Finite Group Databasebeta

← #31902678

Subgroups — #31902678

Order 18176.

1534 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11765848C211yesmaximal, characteristic
2C22×(C2×D71)⋊C8C211yesmaximal, characteristic
3C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
4C2×#17985754C211yesmaximal, characteristic, complemented
5C2×#17985753C211yesmaximal, characteristic, complemented
6C2×#17985753C211yesmaximal, characteristic, complemented
7C2×#336×C71C211yesmaximal, characteristic, complemented
8C23×C4×D71C2211yescharacteristic
9C22×#11765848—22no—
10C22×#11765848—22no—
11C22×#11765848—22no—
12C22×#11765848—22no—
13C22×#11765848—22no—
14C22×#11765848—22no—
15C22×#11765848C414yescomplemented
16C23×C71⋊C8C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C22×(C2×D71)⋊C4C412yes—
19C22×C4×Dic71C2211yescharacteristic
20C2×(C2×D71)⋊C8—22no—
21C2×(C2×D71)⋊C8—22no—
22C2×(C2×D71)⋊C8C414yescomplemented
23C4×(C2×D71)⋊C4—22no—
24C4×(C2×D71)⋊C4—22no—
25C2×C71⋊#95C412yes—
26#17985754—22no—
27#17985753—22no—
28#17985753—22no—
29C23×C8×C71C2211yescharacteristic
30C23×C8×C71C2211yescharacteristic
31C22×C42×C71C2211yescharacteristic
32#336×C71—22no—
33C24×D71C2×C411yescharacteristic
34C23×Dic71C2×C412yes—
35C23×Dic71C2×C411yescharacteristic
36C22×C4×D71—21no—
37C22×C4×D71—21no—
38C22×C4×D71—21no—
39C22×C4×D71—21no—
40C22×C4×D71—21no—
41C22×C4×D71—21no—
42C22×C4×D71—21no—
43C22×C4×D71—21no—
44C22×C4×D71C2×C412yes—
45C22×C4×D71C2×C412yes—
46C22×C4×D71D412yes—
47C22×C4×D71D412yes—
48C22×C4×D71D412yes—
49C22×C4×D71Q812yes—
50C2×#11765848—28no—
51C2×#11765848—28no—
52C2×#11765848—28no—
53C2×#11765848—28no—
54C2×#11765848—28no—
55C2×#11765848—28no—
56C2×#11765848—28no—
57C22×C71⋊C8—21no—
58C22×C71⋊C8—21no—
59C22×C71⋊C8—21no—
60C22×C71⋊C8—21no—
61C22×C71⋊C8—21no—
62C22×C71⋊C8—21no—
63C22×C71⋊C8—21no—
64C22×C71⋊C8—21no—
65C22×C71⋊C8—21no—
66C22×C71⋊C8—21no—
67C22×C71⋊C8C2×C412yes—
68C22×C71⋊C8C2×C412yes—
69C22×C71⋊C8D412yes—
70C22×C71⋊C8D412yes—
71C2×(C2×D71)⋊C4—24no—
72C2×(C2×D71)⋊C4—24no—
73C2×(C2×D71)⋊C4—24no—
74C2×C4×Dic71—21no—
75C2×C4×Dic71—21no—
76C2×C4×Dic71—21no—
77C2×C4×Dic71—21no—
78C2×C4×Dic71—21no—
79C2×C4×Dic71—21no—
80(C2×D71)⋊C8—28no—
81C71⋊#95—24no—
82C23×C4×C71C2×C412yes—
83C23×C4×C71C2311yescharacteristic
84C22×C8×C71—21no—
85C22×C8×C71—21no—
86C22×C8×C71—21no—
87C22×C8×C71—21no—
88C22×C8×C71—21no—
89C22×C8×C71—21no—
90C22×C8×C71—21no—
91C22×C8×C71—21no—
92C22×C8×C71—21no—
93C22×C8×C71—21no—
94C22×C8×C71C2×C412yes—
95C22×C8×C71C2×C412yes—
96C22×C8×C71D412yes—
97C22×C8×C71D412yes—
98C2×C42×C71—21no—
99C2×C42×C71—21no—
100C2×C42×C71—21no—
101C2×C42×C71—21no—
102C2×C42×C71—21no—
103C2×C42×C71—21no—
104C23×D71—21no—
105C23×D71—21no—
106C23×D71—21no—
107C23×D71—21no—
108C23×D71—22no—
109C23×D71—22no—
110C23×D71—22no—
111C23×D71—22no—
112C23×D71C4212yes—
113C23×D71C22⋊C412yes—
114C23×D71C4⋊C412yes—
115C22×Dic71—21no—
116C22×Dic71—21no—
