Finite Group Databasebeta

← #31919839

Subgroups — #31919839

Order 18176.

4166 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D71C211yesmaximal, characteristic
2C2×#17985906C211yesmaximal, characteristic, complemented
3C2×#17985905C211yesmaximal, characteristic, complemented
4C2×#17985904C211yesmaximal, characteristic, complemented
5C2×#17985856C211yesmaximal, characteristic
6C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
7#22586610C214yesmaximal, complemented
8(C2×D71)⋊#95C214yesmaximal
9C2×#391×C71C211yesmaximal, characteristic, complemented
10C23×Dic142C2212yes—
11C23×Dic142C2211yescharacteristic
12C22×Q8×D71—24no—
13C22×Q8×D71—24no—
14C22×Q8×D71—24no—
15C22×Q8×D71—24no—
16C22×Q8×D71—24no—
17C22×Q8×D71—24no—
18C22×Q8×D71C418yescomplemented
19C23×C4×D71C2212yes—
20C23×C4×D71C2211yescharacteristic
21C22×C4⋊Dic71C2211yescharacteristic
22C22×(C2×D71)⋊C4C2212yes—
23C22×(C2×D71)⋊C4C2212yes—
24C22×C4×Dic71C2211yescharacteristic
25#17985906—24no—
26#17985905—24no—
27#17985904—24no—
28#17985856—24no—
29C4×(C2×D71)⋊C4—24no—
30C2×C71⋊#95C2214yes—
31C2×C71⋊#95C2214yes—
32C2×C71⋊#95C2214yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C23×Q8×C71C2211yescharacteristic
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C42×C71C2211yescharacteristic
38#391×C71—24no—
39C2×#95×C71C2214yes—
40C24×D71C2311yescharacteristic
41C22×Dic142—24no—
42C22×Dic142—24no—
43C22×Dic142—24no—
44C22×Dic142—24no—
45C22×Dic142—22no—
46C22×Dic142—22no—
47C22×Dic142—24no—
48C22×Dic142—22no—
49C22×Dic142—24no—
50C22×Dic142—22no—
51C22×Dic142C2×C418yes—
52C22×Dic142C2×C414yes—
53C22×Dic142D414yes—
54C22×Dic142D414yes—
55C2×Q8×D71—232no—
56C2×Q8×D71—232no—
57C2×Q8×D71—232no—
58C2×Q8×D71—232no—
59C2×Q8×D71—232no—
60C2×Q8×D71—232no—
61C2×Q8×D71—232no—
62C23×Dic71C2312yes—
63C23×Dic71C2312yes—
64C23×Dic71C2312yes—
65C23×Dic71C2311yescharacteristic
66C22×C4×D71—24no—
67C22×C4×D71—24no—
68C22×C4×D71—24no—
69C22×C4×D71—24no—
70C22×C4×D71—22no—
71C22×C4×D71—22no—
72C22×C4×D71—24no—
73C22×C4×D71—22no—
74C22×C4×D71—24no—
75C22×C4×D71—22no—
76C22×C4×D71C2×C418yes—
77C22×C4×D71C2×C414yes—
78C22×C4×D71D414yes—
79C22×C4×D71D414yes—
80C2×C4⋊Dic71—22no—
81C2×C4⋊Dic71—22no—
82C2×C4⋊Dic71—22no—
83C2×(C2×D71)⋊C4—24no—
84C2×(C2×D71)⋊C4—24no—
85C2×(C2×D71)⋊C4—24no—
86C2×(C2×D71)⋊C4—28no—
87C2×(C2×D71)⋊C4Q818yescomplemented
88C2×C4×Dic71—22no—
89C2×C4×Dic71—22no—
90C2×C4×Dic71—22no—
91C71⋊#95—24no—
92C71⋊#95—24no—
93C71⋊#95—28no—
94C71⋊#95—28no—
95C71⋊#95—28no—
96C22×Q8×C71—22no—
97C22×Q8×C71—22no—
98C22×Q8×C71—22no—
99C22×Q8×C71—22no—
100C22×Q8×C71C2×C414yes—
101C22×Q8×C71D414yes—
102C22×Q8×C71D414yes—
103C23×C4×C71C2312yes—
