Finite Group Databasebeta

← C2×#22591862 #32165454

Subgroups — C2×#22591862 #32165454

Order 18176.

2790 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
1C22×#14556105C211yesmaximal, characteristic
2C22×C4×Dic142C211yesmaximal, characteristic, complemented
3#22591862C2116yesmaximal, direct product factor
4C2×#17985935C211yesmaximal, characteristic
5C2×#17985935C211yesmaximal, characteristic
6C2×#17985932C211yesmaximal, characteristic, complemented
7C2×#17985931C211yesmaximal, characteristic, complemented
8C2×#17985903C211yesmaximal, characteristic, complemented
9C2×#17985896C211yesmaximal, characteristic, complemented
10C2×#17985892C211yesmaximal, characteristic
11C2×#17985886C211yesmaximal, characteristic, complemented
12C2×#17985883C211yesmaximal, characteristic, complemented
13C2×#17985868C211yesmaximal, characteristic, complemented
14C2×#17985857C211yesmaximal, characteristic
15C2×C22⋊C4×Dic71C211yesmaximal, characteristic
16C2×#388×C71C211yesmaximal, characteristic
17C23×Dic142C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C2×#14556105—28no—
20C2×#14556105C2218yes—
21C2×C4×Dic142—28no—
22C2×C4×Dic142C2218yescomplemented
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C4⋊Dic71C2211yescharacteristic
25C22×C4⋊Dic71C2211yescharacteristic
26C22×C4⋊Dic71C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×C22⋊Dic71C2211yescharacteristic
37C22×C22⋊Dic71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39C22×C4×Dic71C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41#17985935C2218yes—
42#17985935C2218yes—
43#17985932C2218yescomplemented
44#17985931C2218yescomplemented
45#17985903C2218yescomplemented
46#17985896C2218yescomplemented
47#17985892C2218yes—
48#17985886C2218yescomplemented
49#17985883C2218yescomplemented
50#17985868C2218yescomplemented
51#17985857C2218yes—
52C22⋊C4×Dic71C2218yes—
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C22⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic
66#388×C71C2218yes—
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C22×Dic142—24no—
70C22×Dic142—24no—
71C22×Dic142D418yes—
72C22×Dic142C2314yes—
73C23×Dic71—24no—
74C23×Dic71—24no—
75C23×Dic71—24no—
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2314yes—
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85#14556105—232no—
86C4×Dic142—232no—
87C2×C4⋊Dic71—24no—
88C2×C4⋊Dic71—24no—
89C2×C4⋊Dic71—42no—
90C2×C4⋊Dic71—42no—
91C2×C4⋊Dic71C2314yes—
92C2×C4⋊Dic71C2314yes—
93C2×C4⋊Dic71C2314yes—
94C2×C4⋊Dic71C2314yes—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4—24no—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—42no—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×C22⋊Dic71—24no—
112C2×C22⋊Dic71—24no—
113C2×C22⋊Dic71—42no—
114C2×C22⋊Dic71C2314yes—
115C2×C22⋊Dic71C2314yes—
