Finite Group Databasebeta

← #31920580

Subgroups — #31920580

Order 18176.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556108C211yesmaximal, characteristic
2C2×#17985905C211yesmaximal, characteristic, complemented
3C2×#17985904C211yesmaximal, characteristic, complemented
4C2×#17985898C211yesmaximal, characteristic, complemented
5C2×#17985856C211yesmaximal, characteristic
6C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
7#22586607C212yesmaximal, complemented
8#22586586C212yesmaximal
9#22586578C212yesmaximal
10#22586570C212yesmaximal, complemented
11C2×C4×C4⋊C4×C71C211yesmaximal, characteristic, complemented
12C23×Dic142C2211yescharacteristic
13C23×C4×D71C2211yescharacteristic
14C2×#14556108—24no—
15C2×#14556108—24no—
16C2×#14556108C418yescomplemented
17C22×C4⋊Dic71C2211yescharacteristic
18C22×C4⋊Dic71C2212yes—
19C22×C4⋊Dic71C2212yes—
20C22×(C2×D71)⋊C4C2211yescharacteristic
21C22×(C2×D71)⋊C4C2212yes—
22C22×(C2×D71)⋊C4C2212yes—
23C22×(C2×D71)⋊C4C2211yescharacteristic
24C22×C4×Dic71C2211yescharacteristic
25#17985905—24no—
26#17985904—24no—
27#17985898—24no—
28#17985856—24no—
29C4×(C2×D71)⋊C4—24no—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2211yescharacteristic
36C2×C71⋊#95C2212yes—
37C2×C71⋊#95C2211yescharacteristic
38C22×C4⋊C4×C71C2211yescharacteristic
39C22×C4⋊C4×C71C2211yescharacteristic
40C22×C42×C71C2212yes—
41C22×C42×C71C2211yescharacteristic
42C4×C4⋊C4×C71—24no—
43C2×#95×C71C2212yes—
44C24×D71C2311yescharacteristic
45C22×Dic142—22no—
46C22×Dic142—22no—
47C22×Dic142—22no—
48C22×Dic142—22no—
49C22×Dic142—22no—
50C22×Dic142—22no—
51C22×Dic142C2×C414yes—
52C23×Dic71C2312yes—
53C23×Dic71C2311yescharacteristic
54C23×Dic71C2312yes—
55C23×Dic71C2311yescharacteristic
56C23×Dic71C2311yescharacteristic
57C22×C4×D71—22no—
58C22×C4×D71—22no—
59C22×C4×D71—22no—
60C22×C4×D71—22no—
61C22×C4×D71—22no—
62C22×C4×D71—22no—
63C22×C4×D71C2×C414yes—
64#14556108—232no—
65C2×C4⋊Dic71—24no—
66C2×C4⋊Dic71—24no—
67C2×C4⋊Dic71—24no—
68C2×C4⋊Dic71—22no—
69C2×C4⋊Dic71—24no—
70C2×C4⋊Dic71—22no—
71C2×C4⋊Dic71—22no—
72C2×C4⋊Dic71—42no—
73C2×C4⋊Dic71C2×C418yes—
74C2×(C2×D71)⋊C4—22no—
75C2×(C2×D71)⋊C4—22no—
76C2×(C2×D71)⋊C4—24no—
77C2×(C2×D71)⋊C4—22no—
78C2×(C2×D71)⋊C4—22no—
79C2×(C2×D71)⋊C4—24no—
80C2×(C2×D71)⋊C4—24no—
81C2×(C2×D71)⋊C4—24no—
82C2×(C2×D71)⋊C4—22no—
83C2×(C2×D71)⋊C4—42no—
84C2×(C2×D71)⋊C4C2×C418yes—
85C2×(C2×D71)⋊C4Q814yescomplemented
86C2×C4×Dic71—22no—
87C2×C4×Dic71—22no—
88C2×C4×Dic71—22no—
89C71⋊#95—22no—
90C71⋊#95—22no—
91C71⋊#95—24no—
92C71⋊#95—24no—
93C71⋊#95—24no—
94C71⋊#95—24no—
95C71⋊#95—24no—
96C71⋊#95—24no—
97C23×C4×C71C2312yes—
98C23×C4×C71C2311yescharacteristic
99C23×C4×C71C2312yes—
100C23×C4×C71C2311yescharacteristic
