Finite Group Databasebeta

← C2×#22592783 #32167228

Subgroups — C2×#22592783 #32167228

Order 18176.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556110C211yesmaximal, characteristic
2C22×#14556085C211yesmaximal, characteristic, complemented
3#22592783C2116yesmaximal, direct product factor
4C2×#17985941C211yesmaximal, characteristic, complemented
5C2×#17985935C211yesmaximal, characteristic, complemented
6C2×#17985932C211yesmaximal, characteristic, complemented
7C2×#17985927C211yesmaximal, characteristic, complemented
8C2×#17985887C211yesmaximal, characteristic, complemented
9C2×#17985884C211yesmaximal, characteristic, complemented
10C2×#17985883C211yesmaximal, characteristic, complemented
11C2×#17985875C211yesmaximal, characteristic
12C2×#17985875C211yesmaximal, characteristic
13C2×#17985858C211yesmaximal, characteristic, complemented
14C2×#17985856C211yesmaximal, characteristic, complemented
15C2×#95×D71C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556110—28no—
22C2×#14556110C2218yes—
23C2×#14556085—28no—
24C2×#14556085C2218yescomplemented
25C22×C4⋊Dic71C2211yescharacteristic
26C22×C4⋊Dic71C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic
33C22×C22⋊Dic71C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39#17985941C2218yescomplemented
40#17985935C2218yescomplemented
41#17985932C2218yescomplemented
42#17985927C2218yescomplemented
43#17985887C2218yescomplemented
44#17985884C2218yescomplemented
45#17985883C2218yescomplemented
46#17985875C2218yes—
47#17985875C2218yes—
48#17985858C2218yescomplemented
49#17985856C2218yescomplemented
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60#95×D71C2218yescomplemented
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C22⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic
66#388×C71C2218yescomplemented
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C22×C22⋊D71—24no—
71C22×C22⋊D71—24no—
72C22×C22⋊D71—24no—
73C22×C22⋊D71C2314yes—
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C22×C4×D71—24no—
82C22×C4×D71—24no—
83C22×C4×D71—24no—
84C22×C4×D71—24no—
85C22×C4×D71—24no—
86C22×C4×D71—24no—
87C22×C4×D71—42no—
88C22×C4×D71—42no—
89C22×C4×D71D418yes—
90C22×C4×D71C2314yes—
91C22×C4×D71C2314yes—
92C22×C4×D71C2314yes—
93#14556110—232no—
94#14556085—232no—
95C2×C4⋊Dic71—24no—
96C2×C4⋊Dic71—24no—
97C2×C4⋊Dic71C2314yes—
98C2×C4⋊Dic71C2314yes—
99C2×Dic71⋊C4—24no—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—24no—
103C2×Dic71⋊C4—42no—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×C22⋊Dic71—24no—
110C2×C22⋊Dic71—24no—
111C2×C22⋊Dic71—42no—
112C2×C22⋊Dic71C2314yes—
113C2×C22⋊Dic71C2314yes—
114C2×C22⋊Dic71C2314yes—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4C2314yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×C4×Dic71—24no—
122C2×C4×Dic71C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C25×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C2×C4⋊C4×C71—42no—
141C2×C4⋊C4×C71C2314yes—
142C2×C22⋊C4×C71—24no—
