5682no—
555C22×C4—5682no—
556C22×C4—5682no—
557C22×C4—711no—
558C22×C4—711no—
559C22×C4—711no—
560C22×C4—711no—
561C22×C4—1424no—
562C22×C4—1421no—
563C22×C4—1421no—
564C22×C4—1421no—
565C22×C4—1421no—
566C22×C4—1424no—
567C22×C4—1424no—
568C22×C4—1424no—
569C22×C4D4×D7111yescharacteristic
570C22×C4D4×D7111yescharacteristic
571C22×C4C23×D7111yescharacteristic
572D8C2×Dic142116yescomplemented
573C2×C8—22no—
574C2×C8—712no—
575C2×C8—712no—
576C2×C8—1422no—
577C2×C8—1422no—
578C2×C8C2×Dic14214yes—
579C2×C8C23×D7112yes—
580C2×C8C23×D7112yes—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—714no—
584C4⋊C4—714no—
585C4⋊C4—714no—
586C4⋊C4—712no—
587C4⋊C4—712no—
588C4⋊C4—712no—
589C4⋊C4—712no—
590C4⋊C4—1424no—
591C4⋊C4—1424no—
592C4⋊C4—1424no—
593C4⋊C4—1424no—
594C4⋊C4—1424no—
595C4⋊C4—1424no—
596C4⋊C4—1424no—
597C4⋊C4—1424no—
598C4⋊C4—1424no—
599C4⋊C4—1421no—
600C4⋊C4—1421no—
601C4⋊C4—1421no—
602C4⋊C4—1421no—
603C4⋊C4—1424no—
604C4⋊C4C23×D7112yes—
605C4⋊C4C23×D7112yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—1424no—
609C22⋊C4—1424no—
610C22⋊C4—1424no—
611C22⋊C4—1424no—
612C42—712no—
613C42—712no—
614C42—712no—
615C42—712no—
616C42D4×D7112yes—
617C42C23×D7112yes—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23C2×D4×D7111yescharacteristic
627Q8—2844no—
628Q8—5684no—
629Q8—5684no—
630D4—22no—
631D4—22no—
632D4—24no—
633D4—24no—
634D4C22×Dic14214yes—
635D4C22×Dic14214yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—48no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—84no—
644C2×C4—2842no—
645C2×C4—2842no—
646C2×C4—2842no—
647C2×C4—2842no—
648C2×C4—2848no—
649C2×C4—5684no—
650C2×C4—5684no—
651C2×C4—5684no—
652C2×C4—712no—
653C2×C4—712no—
654C2×C4—712no—
655C2×C4—712no—
656C2×C4—1422no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4C2×D4×D7112yes—
665C2×C4C2×D4×D7112yes—
666C2×C4C2×D4×D7111yescharacteristic
667C2×C4C22×Dic14212yes—
668C2×C4#1455617512yes—
669C2×C4C24×D7111yescharacteristic
670C8—22no—
671C8—1422no—
672C8—1422no—
673C8C22×Dic14214yes—
674C22—24no—
675C22—24no—
676C22—42no—
677C22—42no—
678C22—48no—
679C22—48no—
680C22—42no—
681C22—42no—
682C22D4×Dic14212yes—
683C22#1798679512yes—
684C22#1798680312yes—
685C22C22×D4×D7111yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—2842no—
691C4—2842no—
692C4—2842no—
693C4—2842no—
694C4—1422no—
695C4—1422no—
696C4—1422no—
697C4—1422no—
698C4D4×Dic14212yes—
699C4C23×Dic14211yescharacteristic
700C4C2×#1455617511yescharacteristic
701C2—44no—
702C2—44no—
703C2#2260129914yesdirect product factor
704C2C2×D4×Dic14211yescharacteristic
705C2C2×#1798679511yescharacteristic
706C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#442×C71C2
socleC23×C71C22×D4
prime radicalC22×D8×C71C22
hypercenterC2×#442D71
hypocenterC71C2×#3389
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#17986708C2semidirect
2. C2×#17986706C2semidirect
3. #22601299C2direct (N × H)
4. C2×#17986408C2semidirect
5. C2×#17986406C2semidirect
6. C2×#17986399C2semidirect
7. C2×#17986301C2semidirect
8. C2×#17986301C2semidirect
9. C2×#17986299C2semidirect
10. C2×#17986297C2semidirect
11. C2×#17986279C2semidirect
12. C2×#17986277C2semidirect
13. C2×#17986127C2semidirect
18. #17986708C22semidirect
20. #17986706C22semidirect
40. #17986408C22semidirect
41. #17986406C22semidirect
42. #17986399C22semidirect
43. #17986301C22semidirect
44. #17986301C22semidirect
45. #17986299C22semidirect
46. #17986297C22semidirect
47. #17986279C22semidirect
48. #17986277C22semidirect
49. #17986127C22semidirect
160. C2×D8×C71Q8semidirect
251. D8×C71C2×Q8semidirect
350. C2×C71#3389semidirect
370. C71C2×#3389semidirect
442. C2×D8Dic142semidirect
572. D8C2×Dic142semidirect
703. C2#22601299direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867082
C2×#179867062
#226012992
C2×#179864082
C2×#179864062
C2×#179863992
C2×#179863012
C2×#179862992
C2×#179862972
C2×#179862792
C2×#179862772
C2×#179861272
C2×#179861112
C2×D8×Dic712
C2×#442×C712
C2×#338971