117C22×Dic71—21no—
118C22×Dic71—21no—
119C22×Dic71—22no—
120C22×Dic71—22no—
121C22×Dic71—22no—
122C22×Dic71—22no—
123C22×Dic71—22no—
124C22×Dic71—22no—
125C22×Dic71C4212yes—
126C22×Dic71C22⋊C412yes—
127C22×Dic71C4⋊C412yes—
128C22×Dic71M1614yescomplemented
129C2×C4×D71—22no—
130C2×C4×D71—22no—
131C2×C4×D71—22no—
132C2×C4×D71—22no—
133C2×C4×D71—22no—
134C2×C4×D71—22no—
135C2×C4×D71—22no—
136C2×C4×D71—22no—
137C2×C4×D71—22no—
138C2×C4×D71—22no—
139C2×C4×D71—22no—
140C2×C4×D71—22no—
141C2×C4×D71—22no—
142C2×C4×D71—22no—
143C2×C4×D71—22no—
144C2×C4×D71—22no—
145C2×C4×D71—22no—
146C2×C4×D71—22no—
147C2×C4×D71—22no—
148C2×C4×D71—22no—
149C2×C4×D71—22no—
150C2×C4×D71—22no—
151C2×C4×D71—22no—
152C2×C4×D71—22no—
153C2×C4×D71C22⋊C414yes—
154C2×C4×D71C22⋊C414yes—
155C2×C4×D71C4⋊C414yes—
156C2×C4×D71C4⋊C414yes—
157#11765848—232no—
158C2×C71⋊C8—22no—
159C2×C71⋊C8—22no—
160C2×C71⋊C8—22no—
161C2×C71⋊C8—22no—
162C2×C71⋊C8—22no—
163C2×C71⋊C8—22no—
164C2×C71⋊C8—22no—
165C2×C71⋊C8—22no—
166C2×C71⋊C8—22no—
167C2×C71⋊C8—41no—
168C2×C71⋊C8—41no—
169C2×C71⋊C8—41no—
170C2×C71⋊C8—41no—
171C2×C71⋊C8C22⋊C414yescomplemented
172(C2×D71)⋊C4—216no—
173C4×Dic71—41no—
174C4×Dic71—41no—
175C4×Dic71—41no—
176C4×Dic71—41no—
177C24×C71C22×C411yescharacteristic
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—22no—
183C22×C4×C71—22no—
184C22×C4×C71M1614yescomplemented
185C22×C4×C71C22×C411yescharacteristic
186C22×C4×C71C22×C411yescharacteristic
187C22×C4×C71C2×D411yescharacteristic
188C22×C4×C71C2×D411yescharacteristic
189C22×C4×C71C2×D411yescharacteristic
190C22×C4×C71C2×D411yescharacteristic
191C22×C4×C71C2×D411yescharacteristic
192C22×C4×C71C2×D411yescharacteristic
193C22×C4×C71C2×D411yescharacteristic
194C22×C4×C71C2×Q811yescharacteristic
195C22×C4×C71#4111yescharacteristic
196C22×C4×C71#4111yescharacteristic
197C22×C4×C71#4111yescharacteristic
198C22×C4×C71#4111yescharacteristic
199C2×C8×C71—22no—
200C2×C8×C71—22no—
201C2×C8×C71—22no—
202C2×C8×C71—22no—
203C2×C8×C71—22no—
204C2×C8×C71—22no—
205C2×C8×C71—22no—
206C2×C8×C71—22no—
207C2×C8×C71—22no—
208C2×C8×C71—41no—
209C2×C8×C71—41no—
210C2×C8×C71—41no—
211C2×C8×C71—41no—
212C2×C8×C71C22⋊C414yescomplemented
213C42×C71—41no—
214C42×C71—41no—
215C42×C71—41no—
216C42×C71—41no—
217C23×C71C2×C4211yescharacteristic
218C23×C71C2×C22⋊C411yescharacteristic
219C23×C71C2×C4⋊C411yescharacteristic
220C23×C71C4×D411yescharacteristic
221C23×C71C4×D411yescharacteristic
222C23×C71C4×D411yescharacteristic
223C23×C71C4×D411yescharacteristic
224C23×C71C2×M1612yes—
225C23×C71C2×M1612yes—
226C23×C71#13112yes—
227C23×C71#13112yes—
228C22×D71—22no—
229C22×D71—22no—
230C22×D71—22no—
231C22×D71—22no—
232C22×D71—22no—
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—22no—
236C22×D71—22no—
237C22×D71—22no—
238C22×D71—24no—
239C22×D71—24no—
240C22×D71—24no—
241C22×D71—24no—
242C22×D71—42no—
243C22×D71—42no—
244C22×D71—42no—