101C23×C4×C71C2311yescharacteristic
102C2×C4⋊C4×C71—22no—
103C2×C4⋊C4×C71—22no—
104C2×C4⋊C4×C71C2×C414yes—
105C2×C4⋊C4×C71D414yes—
106C2×C4⋊C4×C71D414yes—
107C2×C4⋊C4×C71D414yes—
108C2×C42×C71—22no—
109C2×C42×C71—22no—
110C2×C42×C71—24no—
111C2×C42×C71—24no—
112C2×C42×C71—42no—
113C2×C42×C71D414yes—
114#95×C71—24no—
115C23×D71—21no—
116C23×D71—21no—
117C23×D71—21no—
118C23×D71—21no—
119C23×D71—21no—
120C23×D71—21no—
121C23×D71—21no—
122C23×D71—21no—
123C23×D71—21no—
124C23×D71—21no—
125C23×D71—21no—
126C23×D71—21no—
127C23×D71C22×C412yes—
128C23×D71C2×Q812yes—
129C23×D71#4112yes—
130C2×Dic142—28no—
131C2×Dic142—28no—
132C2×Dic142—28no—
133C2×Dic142—44no—
134C2×Dic142—44no—
135C2×Dic142—44no—
136C2×Dic142—44no—
137C22×Dic71—21no—
138C22×Dic71—21no—
139C22×Dic71—21no—
140C22×Dic71—21no—
141C22×Dic71—22no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71—21no—
146C22×Dic71—21no—
147C22×Dic71—21no—
148C22×Dic71—21no—
149C22×Dic71—21no—
150C22×Dic71—21no—
151C22×Dic71—21no—
152C22×Dic71—21no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—21no—
156C22×Dic71—21no—
157C22×Dic71—21no—
158C22×Dic71—21no—
159C22×Dic71—21no—
160C22×Dic71—21no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71C22×C412yes—
169C22×Dic71C22×C414yes—
170C22×Dic71C2×Q812yes—
171C22×Dic71#4112yes—
172C2×C4×D71—28no—
173C2×C4×D71—28no—
174C2×C4×D71—28no—
175C2×C4×D71—44no—
176C2×C4×D71—44no—
177C2×C4×D71—44no—
178C2×C4×D71—44no—
179C4⋊Dic71—216no—
180C4⋊Dic71—48no—
181C4⋊Dic71—44no—
182(C2×D71)⋊C4—28no—
183(C2×D71)⋊C4—216no—
184(C2×D71)⋊C4—28no—
185(C2×D71)⋊C4—48no—
186C4×Dic71—44no—
187C24×C71C2411yescharacteristic
188C22×C4×C71—21no—
189C22×C4×C71—22no—
190C22×C4×C71—21no—
191C22×C4×C71—22no—
192C22×C4×C71—21no—
193C22×C4×C71—22no—
194C22×C4×C71—22no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—22no—
198C22×C4×C71—22no—
199C22×C4×C71—21no—
200C22×C4×C71—22no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—22no—
204C22×C4×C71—22no—
205C22×C4×C71—21no—
206C22×C4×C71—21no—
207C22×C4×C71—22no—
208C22×C4×C71C22×C414yes—
209C22×C4×C71C22×C412yes—
210C22×C4×C71C2×D414yes—
211C22×C4×C71C2×D412yes—
212C22×C4×C71C2×D412yes—
213C22×C4×C71C2×D414yes—
214C22×C4×C71C2×D414yes—
215C22×C4×C71C2×D412yes—
216C22×C4×C71C2×D412yes—
217C22×C4×C71C2×D412yes—
218C22×C4×C71C2×D412yes—
219C22×C4×C71C2×Q812yes—
220C22×C4×C71#4112yes—
221C22×C4×C71#4112yes—
222C22×C4×C71#4112yes—
223C4⋊C4×C71—28no—
224C4⋊C4×C71C22⋊C4116yescomplemented
225C42×C71—28no—
226C42×C71—48no—
227C23×C71C23×C411yescharacteristic
228C23×C71C22×D411yescharacteristic
229C23×C71C22×D411yescharacteristic
230C23×C71C22×D411yescharacteristic
231C23×C71C22×D411yescharacteristic
232C23×C71C22×Q811yescharacteristic
