Finite Group Databasebeta

← #31920127

Subgroups — #31920127

Order 18176.

1630 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985898C211yesmaximal, characteristic
2C2×#17985897C211yesmaximal, characteristic
3C2×#17985895C211yesmaximal, characteristic
4C2×#17985864C211yesmaximal, characteristic
5C2×C4⋊C4×Dic71C211yesmaximal, characteristic
6C2×C4×Dic71⋊C4C211yesmaximal, characteristic
7#22586604C212yesmaximal
8#22586603C212yesmaximal
9#22586569C212yesmaximal
10Dic71⋊#95C212yesmaximal
11C2×#389×C71C211yesmaximal, characteristic
12C22×C4⋊Dic71C2211yescharacteristic
13C22×C4⋊Dic71C2212yes—
14C22×C4⋊Dic71C2211yescharacteristic
15C22×Dic71⋊C4C2211yescharacteristic
16C22×Dic71⋊C4C2211yescharacteristic
17C22×Dic71⋊C4C2212yes—
18C22×Dic71⋊C4C2212yes—
19C22×C4×Dic71C2211yescharacteristic
20C22×C4×Dic71C2212yes—
21C22×C4×Dic71C2211yescharacteristic
22#17985898—24no—
23#17985897—24no—
24#17985895—24no—
25#17985864—24no—
26C4⋊C4×Dic71C418yescomplemented
27C4×Dic71⋊C4—24no—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2211yescharacteristic
34C2×C71⋊#95C2211yescharacteristic
35C2×C71⋊#95C2212yes—
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C4⋊C4×C71C2212yes—
38C22×C4⋊C4×C71C2211yescharacteristic
39C22×C42×C71C2211yescharacteristic
40#389×C71—24no—
41C2×#95×C71C2212yes—
42C23×Dic71C2312yes—
43C23×Dic71C2311yescharacteristic
44C23×Dic71C2311yescharacteristic
45C23×Dic71C2311yescharacteristic
46C23×Dic71C2311yescharacteristic
47C23×Dic71C2312yes—
48C2×C4⋊Dic71—24no—
49C2×C4⋊Dic71—22no—
50C2×C4⋊Dic71—22no—
51C2×C4⋊Dic71—24no—
52C2×C4⋊Dic71—22no—
53C2×C4⋊Dic71—42no—
54C2×C4⋊Dic71C2×C414yes—
55C2×C4⋊Dic71D414yes—
56C2×C4⋊Dic71Q814yes—
57C2×Dic71⋊C4—22no—
58C2×Dic71⋊C4—22no—
59C2×Dic71⋊C4—22no—
60C2×Dic71⋊C4—22no—
61C2×Dic71⋊C4—24no—
62C2×Dic71⋊C4—24no—
63C2×Dic71⋊C4—24no—
64C2×Dic71⋊C4—22no—
65C2×Dic71⋊C4—22no—
66C2×Dic71⋊C4—24no—
67C2×Dic71⋊C4—42no—
68C2×Dic71⋊C4—42no—
69C2×C4×Dic71—22no—
70C2×C4×Dic71—22no—
71C2×C4×Dic71—22no—
72C2×C4×Dic71—42no—
73C2×C4×Dic71—42no—
74C2×C4×Dic71C2×C418yes—
75C2×C4×Dic71C2×C414yes—
76C2×C4×Dic71D414yes—
77C2×C4×Dic71Q814yes—
78C71⋊#95—22no—
79C71⋊#95—22no—
80C71⋊#95—24no—
81C71⋊#95—24no—
82C71⋊#95—24no—
83C71⋊#95—24no—
84C71⋊#95—24no—
85C71⋊#95C2×C418yes—
86C23×C4×C71C2312yes—
87C23×C4×C71C2311yescharacteristic
88C23×C4×C71C2311yescharacteristic
89C23×C4×C71C2312yes—
90C23×C4×C71C2311yescharacteristic
91C2×C4⋊C4×C71—22no—
92C2×C4⋊C4×C71—22no—
93C2×C4⋊C4×C71—24no—
94C2×C4⋊C4×C71—22no—
95C2×C4⋊C4×C71—24no—
96C2×C4⋊C4×C71—42no—
97C2×C4⋊C4×C71C2×C414yes—
98C2×C4⋊C4×C71D414yes—
99C2×C4⋊C4×C71Q814yes—
100C2×C42×C71—22no—
101C2×C42×C71—22no—
102C2×C42×C71—22no—
