Finite Group Databasebeta

← #31918596

Subgroups — #31918596

Order 18176.

3366 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic
2C23×C4×Dic71C211yesmaximal, characteristic, complemented
3C2×#17985878C211yesmaximal, characteristic
4C2×#17985876C211yesmaximal, characteristic
5C2×C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
6C2×#17985846C212yesmaximal, complemented
7#22586576C212yesmaximal, complemented
8#22586571C212yesmaximal, complemented
9#22586562C211yesmaximal, characteristic, complemented
10#95×Dic71C212yesmaximal, complemented
11C71×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D71C2211yescharacteristic
13C24×Dic71C2211yescharacteristic
14C24×Dic71C2211yescharacteristic
15C23×C4×D71C2211yescharacteristic
16C2×(C22⋊D71)⋊C4—24no—
17C2×(C22⋊D71)⋊C4—24no—
18C2×(C22⋊D71)⋊C4C418yescomplemented
19C22×Dic71⋊C4C2211yescharacteristic
20C22×C22⋊Dic71C2211yescharacteristic
21C22×(C2×D71)⋊C4C2212yes—
22C22×(C2×D71)⋊C4C2211yescharacteristic
23C22×(C2×D71)⋊C4C2212yes—
24C22×C4×Dic71—28no—
25C22×C4×Dic71—24no—
26C22×C4×Dic71C2212yes—
27C22×C4×Dic71C2212yes—
28C22×C4×Dic71C2211yescharacteristic
29C22×C4×Dic71C2212yes—
30#17985878C418yescomplemented
31#17985876C418yescomplemented
32C22⋊C4×Dic71—24no—
33#17985846—28no—
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2212yes—
36C2×C71⋊#95C2212yes—
37C2×C71⋊#95C2212yes—
38C2×C71⋊#95C2212yes—
39C24×C4×C71C2211yescharacteristic
40C22×C22⋊C4×C71C2211yescharacteristic
41C22×C22⋊C4×C71C2211yescharacteristic
42C2×#95×C71C2212yes—
43C2×#95×C71C2212yes—
44C24×D71C2311yescharacteristic
45C22×C22⋊D71—22no—
46C22×C22⋊D71—22no—
47C22×C22⋊D71—22no—
48C22×C22⋊D71—22no—
49C22×C22⋊D71C2×C414yes—
50C22×C22⋊D71C2×C414yes—
51C22×C22⋊D71C2×C414yes—
52C23×Dic71—24no—
53C23×Dic71—24no—
54C23×Dic71—24no—
55C23×Dic71—24no—
56C23×Dic71—22no—
57C23×Dic71—22no—
58C23×Dic71C2×C414yes—
59C23×Dic71C2×C414yescomplemented
60C23×Dic71D414yes—
61C23×Dic71D414yes—
62C23×Dic71C2312yes—
63C23×Dic71C2311yescharacteristic
64C23×Dic71C2311yescharacteristic
65C23×Dic71C2312yes—
66C23×Dic71C2311yescharacteristic
67C22×C4×D71—24no—
68C22×C4×D71—22no—
69C22×C4×D71—22no—
70C22×C4×D71—24no—
71C22×C4×D71C2×C414yescomplemented
72(C22⋊D71)⋊C4—232no—
73C2×Dic71⋊C4—22no—
74C2×Dic71⋊C4—22no—
75C2×Dic71⋊C4C2×C414yescomplemented
76C2×C22⋊Dic71—22no—
77C2×C22⋊Dic71—22no—
78C2×C22⋊Dic71C2×C414yescomplemented
79C2×(C2×D71)⋊C4—24no—
80C2×(C2×D71)⋊C4—22no—
81C2×(C2×D71)⋊C4—22no—
82C2×(C2×D71)⋊C4—24no—
83C2×(C2×D71)⋊C4—24no—
84C2×(C2×D71)⋊C4—24no—
85C2×(C2×D71)⋊C4C2×C418yescomplemented
86C2×(C2×D71)⋊C4C2×C418yescomplemented
87C2×(C2×D71)⋊C4C2×C414yescomplemented
88C2×C4×Dic71—232no—