233C23×C71C2×#4111yescharacteristic
234C23×C71C2×#4111yescharacteristic
235C23×C71C2×#4111yescharacteristic
236C23×C71C2×#4111yescharacteristic
237C23×C71C2×#4111yescharacteristic
238C23×C71H(5,𝔽2)11yescharacteristic
239C23×C712−1+411yescharacteristic
240C23×C712−1+411yescharacteristic
241C23×C712−1+411yescharacteristic
242C22×D71—22no—
243C22×D71—22no—
244C22×D71—22no—
245C22×D71—22no—
246C22×D71—22no—
247C22×D71—22no—
248C22×D71—22no—
249C22×D71—22no—
250C22×D71—22no—
251C22×D71—22no—
252C22×D71—22no—
253C22×D71—22no—
254C22×D71—22no—
255C22×D71—22no—
256C22×D71—22no—
257C22×D71—22no—
258C22×D71—22no—
259C22×D71—22no—
260C22×D71—41no—
261C22×D71—41no—
262C22×D71—41no—
263C22×D71—41no—
264C22×D71—41no—
265C22×D71—41no—
266C22×D71—41no—
267C22×D71—41no—
268C22×D71—41no—
269C22×D71—41no—
270C22×D71—41no—
271C22×D71—41no—
272C22×D71—41no—
273C22×D71—41no—
274C22×D71—41no—
275C22×D71—41no—
276C22×D71C4×Q814yes—
277C2×C4×C71—24no—
278C2×C4×C71—24no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—24no—
283C2×C4×C71—24no—
284C2×C4×C71—24no—
285C2×C4×C71—24no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—24no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—24no—
294C2×C4×C71—24no—
295C2×C4×C71—42no—
296C2×C4×C71—42no—
297C2×C4×C71—42no—
298C2×C4×C71—41no—
299C2×C4×C71—41no—
300C2×C4×C71—42no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71C2×C22⋊C418yes—
304C2×C4×C71C2×C22⋊C414yes—
305C2×C4×C71C4×D414yes—
306C2×C4×C71C4×D414yes—
307C2×C4×C71#12114yes—
308C2×C4×C71#12114yes—
309C2×C4×C71C22⋊Q814yescomplemented
310C2×C4×C71#12414yes—
311C2×C4×C71#12714yes—
312C2×Dic71—24no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—24no—
317C2×Dic71—24no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—41no—
325C2×Dic71—41no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328C2×Dic71—41no—
329C2×Dic71—42no—
330C2×Dic71—41no—
331C2×Dic71—41no—
332C2×Dic71—41no—
333C2×Dic71—42no—
334C2×Dic71—41no—
335C2×Dic71—41no—
336C2×Dic71—41no—
337C2×Dic71—41no—
338C2×Dic71—41no—
339C2×Dic71—41no—
340C2×Dic71—42no—
341C2×Dic71—42no—
342C2×Dic71—42no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345C2×Dic71—42no—
346C2×Dic71—42no—
347C4×D71—416no—
348Dic142—416no—
349C22×C71C22×C22⋊C411yescharacteristic
350C22×C71C2×C4×D411yescharacteristic
351C22×C71C2×C4×D411yescharacteristic
352C22×C71C2×C4×Q811yescharacteristic
353C22×C71C4×#4111yescharacteristic
354C22×C71#51911yescharacteristic
355C22×C71#52011yescharacteristic
356C22×C71C2×#12111yescharacteristic
357C22×C71C2×#12111yescharacteristic
358C22×C71C2×C22⋊Q811yescharacteristic
359C22×C71#52511yescharacteristic
360C22×C71C2×#12411yescharacteristic
361C22×C71#52911yescharacteristic