116C2×C22⋊Dic71C2314yes—
117C2×C4×Dic71—24no—
118C2×C4×Dic71—24no—
119C2×C4×Dic71—24no—
120C2×C4×Dic71C2314yes—
121C2×C4×Dic71C2314yes—
122C2×C4×Dic71C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C25×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C2×C4⋊C4×C71—42no—
139C2×C4⋊C4×C71C2314yes—
140C2×C22⋊C4×C71—24no—
141C2×C22⋊C4×C71—42no—
142C2×C22⋊C4×C71Q818yescomplemented
143C2×C22⋊C4×C71C2314yes—
144C2×C22⋊C4×C71C2314yes—
145C2×C22⋊C4×C71C2314yes—
146C2×C42×C71—24no—
147C2×C42×C71C2314yes—
148#95×C71C2314yes—
149#95×C71C2314yes—
150C2×Dic142—232no—
151C2×Dic142—28no—
152C2×Dic142—28no—
153C2×Dic142C2×D4116yes—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—28no—
174C22×Dic71—28no—
175C22×Dic71—28no—
176C22×Dic71—416no—
177C22×Dic71C2×D414yes—
178C22×Dic71C2×D414yes—
179C22×Dic71#4114yes—
180C22×Dic71#4114yes—
181C22×Dic71#4114yes—
182C22×Dic71C2412yes—
183C22×Dic71C2412yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C4⋊Dic71—28no—
191C4⋊Dic71—28no—
192C4⋊Dic71—44no—
193C4⋊Dic71—44no—
194Dic71⋊C4—28no—
195Dic71⋊C4—28no—
196Dic71⋊C4—28no—
197Dic71⋊C4—28no—
198Dic71⋊C4—28no—
199Dic71⋊C4—28no—
200Dic71⋊C4—28no—
201Dic71⋊C4—44no—
202C22⋊Dic71—28no—
203C22⋊Dic71—28no—
204C22⋊Dic71—44no—
205C4×Dic71—28no—
206C4×Dic71—28no—
207C4×Dic71—28no—
208C24×C71—22no—
209C24×C71—22no—
210C24×C71—22no—
211C24×C71—22no—
212C24×C71—22no—
213C24×C71—22no—
214C24×C71C2×Q814yes—
215C24×C71C2412yes—
216C24×C71C2411yescharacteristic
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71C2×D414yes—
233C22×C4×C71C2×Q814yes—
234C22×C4×C71C2×Q814yes—
235C22×C4×C71C2412yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2412yes—
241C4⋊C4×C71—44no—
242C22⋊C4×C71—28no—
243C22⋊C4×C71—44no—
244C22⋊C4×C71C2×Q8116yescomplemented
245C42×C71—28no—
246C23×C71—28no—
247C23×C71—28no—
248C23×C71—28no—
249C23×C71—22no—
250C23×C71—22no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71—22no—
254C23×C71—22no—
255C23×C71—44no—
256C23×C71—44no—
257C23×C71—44no—
258C23×C71—44no—
259C23×C71C22×D412yes—
260C23×C71C22×Q814yes—
261C23×C71C22×Q812yes—
262C23×C71C2×#4112yes—
263C23×C71C2×#4112yes—
264C23×C71C2×#4112yes—
265C23×C71H(5,𝔽2)12yes—
266C23×C712−1+412yes—
267C23×C71C2511yescharacteristic
268C2×C4×C71—28no—
269C2×C4×C71—28no—
270C2×C4×C71—28no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—44no—
287C2×C4×C71—44no—
288C2×C4×C71—44no—
289C2×C4×C71C22×D414yes—
290C2×C4×C71C22×Q814yes—
291C2×C4×C71C22×Q814yes—
292C2×Dic71—28no—
293C2×Dic71—28no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—44no—
314C2×Dic71—44no—
315C2×Dic71—44no—
316C2×Dic71—44no—
317C2×Dic71—44no—
318C2×Dic71—416no—
319C2×Dic71#123116yes—
320C2×Dic71C22×D414yes—
321C2×Dic71C22×D414yes—
322C2×Dic71C2×#4114yes—
323C2×Dic71C2×#4114yes—
324C2×Dic71C2×#4114yes—
