Finite Group Databasebeta

← #31919824

Subgroups — #31919824

Order 18176.

2458 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556090C211yesmaximal, characteristic
2C2×#17985901C211yesmaximal, characteristic
3C2×#17985900C211yesmaximal, characteristic
4C2×#17985898C211yesmaximal, characteristic, complemented
5C2×#17985856C212yesmaximal, complemented
6#22586586C212yesmaximal, complemented
7#22586582C212yesmaximal, complemented
8#22586569C211yesmaximal, characteristic, complemented
9(C2×D71)⋊#95C212yesmaximal, complemented
10C4×C71⋊#95C211yesmaximal, characteristic, complemented
11C2×#389×C71C211yesmaximal, characteristic, complemented
12C23×D284C2211yescharacteristic
13C23×C4×D71C2212yes—
14C2×#14556090—24no—
15C2×#14556090—24no—
16C2×#14556090C418yescomplemented
17C22×C4⋊Dic71C2211yescharacteristic
18C22×C4⋊Dic71C2212yes—
19C22×(C2×D71)⋊C4C2212yes—
20C22×(C2×D71)⋊C4C2212yes—
21C22×(C2×D71)⋊C4C2212yes—
22C22×(C2×D71)⋊C4C2212yes—
23C22×(C2×D71)⋊C4C2212yes—
24C22×C4×Dic71C2211yescharacteristic
25C22×C4×Dic71C2211yescharacteristic
26#17985901—24no—
27#17985900—24no—
28#17985898—24no—
29#17985856—28no—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2211yescharacteristic
32C2×C71⋊#95C2211yescharacteristic
33C2×C71⋊#95C2211yescharacteristic
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2212yes—
36C2×C71⋊#95C2211yescharacteristic
37C22×C4⋊C4×C71C2211yescharacteristic
38C22×C4⋊C4×C71C2212yes—
39C22×C4⋊C4×C71C2211yescharacteristic
40C22×C42×C71C2211yescharacteristic
41#389×C71—24no—
42C2×#95×C71C2212yes—
43C24×D71C2312yes—
44C22×D284—22no—
45C22×D284—22no—
46C22×D284—22no—
47C22×D284—22no—
48C22×D284C2×C414yes—
49C22×D284D414yes—
50C22×D284Q814yes—
51C23×Dic71C2312yes—
52C23×Dic71C2311yescharacteristic
53C23×Dic71C2311yescharacteristic
54C23×Dic71C2311yescharacteristic
55C23×Dic71C2311yescharacteristic
56C22×C4×D71—24no—
57C22×C4×D71—24no—
58C22×C4×D71—24no—
59C22×C4×D71—24no—
60C22×C4×D71—42no—
61C22×C4×D71—42no—
62C22×C4×D71C2×C418yes—
63#14556090—232no—
64C2×C4⋊Dic71—24no—
65C2×C4⋊Dic71—24no—
66C2×C4⋊Dic71—22no—
67C2×C4⋊Dic71—22no—
68C2×C4⋊Dic71—22no—
69C2×C4⋊Dic71—42no—
70C2×(C2×D71)⋊C4—24no—
71C2×(C2×D71)⋊C4—24no—
72C2×(C2×D71)⋊C4—24no—
73C2×(C2×D71)⋊C4—24no—
74C2×(C2×D71)⋊C4—24no—
75C2×(C2×D71)⋊C4—24no—
76C2×(C2×D71)⋊C4—24no—
77C2×(C2×D71)⋊C4—24no—
78C2×(C2×D71)⋊C4—24no—
79C2×(C2×D71)⋊C4—24no—
80C2×(C2×D71)⋊C4—42no—
81C2×(C2×D71)⋊C4—42no—
82C2×(C2×D71)⋊C4—42no—
83C2×(C2×D71)⋊C4—42no—
84C2×(C2×D71)⋊C4C2×C418yes—
85C2×C4×Dic71—22no—
86C2×C4×Dic71—22no—
87C2×C4×Dic71—22no—
88C2×C4×Dic71—22no—
89C2×C4×Dic71—22no—
90C2×C4×Dic71C2×C414yes—