245C22×D71—42no—
246C22×D71—42no—
247C22×D71—42no—
248C22×D71—42no—
249C22×D71—42no—
250C22×D71#9514yes—
251C2×C4×C71—24no—
252C2×C4×C71—24no—
253C2×C4×C71—24no—
254C2×C4×C71—42no—
255C2×C4×C71—42no—
256C2×C4×C71—42no—
257C2×C4×C71—42no—
258C2×C4×C71C2×C22⋊C411yescharacteristic
259C2×C4×C71C2×C22⋊C411yescharacteristic
260C2×C4×C71C2×C22⋊C411yescharacteristic
261C2×C4×C71C2×C22⋊C411yescharacteristic
262C2×C4×C71C2×C4⋊C411yescharacteristic
263C2×C4×C71C2×C4⋊C411yescharacteristic
264C2×C4×C71#11711yescharacteristic
265C2×C4×C71#11711yescharacteristic
266C2×C4×C71C4×D411yescharacteristic
267C2×C4×C71C4×D411yescharacteristic
268C2×C4×C71C4×D411yescharacteristic
269C2×C4×C71C4×D411yescharacteristic
270C2×C4×C71#12011yescharacteristic
271C2×C4×C71#12011yescharacteristic
272C2×C4×C71#12011yescharacteristic
273C2×C4×C71#12011yescharacteristic
274C2×C4×C71#12111yescharacteristic
275C2×C4×C71#12111yescharacteristic
276C2×C4×C71#12111yescharacteristic
277C2×C4×C71#12111yescharacteristic
278C2×C4×C71C22⋊Q811yescharacteristic
279C2×C4×C71C22⋊Q811yescharacteristic
280C2×C4×C71C22⋊Q811yescharacteristic
281C2×C4×C71C22⋊Q811yescharacteristic
282C2×C4×C71#12311yescharacteristic
283C2×C4×C71#12311yescharacteristic
284C2×C4×C71#12311yescharacteristic
285C2×C4×C71#12311yescharacteristic
286C2×Dic71—22no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—24no—
293C2×Dic71—24no—
294C2×Dic71—24no—
295C2×Dic71—42no—
296C2×Dic71—42no—
297C2×Dic71—42no—
298C2×Dic71—42no—
299C2×Dic71#9514yes—
300C4×D71—24no—
301C4×D71—24no—
302C4×D71—24no—
303C4×D71—24no—
304C4×D71—24no—
305C4×D71—24no—
306C4×D71—24no—
307C4×D71—24no—
308C8×C71—24no—
309C8×C71—42no—
310C71⋊C8—24no—
311C71⋊C8—42no—
312C22×C71C2×#9511yescharacteristic
313C22×C71C4×C22⋊C411yescharacteristic
314C22×C71C4×C22⋊C411yescharacteristic
315C22×C71#38511yescharacteristic
316C22×C71#38511yescharacteristic
317C22×C71#38611yescharacteristic
318C22×C71#38611yescharacteristic
319C22×C71C4×M1611yescharacteristic
320C22×C71C4×M1611yescharacteristic
321C22×C71#40511yescharacteristic
322C22×C71#40511yescharacteristic
323C22×C71#40712yes—
324C22×C71#40812yes—
325C22×C71#42312yes—
326C22×C71#42412yes—
327C22×C71#43512yes—
328C22×C71#43512yes—
329C22×C71#43512yes—
330C22×C71#43512yes—
331C22×C71#43612yes—
332C22×C71#43612yes—
333C22×C71#43612yes—
334C22×C71#43612yes—
335C2×D71—24no—
336C2×D71—24no—
337C2×D71—24no—
338C2×D71—44no—
339C2×D71—44no—
340C2×D71—44no—
341C2×D71—44no—
342C2×D71—42no—
343C2×D71—42no—
344C2×D71—42no—
345C2×D71—42no—
346C4×C71—44no—
347C4×C71#37911yescharacteristic
348C4×C71#38011yescharacteristic
349C4×C71#38011yescharacteristic
350C4×C71#38111yescharacteristic
351C4×C71#38511yescharacteristic
352C4×C71#38511yescharacteristic
353C4×C71#38611yescharacteristic
354C4×C71#38611yescharacteristic
355Dic71—24no—
356Dic71—44no—
357#10715—711nomaximal, Sylow
358C2×C71C22⋊#9511yescharacteristic