143C2×C22⋊C4×C71—24no—
144C2×C22⋊C4×C71—42no—
145C2×C22⋊C4×C71C2314yes—
146C2×C22⋊C4×C71C2314yes—
147C2×C22⋊C4×C71C2314yes—
148C2×C42×C71—24no—
149C2×C42×C71C2314yes—
150#95×C71C2314yes—
151#95×C71C2314yes—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71C2×D414yes—
157C23×D71#4114yes—
158C23×D71#4114yes—
159C23×D71C2412yes—
160C2×C22⋊D71—28no—
161C2×C22⋊D71—28no—
162C2×C22⋊D71—28no—
163C2×C22⋊D71—416no—
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—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71C2×D414yes—
184C22×Dic71#4114yes—
185C22×Dic71C2412yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C2×C4×D71—232no—
193C2×C4×D71—28no—
194C2×C4×D71—28no—
195C2×C4×D71—28no—
196C2×C4×D71—28no—
197C2×C4×D71—28no—
198C2×C4×D71—28no—
199C2×C4×D71—44no—
200C2×C4×D71—44no—
201C2×C4×D71—416no—
202C2×C4×D71—416no—
203C2×C4×D71C2×D4116yes—
204C4⋊Dic71—28no—
205C4⋊Dic71—28no—
206Dic71⋊C4—28no—
207Dic71⋊C4—28no—
208Dic71⋊C4—28no—
209Dic71⋊C4—28no—
210Dic71⋊C4—44no—
211C22⋊Dic71—28no—
212C22⋊Dic71—28no—
213C22⋊Dic71—44no—
214(C2×D71)⋊C4—28no—
215(C2×D71)⋊C4—28no—
216(C2×D71)⋊C4—28no—
217C4×Dic71—28no—
218C24×C71—22no—
219C24×C71—22no—
220C24×C71—22no—
221C24×C71—22no—
222C24×C71—22no—
223C24×C71—22no—
224C24×C71—22no—
225C24×C71C2412yes—
226C24×C71C2411yescharacteristic
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71C2×D414yes—
244C22×C4×C71#4114yes—
245C22×C4×C71C2412yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2412yes—
250C22×C4×C71C2412yes—
251C4⋊C4×C71—44no—
252C22⋊C4×C71—28no—
253C22⋊C4×C71—28no—
254C22⋊C4×C71—44no—
255C42×C71—28no—
256C23×C71—22no—
257C23×C71—22no—
258C23×C71—22no—
259C23×C71—22no—
260C23×C71—22no—
261C23×C71—22no—
262C23×C71—22no—
263C23×C71—44no—
264C23×C71—44no—
265C23×C71—44no—
266C23×C71—44no—
267C23×C71—44no—
268C23×C71—44no—
269C23×C71—44no—
270C23×C71C22×D412yes—
271C23×C71C2×#4112yes—
272C23×C71C2×#4112yes—
273C23×C71C2×#4112yes—
274C23×C71C2×#4112yes—
275C23×C71H(5,𝔽2)12yes—
276C23×C712−1+412yes—
277C23×C71C2511yescharacteristic
278C22×D71—28no—
279C22×D71—28no—
280C22×D71—28no—
281C22×D71—28no—
282C22×D71—28no—
283C22×D71—28no—
284C22×D71—22no—
285C22×D71—22no—
286C22×D71—22no—
287C22×D71—22no—
288C22×D71#123116yes—
289C22×D71C22×D414yes—
290C22×D71C2×#4114yes—
291C22×D71C2×#4114yes—
292C2×C4×C71—28no—
293C2×C4×C71—28no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—44no—
311C2×C4×C71—44no—
312C2×C4×C71—44no—
313C2×C4×C71—44no—
314C2×C4×C71C22×D414yes—
315C2×C4×C71C2×#4114yes—
316C22⋊D71—416no—
317C2×Dic71—28no—
318C2×Dic71—28no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—44no—
339C2×Dic71—44no—
340C2×Dic71—44no—
341C2×Dic71—44no—
342C2×Dic71—44no—
343C2×Dic71C22×D414yes—
344C2×Dic71C2×#4114yes—
345C4×D71—232no—
346C4×D71—416no—
347C4×D71—416no—
348C22×C71—42no—
349C22×C71—42no—
350C22×C71—42no—
351C22×C71—42no—
352C22×C71—42no—
353C22×C71—42no—
354C22×C71—42no—
355C22×C71—88no—
356C22×C71C2×#12314yes—
357C22×C71#53214yes—