325Dic142—232no—
326C22×C71—24no—
327C22×C71—24no—
328C22×C71—24no—
329C22×C71—42no—
330C22×C71—416no—
331C22×C71—42no—
332C22×C71—42no—
333C22×C71—42no—
334C22×C71C2×#12314yes—
335C22×C71#53314yes—
336C22×C71#54214yes—
337C22×C71D4×Q814yes—
338C22×C71#55014yes—
339C22×C71#55214yes—
340C22×C71#55414yes—
341C22×C71C23×D411yescharacteristic
342C22×C71C23×Q811yescharacteristic
343C22×C71C22×#4111yescharacteristic
344C22×C71C22×#4111yescharacteristic
345C22×C71C22×#4111yescharacteristic
346C22×C71C2×H(5,𝔽2)11yescharacteristic
347C22×C71C2×2−1+411yescharacteristic
348C4×C71—24no—
349C4×C71—24no—
350C4×C71—24no—
351C4×C71—42no—
352C4×C71—42no—
353C4×C71—42no—
354Dic71—24no—
355Dic71—24no—
356Dic71—42no—
357Dic71—42no—
358Dic71—42no—
359Dic71—42no—
360Dic71—42no—
361Dic71C2×#12318yes—
362C2×#2423—711nomaximal, Sylow
363C2×C71—44no—
364C2×C71#242318yescomplemented
365C2×C71C22×#12311yescharacteristic
366C2×C71C2×#53311yescharacteristic
367C2×C71C2×#54211yescharacteristic
368C2×C71C2×D4×Q811yescharacteristic
369C2×C71C2×#55011yescharacteristic
370C2×C71C2×#55211yescharacteristic
371C2×C71C2×#55411yescharacteristic
372C22×C22⋊Q8—711no—
373C22×C4×Q8—711no—
374#2423—7116no—
375C2×#399—711no—
376C2×#399—711no—
377C2×#398—711no—
378C2×#398—711no—
379C2×#391—711no—
380C2×#389—711no—
381C2×#388—711no—
382C2×#388D7111yescharacteristic
383C2×#387—711no—
384C2×#387—711no—
385C2×#384—711no—
386C2×#380—711no—
387C2×C4×C22⋊C4—711no—
388C71C2×#242311yescharacteristic, complemented, Sylow
389C23×Q8—711no—
390C24×C4—711no—
391C2×C22⋊Q8—718no—
392C2×C22⋊Q8—1428no—
393C2×C4×Q8—718no—
394C2×C4×Q8—1428no—
395C22×C4⋊C4—711no—
396C22×C4⋊C4—711no—
397C22×C4⋊C4—711no—
398C22×C4⋊C4—711no—
399C22×C4⋊C4—711no—
400C22×C4⋊C4—711no—
401C22×C4⋊C4—711no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4—711no—
405C22×C4⋊C4—711no—
406C22×C4⋊C4—711no—
407C22×C4⋊C4C2×D7111yescharacteristic
408C22×C22⋊C4—711no—
409C22×C22⋊C4—711no—
410C22×C22⋊C4—711no—
411C22×C22⋊C4C2×D7111yescharacteristic
412C22×C22⋊C4C2×D7111yescharacteristic
413C22×C22⋊C4C2×D7111yescharacteristic
414C22×C42—711no—
415C22×C42—711no—
416C22×C42—711no—
417C22×C42C2×D7111yescharacteristic
418#399—718no—
419#399—718no—
420#398—718no—
421#398—718no—
422#391—718no—
423#389—718no—
424#388—718no—
425#388C2×D7118yes—
426#387—718no—
427#387—718no—
428#384—718no—
429#380—718no—
430C4×C22⋊C4—718no—
431C2×#95—711no—
432C2×#95—711no—
433C2×#95—711no—
434C2×#95—711no—
435C2×#95—711no—
436C2×#95—711no—
437C2×#95—711no—
438C2×#95—711no—
439C2×#95C2×D7111yescharacteristic
440C2×#95C2×D7111yescharacteristic
441C25C22×D7111yescharacteristic
442C22×Q8—718no—
443C22×Q8—714no—
444C22×Q8—1424no—
445C22×Q8—1424no—
446C23×C4—711no—
447C23×C4—711no—
448C23×C4—711no—
449C23×C4—714no—
450C23×C4—711no—
451C23×C4—711no—