359C2×C71#172811yescharacteristic
360C2×C71#172911yescharacteristic
361C2×C71#175311yescharacteristic
362C2×C71#175311yescharacteristic
363C2×C71#175311yescharacteristic
364C2×C71#175311yescharacteristic
365C2×C71#185112yes—
366C2×C71#185112yes—
367C2×C71#187012yes—
368C2×C71#187012yes—
369D71—44no—
370C23×M16—711no—
371C22×C22⋊C8—711no—
372C2×C4×C22⋊C4—711no—
373C2×#336—711no—
374C2×#336—711no—
375C2×#336—711no—
376C2×#336D7111yescharacteristic, complemented
377C71#1071511yescharacteristic, complemented, Sylow
378C24×C4—711no—
379C22×M16—714no—
380C22×M16—1422no—
381C22×M16—1422no—
382C22×M16—1422no—
383C22×M16—1422no—
384C22×M16—1422no—
385C22×M16—1422no—
386C23×C8—711no—
387C23×C8—711no—
388C23×C8C2×D7111yescharacteristic
389C23×C8C2×D7111yescharacteristic
390C22×C22⋊C4—712no—
391C22×C42—711no—
392C22×C42C2×D7111yescharacteristic
393C2×C22⋊C8—714no—
394C2×C22⋊C8—1422no—
395C2×C22⋊C8—1422no—
396C4×C22⋊C4—1422no—
397C4×C22⋊C4—1422no—
398C2×#95—712no—
399#336—22no—
400#336—1422no—
401#336—1422no—
402#336—1422no—
403C25—711no—
404C23×C4—711no—
405C23×C4—712no—
406C23×C4—712no—
407C23×C4—712no—
408C23×C4—712no—
409C23×C4—712no—
410C23×C4—712no—
411C23×C4—712no—
412C23×C4—1421no—
413C23×C4—1421no—
414C23×C4—1421no—
415C23×C4—1421no—
416C23×C4—1421no—
417C23×C4—1421no—
418C23×C4—1421no—
419C23×C4—1421no—
420C23×C4C4×D7112yes—
421C23×C4C22×D7111yescharacteristic
422C2×M16—1428no—
423C2×M16—1428no—
424C2×M16—1428no—
425C2×M16—1428no—
426C2×M16—1428no—
427C2×M16—1428no—
428C2×M16—1428no—
429C22×C8—21no—
430C22×C8—21no—
431C22×C8—21no—
432C22×C8—21no—
433C22×C8—21no—
434C22×C8—21no—
435C22×C8—21no—
436C22×C8—21no—
437C22×C8—21no—
438C22×C8—21no—
439C22×C8—712no—
440C22×C8—712no—
441C22×C8—712no—
442C22×C8—712no—
443C22×C8—1421no—
444C22×C8—1421no—
445C22×C8—1421no—
446C22×C8—1421no—
447C22×C8—1421no—
448C22×C8—1421no—
449C22×C8—1421no—
450C22×C8—1421no—
451C22×C8—1421no—
452C22×C8—1421no—
453C22×C8C4×D7112yes—
454C22×C8C4×D7112yes—
455C22×C8D28412yes—
456C22×C8C22⋊D7112yes—
457C2×C22⋊C4—1424no—
458C2×C22⋊C4—1424no—
459C2×C22⋊C4—1424no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—1421no—
467C2×C42—1421no—
468C2×C42—1421no—
469C2×C42—1421no—
470C2×C42—1421no—
471C2×C42—1421no—
472C22⋊C8—1428no—
473#95—1424no—
474C24—712no—
475C24—712no—
476C24—712no—
477C24—1421no—
478C24—1421no—
479C24—1421no—
480C24—1421no—
481C24—1422no—
482C24—1422no—
483C24—1422no—
484C24—1422no—
485C24C2×C4×D7111yescharacteristic
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—712no—
493C22×C4—712no—
494C22×C4—712no—
495C22×C4—714no—
496C22×C4—714no—
497C22×C4—714no—
498C22×C4—714no—
499C22×C4—714no—
500C22×C4—1422no—
501C22×C4—1422no—
502C22×C4—1422no—
503C22×C4—1422no—
504C22×C4—1422no—
505C22×C4—1422no—
506C22×C4—1421no—
507C22×C4—1421no—
508C22×C4—1421no—
509C22×C4—1421no—
510C22×C4—1422no—
511C22×C4—1422no—
512C22×C4—1422no—
513C22×C4—1422no—
514C22×C4—1422no—