358C22×C71#53714yes—
359C22×C71#55114yes—
360C22×C71#55114yes—
361C22×C71#55214yes—
362C22×C71#55214yes—
363C22×C71C23×D411yescharacteristic
364C22×C71C22×#4111yescharacteristic
365C22×C71C22×#4111yescharacteristic
366C22×C71C22×#4111yescharacteristic
367C22×C71C22×#4111yescharacteristic
368C22×C71C2×H(5,𝔽2)11yescharacteristic
369C22×C71C2×2−1+411yescharacteristic
370C2×D71—24no—
371C2×D71—24no—
372C2×D71—24no—
373C2×D71—24no—
374C2×D71—24no—
375C2×D71—24no—
376C2×D71—232no—
377C2×D71C2×#12318yes—
378C4×C71—24no—
379C4×C71—24no—
380C4×C71—42no—
381C4×C71—42no—
382C4×C71—42no—
383C4×C71—42no—
384Dic71—24no—
385Dic71—24no—
386Dic71—42no—
387Dic71—42no—
388Dic71—42no—
389Dic71—42no—
390Dic71—42no—
391C2×#2498—711nomaximal, Sylow
392C2×C71—82no—
393C2×C71#249818yescomplemented
394C2×C71C22×#12311yescharacteristic
395C2×C71C2×#53211yescharacteristic
396C2×C71C2×#53711yescharacteristic
397C2×C71C2×#55111yescharacteristic
398C2×C71C2×#55111yescharacteristic
399C2×C71C2×#55211yescharacteristic
400C2×C71C2×#55211yescharacteristic
401D71—28no—
402C22×#123—711no—
403C22×#117—711no—
404#2498—7116no—
405C2×#400—711no—
406C2×#399—711no—
407C2×#398—711no—
408C2×#397—711no—
409C2×#388—711no—
410C2×#388D7111yescharacteristic, complemented
411C2×#387—711no—
412C2×#387—711no—
413C2×#386—711no—
414C2×#386—711no—
415C2×#380—711no—
416C2×#380—711no—
417C22×#95—711no—
418C71C2×#249811yescharacteristic, complemented, Sylow
419C23×D4—711no—
420C24×C4—711no—
421C24×C4—711no—
422C24×C4—711no—
423C2×#123—718no—
424C2×#123—1428no—
425C2×#117—718no—
426C2×#117—1428no—
427C22×C4⋊C4—711no—
428C22×C4⋊C4—711no—
429C22×C4⋊C4—711no—
430C22×C4⋊C4—711no—
431C22×C4⋊C4—711no—
432C22×C4⋊C4—711no—
433C22×C4⋊C4—711no—
434C22×C4⋊C4C2×D7111yescharacteristic
435C22×C22⋊C4—711no—
436C22×C22⋊C4—711no—
437C22×C22⋊C4—711no—
438C22×C22⋊C4—711no—
439C22×C22⋊C4—711no—
440C22×C22⋊C4—711no—
441C22×C22⋊C4C2×D7111yescharacteristic
442C22×C22⋊C4C2×D7111yescharacteristic
443C22×C22⋊C4C2×D7111yescharacteristic
444C22×C42—711no—
445C22×C42C2×D7111yescharacteristic
446#400—718no—
447#399—718no—
448#398—718no—
449#397—718no—
450#388—718no—
451#388C2×D7118yescomplemented
452#387—718no—
453#387—718no—
454#386—718no—
455#386—718no—
456#380—718no—
457#380—718no—
458C2×#95—711no—
459C2×#95—711no—
460C2×#95—711no—
461C2×#95—711no—
462C2×#95—711no—
463C2×#95—711no—
464C2×#95—711no—
465C2×#95—711no—
466C2×#95—711no—
467C2×#95—711no—
468C2×#95—718no—
469C2×#95C2×D7111yescharacteristic
470C2×#95C2×D7111yescharacteristic
471C25—711no—
472C25C22×D7111yescharacteristic
473C22×D4—714no—
474C22×D4—1424no—
475C22×D4—1424no—
476C22×D4—1424no—
477C23×C4—2842no—
478C23×C4—2842no—
479C23×C4—714no—
480C23×C4—714no—
481C23×C4—711no—
482C23×C4—711no—
483C23×C4—718no—
484C23×C4—714no—
485C23×C4—711no—
486C23×C4—711no—
487C23×C4—711no—
488C23×C4—711no—
489C23×C4—711no—
490C23×C4—1424no—
491C23×C4—1424no—
492C23×C4—1424no—
493C23×C4—1424no—
494C23×C4—1424no—
495C23×C4—1424no—