89C2×C4×Dic71—24no—
90C2×C4×Dic71—24no—
91C2×C4×Dic71—24no—
92C2×C4×Dic71—24no—
93C2×C4×Dic71—22no—
94C2×C4×Dic71—22no—
95C2×C4×Dic71—24no—
96C2×C4×Dic71—24no—
97C2×C4×Dic71—24no—
98C2×C4×Dic71—24no—
99C2×C4×Dic71C2×C414yescomplemented
100C2×C4×Dic71D418yescomplemented
101C71⋊#95—24no—
102C71⋊#95—24no—
103C71⋊#95—24no—
104C71⋊#95C2×C418yescomplemented
105C71⋊#95C2×C418yescomplemented
106C25×C71C2311yescharacteristic
107C23×C4×C71—22no—
108C23×C4×C71—22no—
109C23×C4×C71—24no—
110C23×C4×C71—24no—
111C23×C4×C71C2×C414yescomplemented
112C23×C4×C71C2311yescharacteristic
113C23×C4×C71C2312yes—
114C23×C4×C71C2311yescharacteristic
115C23×C4×C71C2312yes—
116C2×C22⋊C4×C71—22no—
117C2×C22⋊C4×C71—22no—
118C2×C22⋊C4×C71—22no—
119C2×C22⋊C4×C71—22no—
120C2×C22⋊C4×C71C2×C414yes—
121C2×C22⋊C4×C71C2×C414yescomplemented
122#95×C71—24no—
123#95×C71—24no—
124C23×D71—21no—
125C23×D71—21no—
126C23×D71—22no—
127C23×D71—22no—
128C23×D71—21no—
129C23×D71—21no—
130C23×D71—22no—
131C23×D71—22no—
132C23×D71C22×C412yes—
133C23×D71C22×C412yes—
134C23×D71C22×C412yes—
135C2×C22⋊D71—28no—
136C2×C22⋊D71—28no—
137C2×C22⋊D71—28no—
138C2×C22⋊D71—28no—
139C2×C22⋊D71—28no—
140C2×C22⋊D71—28no—
141C2×C22⋊D71C42116yescomplemented
142C22×Dic71—216no—
143C22×Dic71—28no—
144C22×Dic71—28no—
145C22×Dic71—28no—
146C22×Dic71—22no—
147C22×Dic71—22no—
148C22×Dic71—22no—
149C22×Dic71—21no—
150C22×Dic71—21no—
151C22×Dic71—22no—
152C22×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—21no—
155C22×Dic71—21no—
156C22×Dic71—216no—
157C22×Dic71—216no—
158C22×Dic71—28no—
159C22×Dic71—216no—
160C22×Dic71—28no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71C22⋊C4116yescomplemented
168C22×Dic71C22×C414yes—
169C22×Dic71C22×C412yes—
170C22×Dic71C22×C412yes—
171C22×Dic71C22×C412yes—
172C22×Dic71C22×C412yes—
173C22×Dic71C22×C414yes—
174C22×Dic71C22×C412yes—
175C22×Dic71C2×D412yes—
176C22×Dic71C2×D412yes—
177C22×Dic71C2×D414yes—
178C22×Dic71C2×D412yes—
179C22×Dic71C2×D412yes—
180C22×Dic71C2×D414yes—
181C22×Dic71#4114yes—
182C22×Dic71#4114yes—
183C2×C4×D71—28no—
184C2×C4×D71—216no—
185C2×C4×D71—44no—
186C2×C4×D71—48no—
187C2×C4×D71—44no—
188Dic71⋊C4—28no—
189C22⋊Dic71—28no—
190(C2×D71)⋊C4—216no—
191(C2×D71)⋊C4—28no—
192(C2×D71)⋊C4—216no—
193C4×Dic71—216no—
194C4×Dic71—28no—
195C4×Dic71—216no—
196C4×Dic71—48no—
197C24×C71—22no—
198C24×C71—22no—
199C24×C71—22no—
200C24×C71—22no—
201C24×C71C22×C412yes—
202C24×C71C22×C412yes—
203C24×C71C22×C412yes—
204C24×C71C2×D412yes—
205C24×C71C2×D412yes—
206C24×C71#4112yes—
207C24×C71#4112yes—
208C24×C71C2411yescharacteristic
209C22×C4×C71—216no—
210C22×C4×C71—28no—
211C22×C4×C71—28no—