362C22×C71C2×#12711yescharacteristic
363C22×C71#53311yescharacteristic
364C22×C71#53611yescharacteristic
365C22×C71#53711yescharacteristic
366C22×C71#54111yescharacteristic
367C22×C71#54211yescharacteristic
368C22×C71#54611yescharacteristic
369C22×C71#54611yescharacteristic
370C22×C71#54611yescharacteristic
371C22×C71#54711yescharacteristic
372C22×C71#54711yescharacteristic
373C22×C71#54711yescharacteristic
374C22×C71#54811yescharacteristic
375C22×C71#54811yescharacteristic
376C22×C71#54811yescharacteristic
377C22×C71D4×Q811yescharacteristic
378C22×C71D4×Q811yescharacteristic
379C22×C71D4×Q811yescharacteristic
380C22×C71#55211yescharacteristic
381C22×C71#55211yescharacteristic
382C22×C71#55411yescharacteristic
383C22×C71#55611yescharacteristic
384C2×D71—24no—
385C2×D71—24no—
386C2×D71—24no—
387C2×D71—42no—
388C2×D71—42no—
389C2×D71—42no—
390C2×D71—42no—
391C2×D71—42no—
392C2×D71—42no—
393C2×D71—42no—
394C2×D71—42no—
395C2×D71—42no—
396C2×D71—42no—
397C2×D71—42no—
398C2×D71—42no—
399C4×C71—28no—
400C4×C71—24no—
401C4×C71—42no—
402C4×C71—44no—
403C4×C71#39018yes—
404Dic71—42no—
405Dic71—42no—
406Dic71—44no—
407Dic71—42no—
408Dic71—82no—
409#13997—711nomaximal, Sylow
410C2×C71C2×#39011yescharacteristic
411C2×C71C4×C22⋊Q811yescharacteristic
412C2×C71#232311yescharacteristic
413C2×C71#233911yescharacteristic
414C2×C71Q8×C22⋊C411yescharacteristic
415C2×C71#236011yescharacteristic
416C2×C71#236211yescharacteristic
417C2×C71#241511yescharacteristic
418C2×C71#241711yescharacteristic
419C2×C71#242711yescharacteristic
420C2×C71#242911yescharacteristic
421C2×C71#248911yescharacteristic
422C2×C71#249211yescharacteristic
423C2×C71#254011yescharacteristic
424C2×C71#254211yescharacteristic
425D71—44no—
426C22×C22⋊Q8—711no—
427C2×#391—711no—
428C2×#391—711no—
429C2×#389—711no—
430C2×#380—711no—
431C2×C4×C4⋊C4D7111yescharacteristic, complemented
432C2×C4×C22⋊C4—711no—
433#1445—712no—
434#1439—712no—
435#1437—712no—
436C4⋊#95—712no—
437C71#1399711yescharacteristic, complemented, Sylow
438C23×Q8—711no—
439C24×C4—711no—
440C2×C22⋊Q8—718no—
441C2×C22⋊Q8—1424no—
442C2×C22⋊Q8—1424no—
443C22×C4⋊C4—712no—
444C22×C4⋊C4—712no—
445C22×C4⋊C4—711no—
446C22×C4⋊C4C2×D7111yescharacteristic
447C22×C4⋊C4C2×D7111yescharacteristic
448C22×C22⋊C4—712no—
449C22×C22⋊C4—712no—
450C22×C22⋊C4—711no—
451C22×C22⋊C4—711no—
452C22×C42—711no—
453C22×C42C2×D7112yes—
454C22×C42C2×D7111yescharacteristic
455#391—1424no—
456#391—1424no—
457#389—1424no—
458#380—1424no—
459C4×C4⋊C4—24no—
460C4×C22⋊C4—1424no—
461C2×#95—711no—
462C2×#95—712no—
463C2×#95—712no—
464C2×#95—712no—
465C2×#95—712no—
466C2×#95—712no—
467C2×#95—712no—
468C2×#95—711no—
469C2×#95C2×D7112yes—
470C25—711no—