104C23×C4×C71C2312yes—
105C23×C4×C71C2312yes—
106C23×C4×C71C2311yescharacteristic
107C2×C4⋊C4×C71—22no—
108C2×C4⋊C4×C71—22no—
109C2×C4⋊C4×C71—22no—
110C2×C42×C71—22no—
111C2×C42×C71—22no—
112C2×C42×C71—22no—
113#95×C71—28no—
114C23×D71—21no—
115C23×D71—21no—
116C23×D71—21no—
117C23×D71—21no—
118C23×D71—22no—
119C23×D71—22no—
120C23×D71C22×C412yes—
121C23×D71C2×D412yes—
122C23×D71C2×D412yes—
123C23×D71C2×Q814yes—
124C23×D71#4114yes—
125C2×Dic142—216no—
126C2×Dic142—216no—
127C2×Dic142—216no—
128C2×Dic142—216no—
129C2×Dic142—28no—
130C2×Dic142—216no—
131C2×Dic142—28no—
132C2×Dic142—28no—
133C2×Dic142—28no—
134C2×Dic142—28no—
135C2×Dic142—28no—
136C2×Dic142—216no—
137C2×Dic142—216no—
138C2×Dic142C22⋊C4116yescomplemented
139Q8×D71—2256no—
140C22×Dic71—22no—
141C22×Dic71—22no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—22no—
145C22×Dic71—21no—
146C22×Dic71—22no—
147C22×Dic71—21no—
148C22×Dic71—22no—
149C22×Dic71—22no—
150C22×Dic71—22no—
151C22×Dic71—22no—
152C22×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—24no—
158C22×Dic71—24no—
159C22×Dic71C22×C414yes—
160C22×Dic71C22×C412yes—
161C22×Dic71C2×D414yes—
162C22×Dic71C2×D414yes—
163C22×Dic71C2×D412yes—
164C22×Dic71C2×D412yes—
165C22×Dic71C2×Q814yescomplemented
166C2×C4×D71—216no—
167C2×C4×D71—216no—
168C2×C4×D71—216no—
169C2×C4×D71—216no—
170C2×C4×D71—216no—
171C2×C4×D71—28no—
172C2×C4×D71—216no—
173C2×C4×D71—28no—
174C2×C4×D71—28no—
175C2×C4×D71—28no—
176C2×C4×D71—28no—
177C2×C4×D71—28no—
178C2×C4×D71—216no—
179C2×C4×D71C22⋊C4116yes—
180C4⋊Dic71—44no—
181(C2×D71)⋊C4—216no—
182(C2×D71)⋊C4—48no—
183C4×Dic71—44no—
184C24×C71C2411yescharacteristic
185C2×Q8×C71—28no—
186C2×Q8×C71—28no—
187C2×Q8×C71—28no—
188C2×Q8×C71—28no—
189C2×Q8×C71—28no—
190C2×Q8×C71—28no—
191C2×Q8×C71C22⋊C4116yescomplemented
192C22×C4×C71—22no—
193C22×C4×C71—22no—
194C22×C4×C71—22no—
195C22×C4×C71—22no—
196C22×C4×C71—22no—
197C22×C4×C71—22no—
198C22×C4×C71—22no—
199C22×C4×C71—22no—
200C22×C4×C71—22no—
201C22×C4×C71—22no—
202C22×C4×C71—22no—
203C22×C4×C71—22no—
204C22×C4×C71—22no—
205C22×C4×C71—24no—
206C22×C4×C71—24no—
207C22×C4×C71C22×C414yes—
208C22×C4×C71C22×C412yes—
209C22×C4×C71C2×D412yes—
210C22×C4×C71C2×D412yes—
211C22×C4×C71C2×D412yes—
212C22×C4×C71C2×D412yes—
213C22×C4×C71C2×D414yes—
214C22×C4×C71C2×D412yes—
215C22×C4×C71C2×D414yes—
216C22×C4×C71C2×D412yes—
217C22×C4×C71C2×Q814yescomplemented
218C4⋊C4×C71—44no—
219C42×C71—44no—
220C23×C71C23×C411yescharacteristic
221C23×C71C22×D411yescharacteristic
222C23×C71C22×D411yescharacteristic
223C23×C71C22×D411yescharacteristic
224C23×C71C22×D411yescharacteristic
225C23×C71C22×D411yescharacteristic