103#95×C71—24no—
104C22×Dic71—21no—
105C22×Dic71—21no—
106C22×Dic71—22no—
107C22×Dic71—21no—
108C22×Dic71—21no—
109C22×Dic71—22no—
110C22×Dic71—21no—
111C22×Dic71—21no—
112C22×Dic71—22no—
113C22×Dic71—22no—
114C22×Dic71—21no—
115C22×Dic71—21no—
116C22×Dic71—21no—
117C22×Dic71—21no—
118C22×Dic71—21no—
119C22×Dic71—21no—
120C22×Dic71—21no—
121C22×Dic71—21no—
122C22×Dic71—21no—
123C22×Dic71—21no—
124C22×Dic71—21no—
125C22×Dic71—21no—
126C22×Dic71—21no—
127C22×Dic71—21no—
128C22×Dic71—22no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71C22×C412yes—
136C22×Dic71C22×C414yes—
137C22×Dic71C22×C412yes—
138C22×Dic71C2×D412yes—
139C22×Dic71C2×D412yes—
140C22×Dic71C2×D414yes—
141C22×Dic71C2×Q812yes—
142C22×Dic71C2×Q812yes—
143C22×Dic71C2×Q814yes—
144C22×Dic71#4112yes—
145C22×Dic71#4112yes—
146C4⋊Dic71—48no—
147C4⋊Dic71—44no—
148C4⋊Dic71C4⋊C4116yescomplemented
149Dic71⋊C4—28no—
150Dic71⋊C4—28no—
151Dic71⋊C4—48no—
152Dic71⋊C4—48no—
153C4×Dic71—48no—
154C4×Dic71—44no—
155C4×Dic71C4⋊C4116yescomplemented
156C24×C71C2411yescharacteristic
157C22×C4×C71—22no—
158C22×C4×C71—22no—
159C22×C4×C71—22no—
160C22×C4×C71—22no—
161C22×C4×C71—21no—
162C22×C4×C71—21no—
163C22×C4×C71—21no—
164C22×C4×C71—21no—
165C22×C4×C71—21no—
166C22×C4×C71—21no—
167C22×C4×C71—21no—
168C22×C4×C71—21no—
169C22×C4×C71—21no—
170C22×C4×C71—21no—
171C22×C4×C71—21no—
172C22×C4×C71—21no—
173C22×C4×C71—22no—
174C22×C4×C71—22no—
175C22×C4×C71—22no—
176C22×C4×C71—22no—
177C22×C4×C71—22no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71C22×C414yes—
181C22×C4×C71C22×C412yes—
182C22×C4×C71C2×D412yes—
183C22×C4×C71C2×D412yes—
184C22×C4×C71C2×D414yes—
185C22×C4×C71C2×D412yes—
186C22×C4×C71C2×Q812yes—
187C22×C4×C71C2×Q812yes—
188C22×C4×C71C2×Q814yes—
189C22×C4×C71C2×Q812yes—
190C22×C4×C71#4112yes—
191C22×C4×C71#4112yes—
192C4⋊C4×C71—48no—
193C4⋊C4×C71—44no—
194C4⋊C4×C71C4⋊C4116yescomplemented
195C42×C71—44no—
196C23×C71C23×C411yescharacteristic
197C23×C71C22×D411yescharacteristic
198C23×C71C22×D411yescharacteristic
199C23×C71C22×D411yescharacteristic
200C23×C71C22×Q811yescharacteristic
201C23×C71C22×Q811yescharacteristic
202C23×C71C22×Q811yescharacteristic
203C23×C71C2×#4111yescharacteristic
204C23×C71C2×#4111yescharacteristic
205C23×C71C2×#4111yescharacteristic
206C23×C71C2×#4111yescharacteristic
207C23×C71H(5,𝔽2)11yescharacteristic
208C23×C71H(5,𝔽2)11yescharacteristic
209C23×C712−1+411yescharacteristic
210C23×C712−1+411yescharacteristic
211C2×C4×C71—24no—
212C2×C4×C71—24no—
213C2×C4×C71—24no—
214C2×C4×C71—24no—
215C2×C4×C71—24no—
216C2×C4×C71—24no—
217C2×C4×C71—22no—
218C2×C4×C71—22no—
219C2×C4×C71—22no—
220C2×C4×C71—22no—