452C23×C4—711no—
453C23×C4—711no—
454C23×C4—711no—
455C23×C4—1424no—
456C23×C4—1424no—
457C23×C4—1424no—
458C23×C4C22×D7111yescharacteristic
459C23×C4C22×D7111yescharacteristic
460C23×C4C22×D7111yescharacteristic
461C23×C4C22×D7111yescharacteristic
462C23×C4C22×D7111yescharacteristic
463C23×C4C22×D7111yescharacteristic
464C22⋊Q8—14232no—
465C4×Q8—14232no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—2842no—
468C2×C4⋊C4—2842no—
469C2×C4⋊C4—2842no—
470C2×C4⋊C4—714no—
471C2×C4⋊C4—714no—
472C2×C4⋊C4—714no—
473C2×C4⋊C4—714no—
474C2×C4⋊C4—714no—
475C2×C4⋊C4—714no—
476C2×C4⋊C4—714no—
477C2×C4⋊C4—714no—
478C2×C4⋊C4—714no—
479C2×C4⋊C4—714no—
480C2×C4⋊C4—714no—
481C2×C4⋊C4—714no—
482C2×C4⋊C4—1424no—
483C2×C4⋊C4—1424no—
484C2×C4⋊C4—1424no—
485C2×C4⋊C4—1424no—
486C2×C4⋊C4—1424no—
487C2×C4⋊C4—1424no—
488C2×C4⋊C4—1424no—
489C2×C4⋊C4—1424no—
490C2×C4⋊C4—1424no—
491C2×C4⋊C4C22×D7114yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—2842no—
495C2×C22⋊C4—714no—
496C2×C22⋊C4—714no—
497C2×C22⋊C4—714no—
498C2×C22⋊C4—1424no—
499C2×C22⋊C4—1424no—
500C2×C22⋊C4Dic14218yescomplemented
501C2×C22⋊C4C22×D7114yes—
502C2×C22⋊C4C22×D7114yes—
503C2×C22⋊C4C22×D7114yes—
504C2×C42—24no—
505C2×C42—714no—
506C2×C42—714no—
507C2×C42—714no—
508C2×C42—1424no—
509C2×C42—1424no—
510C2×C42—1424no—
511C2×C42C22×D7114yes—
512#95—714no—
513#95—714no—
514#95—714no—
515#95—714no—
516#95—714no—
517#95—714no—
518#95—714no—
519#95—714no—
520#95C22×D7114yes—
521#95C22×D7114yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24C2×Dic14214yes—
529C24C23×D7112yes—
530C24C23×D7111yescharacteristic
531C2×Q8—7116no—
532C2×Q8—1428no—
533C2×Q8—1428no—
534C2×Q8—14232no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—28416no—
551C22×C4—714no—
552C22×C4—714no—
553C22×C4—714no—
554C22×C4—712no—
555C22×C4—714no—
556C22×C4—714no—
557C22×C4—712no—
558C22×C4—712no—
559C22×C4—712no—
560C22×C4—712no—
561C22×C4—712no—
562C22×C4—712no—
563C22×C4—712no—
564C22×C4—1428no—
565C22×C4—1428no—
566C22×C4—1428no—
567C22×C4—1422no—
568C22×C4—1422no—
569C22×C4—1422no—
570C22×C4—1422no—
571C22×C4—1422no—
572C22×C4—1422no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1422no—
586C22×C4D4×D7114yes—
587C22×C4C2×Dic14214yes—
588C22×C4C2×Dic14214yes—
589C22×C4C23×D7112yes—
590C22×C4C23×D7112yes—
591C22×C4C23×D7112yes—
592C22×C4C23×D7112yes—
593C22×C4C23×D7112yes—
594C22×C4C23×D7112yes—
595C4⋊C4—44no—
596C4⋊C4—2844no—
597C4⋊C4—2844no—
598C4⋊C4—2844no—
599C4⋊C4—1428no—
600C4⋊C4—1428no—
601C4⋊C4—1428no—
602C4⋊C4—1428no—
603C4⋊C4—1428no—
604C4⋊C4—1428no—
605C4⋊C4—1428no—
606C4⋊C4—1428no—
607C4⋊C4—1428no—
608C22⋊C4—28no—
609C22⋊C4—44no—
610C22⋊C4—2844no—
611C22⋊C4—1428no—
612C22⋊C4—1428no—
613C22⋊C4C2×Dic142116yescomplemented
614C42—28no—
615C42—1428no—
616C42—1428no—