91C71⋊#95—24no—
92C71⋊#95—22no—
93C71⋊#95—22no—
94C71⋊#95—24no—
95C71⋊#95—22no—
96C71⋊#95—42no—
97C71⋊#95D414yescomplemented
98C23×C4×C71C2312yes—
99C23×C4×C71C2311yescharacteristic
100C23×C4×C71C2311yescharacteristic
101C23×C4×C71C2312yes—
102C23×C4×C71C2311yescharacteristic
103C2×C4⋊C4×C71—24no—
104C2×C4⋊C4×C71—22no—
105C2×C4⋊C4×C71—24no—
106C2×C4⋊C4×C71—22no—
107C2×C4⋊C4×C71—22no—
108C2×C4⋊C4×C71—42no—
109C2×C4⋊C4×C71C2×C414yes—
110C2×C4⋊C4×C71D414yes—
111C2×C4⋊C4×C71D414yes—
112C2×C42×C71—22no—
113C2×C42×C71—22no—
114C2×C42×C71—22no—
115#95×C71—24no—
116C23×D71—22no—
117C23×D71—22no—
118C23×D71—22no—
119C23×D71—22no—
120C23×D71—22no—
121C23×D71—22no—
122C23×D71—22no—
123C23×D71—22no—
124C23×D71—22no—
125C23×D71—22no—
126C23×D71—22no—
127C23×D71—22no—
128C23×D71C22×C414yes—
129C23×D71C2×D414yes—
130C23×D71C2×Q814yes—
131C2×D284—28no—
132C2×D284—28no—
133C2×D284—28no—
134C2×D284—28no—
135C2×D284—28no—
136C2×D284—28no—
137C2×D284C4⋊C4116yescomplemented
138C22×Dic71—21no—
139C22×Dic71—21no—
140C22×Dic71—21no—
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
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—21no—
154C22×Dic71—21no—
155C22×Dic71—21no—
156C22×Dic71—21no—
157C22×Dic71—21no—
158C22×Dic71—21no—
159C22×Dic71—21no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71C22×C412yes—
168C22×Dic71C22×C412yes—
169C22×Dic71C2×D412yes—
170C22×Dic71C2×D412yes—
171C22×Dic71#4112yes—
172C22×Dic71#4112yes—
173C2×C4×D71—216no—
174C2×C4×D71—216no—
175C2×C4×D71—48no—
176C2×C4×D71—48no—
177C2×C4×D71—48no—
178C2×C4×D71—48no—
179C2×C4×D71—48no—
180C4⋊Dic71—48no—
181C4⋊Dic71—44no—
182(C2×D71)⋊C4—216no—
183(C2×D71)⋊C4—48no—
184(C2×D71)⋊C4—48no—
185(C2×D71)⋊C4—48no—
186(C2×D71)⋊C4—48no—
187C4×Dic71—28no—
188C4×Dic71—44no—
189C24×C71C2411yescharacteristic
190C22×C4×C71—22no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—22no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71C22×C414yes—
214C22×C4×C71C22×C412yes—
215C22×C4×C71C2×D412yes—
216C22×C4×C71C2×D412yes—
217C22×C4×C71C2×D414yes—
218C22×C4×C71C2×D412yes—
219C22×C4×C71C2×D414yes—
220C22×C4×C71C2×D412yes—
221C22×C4×C71C2×Q812yes—
222C22×C4×C71#4112yes—
223C22×C4×C71#4112yes—
224C22×C4×C71#4112yes—
225C4⋊C4×C71—48no—
226C4⋊C4×C71—44no—
227C4⋊C4×C71C22⋊C4116yescomplemented
228C42×C71—44no—
229C23×C71C23×C411yescharacteristic
230C23×C71C22×D411yescharacteristic
231C23×C71C22×D411yescharacteristic
232C23×C71C22×D411yescharacteristic
233C23×C71C22×D411yescharacteristic
234C23×C71C22×Q811yescharacteristic
235C23×C71C2×#4111yescharacteristic
236C23×C71C2×#4111yescharacteristic
237C23×C71C2×#4111yescharacteristic
