Finite Group Databasebeta

← #31920893

Subgroups — #31920893

Order 18176.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985901C211yesmaximal, characteristic
2C2×#17985901C211yesmaximal, characteristic
3C2×#17985901C211yesmaximal, characteristic
4C2×#17985889C212yesmaximal, complemented
5C2×C4×C4⋊Dic71C211yesmaximal, characteristic, complemented
6#22586588C212yesmaximal, complemented
7#22586582C212yesmaximal, complemented
8#22586576C212yesmaximal, complemented
9#22586570C211yesmaximal, characteristic, complemented
10#22586570C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C71C211yesmaximal, characteristic, complemented
12C23×D284C2211yescharacteristic
13C22×C4⋊Dic71C2211yescharacteristic
14C22×C4⋊Dic71C2211yescharacteristic
15C22×C4⋊Dic71C2211yescharacteristic
16C22×(C2×D71)⋊C4C2212yes—
17C22×(C2×D71)⋊C4C2212yes—
18C22×(C2×D71)⋊C4C2212yes—
19C22×(C2×D71)⋊C4C2212yes—
20C22×(C2×D71)⋊C4C2212yes—
21C22×(C2×D71)⋊C4C2212yes—
22C22×C4×Dic71C2212yes—
23#17985901—24no—
24#17985901—24no—
25#17985901C418yescomplemented
26#17985889—28no—
27C4×C4⋊Dic71—24no—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C22×C4⋊C4×C71C2211yescharacteristic
34C22×C4⋊C4×C71C2211yescharacteristic
35C22×C42×C71C2211yescharacteristic
36C22×C42×C71C2211yescharacteristic
37C22×C42×C71C2211yescharacteristic
38C4×C4⋊C4×C71—24no—
39C2×#95×C71C2211yescharacteristic
40C2×#95×C71C2211yescharacteristic
41C24×D71C2312yes—
42C22×D284—22no—
43C22×D284—22no—
44C22×D284—22no—
45C22×D284—22no—
46C22×D284—22no—
47C22×D284—22no—
48C22×D284C2×C414yes—
49C23×Dic71C2312yes—
50C23×Dic71C2312yes—
51C23×Dic71C2312yes—
52C2×C4⋊Dic71—22no—
53C2×C4⋊Dic71—22no—
54C2×C4⋊Dic71—22no—
55C2×C4⋊Dic71—22no—
56C2×C4⋊Dic71—22no—
57C2×C4⋊Dic71—22no—
58C2×C4⋊Dic71—22no—
59C2×C4⋊Dic71C2×C414yes—
60C2×C4⋊Dic71D414yes—
61C2×(C2×D71)⋊C4—24no—
62C2×(C2×D71)⋊C4—24no—
63C2×(C2×D71)⋊C4—24no—
64C2×(C2×D71)⋊C4—24no—
65C2×(C2×D71)⋊C4—24no—
66C2×(C2×D71)⋊C4—24no—
67C2×(C2×D71)⋊C4—24no—
68C2×(C2×D71)⋊C4—24no—
69C2×(C2×D71)⋊C4—24no—
70C2×(C2×D71)⋊C4—24no—
71C2×(C2×D71)⋊C4—42no—
72C2×(C2×D71)⋊C4—42no—
73C2×(C2×D71)⋊C4—42no—
74C2×(C2×D71)⋊C4—42no—
75C2×(C2×D71)⋊C4—42no—
76C2×(C2×D71)⋊C4—42no—
77C2×(C2×D71)⋊C4C2×C418yes—
78C2×(C2×D71)⋊C4C2×C418yes—
79C2×C4×Dic71—24no—
80C2×C4×Dic71—24no—
81C2×C4×Dic71—42no—
82C71⋊#95—24no—
83C71⋊#95—24no—
84C71⋊#95—24no—
85C71⋊#95—42no—
86C71⋊#95—42no—
87C23×C4×C71C2311yescharacteristic
88C23×C4×C71C2311yescharacteristic
89C23×C4×C71C2311yescharacteristic
90C23×C4×C71C2311yescharacteristic
91C23×C4×C71C2311yescharacteristic
92C23×C4×C71C2311yescharacteristic
93C23×C4×C71C2311yescharacteristic
94C2×C4⋊C4×C71—22no—
95C2×C4⋊C4×C71—22no—
96C2×C4⋊C4×C71—22no—
97C2×C4⋊C4×C71—22no—
98C2×C4⋊C4×C71—22no—
99C2×C4⋊C4×C71D414yescomplemented
100C2×C42×C71—22no—
101C2×C42×C71—22no—
102C2×C42×C71—22no—
103C2×C42×C71—22no—
104C2×C42×C71—22no—
105C2×C42×C71—22no—
106C2×C42×C71—22no—
107C2×C42×C71C2×C414yes—
108C2×C42×C71D414yes—
109#95×C71—22no—
110#95×C71—22no—
111C23×D71—22no—
112C23×D71—22no—
113C23×D71—22no—
114C23×D71—22no—
115C23×D71—22no—
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×D71C22×C414yes—