515C22×C4—1422no—
516C22×C4—1422no—
517C22×C4—1422no—
518C22×C4—1422no—
519C22×C4—1422no—
520C22×C4—1422no—
521C22×C4—1422no—
522C22×C4—1422no—
523C22×C4—1422no—
524C22×C4—1422no—
525C22×C4—1422no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1422no—
529C22×C4—1422no—
530C22×C4—1422no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—1422no—
534C22×C4#1176584814yescomplemented
535C22×C4C2×C4×D7111yescharacteristic
536C22×C4C2×C4×D7111yescharacteristic
537C22×C4D4×D7111yescharacteristic
538C22×C4D4×D7111yescharacteristic
539C22×C4D4×D7111yescharacteristic
540C22×C4D4×D7111yescharacteristic
541C22×C4D4×D7111yescharacteristic
542C22×C4C2×C22⋊D7111yescharacteristic
543C22×C4C2×D28411yescharacteristic
544C22×C4Q8×D7111yescharacteristic
545C22×C4#1176586411yescharacteristic
546C22×C4#1176586511yescharacteristic
547C22×C4#1176586511yescharacteristic
548C22×C4#1176586611yescharacteristic
549M16—14232no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—2841no—
564C2×C8—2841no—
565C2×C8—2841no—
566C2×C8—2841no—
567C2×C8—714no—
568C2×C8—1422no—
569C2×C8—1422no—
570C2×C8—1422no—
571C2×C8—1422no—
572C2×C8—1422no—
573C2×C8—1422no—
574C2×C8—1422no—
575C2×C8—1422no—
576C2×C8—1422no—
577C2×C8(C2×D71)⋊C414yescomplemented
578C22⋊C4—14216no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—2841no—
584C42—2841no—
585C42—2841no—
586C42—2841no—
587C23—2842no—
588C23—2842no—
589C23—2842no—
590C23—2842no—
591C23—2842no—
592C23—2842no—
593C23—2842no—
594C23—2842no—
595C23—714no—
596C23—1422no—
597C23—1422no—
598C23—1422no—
599C23—1422no—
600C23—1422no—
601C23—1422no—
602C23—1422no—
603C23—1422no—
604C23—1422no—
605C23—1422no—
606C23—1424no—
607C23—1424no—
608C23—1424no—
609C23—1424no—
610C23C42×D7111yescharacteristic
611C23C22⋊C4×D7111yescharacteristic
612C23C4⋊C4×D7111yescharacteristic
613C23(C22⋊D71)⋊C411yescharacteristic
614C23C4×C22⋊D7111yescharacteristic
615C23#1455609011yescharacteristic
616C23C4×D28411yescharacteristic
617C23M16×D7112yes—
618C23C2×#1176584812yes—
619C23#1455613412yes—
620C23#1455613612yes—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—2842no—
629C2×C4—2842no—
630C2×C4—2842no—
631C2×C4—2842no—
632C2×C4—714no—
633C2×C4—1424no—
634C2×C4—1424no—
635C2×C4—1424no—
636C2×C4—1422no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1424no—
643C2×C4—1424no—
644C2×C4—1424no—
645C2×C4—1424no—
646C2×C4—1424no—
647C2×C4—1424no—
648C2×C4—1424no—
649C2×C4—1424no—
650C2×C4C22⋊C4×D7111yescharacteristic
651C2×C4C22⋊C4×D7111yescharacteristic
652C2×C4C22⋊C4×D7111yescharacteristic
653C2×C4C2×(C2×D71)⋊C411yescharacteristic
654C2×C4C4⋊C4×D7111yescharacteristic
655C2×C4C4⋊C4×D7111yescharacteristic
656C2×C4#1455608511yescharacteristic
657C2×C4#1455608611yescharacteristic
658C2×C4(C22⋊D71)⋊C411yescharacteristic
659C2×C4C4×C22⋊D7111yescharacteristic
660C2×C4#1455609011yescharacteristic
661C2×C4C4×D28411yescharacteristic
662C2×C4#1455609611yescharacteristic