238C23×C71C2×#4111yescharacteristic
239C23×C71C2×#4111yescharacteristic
240C23×C71H(5,𝔽2)11yescharacteristic
241C23×C71H(5,𝔽2)11yescharacteristic
242C23×C71H(5,𝔽2)11yescharacteristic
243C23×C712−1+411yescharacteristic
244C22×D71—24no—
245C22×D71—24no—
246C22×D71—24no—
247C22×D71—24no—
248C22×D71—24no—
249C22×D71—24no—
250C22×D71—24no—
251C22×D71—24no—
252C22×D71—24no—
253C22×D71—24no—
254C22×D71—24no—
255C22×D71—24no—
256C22×D71—24no—
257C22×D71—24no—
258C22×D71—24no—
259C22×D71—24no—
260C22×D71—24no—
261C22×D71—24no—
262C22×D71—42no—
263C22×D71—42no—
264C22×D71—42no—
265C22×D71—42no—
266C22×D71—42no—
267C22×D71—42no—
268C22×D71—42no—
269C22×D71—42no—
270C22×D71—42no—
271C22×D71—42no—
272C22×D71—42no—
273C22×D71—42no—
274C22×D71—42no—
275C22×D71—42no—
276C22×D71—42no—
277C22×D71—42no—
278C22×D71C2×C4⋊C418yes—
279C2×C4×C71—24no—
280C2×C4×C71—24no—
281C2×C4×C71—24no—
282C2×C4×C71—24no—
283C2×C4×C71—24no—
284C2×C4×C71—24no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—41no—
292C2×C4×C71—41no—
293C2×C4×C71—41no—
294C2×C4×C71—41no—
295C2×C4×C71—41no—
296C2×C4×C71—41no—
297C2×C4×C71—41no—
298C2×C4×C71—41no—
299C2×C4×C71—42no—
300C2×C4×C71—42no—
301C2×C4×C71—42no—
302C2×C4×C71—42no—
303C2×C4×C71—42no—
304C2×C4×C71—42no—
305C2×C4×C71—42no—
306C2×C4×C71C2×C22⋊C418yes—
307C2×C4×C71C2×C22⋊C414yes—
308C2×C4×C71C2×C4⋊C414yes—
309C2×C4×C71#11714yes—
310C2×C4×C71#12114yes—
311C2×C4×C71#12114yes—
312C2×C4×C71C22⋊Q814yes—
313C2×C4×C71C22⋊Q814yes—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
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—41no—
330C2×Dic71—41no—
331C2×Dic71—41no—
332C2×Dic71—41no—
333C2×Dic71—41no—
334C2×Dic71—41no—
335C2×Dic71—41no—
336C2×Dic71—41no—
337C2×Dic71—41no—
338C2×Dic71—41no—
339C2×Dic71—41no—
340C2×Dic71—41no—
341C2×Dic71—42no—
342C2×Dic71—42no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345C2×Dic71—42no—
346C2×Dic71—42no—
347C2×Dic71—42no—
348C2×Dic71C4×D414yes—
349D284—232no—
350C4×D71—432no—
351C22×C71C22×C22⋊C411yescharacteristic
352C22×C71C22×C4⋊C411yescharacteristic
353C22×C71C2×#11711yescharacteristic
354C22×C71C2×C4×D411yescharacteristic
355C22×C71C4×#4111yescharacteristic
356C22×C71#51811yescharacteristic
357C22×C71#52011yescharacteristic
358C22×C71C2×#12111yescharacteristic
359C22×C71C2×#12111yescharacteristic
360C22×C71C2×C22⋊Q811yescharacteristic
361C22×C71C2×C22⋊Q811yescharacteristic
362C22×C71#52911yescharacteristic
363C22×C71#52911yescharacteristic
364C22×C71#53211yescharacteristic
365C22×C71#53211yescharacteristic
366C22×C71#54011yescharacteristic
367C22×C71#54011yescharacteristic