226C23×C71C22×D411yescharacteristic
227C23×C71C22×Q812yes—
228C23×C71C2×#4112yes—
229C23×C712−1+412yes—
230C23×C712−1+412yes—
231C22×D71—22no—
232C22×D71—22no—
233C22×D71—24no—
234C22×D71—22no—
235C22×D71—22no—
236C22×D71—22no—
237C22×D71—22no—
238C22×D71—22no—
239C22×D71—24no—
240C22×D71—22no—
241C22×D71—24no—
242C22×D71—24no—
243C22×D71—24no—
244C22×D71—24no—
245C22×D71—24no—
246C22×D71—24no—
247C22×D71—24no—
248C22×D71—24no—
249C22×D71C2×C22⋊C414yes—
250C22×D71C4×Q818yes—
251C22×D71C22⋊Q818yes—
252C22×D71#12414yes—
253C22×D71C4⋊Q814yes—
254Q8×C71—232no—
255C2×C4×C71—24no—
256C2×C4×C71—24no—
257C2×C4×C71—24no—
258C2×C4×C71—24no—
259C2×C4×C71—24no—
260C2×C4×C71—24no—
261C2×C4×C71—24no—
262C2×C4×C71—24no—
263C2×C4×C71—24no—
264C2×C4×C71—42no—
265C2×C4×C71—42no—
266C2×C4×C71—42no—
267C2×C4×C71—42no—
268C2×C4×C71—42no—
269C2×C4×C71—42no—
270C2×C4×C71—42no—
271C2×C4×C71—44no—
272C2×C4×C71—44no—
273C2×C4×C71C2×C22⋊C414yes—
274C2×C4×C71C2×C22⋊C414yes—
275C2×C4×C71C2×C22⋊C418yes—
276C2×C4×C71C2×C22⋊C414yes—
277C2×C4×C71#12014yes—
278C2×C4×C71#12014yes—
279C2×C4×C71#12014yes—
280C2×C4×C71#12014yes—
281C2×Dic71—24no—
282C2×Dic71—22no—
283C2×Dic71—22no—
284C2×Dic71—24no—
285C2×Dic71—24no—
286C2×Dic71—22no—
287C2×Dic71—24no—
288C2×Dic71—22no—
289C2×Dic71—24no—
290C2×Dic71—22no—
291C2×Dic71—24no—
292C2×Dic71—22no—
293C2×Dic71—24no—
294C2×Dic71—24no—
295C2×Dic71—24no—
296C2×Dic71—42no—
297C2×Dic71—42no—
298C2×Dic71—42no—
299C2×Dic71—42no—
300C2×Dic71—42no—
301C2×Dic71—42no—
302C2×Dic71—42no—
303C2×Dic71—44no—
304C2×Dic71—44no—
305C2×Dic71C2×C22⋊C418yes—
306C2×Dic71C2×C22⋊C414yes—
307C4×D71—264no—
308C4×D71—232no—
309Dic142—264no—
310Dic142—232no—
311C22×C71C22×C22⋊C411yescharacteristic
312C22×C71C22×C22⋊C411yescharacteristic
313C22×C71C22×C22⋊C411yescharacteristic
314C22×C71C2×C4×Q812yes—
315C22×C71#51912yes—
316C22×C71C2×#12011yescharacteristic
317C22×C71C2×#12011yescharacteristic
318C22×C71C2×#12011yescharacteristic
319C22×C71C2×#12011yescharacteristic
320C22×C71C2×C22⋊Q812yes—
321C22×C71C2×#12411yescharacteristic
322C22×C71C2×C4⋊Q811yescharacteristic
323C22×C71#53611yescharacteristic
324C22×C71#53612yes—
325C22×C71#53611yescharacteristic
326C22×C71#54812yes—
327C22×C71#54812yes—
328C22×C71#54812yes—
329C22×C71#54812yes—
330C22×C71D4×Q812yes—
331C22×C71D4×Q812yes—
332C22×C71D4×Q812yes—
333C22×C71D4×Q812yes—
334C2×D71—24no—
335C2×D71—28no—
336C2×D71—28no—
337C2×D71—28no—
338C2×D71—28no—
339C2×D71—24no—
340C2×D71—24no—
341C2×D71—24no—
342C2×D71—24no—
343C2×D71—24no—
344C2×D71#39118yescomplemented
345C4×C71—28no—
346C4×C71—44no—
347C4×C71—82no—
348C4×C71#37918yes—
349Dic71—24no—
350Dic71—28no—