221C2×C4×C71—22no—
222C2×C4×C71—22no—
223C2×C4×C71—41no—
224C2×C4×C71—41no—
225C2×C4×C71—41no—
226C2×C4×C71—41no—
227C2×C4×C71—41no—
228C2×C4×C71—41no—
229C2×C4×C71—41no—
230C2×C4×C71—41no—
231C2×C4×C71—42no—
232C2×C4×C71—42no—
233C2×C4×C71—42no—
234C2×C4×C71—42no—
235C2×C4×C71—42no—
236C2×C4×C71—42no—
237C2×C4×C71—42no—
238C2×C4×C71C2×C4⋊C414yes—
239C2×C4×C71C2×C4⋊C414yes—
240C2×C4×C71C2×C4⋊C418yes—
241C2×C4×C71C2×C4⋊C414yes—
242C2×C4×C71#12714yes—
243C2×C4×C71C4⋊Q814yes—
244C2×C4×C71C4⋊Q814yes—
245C2×C4×C71C4⋊Q814yes—
246C2×Dic71—22no—
247C2×Dic71—24no—
248C2×Dic71—22no—
249C2×Dic71—22no—
250C2×Dic71—24no—
251C2×Dic71—22no—
252C2×Dic71—22no—
253C2×Dic71—22no—
254C2×Dic71—22no—
255C2×Dic71—22no—
256C2×Dic71—22no—
257C2×Dic71—22no—
258C2×Dic71—22no—
259C2×Dic71—22no—
260C2×Dic71—24no—
261C2×Dic71—24no—
262C2×Dic71—24no—
263C2×Dic71—24no—
264C2×Dic71—22no—
265C2×Dic71—22no—
266C2×Dic71—22no—
267C2×Dic71—22no—
268C2×Dic71—22no—
269C2×Dic71—22no—
270C2×Dic71—41no—
271C2×Dic71—41no—
272C2×Dic71—41no—
273C2×Dic71—41no—
274C2×Dic71—41no—
275C2×Dic71—41no—
276C2×Dic71—41no—
277C2×Dic71—41no—
278C2×Dic71—42no—
279C2×Dic71—42no—
280C2×Dic71—42no—
281C2×Dic71—42no—
282C2×Dic71—42no—
283C2×Dic71—42no—
284C2×Dic71—42no—
285C2×Dic71C2×C4⋊C414yes—
286C2×Dic71C2×C4⋊C414yes—
287C2×Dic71C2×C4⋊C418yes—
288C22×C71C22×C4⋊C411yescharacteristic
289C22×C71C22×C4⋊C411yescharacteristic
290C22×C71C22×C4⋊C411yescharacteristic
291C22×C71C4×#4111yescharacteristic
292C22×C71C4×#4111yescharacteristic
293C22×C71#51811yescharacteristic
294C22×C71#51911yescharacteristic
295C22×C71#52511yescharacteristic
296C22×C71#52511yescharacteristic
297C22×C71C2×#12711yescharacteristic
298C22×C71C2×C4⋊Q811yescharacteristic
299C22×C71C2×C4⋊Q811yescharacteristic
300C22×C71C2×C4⋊Q811yescharacteristic
301C22×C71#53311yescharacteristic
302C22×C71#53311yescharacteristic
303C22×C71#53711yescharacteristic
304C22×C71#53711yescharacteristic
305C22×C71#54411yescharacteristic
306C22×C71#54411yescharacteristic
307C22×C71#54611yescharacteristic
308C22×C71#54611yescharacteristic
309C22×C71#54611yescharacteristic
310C22×C71#54611yescharacteristic
311C22×C71#54811yescharacteristic
312C22×C71#54811yescharacteristic
313C22×C71#54811yescharacteristic
314C22×C71#54811yescharacteristic
315C22×C71#55411yescharacteristic
316C22×C71#55411yescharacteristic
317C22×C71#55411yescharacteristic
318C22×C71#55411yescharacteristic
319C22×C71#55711yescharacteristic
320C22×C71#55711yescharacteristic
321C22×C71#55711yescharacteristic
322C22×C71#55711yescharacteristic
323C4×C71—28no—
324C4×C71—42no—
325C4×C71—42no—
326C4×C71—82no—
327C4×C71#38418yes—
328Dic71—24no—
329Dic71—28no—