126C2×D284—28no—
127C2×D284—28no—
128C2×D284—28no—
129C2×D284—44no—
130C2×D284—44no—
131C2×D284—44no—
132C2×D284—44no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71—22no—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71—22no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71—22no—
146C22×Dic71—22no—
147C22×Dic71—22no—
148C22×Dic71—22no—
149C22×Dic71—22no—
150C22×Dic71—22no—
151C22×Dic71—22no—
152C22×Dic71C22×C414yes—
153C22×Dic71C2×D414yes—
154C4⋊Dic71—28no—
155C4⋊Dic71—28no—
156C4⋊Dic71—44no—
157(C2×D71)⋊C4—216no—
158(C2×D71)⋊C4—48no—
159(C2×D71)⋊C4—48no—
160(C2×D71)⋊C4—48no—
161(C2×D71)⋊C4—48no—
162(C2×D71)⋊C4—48no—
163C4×Dic71—48no—
164C24×C71C2411yescharacteristic
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—21no—
174C22×C4×C71—21no—
175C22×C4×C71—21no—
176C22×C4×C71—21no—
177C22×C4×C71—21no—
178C22×C4×C71—21no—
179C22×C4×C71—21no—
180C22×C4×C71—21no—
181C22×C4×C71—21no—
182C22×C4×C71—21no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—21no—
187C22×C4×C71—21no—
188C22×C4×C71—21no—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71C22×C412yes—
198C22×C4×C71C22×C412yes—
199C22×C4×C71C22×C412yes—
200C22×C4×C71C2×D412yes—
201C22×C4×C71C2×D412yes—
202C22×C4×C71C2×D412yes—
203C22×C4×C71C2×D412yes—
204C22×C4×C71C2×D412yes—
205C22×C4×C71C2×D412yes—
206C22×C4×C71C2×D412yes—
207C22×C4×C71#4112yes—
208C22×C4×C71#4112yes—
209C22×C4×C71#4112yes—
210C22×C4×C71#4112yes—
211C22×C4×C71#4112yes—
212C22×C4×C71#4112yes—
213C22×C4×C71#4112yes—
214C4⋊C4×C71—28no—
215C4⋊C4×C71—28no—
216C42×C71—28no—
217C42×C71—28no—
218C42×C71—44no—
219C23×C71C23×C411yescharacteristic
220C23×C71C22×D411yescharacteristic
221C23×C71C22×D411yescharacteristic
222C23×C71C22×D411yescharacteristic
223C23×C71C2×#4111yescharacteristic
224C23×C71C2×#4111yescharacteristic
225C23×C71C2×#4111yescharacteristic
226C23×C71C2×#4111yescharacteristic
227C23×C71C2×#4111yescharacteristic
228C23×C71C2×#4111yescharacteristic
229C23×C71C2×#4111yescharacteristic
230C23×C71H(5,𝔽2)11yescharacteristic
231C23×C71H(5,𝔽2)11yescharacteristic
232C23×C71H(5,𝔽2)11yescharacteristic
233C23×C712−1+411yescharacteristic
234C22×D71—24no—
235C22×D71—24no—
236C22×D71—24no—
237C22×D71—24no—
238C22×D71—24no—
239C22×D71—24no—
240C22×D71—24no—
241C22×D71—42no—
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—42no—
251C22×D71—42no—
252C22×D71—42no—
253C22×D71—42no—
254C22×D71—42no—
255C22×D71—42no—
256C22×D71—42no—
257C22×D71—42no—
258C22×D71—42no—
259C22×D71—42no—
260C22×D71—42no—
261C22×D71—42no—
262C22×D71—42no—
263C22×D71—42no—
264C22×D71—42no—
265C22×D71—42no—
266C22×D71—42no—
267C22×D71—42no—
268C22×D71—42no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
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—22no—
292C2×C4×C71—22no—
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—41no—
300C2×C4×C71—41no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71—41no—
304C2×C4×C71—41no—
305C2×C4×C71—41no—
306C2×C4×C71—41no—
307C2×C4×C71—41no—
308C2×C4×C71—41no—
309C2×C4×C71#11714yes—
310C2×C4×C71C4×D414yes—
311C2×C4×C71C4×D414yes—
312C2×C4×C71C4×D414yes—
313C2×C4×C71#12114yes—
314C2×C4×C71#12114yes—