212C22×C4×C71—28no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—216no—
218C22×C4×C71—22no—
219C22×C4×C71—21no—
220C22×C4×C71—21no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—21no—
224C22×C4×C71—21no—
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×C71C22×C412yes—
233C22×C4×C71C22×C412yes—
234C22×C4×C71C22×C414yes—
235C22×C4×C71C22×C414yes—
236C22×C4×C71C2×D414yes—
237C22×C4×C71#4114yes—
238C22⋊C4×C71—28no—
239C22⋊C4×C71—28no—
240C23×C71—24no—
241C23×C71—24no—
242C23×C71—24no—
243C23×C71—24no—
244C23×C71—24no—
245C23×C71—24no—
246C23×C71—22no—
247C23×C71—24no—
248C23×C71—22no—
249C23×C71—22no—
250C23×C71—24no—
251C23×C71—22no—
252C23×C71—24no—
253C23×C71—24no—
254C23×C71—24no—
255C23×C71—24no—
256C23×C71C2×C4214yes—
257C23×C71C2×C22⋊C414yes—
258C23×C71#11714yes—
259C23×C71C4×D414yes—
260C23×C71C4×D414yes—
261C23×C71C4×D414yes—
262C23×C71C4×D414yes—
263C23×C71C23×C411yescharacteristic
264C23×C71C23×C411yescharacteristic
265C23×C71C23×C411yescharacteristic
266C23×C71C22×D411yescharacteristic
267C23×C71C22×D411yescharacteristic
268C23×C71C22×D412yes—
269C23×C71C2×#4112yes—
270C23×C71C2×#4112yes—
271C23×C71C2×#4111yescharacteristic
272C23×C71C2×#4112yes—
273C23×C71C2×#4111yescharacteristic
274C22×D71—22no—
275C22×D71—22no—
276C22×D71—24no—
277C22×D71—24no—
278C22×D71—24no—
279C22×D71—22no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—24no—
284C22×D71—24no—
285C22×D71—24no—
286C22×D71—41no—
287C22×D71—42no—
288C22×D71—41no—
289C22×D71—42no—
290C22×D71—41no—
291C22×D71—41no—
292C22×D71—42no—
293C22×D71—42no—
294C22×D71—42no—
295C22×D71—42no—
296C22×D71C2×C4214yescomplemented
297C2×C4×C71—232no—
298C2×C4×C71—24no—
299C2×C4×C71—24no—
300C2×C4×C71—24no—
301C2×C4×C71—24no—
302C2×C4×C71—24no—
303C2×C4×C71—24no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—24no—
307C2×C4×C71—24no—
308C2×C4×C71—24no—
309C2×C4×C71—24no—
310C2×C4×C71—24no—
311C2×C4×C71—41no—
312C2×C4×C71—42no—
313C2×C4×C71—42no—
314C2×C4×C71—41no—
315C2×C4×C71—41no—
316C2×C4×C71—42no—
317C2×C4×C71—41no—
318C2×C4×C71—42no—
319C2×C4×C71—42no—
320C2×C4×C71—42no—
321C2×C4×C71C4×D418yescomplemented
322C22⋊D71—232no—
323C2×Dic71—232no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—24no—
327C2×Dic71—24no—
328C2×Dic71—24no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—24no—
335C2×Dic71—24no—
336C2×Dic71—22no—
337C2×Dic71—24no—
338C2×Dic71—24no—
339C2×Dic71—24no—
340C2×Dic71—232no—
341C2×Dic71—24no—
342C2×Dic71—24no—
343C2×Dic71—24no—
344C2×Dic71—42no—
345C2×Dic71—42no—
346C2×Dic71—42no—
347C2×Dic71—42no—
348C2×Dic71C2×C4214yescomplemented
349C2×Dic71C2×C22⋊C414yes—
350C2×Dic71C2×C22⋊C414yes—