330Dic71—24no—
331Dic71—42no—
332Dic71—42no—
333Dic71—82no—
334#13954—711nomaximal, Sylow
335C2×C71C2×#38411yescharacteristic
336C2×C71#229611yescharacteristic
337C2×C71#231611yescharacteristic
338C2×C71#234911yescharacteristic
339C2×C71#234911yescharacteristic
340C2×C71#235111yescharacteristic
341C2×C71#235111yescharacteristic
342C2×C71#254011yescharacteristic
343C2×C71#254011yescharacteristic
344C2×C71#255011yescharacteristic
345C2×C71#255011yescharacteristic
346C2×C71#255011yescharacteristic
347C2×C71#255011yescharacteristic
348C2×C71#258411yescharacteristic
349C2×C71#258411yescharacteristic
350C2×#389—711no—
351C2×#389—711no—
352C2×#389—711no—
353C2×#389D7111yescharacteristic
354C2×#382—711no—
355C2×C4×C4⋊C4—711no—
356C2×C4×C4⋊C4—711no—
357#1444—712no—
358#1444—712no—
359C4⋊#95—712no—
360C4⋊#95—712no—
361C71#1395411yescharacteristic, complemented, Sylow
362C22×C4⋊C4—712no—
363C22×C4⋊C4—712no—
364C22×C4⋊C4—712no—
365C22×C4⋊C4—711no—
366C22×C4⋊C4—711no—
367C22×C4⋊C4—711no—
368C22×C4⋊C4—711no—
369C22×C4⋊C4C2×D7111yescharacteristic
370C22×C4⋊C4C2×D7112yes—
371C22×C4⋊C4C2×D7111yescharacteristic
372C22×C42—712no—
373C22×C42—711no—
374C22×C42—711no—
375C22×C42C2×D7111yescharacteristic
376#389—24no—
377#389—1424no—
378#389—1424no—
379#389—1424no—
380#382—1424no—
381C4×C4⋊C4—718no—
382C4×C4⋊C4—1424no—
383C2×#95—712no—
384C2×#95—711no—
385C2×#95—711no—
386C2×#95—712no—
387C2×#95—712no—
388C2×#95—712no—
389C2×#95—712no—
390C2×#95—712no—
391C2×#95C2×D7112yes—
392C23×C4—712no—
393C23×C4—711no—
394C23×C4—711no—
395C23×C4—711no—
396C23×C4—711no—
397C23×C4—712no—
398C23×C4C22×D7112yes—
399C23×C4C22×D7111yescharacteristic
400C23×C4C22×D7111yescharacteristic
401C23×C4C22×D7112yes—
402C23×C4C22×D7111yescharacteristic
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—2842no—
410C2×C4⋊C4—2842no—
411C2×C4⋊C4—2842no—
412C2×C4⋊C4—714no—
413C2×C4⋊C4—714no—
414C2×C4⋊C4—714no—
415C2×C4⋊C4—1424no—
416C2×C4⋊C4—1424no—
417C2×C4⋊C4—1424no—
418C2×C4⋊C4—1424no—
419C2×C4⋊C4—1422no—
420C2×C4⋊C4—1422no—
421C2×C4⋊C4—1424no—
422C2×C4⋊C4—1422no—
423C2×C4⋊C4—1424no—
424C2×C4⋊C4—1422no—
425C2×C4⋊C4—1422no—
426C2×C4⋊C4—1422no—
427C2×C4⋊C4—1422no—
428C2×C4⋊C4—1422no—
429C2×C4⋊C4—1422no—
430C2×C4⋊C4Dic14214yes—
431C2×C4⋊C4C4×D7114yes—
432C2×C4⋊C4C22⋊D7114yes—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—2842no—
437C2×C42—2842no—
438C2×C42—718no—
439C2×C42—714no—
440C2×C42—714no—
441C2×C42—714no—
442C2×C42—1422no—
443C2×C42—1422no—
444C2×C42—1422no—
445#95—24no—
446#95—718no—
447#95—1422no—
448#95—1422no—
449#95—1424no—
450#95—1424no—
451#95—1424no—
452#95—1424no—
453#95—1424no—
454C24C23×D7111yescharacteristic