617C42—1428no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C2×D4×D7112yes—
632C23C22×Dic14214yes—
633C23C22×Dic14212yes—
634C23#41×D7112yes—
635C23#41×D7112yes—
636C23#41×D7112yes—
637C23#1455617312yes—
638C23#1455617512yes—
639C23C24×D7111yescharacteristic
640Q8—14232no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—2844no—
663C2×C4—2844no—
664C2×C4—2844no—
665C2×C4—2844no—
666C2×C4—2844no—
667C2×C4—28416no—
668C2×C4—714no—
669C2×C4—714no—
670C2×C4—714no—
671C2×C4—7116no—
672C2×C4—714no—
673C2×C4—714no—
674C2×C4—1422no—
675C2×C4—1422no—
676C2×C4—1422no—
677C2×C4—1422no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4—1422no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1428no—
694C2×C4—1428no—
695C2×C4C2×D4×D7114yes—
696C2×C4C22×Dic14214yes—
697C2×C4C22×Dic14214yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—416no—
704C22—42no—
705C22—42no—
706C22#123×D7114yes—
707C22#1798655214yes—
708C22#1798661314yes—
709C22D4×Dic14214yes—
710C22#1798666714yes—
711C22#1798668514yes—
712C22#1798670814yes—
713C22C22×D4×D7111yescharacteristic
714C22C23×Dic14211yescharacteristic
715C22C2×#41×D7111yescharacteristic
716C22C2×#41×D7111yescharacteristic
717C22C2×#41×D7111yescharacteristic
718C22C2×#1455617311yescharacteristic
719C22C2×#1455617511yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—2842no—
727C4—2842no—
728C4—2842no—
729C4—2842no—
730C4—2842no—
731C4—718no—
732C4—1424no—
733C4—1424no—
734C2—44no—
735C2#2259186218yesdirect product factor
736C2C2×#123×D7111yescharacteristic
737C2C2×#1798655211yescharacteristic
738C2C2×#1798661311yescharacteristic
739C2C2×D4×Dic14211yescharacteristic
740C2C2×#1798666711yescharacteristic
741C2C2×#1798668511yescharacteristic
742C2C2×#1798670811yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#388D71
hypocenterC71C2×#2423
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic142C2semidirect
3. #22591862C2direct (N × H)
6. C2×#17985932C2semidirect
7. C2×#17985931C2semidirect
8. C2×#17985903C2semidirect
9. C2×#17985896C2semidirect
11. C2×#17985886C2semidirect
12. C2×#17985883C2semidirect
13. C2×#17985868C2semidirect
22. C2×C4×Dic142C22semidirect
43. #17985932C22semidirect
44. #17985931C22semidirect
45. #17985903C22semidirect
46. #17985896C22semidirect
48. #17985886C22semidirect
49. #17985883C22semidirect
50. #17985868C22semidirect
142. C2×C22⋊C4×C71Q8semidirect
244. C22⋊C4×C71C2×Q8semidirect
364. C2×C71#2423semidirect
388. C71C2×#2423semidirect
500. C2×C22⋊C4Dic142semidirect
613. C22⋊C4C2×Dic142semidirect
735. C2#22591862direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561052
C22×C4×Dic1422
#225918622
C2×#179859352
C2×#179859322
C2×#179859312
C2×#179859032
C2×#179858962
C2×#179858922
C2×#179858862
C2×#179858832
C2×#179858682
C2×#179858572
C2×C22⋊C4×Dic712
C2×#388×C712
C2×#242371