351C2×Dic71C4×D418yes—
352C2×Dic71C4×D418yescomplemented
353C2×Dic71#12014yes—
354C2×Dic71#12118yes—
355C2×Dic71#12314yes—
356C4×D71—416no—
357C22×C71—28no—
358C22×C71—24no—
359C22×C71—28no—
360C22×C71—24no—
361C22×C71—24no—
362C22×C71—24no—
363C22×C71—28no—
364C22×C71—28no—
365C22×C71—24no—
366C22×C71—24no—
367C22×C71C4×C22⋊C418yescomplemented
368C22×C71C22×C4211yescharacteristic
369C22×C71C22×C22⋊C411yescharacteristic
370C22×C71C2×#11711yescharacteristic
371C22×C71C2×C4×D412yes—
372C22×C71C2×C4×D412yes—
373C22×C71C2×C4×D411yescharacteristic
374C22×C71C2×C4×D411yescharacteristic
375C22×C71C2×C4×D412yes—
376C22×C71C2×C4×D411yescharacteristic
377C22×C71C2×C4×D411yescharacteristic
378C22×C71C4×#4112yes—
379C22×C71C4×#4112yes—
380C22×C71C4×#4112yes—
381C22×C71C2×#12011yescharacteristic
382C22×C71C2×#12112yes—
383C22×C71C2×#12311yescharacteristic
384C22×C71#52512yes—
385C22×C71#52511yescharacteristic
386C22×C71#52511yescharacteristic
387C22×C71#52512yes—
388C22×C71#52912yes—
389C22×C71#52912yes—
390C22×C71#53212yes—
391C2×D71—24no—
392C2×D71—28no—
393C2×D71—42no—
394C2×D71—44no—
395C2×D71—42no—
396C2×D71—42no—
397C2×D71—42no—
398C2×D71—44no—
399C2×D71—44no—
400C2×D71—42no—
401C2×D71—42no—
402C4×C71—28no—
403C4×C71—42no—
404C4×C71—42no—
405C4×C71—44no—
406Dic71—24no—
407Dic71—24no—
408Dic71—28no—
409Dic71—44no—
410Dic71#38618yescomplemented
411C4×#386—711nomaximal, Sylow
412C2×C71—28no—
413C2×C71C2×C4×C22⋊C411yescharacteristic
414C2×C71C42×D412yes—
415C2×C71C2×#38611yescharacteristic
416C2×C71#229012yes—
417C2×C71#229711yescharacteristic
418C2×C71C4×#12011yescharacteristic
419C2×C71C4×#12011yescharacteristic
420C2×C71C4×#12112yes—
421C2×C71C4×#12112yes—
422C2×C71C4×#12311yescharacteristic
423C2×C71C4×#12311yescharacteristic
424D71—44no—
425C22×C4×D4—711no—
426C23×C42—711no—
427C2×#386—711no—
428C2×#386—711no—
429C2×C4×C22⋊C4—712no—
430C2×C4×C22⋊C4—711no—
431#1437—712no—
432#1436—712no—
433C22⋊#95—711no—
434C22⋊#95D7111yescharacteristic, complemented
435C4×#95—712no—
436C71C4×#38611yescharacteristic, complemented, Sylow
437C23×D4—711no—
438C24×C4—711no—
439C24×C4—711no—
440C24×C4—711no—
441C24×C4C2×D7111yescharacteristic
442C2×C4×D4—718no—
443C2×C4×D4—1424no—
444C2×C4×D4—1424no—
445C22×C4⋊C4—711no—
446C22×C22⋊C4—711no—
447C22×C22⋊C4—711no—
448C22×C22⋊C4—712no—
449C22×C22⋊C4—712no—
450C22×C22⋊C4C2×D7111yescharacteristic
451C22×C22⋊C4C2×D7111yescharacteristic
452C22×C42—712no—
453C22×C42—711no—
454C22×C42—712no—
455C22×C42—712no—
456C22×C42—1428no—
457C22×C42—1424no—
458#386—718no—
459#386—718no—
460C4×C22⋊C4—1428no—
461C4×C22⋊C4—1424no—
462C2×#95—712no—
463C2×#95—712no—
464C2×#95—712no—