496C23×C4C22×D7111yescharacteristic
497C23×C4C22×D7111yescharacteristic
498C23×C4C22×D7111yescharacteristic
499C23×C4C22×D7111yescharacteristic
500C23×C4C22×D7111yescharacteristic
501C23×C4C22×D7111yescharacteristic
502#123—14232no—
503#117—14232no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4—2842no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4—714no—
508C2×C4⋊C4—714no—
509C2×C4⋊C4—714no—
510C2×C4⋊C4—714no—
511C2×C4⋊C4—714no—
512C2×C4⋊C4—714no—
513C2×C4⋊C4—1424no—
514C2×C4⋊C4—1424no—
515C2×C4⋊C4—1424no—
516C2×C4⋊C4—1424no—
517C2×C4⋊C4—1424no—
518C2×C4⋊C4—1424no—
519C2×C4⋊C4C22×D7114yes—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—2842no—
524C2×C22⋊C4—714no—
525C2×C22⋊C4—714no—
526C2×C22⋊C4—714no—
527C2×C22⋊C4—714no—
528C2×C22⋊C4—714no—
529C2×C22⋊C4—714no—
530C2×C22⋊C4—1424no—
531C2×C22⋊C4—1424no—
532C2×C22⋊C4—1424no—
533C2×C22⋊C4—1424no—
534C2×C22⋊C4—1424no—
535C2×C22⋊C4C22×D7114yes—
536C2×C22⋊C4C22×D7114yes—
537C2×C22⋊C4C22×D7114yes—
538C2×C42—24no—
539C2×C42—714no—
540C2×C42—1424no—
541C2×C42C22×D7114yes—
542#95—714no—
543#95—714no—
544#95—714no—
545#95—714no—
546#95—714no—
547#95—714no—
548#95—714no—
549#95—714no—
550#95—714no—
551#95—714no—
552#95C22×D7114yes—
553#95C22×D7114yes—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—714no—
562C24—714no—
563C24—714no—
564C24—712no—
565C24—1422no—
566C24—1422no—
567C24—1422no—
568C24—1422no—
569C24C23×D7112yes—
570C24C23×D7111yescharacteristic
571C2×D4—28416no—
572C2×D4—1428no—
573C2×D4—1428no—
574C2×D4—1428no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—28416no—
592C22×C4—2844no—
593C22×C4—2844no—
594C22×C4—28416no—
595C22×C4—714no—
596C22×C4—714no—
597C22×C4—712no—
598C22×C4—712no—
599C22×C4—7116no—
600C22×C4—712no—
601C22×C4—712no—
602C22×C4—712no—
603C22×C4—712no—
604C22×C4—712no—
605C22×C4—1428no—
606C22×C4—1428no—
607C22×C4—1428no—
608C22×C4—1428no—
609C22×C4—1428no—
610C22×C4—14232no—
611C22×C4—1422no—
612C22×C4—1422no—
613C22×C4—1422no—
614C22×C4—1422no—
615C22×C4—1422no—
616C22×C4—1422no—
617C22×C4—1422no—
618C22×C4—1422no—
619C22×C4—1422no—
620C22×C4—1422no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4—1422no—
624C22×C4—1422no—
625C22×C4—1422no—
626C22×C4—1428no—
627C22×C4—1422no—
628C22×C4—1422no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4D4×D7114yes—
632C22×C4#1176586514yes—
633C22×C4C23×D7112yes—
634C22×C4C23×D7112yes—
635C22×C4C23×D7112yes—
636C22×C4C23×D7112yes—
637C22×C4C23×D7112yes—
638C22×C4C23×D7112yes—
639C4⋊C4—44no—
640C4⋊C4—2844no—
641C4⋊C4—1428no—
642C4⋊C4—1428no—
643C4⋊C4—1428no—
644C4⋊C4—1428no—
645C4⋊C4—1428no—
646C4⋊C4—1428no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—44no—
650C22⋊C4—2844no—
651C22⋊C4—1428no—
652C22⋊C4—1428no—
653C22⋊C4—1428no—
654C22⋊C4—1428no—
655C22⋊C4—1428no—
656C42—28no—
657C42—1428no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—714no—
673C23—714no—
674C23—714no—
675C23—7116no—
676C23—1422no—
677C23—1422no—
678C23—1422no—
679C23—1422no—