351Dic71—44no—
352Dic71—82no—
353#13922—711nomaximal, Sylow
354C2×C71C2×#37911yescharacteristic
355C2×C71C2×#39111yescharacteristic
356C2×C71#231011yescharacteristic
357C2×C71Q8×C22⋊C412yes—
358C2×C71Q8×C22⋊C412yes—
359C2×C71#240912yes—
360C2×C71#240912yes—
361C2×C71#243411yescharacteristic
362C2×C71#243411yescharacteristic
363C2×C71#243611yescharacteristic
364C2×C71#243611yescharacteristic
365D71—28no—
366C24×Q8—711no—
367C2×#391—711no—
368C2×#391—711no—
369C2×#391—711no—
370C2×#391D7111yescharacteristic, complemented
371C2×#380—711no—
372C2×C4×C22⋊C4—711no—
373#1446—714no—
374C22⋊#95—714no—
375C71#1392211yescharacteristic, complemented, Sylow
376C23×Q8—718no—
377C23×Q8—711no—
378C23×Q8—712no—
379C23×Q8—1424no—
380C23×Q8—1424no—
381C23×Q8—1424no—
382C23×Q8—1424no—
383C23×Q8—1424no—
384C23×Q8—1424no—
385C23×Q8C2×D7111yescharacteristic
386C24×C4—711no—
387C24×C4—712no—
388C22×C4⋊C4—711no—
389C22×C4⋊C4C2×D7111yescharacteristic
390C22×C22⋊C4—712no—
391C22×C22⋊C4—712no—
392C22×C42—711no—
393C22×C42C2×D7111yescharacteristic
394#391—24no—
395#391—1424no—
396#391—1424no—
397#391—1424no—
398#380—1424no—
399C4×C22⋊C4—1424no—
400C2×#95—714no—
401C2×#95—714no—
402C2×#95—714no—
403C2×#95—712no—
404C2×#95—712no—
405C2×#95C2×D7114yes—
406C25—711no—
407C22×Q8—22no—
408C22×Q8—22no—
409C22×Q8—22no—
410C22×Q8—22no—
411C22×Q8—714no—
412C22×Q8—718no—
413C22×Q8—714no—
414C22×Q8—714no—
415C22×Q8—1424no—
416C22×Q8—1424no—
417C22×Q8—1424no—
418C22×Q8—1424no—
419C22×Q8—14232no—
420C22×Q8—14232no—
421C22×Q8—14232no—
422C22×Q8—14232no—
423C22×Q8—14232no—
424C22×Q8—14232no—
425C22×Q8—14232no—
426C22×Q8—1422no—
427C22×Q8—1422no—
428C22×Q8—1424no—
429C22×Q8—1422no—
430C22×Q8—1424no—
431C22×Q8—1422no—
432C22×Q8C4×D7114yes—
433C22×Q8D28414yes—
434C22×Q8C22⋊D7114yes—
435C23×C4—711no—
436C23×C4—712no—
437C23×C4—714no—
438C23×C4—714no—
439C23×C4—714no—
440C23×C4—712no—
441C23×C4—718no—
442C23×C4—712no—
443C23×C4—1424no—
444C23×C4—1424no—
445C23×C4—1424no—
446C23×C4—1424no—
447C23×C4—1422no—
448C23×C4—1422no—
449C23×C4—1424no—
450C23×C4—1422no—
451C23×C4—1424no—
452C23×C4—1422no—
453C23×C4C22×D7112yes—
454C23×C4C22×D7112yes—
455C23×C4C22×D7112yes—
456C23×C4C22×D7111yescharacteristic
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—1422no—
461C2×C4⋊C4—1422no—
462C2×C4⋊C4—1422no—
463C2×C22⋊C4—718no—
464C2×C22⋊C4—1424no—
465C2×C22⋊C4—1428no—
466C2×C22⋊C4—1424no—
467C2×C22⋊C4—1424no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—1422no—
472C2×C42—1422no—
473C2×C42—1422no—
474#95—28no—
475#95—1424no—
476#95—1424no—
477#95—1428no—
478#95—1428no—
479#95—1428no—
480C24—712no—
481C24—712no—
482C24—712no—