465C2×#95—712no—
466C2×#95—712no—
467C2×#95C2×D7112yes—
468C2×#95C2×D7112yes—
469C25—711no—
470C25C22×D7111yescharacteristic
471C22×D4—714no—
472C22×D4—714no—
473C22×D4—714no—
474C22×D4—1422no—
475C22×D4—1422no—
476C22×D4—1422no—
477C22×D4—1422no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—711no—
483C23×C4—714no—
484C23×C4—714no—
485C23×C4—714no—
486C23×C4—711no—
487C23×C4—712no—
488C23×C4—711no—
489C23×C4—714no—
490C23×C4—712no—
491C23×C4—714no—
492C23×C4—1422no—
493C23×C4—1422no—
494C23×C4—1424no—
495C23×C4—1424no—
496C23×C4—1424no—
497C23×C4—1424no—
498C23×C4—1424no—
499C23×C4—1424no—
500C23×C4—1422no—
501C23×C4—1422no—
502C23×C4C4×D7114yescomplemented
503C23×C4C22×D7112yes—
504C23×C4C22×D7111yescharacteristic
505C23×C4C22×D7111yescharacteristic
506C23×C4C22×D7112yes—
507C4×D4—14232no—
508C2×C4⋊C4—714no—
509C2×C4⋊C4—1422no—
510C2×C4⋊C4—1422no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—714no—
516C2×C22⋊C4—714no—
517C2×C22⋊C4—718no—
518C2×C22⋊C4—718no—
519C2×C22⋊C4—1422no—
520C2×C22⋊C4—1422no—
521C2×C22⋊C4—1424no—
522C2×C22⋊C4—1424no—
523C2×C22⋊C4—1422no—
524C2×C22⋊C4—1422no—
525C2×C22⋊C4—1424no—
526C2×C22⋊C4—1424no—
527C2×C22⋊C4C4×D7114yes—
528C2×C22⋊C4C4×D7114yescomplemented
529C2×C42—714no—
530C2×C42—718no—
531C2×C42—1424no—
532C2×C42—1424no—
533C2×C42—1424no—
534C2×C42—1422no—
535C2×C42—1422no—
536C2×C42—1424no—
537C2×C42—1424no—
538C2×C42—1424no—
539C2×C42—1424no—
540C2×C42—14232no—
541C2×C42—1424no—
542#95—24no—
543#95—24no—
544#95—718no—
545#95—718no—
546#95—1424no—
547#95—1424no—
548#95—1424no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—712no—
554C24—712no—
555C24—712no—
556C24—1422no—
557C24—1421no—
558C24—1421no—
559C24—1422no—
560C24—1422no—
561C24—1422no—
562C24—1421no—
563C24—1421no—
564C24C2×C4×D7112yes—
565C24C2×C4×D7112yes—
566C24C2×C4×D7112yes—
567C24D4×D7112yes—
568C24D4×D7112yes—
569C24#1176586412yes—
570C24#1176586612yes—
571C24C23×D7111yescharacteristic
572C2×D4—7116no—
573C2×D4—1428no—
574C2×D4—1428no—
575C2×D4—1428no—
576C2×D4—1428no—
577C2×D4—1428no—
578C2×D4—1428no—
579C22×C4—28no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—28no—
587C22×C4—216no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—2844no—
603C22×C4—2848no—
604C22×C4—2844no—
605C22×C4—712no—
606C22×C4—714no—
607C22×C4—712no—
608C22×C4—712no—
609C22×C4—714no—
610C22×C4—712no—
611C22×C4—712no—
612C22×C4—714no—
613C22×C4—712no—
614C22×C4—712no—
615C22×C4—712no—
616C22×C4—714no—
617C22×C4—712no—
618C22×C4—714no—
619C22×C4—7116no—
620C22×C4—714no—
621C22×C4—1428no—
622C22×C4—14216no—
623C22×C4—1422no—
624C22×C4—1422no—
625C22×C4—1422no—
626C22×C4—1422no—