471C22×Q8—714no—
472C22×Q8—1422no—
473C22×Q8—1422no—
474C22×Q8—1422no—
475C22×Q8—1422no—
476C22×Q8—1422no—
477C22×Q8—1422no—
478C23×C4—711no—
479C23×C4—712no—
480C23×C4—711no—
481C23×C4—711no—
482C23×C4—714no—
483C23×C4—712no—
484C23×C4—1422no—
485C23×C4—1422no—
486C23×C4—1422no—
487C23×C4—1422no—
488C23×C4—1422no—
489C23×C4—1422no—
490C23×C4C22×D7112yes—
491C23×C4C22×D7111yescharacteristic
492C23×C4C22×D7112yes—
493C23×C4C22×D7111yescharacteristic
494C23×C4C22×D7111yescharacteristic
495C22⋊Q8—14232no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—2842no—
499C2×C4⋊C4—718no—
500C2×C4⋊C4—1424no—
501C2×C4⋊C4—1422no—
502C2×C4⋊C4—1424no—
503C2×C4⋊C4—1422no—
504C2×C4⋊C4—1422no—
505C2×C4⋊C4—1424no—
506C2×C4⋊C4—1424no—
507C2×C4⋊C4C4×D7114yes—
508C2×C4⋊C4D28414yes—
509C2×C4⋊C4D28414yes—
510C2×C4⋊C4C22⋊D7114yes—
511C2×C22⋊C4—2842no—
512C2×C22⋊C4—718no—
513C2×C22⋊C4—714no—
514C2×C22⋊C4—1424no—
515C2×C22⋊C4—1424no—
516C2×C22⋊C4—1422no—
517C2×C22⋊C4—1422no—
518C2×C22⋊C4—1424no—
519C2×C22⋊C4—1424no—
520C2×C22⋊C4—1422no—
521C2×C22⋊C4—1422no—
522C2×C22⋊C4—1422no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—24no—
526C2×C42—24no—
527C2×C42—42no—
528C2×C42—1422no—
529C2×C42—1422no—
530C2×C42—1422no—
531C2×C42D28414yes—
532#95—24no—
533#95—1422no—
534#95—1422no—
535#95—1424no—
536#95—1424no—
537#95—1424no—
538#95—1424no—
539#95—1424no—
540#95—1424no—
541C24—712no—
542C24—712no—
543C24—712no—
544C24—1421no—
545C24—1421no—
546C24—1421no—
547C24—1421no—
548C24—1421no—
549C24—1421no—
550C24—1421no—
551C24—1421no—
552C24—1421no—
553C24—1421no—
554C24—1421no—
555C24—1421no—
556C24C23×D7111yescharacteristic
557C2×Q8—2844no—
558C2×Q8—2844no—
559C2×Q8—2844no—
560C2×Q8—2844no—
561C2×Q8—1428no—
562C2×Q8—1428no—
563C2×Q8—1428no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—2844no—
585C22×C4—2844no—
586C22×C4—2844no—
587C22×C4—2844no—
588C22×C4—714no—
589C22×C4—712no—
590C22×C4—712no—
591C22×C4—712no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1422no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4—1422no—
599C22×C4—1422no—
600C22×C4—1421no—
601C22×C4—1421no—
602C22×C4—1421no—
603C22×C4—1421no—
604C22×C4—1421no—
605C22×C4—1421no—
606C22×C4—1422no—
607C22×C4—1422no—
608C22×C4—1421no—
609C22×C4—1421no—
610C22×C4—1421no—
611C22×C4—1422no—
612C22×C4—1421no—
613C22×C4—1421no—
614C22×C4—1421no—
615C22×C4—1421no—
616C22×C4—1421no—
617C22×C4—1422no—
618C22×C4—1422no—
619C22×C4—1421no—
620C22×C4—1421no—
621C22×C4—1421no—
622C22×C4—1421no—
623C22×C4—1428no—
624C22×C4—1428no—
625C22×C4—1428no—
626C22×C4C2×C4×D7114yes—
627C22×C4C2×C4×D7112yes—
628C22×C4C2×C22⋊D7114yes—
629C22×C4C2×C22⋊D7112yes—
630C22×C4C2×D28412yes—
631C22×C4C2×D28414yes—