368C22×C71#54211yescharacteristic
369C22×C71#54211yescharacteristic
370C22×C71D4211yescharacteristic
371C22×C71D4211yescharacteristic
372C22×C71D4211yescharacteristic
373C22×C71#54611yescharacteristic
374C22×C71#54611yescharacteristic
375C22×C71#54611yescharacteristic
376C22×C71#54611yescharacteristic
377C22×C71#54711yescharacteristic
378C22×C71#54811yescharacteristic
379C22×C71#54811yescharacteristic
380C22×C71D4×Q811yescharacteristic
381C22×C71#55011yescharacteristic
382C22×C71#55011yescharacteristic
383C22×C71#55411yescharacteristic
384C22×C71#55411yescharacteristic
385C22×C71#55411yescharacteristic
386C2×D71—28no—
387C2×D71—28no—
388C2×D71—28no—
389C2×D71—44no—
390C2×D71—44no—
391C2×D71—44no—
392C2×D71—44no—
393C2×D71—44no—
394C2×D71—44no—
395C2×D71—44no—
396C2×D71—44no—
397C2×D71—44no—
398C2×D71—44no—
399C2×D71—44no—
400C2×D71—44no—
401C4×C71—28no—
402C4×C71—42no—
403C4×C71—42no—
404C4×C71—82no—
405C4×C71#38018yescomplemented
406Dic71—24no—
407Dic71—42no—
408Dic71—42no—
409Dic71—42no—
410Dic71—82no—
411#13920—711nomaximal, Sylow
412C2×C71C2×#38011yescharacteristic
413C2×C71#229311yescharacteristic
414C2×C71#231911yescharacteristic
415C2×C71D4×C22⋊C411yescharacteristic
416C2×C71#234111yescharacteristic
417C2×C71D4×C4⋊C411yescharacteristic
418C2×C71#234911yescharacteristic
419C2×C71#242711yescharacteristic
420C2×C71#242711yescharacteristic
421C2×C71#242811yescharacteristic
422C2×C71#242811yescharacteristic
423C2×C71#245211yescharacteristic
424C2×C71#245211yescharacteristic
425C2×C71#245411yescharacteristic
426C2×C71#245411yescharacteristic
427D71—48no—
428C22×C4×D4—711no—
429C2×#390—711no—
430C2×#390—711no—
431C2×#389—711no—
432C2×#389D7111yescharacteristic, complemented
433C2×#380—712no—
434#1439—712no—
435#1439—712no—
436C4⋊#95—711no—
437C22⋊#95—712no—
438C4×#95—711no—
439C71#1392011yescharacteristic, complemented, Sylow
440C23×D4—711no—
441C24×C4—712no—
442C2×C4×D4—718no—
443C2×C4×D4—1424no—
444C2×C4×D4—1424no—
445C22×C4⋊C4—712no—
446C22×C4⋊C4—711no—
447C22×C4⋊C4C2×D7111yescharacteristic
448C22×C4⋊C4C2×D7112yes—
449C22×C4⋊C4C2×D7111yescharacteristic
450C22×C22⋊C4—712no—
451C22×C22⋊C4—712no—
452C22×C22⋊C4—712no—
453C22×C22⋊C4—712no—
454C22×C22⋊C4—712no—
455C22×C42—711no—
456C22×C42—711no—
457C22×C42C2×D7111yescharacteristic
458#390—1424no—
459#390—1424no—
460#389—24no—
461#389—1424no—
462#380—1428no—
463C2×#95—712no—
464C2×#95—711no—
465C2×#95—711no—
466C2×#95—711no—
467C2×#95—711no—
468C2×#95—712no—
469C2×#95—712no—
470C2×#95C2×D7112yes—
471C25—712no—
472C22×D4—714no—
473C22×D4—714no—
474C22×D4—714no—
475C22×D4—1422no—
476C22×D4—1422no—