315C2×C4×C71#12314yes—
316C2×C4×C71#12414yes—
317C2×C4×C71#12614yes—
318C2×Dic71—24no—
319C2×Dic71—24no—
320C2×Dic71—24no—
321C2×Dic71—24no—
322C2×Dic71—24no—
323C2×Dic71—24no—
324C2×Dic71—42no—
325C2×Dic71—42no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330C2×Dic71—42no—
331C2×Dic71—42no—
332C2×Dic71—42no—
333C2×Dic71—42no—
334C2×Dic71—42no—
335C2×Dic71—42no—
336C2×Dic71—42no—
337C2×Dic71—42no—
338C2×Dic71—42no—
339D284—416no—
340C22×C71C2×#11711yescharacteristic
341C22×C71C2×C4×D411yescharacteristic
342C22×C71C2×C4×D411yescharacteristic
343C22×C71C2×C4×D411yescharacteristic
344C22×C71C4×#4111yescharacteristic
345C22×C71#51811yescharacteristic
346C22×C71#52011yescharacteristic
347C22×C71C2×#12111yescharacteristic
348C22×C71C2×#12111yescharacteristic
349C22×C71C2×#12311yescharacteristic
350C22×C71#52511yescharacteristic
351C22×C71C2×#12411yescharacteristic
352C22×C71C2×#12611yescharacteristic
353C22×C71#52911yescharacteristic
354C22×C71#53211yescharacteristic
355C22×C71#53511yescharacteristic
356C22×C71#53711yescharacteristic
357C22×C71#54011yescharacteristic
358C22×C71#54211yescharacteristic
359C22×C71D4211yescharacteristic
360C22×C71#54611yescharacteristic
361C22×C71#54711yescharacteristic
362C22×C71#54811yescharacteristic
363C22×C71#55011yescharacteristic
364C22×C71#55011yescharacteristic
365C22×C71#55011yescharacteristic
366C22×C71#55311yescharacteristic
367C22×C71#55311yescharacteristic
368C22×C71#55511yescharacteristic
369C22×C71#55611yescharacteristic
370C22×C71#55611yescharacteristic
371C22×C71#55911yescharacteristic
372C22×C71#55911yescharacteristic
373C22×C71#55911yescharacteristic
374C22×C71#55911yescharacteristic
375C2×D71—44no—
376C2×D71—44no—
377C2×D71—44no—
378C2×D71—44no—
379C2×D71—44no—
380C2×D71—44no—
381C2×D71—44no—
382C2×D71—82no—
383C2×D71—82no—
384C2×D71—82no—
385C2×D71—82no—
386C2×D71—82no—
387C2×D71—82no—
388C2×D71—82no—
389C2×D71—82no—
390C4×C71—24no—
391C4×C71—24no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71—42no—
395C4×C71—42no—
396C4×C71#38818yescomplemented
397Dic71—44no—
398Dic71—44no—
399Dic71—82no—
400#14022—711nomaximal, Sylow
401C2×C71C2×#38811yescharacteristic
402C2×C71C4×#12111yescharacteristic
403C2×C71#232411yescharacteristic
404C2×C71#235411yescharacteristic
405C2×C71#235711yescharacteristic
406C2×C71#236611yescharacteristic
407C2×C71#236711yescharacteristic
408C2×C71#241411yescharacteristic
409C2×C71#241611yescharacteristic
410C2×C71#244511yescharacteristic
411C2×C71#244811yescharacteristic
412C2×C71#251211yescharacteristic
413C2×C71#251311yescharacteristic
414C2×C71#254811yescharacteristic
415C2×C71#259211yescharacteristic
416D71—84no—
417C2×#390—711no—
418C2×#390—711no—
419C2×#390—711no—
420C2×#388—712no—
421C2×C4×C4⋊C4—711no—
422C2×C4×C4⋊C4D7111yescharacteristic, complemented
423#1440—712no—
424#1439—712no—
425#1437—712no—
426C4⋊#95—711no—
427C4⋊#95—711no—
428C71#1402211yescharacteristic, complemented, Sylow
429C23×D4—711no—
430C22×C4⋊C4—711no—
431C22×C4⋊C4—711no—
432C22×C4⋊C4—711no—
433C22×C4⋊C4C2×D7111yescharacteristic
434C22×C4⋊C4C2×D7111yescharacteristic
435C22×C22⋊C4—712no—
436C22×C22⋊C4—712no—