632C22×C4C2×D28414yes—
633C22×C4C2×D28412yes—
634C22×C4C2×D28412yes—
635C22×C4C2×D28412yes—
636C22×C4C2×D28412yes—
637C22×C4Q8×D7112yes—
638C22×C4#1176586412yes—
639C22×C4#1176586512yes—
640C22×C4#1176586512yes—
641C4⋊C4—28no—
642C4⋊C4—2848no—
643C4⋊C4—2844no—
644C4⋊C4—14216no—
645C4⋊C4(C2×D71)⋊C4116yescomplemented
646C22⋊C4—2848no—
647C22⋊C4—1428no—
648C22⋊C4—14216no—
649C22⋊C4—1428no—
650C42—28no—
651C42—48no—
652C42—2844no—
653C23—2841no—
654C23—2841no—
655C23—2841no—
656C23—2841no—
657C23—2841no—
658C23—2841no—
659C23—2841no—
660C23—2841no—
661C23—2841no—
662C23—2841no—
663C23—2841no—
664C23—2841no—
665C23—2841no—
666C23—2841no—
667C23—2841no—
668C23—2841no—
669C23—714no—
670C23—1422no—
671C23—1422no—
672C23—1422no—
673C23—1422no—
674C23—1422no—
675C23—1422no—
676C23—1422no—
677C23—1422no—
678C23—1422no—
679C23—1422no—
680C23—1422no—
681C23—1422no—
682C23—1422no—
683C23—1422no—
684C23—1422no—
685C23—1422no—
686C23—1422no—
687C23—1422no—
688C23C22×C4×D7111yescharacteristic
689C23C22×C22⋊D7111yescharacteristic
690C23C22×D28411yescharacteristic
691C23C22×D28411yescharacteristic
692C23C22×D28411yescharacteristic
693C23C2×Q8×D7111yescharacteristic
694C23#41×D7111yescharacteristic
695C23#41×D7111yescharacteristic
696C23C2×#1176586411yescharacteristic
697C23C2×#1176586511yescharacteristic
698C23C2×#1176586511yescharacteristic
699C23#1455617311yescharacteristic
700C23#1455617511yescharacteristic
701C23#1455617511yescharacteristic
702C23#1455617611yescharacteristic
703Q8—28416no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—2841no—
731C2×C4—2841no—
732C2×C4—2841no—
733C2×C4—2841no—
734C2×C4—2841no—
735C2×C4—2841no—
736C2×C4—2841no—
737C2×C4—2841no—
738C2×C4—2842no—
739C2×C4—2842no—
740C2×C4—2841no—
741C2×C4—2842no—
742C2×C4—2841no—
743C2×C4—2841no—
744C2×C4—2841no—
745C2×C4—2842no—
746C2×C4—28416no—
747C2×C4—2842no—
748C2×C4—2842no—
749C2×C4—2842no—
750C2×C4—2842no—
751C2×C4—2842no—
752C2×C4—2842no—
753C2×C4—2842no—
754C2×C4—1422no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1424no—
759C2×C4—1422no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1424no—
763C2×C4—1424no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4C2×(C2×D71)⋊C418yes—
767C2×C4C2×(C2×D71)⋊C414yes—
768C2×C4C4×D28414yes—
769C2×C4C4×D28414yes—
770C2×C4#1455610214yes—
771C2×C4#1455610214yes—
772C2×C4#1455610814yescomplemented
773C2×C4#1455611614yes—
774C2×C4#1455612514yes—
775C22—2842no—
776C22—2842no—
777C22—2842no—
778C22—2842no—
779C22—2842no—
780C22—2842no—
781C22—2842no—
782C22—2842no—
783C22—2842no—
784C22—2842no—
785C22—2842no—
786C22—2842no—
787C22—1424no—
788C22—1424no—
789C22—1424no—
790C22C22×(C2×D71)⋊C411yescharacteristic
791C22C2×C4×D28411yescharacteristic