477C22×D4—1422no—
478C22×D4—1422no—
479C23×C4—2842no—
480C23×C4—2842no—
481C23×C4—718no—
482C23×C4—711no—
483C23×C4—711no—
484C23×C4—711no—
485C23×C4—711no—
486C23×C4—712no—
487C23×C4—1424no—
488C23×C4—1424no—
489C23×C4—1424no—
490C23×C4—1424no—
491C23×C4C22×D7112yes—
492C23×C4C22×D7111yescharacteristic
493C23×C4C22×D7111yescharacteristic
494C23×C4C22×D7112yes—
495C23×C4C22×D7111yescharacteristic
496C4×D4—14232no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—42no—
503C2×C4⋊C4—2842no—
504C2×C4⋊C4—1424no—
505C2×C4⋊C4—1422no—
506C2×C4⋊C4—1424no—
507C2×C4⋊C4—1422no—
508C2×C4⋊C4—1422no—
509C2×C4⋊C4C4×D7114yes—
510C2×C4⋊C4D28414yes—
511C2×C4⋊C4C22⋊D7114yes—
512C2×C22⋊C4—2842no—
513C2×C22⋊C4—2842no—
514C2×C22⋊C4—2842no—
515C2×C22⋊C4—2842no—
516C2×C22⋊C4—718no—
517C2×C22⋊C4—1424no—
518C2×C22⋊C4—1424no—
519C2×C22⋊C4—1424no—
520C2×C22⋊C4—1424no—
521C2×C22⋊C4—1424no—
522C2×C22⋊C4—1424no—
523C2×C22⋊C4—1424no—
524C2×C22⋊C4—1424no—
525C2×C22⋊C4—1424no—
526C2×C22⋊C4—1424no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—714no—
531C2×C42—1422no—
532C2×C42—1422no—
533C2×C42—1422no—
534C2×C42—1422no—
535C2×C42—1422no—
536#95—24no—
537#95—2842no—
538#95—714no—
539#95—1424no—
540#95—1422no—
541#95—1422no—
542#95—1424no—
543#95—1422no—
544C24—714no—
545C24—714no—
546C24—714no—
547C24—1422no—
548C24—1422no—
549C24—1422no—
550C24—1422no—
551C24—1422no—
552C24—1422no—
553C24—1422no—
554C24—1422no—
555C24—1422no—
556C24—1422no—
557C24—1422no—
558C24—1422no—
559C24C23×D7111yescharacteristic
560C2×D4—7116no—
561C2×D4—1428no—
562C2×D4—1428no—
563C2×D4—1428no—
564C2×D4—1428no—
565C2×D4—1428no—
566C2×D4—1428no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—2848no—
591C22×C4—2848no—
592C22×C4—2848no—
593C22×C4—2848no—
594C22×C4—2848no—
595C22×C4—712no—
596C22×C4—712no—
597C22×C4—712no—
598C22×C4—712no—
599C22×C4—712no—
600C22×C4—712no—
601C22×C4—14216no—
602C22×C4—1422no—
603C22×C4—1422no—
604C22×C4—1422no—
605C22×C4—1422no—
606C22×C4—1422no—
607C22×C4—1422no—
608C22×C4—1422no—
609C22×C4—1421no—
610C22×C4—1421no—
611C22×C4—1421no—
612C22×C4—1421no—
613C22×C4—1421no—
614C22×C4—1421no—
615C22×C4—1421no—
616C22×C4—1421no—
617C22×C4—1421no—
618C22×C4—1421no—
619C22×C4—1421no—
620C22×C4—1421no—
621C22×C4—1421no—
622C22×C4—1421no—
623C22×C4—1421no—
624C22×C4—1421no—
625C22×C4—1421no—
626C22×C4—1421no—
627C22×C4—14216no—
628C22×C4—1421no—
629C22×C4—1421no—
630C22×C4—1421no—
631C22×C4—1421no—
632C22×C4C2×C4×D7114yes—
633C22×C4C2×C4×D7112yes—
634C22×C4D4×D7112yes—
635C22×C4D4×D7112yes—
636C22×C4C2×C22⋊D7114yes—
637C22×C4C2×C22⋊D7112yes—
638C22×C4C2×D28414yes—
639C22×C4C2×D28412yes—