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—712no—
479C22×C4—714no—
480C22×C4—712no—
481C22×C4—712no—
482C22×C4—712no—
483C22×C4—714no—
484C22×C4—712no—
485C22×C4—712no—
486C22×C4—714no—
487C22×C4—712no—
488C22×C4—712no—
489C22×C4—1422no—
490C22×C4—1422no—
491C22×C4—1422no—
492C22×C4—1422no—
493C22×C4—1422no—
494C22×C4—1422no—
495C22×C4—1422no—
496C22×C4—1421no—
497C22×C4—1421no—
498C22×C4—1421no—
499C22×C4—1421no—
500C22×C4—1421no—
501C22×C4—1421no—
502C22×C4—1421no—
503C22×C4—1421no—
504C22×C4—1421no—
505C22×C4—1421no—
506C22×C4—1421no—
507C22×C4—1421no—
508C22×C4—1422no—
509C22×C4—1421no—
510C22×C4—1421no—
511C22×C4—1421no—
512C22×C4—1422no—
513C22×C4—1421no—
514C22×C4—1421no—
515C22×C4—1422no—
516C22×C4—1421no—
517C22×C4—1422no—
518C22×C4—1421no—
519C22×C4—1421no—
520C22×C4C2×C4×D7114yes—
521C22×C4C2×C4×D7112yes—
522C22×C4D4×D7112yes—
523C22×C4D4×D7112yes—
524C22×C4C2×C22⋊D7114yes—
525C22×C4C2×C22⋊D7112yes—
526C22×C4Q8×D7112yes—
527C22×C4Q8×D7112yes—
528C22×C4C2×Dic14214yes—
529C22×C4C2×Dic14212yes—
530C22×C4#1176586412yes—
531C22×C4#1176586612yes—
532C4⋊C4—48no—
533C4⋊C4—44no—
534C4⋊C4—2848no—
535C4⋊C4—2848no—
536C4⋊C4—2848no—
537C4⋊C4—2844no—
538C4⋊C4—7116no—
539C4⋊C4—1428no—
540C4⋊C4—1428no—
541C4⋊C4Dic71⋊C4116yescomplemented
542C42—44no—
543C42—2848no—
544C42—2844no—
545C42—7116no—
546C23C22×C4×D7111yescharacteristic
547C23C2×D4×D7111yescharacteristic
548C23C2×D4×D7111yescharacteristic
549C23C22×C22⋊D7111yescharacteristic
550C23C2×Q8×D7111yescharacteristic
551C23C2×Q8×D7111yescharacteristic
552C23C22×Dic14211yescharacteristic
553C23#41×D7111yescharacteristic
554C23#41×D7111yescharacteristic
555C23C2×#1176586411yescharacteristic
556C23C2×#1176586611yescharacteristic
557C23#1455617311yescharacteristic
558C23#1455617411yescharacteristic
559C23#1455617511yescharacteristic
560C23#1455617611yescharacteristic
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—2841no—
589C2×C4—2841no—
590C2×C4—2841no—
591C2×C4—2841no—
592C2×C4—2841no—
593C2×C4—2841no—
594C2×C4—2841no—
595C2×C4—2841no—
596C2×C4—2842no—
597C2×C4—2842no—
598C2×C4—2842no—
599C2×C4—2842no—
600C2×C4—2842no—
601C2×C4—2842no—
602C2×C4—2842no—
603C2×C4—714no—
604C2×C4—714no—
605C2×C4—718no—
606C2×C4—1422no—
607C2×C4—1422no—
608C2×C4—1422no—
609C2×C4—1422no—
610C2×C4—1422no—
611C2×C4—1422no—
612C2×C4—1422no—
613C2×C4—1422no—
614C2×C4—1422no—
615C2×C4—1422no—
616C2×C4—1424no—
617C2×C4—1424no—
618C2×C4—1424no—
619C2×C4—1424no—
620C2×C4—1422no—
621C2×C4—1424no—
622C2×C4—1422no—
623C2×C4—1422no—
624C2×C4—1424no—
625C2×C4—1422no—
626C2×C4—1422no—
627C2×C4—1422no—
628C2×C4—1422no—
629C2×C4—1422no—
630C2×C4C4⋊C4×D7114yes—