792C22C2×C4×D28411yescharacteristic
793C22C4×Q8×D7111yescharacteristic
794C22C4×#1176586411yescharacteristic
795C22#1798647511yescharacteristic
796C22#1798647811yescharacteristic
797C22C2×#1455610211yescharacteristic
798C22C2×#1455610211yescharacteristic
799C22C2×#1455610811yescharacteristic
800C22#1798651111yescharacteristic
801C22C2×#1455611611yescharacteristic
802C22#1798653111yescharacteristic
803C22C2×#1455612511yescharacteristic
804C22#1798655311yescharacteristic
805C22#1798657511yescharacteristic
806C22#1798658011yescharacteristic
807C22#1798660711yescharacteristic
808C22#1798661411yescharacteristic
809C22#1798664311yescharacteristic
810C22#1798664411yescharacteristic
811C22#1798664411yescharacteristic
812C22#1798664811yescharacteristic
813C22#1798665311yescharacteristic
814C22#1798665311yescharacteristic
815C22#1798665611yescharacteristic
816C22#1798666111yescharacteristic
817C22#1798666111yescharacteristic
818C22Q8×C22⋊D7111yescharacteristic
819C22Q8×D28411yescharacteristic
820C22Q8×D28411yescharacteristic
821C22#1798668411yescharacteristic
822C22#1798668811yescharacteristic
823C22#1798670411yescharacteristic
824C22#1798671711yescharacteristic
825C4—24no—
826C4—28no—
827C4—42no—
828C4—44no—
829C4—2842no—
830C4—2842no—
831C4—2844no—
832C4—2842no—
833C4—5682no—
834C4#1798590118yes—
835C2—2844no—
836C2C2×#1798590111yescharacteristic
837C2C4×#1455610811yescharacteristic
838C2#2259102311yescharacteristic
839C2#2259116511yescharacteristic
840C2Q8×(C2×D71)⋊C411yescharacteristic
841C2#2259134711yescharacteristic
842C2#2259136911yescharacteristic
843C2#2259176311yescharacteristic
844C2#2259178511yescharacteristic
845C2#2259191111yescharacteristic
846C2#2259193311yescharacteristic
847C2#2259267511yescharacteristic
848C2#2259270811yescharacteristic
849C2#2259327411yescharacteristic
850C2#2259328911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×C4×C4⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×C4×C4⋊C4D71
hypocenterC71#13997
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#17985905C2semidirect
3. C2×#17985904C2semidirect
4. C2×#17985898C2semidirect
7. #22586607C2semidirect
10. #22586570C2semidirect
11. C2×C4×C4⋊C4×C71C2semidirect
16. C2×#14556108C4semidirect
85. C2×(C2×D71)⋊C4Q8semidirect
224. C4⋊C4×C71C22⋊C4semidirect
309. C2×C4×C71C22⋊Q8semidirect
431. C2×C4×C4⋊C4D71semidirect
437. C71#13997semidirect
645. C4⋊C4(C2×D71)⋊C4semidirect
772. C2×C4#14556108semidirect

Maximal subgroups

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

subgroupindex
C22×#145561082
C2×#179859052
C2×#179859042
C2×#179858982
C2×#179858562
C2×C4×(C2×D71)⋊C42
#225866072
#225865862
#225865782
#225865702
C2×C4×C4⋊C4×C712
#1399771