640C22×C4Q8×D7112yes—
641C22×C4#1176586412yes—
642C22×C4#1176586612yes—
643C22×C4#1176586612yes—
644C4⋊C4—48no—
645C4⋊C4—44no—
646C4⋊C4—2848no—
647C4⋊C4—2844no—
648C4⋊C4(C2×D71)⋊C4116yescomplemented
649C22⋊C4—2848no—
650C22⋊C4—2848no—
651C22⋊C4—2848no—
652C22⋊C4—2848no—
653C22⋊C4—14216no—
654C42—44no—
655C42—2844no—
656C42—1428no—
657C23—2842no—
658C23—2842no—
659C23—2842no—
660C23—2842no—
661C23—2842no—
662C23—2842no—
663C23—2842no—
664C23—2842no—
665C23—2842no—
666C23—2842no—
667C23—2842no—
668C23—2842no—
669C23—2842no—
670C23—2842no—
671C23—2842no—
672C23—2842no—
673C23—718no—
674C23—1424no—
675C23—1424no—
676C23—1424no—
677C23—1424no—
678C23—1424no—
679C23—1424no—
680C23—1424no—
681C23—1424no—
682C23—1424no—
683C23—1424no—
684C23—1424no—
685C23—1424no—
686C23—1424no—
687C23—1424no—
688C23—1424no—
689C23—1424no—
690C23—1424no—
691C23—1424no—
692C23C22×C4×D7111yescharacteristic
693C23C2×D4×D7111yescharacteristic
694C23C2×D4×D7111yescharacteristic
695C23C22×C22⋊D7111yescharacteristic
696C23C22×D28411yescharacteristic
697C23C2×Q8×D7111yescharacteristic
698C23#41×D7111yescharacteristic
699C23#41×D7111yescharacteristic
700C23C2×#1176586411yescharacteristic
701C23C2×#1176586611yescharacteristic
702C23C2×#1176586611yescharacteristic
703C23#1455617311yescharacteristic
704C23#1455617411yescharacteristic
705C23#1455617411yescharacteristic
706C23#1455617611yescharacteristic
707D4—14232no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—28432no—
736C2×C4—2841no—
737C2×C4—2841no—
738C2×C4—2841no—
739C2×C4—2841no—
740C2×C4—2841no—
741C2×C4—2841no—
742C2×C4—2841no—
743C2×C4—2841no—
744C2×C4—2841no—
745C2×C4—2841no—
746C2×C4—2841no—
747C2×C4—2841no—
748C2×C4—2842no—
749C2×C4—2842no—
750C2×C4—2842no—
751C2×C4—2842no—
752C2×C4—2842no—
753C2×C4—2842no—
754C2×C4—2842no—
755C2×C4—714no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1422no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1422no—
770C2×C4—1422no—
771C2×C4C2×(C2×D71)⋊C418yes—
772C2×C4C2×(C2×D71)⋊C414yes—
773C2×C4C4⋊C4×D7114yes—
774C2×C4#1455608614yes—
775C2×C4#1455609914yes—
776C2×C4#1455610314yes—
777C2×C4#1455610414yes—
778C2×C4#1455610814yes—
779C22—2844no—
780C22—2844no—
781C22—2844no—
782C22—2844no—
783C22—2844no—
784C22—2844no—
785C22—2844no—
786C22—2844no—
787C22—2844no—
788C22—2844no—
789C22—2844no—
790C22—2844no—
791C22—1428no—
792C22—1428no—
793C22—1428no—
794C22C22×(C2×D71)⋊C411yescharacteristic
795C22C2×C4⋊C4×D7111yescharacteristic
796C22C2×#1455608611yescharacteristic
797C22C4×D4×D7111yescharacteristic
798C22C4×#1176586611yescharacteristic
799C22#1798647111yescharacteristic