631C2×C4C4⋊C4×D7114yes—
632C2×C4C2×Dic71⋊C418yes—
633C2×C4C2×Dic71⋊C414yes—
634C2×C4#1455612414yes—
635C2×C4#1455612614yes—
636C2×C4#1455612714yes—
637C2×C4#1455612714yes—
638C22C2×C4⋊C4×D7111yescharacteristic
639C22C2×C4⋊C4×D7111yescharacteristic
640C22C22×Dic71⋊C411yescharacteristic
641C22C4×#1176586411yescharacteristic
642C22C4×#1176586611yescharacteristic
643C22#1798647111yescharacteristic
644C22#1798647511yescharacteristic
645C22#1798650911yescharacteristic
646C22#1798651211yescharacteristic
647C22C2×#1455612411yescharacteristic
648C22C2×#1455612611yescharacteristic
649C22C2×#1455612711yescharacteristic
650C22C2×#1455612711yescharacteristic
651C22#1798655411yescharacteristic
652C22#1798655511yescharacteristic
653C22#1798657811yescharacteristic
654C22#1798657911yescharacteristic
655C22#1798662611yescharacteristic
656C22#1798662911yescharacteristic
657C22#1798663711yescharacteristic
658C22#1798664011yescharacteristic
659C22#1798664311yescharacteristic
660C22#1798664611yescharacteristic
661C22#1798665511yescharacteristic
662C22#1798665611yescharacteristic
663C22#1798665911yescharacteristic
664C22#1798666011yescharacteristic
665C22#1798670511yescharacteristic
666C22#1798670611yescharacteristic
667C22#1798670811yescharacteristic
668C22#1798671011yescharacteristic
669C22#1798672411yescharacteristic
670C22#1798672511yescharacteristic
671C22#1798672611yescharacteristic
672C22#1798672811yescharacteristic
673C4—28no—
674C4—42no—
675C4—42no—
676C4—82no—
677C4—2842no—
678C4—2842no—
679C4—5682no—
680C4—1428no—
681C4—1424no—
682C4—1424no—
683C4#1798586818yes—
684C2C2×#1798586811yescharacteristic
685C2#2259082111yescharacteristic
686C2#2259095511yescharacteristic
687C2#2259124511yescharacteristic
688C2#2259124911yescharacteristic
689C2#2259125811yescharacteristic
690C2#2259125911yescharacteristic
691C2#2259327611yescharacteristic
692C2#2259327811yescharacteristic
693C2#2259335711yescharacteristic
694C2#2259335911yescharacteristic
695C2#2259336311yescharacteristic
696C2#2259336411yescharacteristic
697C2#2259372511yescharacteristic
698C2#2259372711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#389×C71C2
socle, prime radical, cosocleC24×C71C24
hypercenterC2×#389D71
hypocenterC71#13954
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
26. C4⋊C4×Dic71C4semidirect
148. C4⋊Dic71C4⋊C4semidirect
155. C4×Dic71C4⋊C4semidirect
194. C4⋊C4×C71C4⋊C4semidirect
361. C71#13954semidirect
541. C4⋊C4Dic71⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#179858982
C2×#179858972
C2×#179858952
C2×#179858642
C2×C4⋊C4×Dic712
C2×C4×Dic71⋊C42
#225866042
#225866032
#225865692
Dic71⋊#952
C2×#389×C712
#1395471