663C2×C4#1455609611yescharacteristic
664C2×C4#1455609811yescharacteristic
665C2×C4#1455609811yescharacteristic
666C2×C4#1455609911yescharacteristic
667C2×C4#1455610111yescharacteristic
668C2×C4#1455610111yescharacteristic
669C2×C4#1455610311yescharacteristic
670C2×C4#1455610411yescharacteristic
671C2×C4#1455610611yescharacteristic
672C2×C4#1455610611yescharacteristic
673C2×C4#1455610811yescharacteristic
674C2×C4#1455611011yescharacteristic
675C2×C4#1455611011yescharacteristic
676C2×C4#1455611311yescharacteristic
677C2×C4#1455611311yescharacteristic
678C8—24no—
679C8—42no—
680C8—2842no—
681C8—1424no—
682C22—2844no—
683C22—2844no—
684C22—2842no—
685C22—2842no—
686C22—2844no—
687C22—2842no—
688C22—2844no—
689C22—2842no—
690C22—1424no—
691C22—1424no—
692C22—1424no—
693C22#95×D7111yescharacteristic
694C22#1798584611yescharacteristic
695C22C4×(C2×D71)⋊C411yescharacteristic
696C22#1798587011yescharacteristic
697C22#1798587311yescharacteristic
698C22#1798587511yescharacteristic
699C22#1798587711yescharacteristic
700C22C4×#1176584811yescharacteristic
701C22#1798595111yescharacteristic
702C22#1798595311yescharacteristic
703C22#1798595611yescharacteristic
704C22#1798596112yes—
705C22#1798596412yes—
706C22#1798602112yes—
707C22#1798602412yes—
708C22#1798606712yes—
709C22#1798606912yes—
710C22#1798607012yes—
711C22#1798607212yes—
712C22#1798607412yes—
713C22#1798607512yes—
714C22#1798607612yes—
715C22#1798607812yes—
716C4—44no—
717C4—2844no—
718C4—1424no—
719C4#1798585411yescharacteristic
720C4#1798585611yescharacteristic
721C4#1798585811yescharacteristic
722C4#1798586111yescharacteristic
723C4#1798587011yescharacteristic
724C4#1798587311yescharacteristic
725C4#1798587511yescharacteristic
726C4#1798587711yescharacteristic
727C2—2844no—
728C2(C2×D71)⋊#9511yescharacteristic
729C2#2258803211yescharacteristic
730C2#2258803511yescharacteristic
731C2#2258812011yescharacteristic
732C2#2258812211yescharacteristic
733C2#2258812311yescharacteristic
734C2#2258812511yescharacteristic
735C2#2258852112yes—
736C2#2258852412yes—
737C2#2258863412yes—
738C2#2258863612yes—
subgroupG/H
center, FrattiniC23×C4C22×D71
commutatorC23×C71C2×C42
FittingC2×#336×C71C2
socleC24×C71C22×C4
prime radicalC24×D71C2×C4
cosocleC23×C4×C71C23
hypercenterC2×#336D71
hypocenterC71#10715
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. C2×#17985754C2semidirect
5. C2×#17985753C2semidirect
6. C2×#17985753C2semidirect
7. C2×#336×C71C2semidirect
15. C22×#11765848C4semidirect
22. C2×(C2×D71)⋊C8C4semidirect
128. C22×Dic71M16semidirect
171. C2×C71⋊C8C22⋊C4semidirect
184. C22×C4×C71M16semidirect
212. C2×C8×C71C22⋊C4semidirect
376. C2×#336D71semidirect
377. C71#10715semidirect
534. C22×C4#11765848semidirect
577. C2×C8(C2×D71)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×#117658482
C22×(C2×D71)⋊C82
C2×C4×(C2×D71)⋊C42
C2×#179857542
C2×#179857532
C2×#336×C712
#1071571