680C23—1428no—
681C23—1428no—
682C23—1428no—
683C23—1428no—
684C23—1428no—
685C23—1428no—
686C23C2×D4×D7112yes—
687C23#41×D7112yes—
688C23#41×D7112yes—
689C23#41×D7112yes—
690C23C2×#1176586512yes—
691C23#1455617312yes—
692C23#1455617512yes—
693C23C24×D7111yescharacteristic
694D4—28416no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—28416no—
718C2×C4—28416no—
719C2×C4—2844no—
720C2×C4—2844no—
721C2×C4—2844no—
722C2×C4—2844no—
723C2×C4—2844no—
724C2×C4—714no—
725C2×C4—714no—
726C2×C4—14232no—
727C2×C4—1422no—
728C2×C4—1422no—
729C2×C4—1422no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4—1422no—
745C2×C4—1422no—
746C2×C4—1428no—
747C2×C4—1428no—
748C2×C4C2×D4×D7114yes—
749C2×C4C2×#1176586514yes—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—88no—
758C22—718no—
759C22—14232no—
760C22—1424no—
761C22—1424no—
762C22—1424no—
763C22—1424no—
764C22—1424no—
765C22—1424no—
766C22#123×D7114yes—
767C22#1798654614yes—
768C22#1798657814yes—
769C22#1798667814yes—
770C22#1798667914yes—
771C22#1798668514yes—
772C22#1798668814yes—
773C22C22×D4×D7111yescharacteristic
774C22C2×#41×D7111yescharacteristic
775C22C2×#41×D7111yescharacteristic
776C22C2×#41×D7111yescharacteristic
777C22C22×#1176586511yescharacteristic
778C22C2×#1455617311yescharacteristic
779C22C2×#1455617511yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—2842no—
787C4—2842no—
788C4—2842no—
789C4—2842no—
790C4—2842no—
791C4—1424no—
792C4—1424no—
793C2—82no—
794C2—1428no—
795C2#2259278318yesdirect product factor
796C2C2×#123×D7111yescharacteristic
797C2C2×#1798654611yescharacteristic
798C2C2×#1798657811yescharacteristic
799C2C2×#1798667811yescharacteristic
800C2C2×#1798667911yescharacteristic
801C2C2×#1798668511yescharacteristic
802C2C2×#1798668811yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC2×#388D71
hypocenterC71C2×#2498
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14556085C2semidirect
3. #22592783C2direct (N × H)
4. C2×#17985941C2semidirect
5. C2×#17985935C2semidirect
6. C2×#17985932C2semidirect
7. C2×#17985927C2semidirect
8. C2×#17985887C2semidirect
9. C2×#17985884C2semidirect
10. C2×#17985883C2semidirect
13. C2×#17985858C2semidirect
14. C2×#17985856C2semidirect
15. C2×#95×D71C2semidirect
16. C2×#388×C71C2semidirect
24. C2×#14556085C22semidirect
39. #17985941C22semidirect
40. #17985935C22semidirect
41. #17985932C22semidirect
42. #17985927C22semidirect
43. #17985887C22semidirect
44. #17985884C22semidirect
45. #17985883C22semidirect
48. #17985858C22semidirect
49. #17985856C22semidirect
60. #95×D71C22semidirect
66. #388×C71C22semidirect
393. C2×C71#2498semidirect
410. C2×#388D71semidirect
418. C71C2×#2498semidirect
451. #388C2×D71semidirect
795. C2#22592783direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561102
C22×#145560852
#225927832
C2×#179859412
C2×#179859352
C2×#179859322
C2×#179859272
C2×#179858872
C2×#179858842
C2×#179858832
C2×#179858752
C2×#179858582
C2×#179858562
C2×#95×D712
C2×#388×C712
C2×#249871