627C22×C4—1422no—
628C22×C4—1422no—
629C22×C4—1428no—
630C22×C4—14216no—
631C22×C4—14216no—
632C22×C4—1428no—
633C22×C4—14216no—
634C22×C4—1428no—
635C22×C4—1428no—
636C22×C4—14216no—
637C22×C4—1422no—
638C22×C4—1422no—
639C22×C4—1422no—
640C22×C4—1421no—
641C22×C4—1421no—
642C22×C4—1422no—
643C22×C4—1422no—
644C22×C4—1421no—
645C22×C4—1422no—
646C22×C4—1421no—
647C22×C4—1428no—
648C22×C4C2×C4×D7114yes—
649C22×C4C2×C4×D7112yes—
650C22×C4C2×C4×D7112yes—
651C22×C4C2×C4×D7114yes—
652C22×C4D4×D7114yes—
653C22×C4#1176586414yes—
654C4⋊C4—1428no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—14216no—
658C22⋊C4—1428no—
659C22⋊C4—1428no—
660C22⋊C4—14216no—
661C42—2848no—
662C42—14216no—
663C42—1428no—
664C42—14216no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—2841no—
682C23—2842no—
683C23—2841no—
684C23—2842no—
685C23—2841no—
686C23—2841no—
687C23—2842no—
688C23—2842no—
689C23—2842no—
690C23—2842no—
691C23—714no—
692C23—1422no—
693C23—1422no—
694C23—1424no—
695C23—1424no—
696C23—1424no—
697C23—1422no—
698C23—1422no—
699C23—1422no—
700C23—1422no—
701C23—1424no—
702C23—1424no—
703C23—1424no—
704C23C42×D7114yes—
705C23C22⋊C4×D7114yes—
706C23#1455608614yes—
707C23(C22⋊D71)⋊C414yes—
708C23(C22⋊D71)⋊C414yes—
709C23#1455609014yes—
710C23#1455609014yes—
711C23C22×C4×D7111yescharacteristic
712C23C22×C4×D7111yescharacteristic
713C23C22×C4×D7111yescharacteristic
714C23C2×D4×D7111yescharacteristic
715C23C2×D4×D7111yescharacteristic
716C23C2×D4×D7112yes—
717C23#41×D7112yes—
718C23#41×D7112yes—
719C23C2×#1176586411yescharacteristic
720C23C2×#1176586412yes—
721C23C2×#1176586611yescharacteristic
722D4—14232no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—28416no—
748C2×C4—2842no—
749C2×C4—2842no—
750C2×C4—2842no—
751C2×C4—2842no—
752C2×C4—714no—
753C2×C4—718no—
754C2×C4—714no—
755C2×C4—718no—
756C2×C4—714no—
757C2×C4—714no—
758C2×C4—714no—
759C2×C4—718no—
760C2×C4—1424no—
761C2×C4—1424no—
762C2×C4—1424no—
763C2×C4—14232no—
764C2×C4—14232no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1424no—
768C2×C4—1424no—
769C2×C4—1422no—
770C2×C4—1422no—
771C2×C4—1424no—
772C2×C4—1422no—
773C2×C4—1422no—
774C2×C4—1422no—
775C2×C4—1424no—
776C2×C4—1424no—
777C2×C4—1422no—
778C2×C4—1424no—
779C2×C4—1424no—
780C2×C4—1424no—
781C2×C4(C22⋊D71)⋊C418yescomplemented
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—28no—
788C22—28no—
789C22—24no—
790C22—24no—
791C22—28no—
792C22—2842no—
793C22—2844no—
794C22—2842no—
795C22—2842no—
796C22—2842no—
797C22—2844no—
798C22—2844no—
799C22—2842no—
800C22—2842no—
801C22—1424no—
802C22—1428no—
803C22#1798584618yescomplemented
804C22C2×C42×D7111yescharacteristic