483C24—714no—
484C24—714no—
485C24—1421no—
486C24—1421no—
487C24—1421no—
488C24—1421no—
489C24—1422no—
490C24—1422no—
491C24C23×D7111yescharacteristic
492C2×Q8—28no—
493C2×Q8—28no—
494C2×Q8—28no—
495C2×Q8—28no—
496C2×Q8—28no—
497C2×Q8—28no—
498C2×Q8—7116no—
499C2×Q8—14216no—
500C2×Q8—14216no—
501C2×Q8—14216no—
502C2×Q8—14216no—
503C2×Q8—14216no—
504C2×Q8—14216no—
505C2×Q8—142256no—
506C2×Q8—1428no—
507C2×Q8—14216no—
508C2×Q8—1428no—
509C2×Q8—1428no—
510C2×Q8—1428no—
511C2×Q8—1428no—
512C2×Q8—1428no—
513C2×Q8(C2×D71)⋊C4116yescomplemented
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—712no—
530C22×C4—714no—
531C22×C4—712no—
532C22×C4—712no—
533C22×C4—714no—
534C22×C4—714no—
535C22×C4—7116no—
536C22×C4—714no—
537C22×C4—14216no—
538C22×C4—14216no—
539C22×C4—14216no—
540C22×C4—14216no—
541C22×C4—14216no—
542C22×C4—14216no—
543C22×C4—1422no—
544C22×C4—1422no—
545C22×C4—1422no—
546C22×C4—1424no—
547C22×C4—1424no—
548C22×C4—1422no—
549C22×C4—1422no—
550C22×C4—1422no—
551C22×C4—1422no—
552C22×C4—1422no—
553C22×C4—1422no—
554C22×C4—1422no—
555C22×C4—1422no—
556C22×C4—1421no—
557C22×C4—1421no—
558C22×C4—1421no—
559C22×C4—1422no—
560C22×C4—1421no—
561C22×C4—1422no—
562C22×C4—1428no—
563C22×C4—14216no—
564C22×C4—1428no—
565C22×C4—1428no—
566C22×C4—1428no—
567C22×C4—1428no—
568C22×C4—1428no—
569C22×C4C2×C4×D7114yes—
570C22×C4C2×C4×D7112yes—
571C22×C4D4×D7112yes—
572C22×C4D4×D7112yes—
573C22×C4D4×D7112yes—
574C22×C4D4×D7112yes—
575C22×C4C2×C22⋊D7114yes—
576C22×C4C2×C22⋊D7112yes—
577C22×C4C2×D28414yes—
578C22×C4C2×D28412yes—
579C22×C4Q8×D7114yescomplemented
580C4⋊C4—44no—
581C4⋊C4—2844no—
582C22⋊C4—2848no—
583C22⋊C4—14216no—
584C42—44no—
585C42—2844no—
586C23—714no—
587C23—718no—
588C23—718no—
589C23—714no—
590C23—714no—
591C23—1422no—
592C23—1424no—
593C23—1422no—
594C23—1424no—
595C23—1424no—
596C23—1424no—
597C23—1424no—
598C23—1424no—
599C23—1424no—
600C23—1424no—
601C23—1424no—
602C23—1422no—
603C23—1422no—
604C23—1424no—
605C23—1422no—
606C23—1422no—
607C23—1422no—
608C23—1422no—
609C23C22×C4×D7111yescharacteristic
610C23C2×D4×D7111yescharacteristic
611C23C2×D4×D7111yescharacteristic
612C23C2×D4×D7111yescharacteristic
613C23C2×D4×D7111yescharacteristic
614C23C22×C22⋊D7111yescharacteristic
615C23C22×D28411yescharacteristic
616C23C2×Q8×D7112yes—
617C23#41×D7112yes—
618C23#1455617512yes—
619C23#1455617612yes—
620Q8—232no—
621Q8—14264no—
622Q8—14232no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—2842no—
642C2×C4—2842no—
643C2×C4—2842no—
644C2×C4—2842no—
645C2×C4—2842no—
646C2×C4—2844no—
647C2×C4—2844no—
648C2×C4—2842no—
649C2×C4—2842no—
650C2×C4—714no—
651C2×C4—718no—
652C2×C4—14264no—