800C22#1798648111yescharacteristic
801C22C2×#1455609911yescharacteristic
802C22C2×#1455610311yescharacteristic
803C22C2×#1455610411yescharacteristic
804C22C2×#1455610811yescharacteristic
805C22#1798653411yescharacteristic
806C22#1798653511yescharacteristic
807C22#1798654411yescharacteristic
808C22#1798655011yescharacteristic
809C22#1798660211yescharacteristic
810C22#1798660511yescharacteristic
811C22#1798662211yescharacteristic
812C22#1798662311yescharacteristic
813C22D4×C22⋊D7111yescharacteristic
814C22#1798663311yescharacteristic
815C22D4×D28411yescharacteristic
816C22#1798663711yescharacteristic
817C22#1798664011yescharacteristic
818C22#1798664411yescharacteristic
819C22#1798664611yescharacteristic
820C22#1798665111yescharacteristic
821C22#1798666011yescharacteristic
822C22#1798666111yescharacteristic
823C22#1798666411yescharacteristic
824C22#1798666811yescharacteristic
825C22#1798667111yescharacteristic
826C22#1798670511yescharacteristic
827C22#1798670511yescharacteristic
828C22#1798671011yescharacteristic
829C4—28no—
830C4—42no—
831C4—42no—
832C4—82no—
833C4—2842no—
834C4—2842no—
835C4—2842no—
836C4—5682no—
837C4—1424no—
838C4#1798585618yescomplemented
839C2—2848no—
840C2C2×#1798585611yescharacteristic
841C2#2259079811yescharacteristic
842C2#2259097911yescharacteristic
843C2D4×(C2×D71)⋊C411yescharacteristic
844C2#2259117811yescharacteristic
845C2#2259124111yescharacteristic
846C2#2259124911yescharacteristic
847C2#2259191311yescharacteristic
848C2#2259191511yescharacteristic
849C2#2259192411yescharacteristic
850C2#2259192611yescharacteristic
851C2#2259218611yescharacteristic
852C2#2259218811yescharacteristic
853C2#2259220811yescharacteristic
854C2#2259221011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#389×C71C2
socle, cosocleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×#389D71
hypocenterC71#13920
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#17985898C2semidirect
5. C2×#17985856C2semidirect
6. #22586586C2semidirect
7. #22586582C2semidirect
8. #22586569C2semidirect
9. (C2×D71)⋊#95C2semidirect
10. C4×C71⋊#95C2semidirect
11. C2×#389×C71C2semidirect
16. C2×#14556090C4semidirect
97. C71⋊#95D4semidirect
137. C2×D284C4⋊C4semidirect
227. C4⋊C4×C71C22⋊C4semidirect
405. C4×C71#380semidirect
432. C2×#389D71semidirect
439. C71#13920semidirect
648. C4⋊C4(C2×D71)⋊C4semidirect
838. C4#17985856semidirect

Maximal subgroups

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

subgroupindex
C22×#145560902
C2×#179859012
C2×#179859002
C2×#179858982
C2×#179858562
#225865862
#225865822
#225865692
(C2×D71)⋊#952
C4×C71⋊#952
C2×#389×C712
#1392071