805C22C2×C22⋊C4×D7111yescharacteristic
806C22C2×#1455608611yescharacteristic
807C22C4×D4×D7112yes—
808C22C4×D4×D7112yes—
809C22C2×(C22⋊D71)⋊C412yes—
810C22C2×(C22⋊D71)⋊C411yescharacteristic
811C22C2×(C22⋊D71)⋊C411yescharacteristic
812C22C2×#1455609011yescharacteristic
813C22C2×#1455609011yescharacteristic
814C22C4×#1176586412yes—
815C22C4×#1176586412yes—
816C22#1798646712yes—
817C22#120×D7111yescharacteristic
818C22#121×D7112yes—
819C22#123×D7111yescharacteristic
820C22#1798650512yes—
821C22#1798650511yescharacteristic
822C22#1798650711yescharacteristic
823C22#1798651212yes—
824C22#1798652612yes—
825C22#1798653512yes—
826C22#1798654412yes—
827C4—28no—
828C4—42no—
829C4—42no—
830C4—44no—
831C4—2844no—
832C4—718no—
833C4—1424no—
834C4—1428no—
835C4—1424no—
836C2—28no—
837C2—2844no—
838C2C2×#1798584611yescharacteristic
839C2C4×(C22⋊D71)⋊C412yes—
840C2#386×D7111yescharacteristic
841C2#2259077612yes—
842C2#2259082511yescharacteristic
843C2#2259083911yescharacteristic
844C2#2259084111yescharacteristic
845C2#2259084612yes—
846C2#2259085012yes—
847C2#2259085711yescharacteristic
848C2#2259085911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC71×C22⋊#95C2
socle, cosocleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC22⋊#95D71
hypocenterC71C4×#386
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C23×C4×Dic71C2semidirect
5. C2×C22⋊C4×Dic71C2semidirect
6. C2×#17985846C2semidirect
7. #22586576C2semidirect
8. #22586571C2semidirect
9. #22586562C2semidirect
10. #95×Dic71C2semidirect
11. C71×C22⋊#95C2semidirect
18. C2×(C22⋊D71)⋊C4C4semidirect
30. #17985878C4semidirect
31. #17985876C4semidirect
59. C23×Dic71C2×C4semidirect
71. C22×C4×D71C2×C4semidirect
75. C2×Dic71⋊C4C2×C4semidirect
78. C2×C22⋊Dic71C2×C4semidirect
85. C2×(C2×D71)⋊C4C2×C4semidirect
86. C2×(C2×D71)⋊C4C2×C4semidirect
87. C2×(C2×D71)⋊C4C2×C4semidirect
99. C2×C4×Dic71C2×C4semidirect
100. C2×C4×Dic71D4semidirect
104. C71⋊#95C2×C4semidirect
105. C71⋊#95C2×C4semidirect
111. C23×C4×C71C2×C4semidirect
121. C2×C22⋊C4×C71C2×C4semidirect
141. C2×C22⋊D71C42semidirect
167. C22×Dic71C22⋊C4semidirect
296. C22×D71C2×C42semidirect
321. C2×C4×C71C4×D4semidirect
348. C2×Dic71C2×C42semidirect
352. C2×Dic71C4×D4semidirect
367. C22×C71C4×C22⋊C4semidirect
410. Dic71#386semidirect
434. C22⋊#95D71semidirect
436. C71C4×#386semidirect
502. C23×C4C4×D71semidirect
528. C2×C22⋊C4C4×D71semidirect
781. C2×C4(C22⋊D71)⋊C4semidirect
803. C22#17985846semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D71)⋊C42
C23×C4×Dic712
C2×#179858782
C2×#179858762
C2×C22⋊C4×Dic712
C2×#179858462
#225865762
#225865712
#225865622
#95×Dic712
C71×C22⋊#952
C4×#38671