653C2×C4—1424no—
654C2×C4—1424no—
655C2×C4—1424no—
656C2×C4—1424no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1424no—
660C2×C4—1422no—
661C2×C4—1424no—
662C2×C4—1422no—
663C2×C4—1424no—
664C2×C4—1422no—
665C2×C4—1424no—
666C2×C4—1422no—
667C2×C4—1424no—
668C2×C4—14232no—
669C2×C4C22⋊C4×D7114yes—
670C2×C4C22⋊C4×D7114yes—
671C2×C4C2×(C2×D71)⋊C418yes—
672C2×C4C2×(C2×D71)⋊C414yes—
673C2×C4#1455609614yes—
674C2×C4#1455609614yes—
675C2×C4#1455609814yes—
676C2×C4#1455609814yes—
677C22—718no—
678C22—1428no—
679C22—1428no—
680C22—1424no—
681C22—1428no—
682C22—1428no—
683C22—1424no—
684C22—1424no—
685C22—1424no—
686C22—1424no—
687C22—1424no—
688C22C2×C22⋊C4×D7111yescharacteristic
689C22C2×C22⋊C4×D7111yescharacteristic
690C22C22×(C2×D71)⋊C411yescharacteristic
691C22C4×Q8×D7112yes—
692C22#1798647512yes—
693C22C2×#1455609611yescharacteristic
694C22C2×#1455609611yescharacteristic
695C22C2×#1455609811yescharacteristic
696C22C2×#1455609811yescharacteristic
697C22C22⋊Q8×D7112yes—
698C22#124×D7111yescharacteristic
699C22C4⋊Q8×D7111yescharacteristic
700C22#1798656911yescharacteristic
701C22#1798657212yes—
702C22#1798657411yescharacteristic
703C22#1798665612yes—
704C22#1798665712yes—
705C22#1798665912yes—
706C22#1798666112yes—
707C22#1798666212yes—
708C22Q8×C22⋊D7112yes—
709C22#1798666412yes—
710C22Q8×D28412yes—
711C4—28no—
712C4—44no—
713C4—82no—
714C4—2844no—
715C4—5682no—
716C4—1424no—
717C4—1428no—
718C4#1798585418yes—
719C2—1428no—
720C2C2×#1798585411yescharacteristic
721C2#391×D7111yescharacteristic
722C2#2259092311yescharacteristic
723C2Q8×(C2×D71)⋊C412yes—
724C2#2259117412yes—
725C2#2259170112yes—
726C2#2259170312yes—
727C2#2259198111yescharacteristic
728C2#2259198311yescharacteristic
729C2#2259199511yescharacteristic
730C2#2259199711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#391×C71C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×#391D71
hypocenterC71#13922
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#17985906C2semidirect
3. C2×#17985905C2semidirect
4. C2×#17985904C2semidirect
7. #22586610C2semidirect
9. C2×#391×C71C2semidirect
18. C22×Q8×D71C4semidirect
87. C2×(C2×D71)⋊C4Q8semidirect
138. C2×Dic142C22⋊C4semidirect
165. C22×Dic71C2×Q8semidirect
191. C2×Q8×C71C22⋊C4semidirect
217. C22×C4×C71C2×Q8semidirect
344. C2×D71#391semidirect
370. C2×#391D71semidirect
375. C71#13922semidirect
513. C2×Q8(C2×D71)⋊C4semidirect
579. C22×C4Q8×D71semidirect

Maximal subgroups

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

subgroupindex
C23×Q8×D712
C2×#179859062
C2×#179859052
C2×#179859042
C2×#179858562
C2×C4×(C2×D71)⋊C42
#225866102
(C2×D71)⋊#952
C2×#391×C712
#1392271