437C22×C22⋊C4—712no—
438C22×C22⋊C4—712no—
439C22×C22⋊C4—712no—
440C22×C22⋊C4—712no—
441C22×C42—712no—
442C22×C42C2×D7111yescharacteristic
443C22×C42C2×D7111yescharacteristic
444C22×C42C2×D7111yescharacteristic
445#390—718no—
446#390—1424no—
447#390—1424no—
448#388—1428no—
449C4×C4⋊C4—24no—
450C4×C4⋊C4—1424no—
451C2×#95—712no—
452C2×#95—712no—
453C2×#95—712no—
454C2×#95—712no—
455C2×#95—712no—
456C2×#95C2×D7111yescharacteristic
457C2×#95C2×D7111yescharacteristic
458C25—712no—
459C22×D4—714no—
460C22×D4—1422no—
461C22×D4—1422no—
462C22×D4—1422no—
463C22×D4—1422no—
464C22×D4—1422no—
465C22×D4—1422no—
466C23×C4—712no—
467C23×C4—712no—
468C23×C4—712no—
469C23×C4C22×D7111yescharacteristic
470C23×C4C22×D7111yescharacteristic
471C23×C4C22×D7111yescharacteristic
472C23×C4C22×D7111yescharacteristic
473C23×C4C22×D7111yescharacteristic
474C23×C4C22×D7111yescharacteristic
475C23×C4C22×D7111yescharacteristic
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—714no—
482C2×C4⋊C4—714no—
483C2×C4⋊C4—1422no—
484C2×C4⋊C4—1422no—
485C2×C4⋊C4—1422no—
486C2×C4⋊C4—1422no—
487C2×C4⋊C4—1422no—
488C2×C4⋊C4—1422no—
489C2×C4⋊C4—1422no—
490C2×C4⋊C4D28414yescomplemented
491C2×C22⋊C4—2842no—
492C2×C22⋊C4—2842no—
493C2×C22⋊C4—2842no—
494C2×C22⋊C4—2842no—
495C2×C22⋊C4—2842no—
496C2×C22⋊C4—2842no—
497C2×C22⋊C4—718no—
498C2×C22⋊C4—718no—
499C2×C22⋊C4—1424no—
500C2×C22⋊C4—1424no—
501C2×C22⋊C4—1424no—
502C2×C22⋊C4—1424no—
503C2×C22⋊C4—1424no—
504C2×C22⋊C4—1424no—
505C2×C22⋊C4—1424no—
506C2×C22⋊C4—1424no—
507C2×C22⋊C4—1424no—
508C2×C22⋊C4—1424no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42—2842no—
517C2×C42—1424no—
518C2×C42—1424no—
519C2×C42C4×D7114yes—
520C2×C42C22⋊D7114yes—
521#95—22no—
522#95—22no—
523#95—2842no—
524#95—2842no—
525#95—1424no—
526#95—1424no—
527#95—1424no—
528C24—714no—
529C24—1422no—
530C24—1422no—
531C24—1422no—
532C24—1422no—
533C24—1422no—
534C24—1422no—
535C24—1422no—
536C24—1422no—
537C24—1422no—
538C24—1422no—
539C24—1422no—
540C24—1422no—
541C24—1422no—
542C24—1422no—
543C24C23×D7111yescharacteristic
544C2×D4—2844no—
545C2×D4—2844no—
546C2×D4—2844no—
547C2×D4—2844no—
548C2×D4—1428no—
549C2×D4—1428no—
550C2×D4—1428no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
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—714no—
584C22×C4—714no—
585C22×C4—1422no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4—1422no—
589C22×C4—1422no—
590C22×C4—1422no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1422no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4—1422no—
599C22×C4—1422no—
600C22×C4—1422no—
601C22×C4—1422no—
602C22×C4—1422no—
603C22×C4—1422no—
604C22×C4C2×C4×D7112yes—
605C22×C4C2×C4×D7112yes—
606C22×C4C2×C4×D7112yes—
607C22×C4D4×D7112yes—
608C22×C4C2×C22⋊D7112yes—
609C22×C4C2×C22⋊D7112yes—
610C22×C4C2×C22⋊D7112yes—
611C22×C4C2×D28412yes—
612C22×C4C2×D28412yes—
613C22×C4C2×D28412yes—
614C22×C4#1176586412yes—
615C22×C4#1176586512yes—
616C22×C4#1176586512yes—
617C22×C4#1176586512yes—
618C22×C4#1176586512yes—
619C22×C4#1176586612yes—
620C22×C4#1176586612yes—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—2844no—
624C4⋊C4—1428no—
625C4⋊C4—1428no—
626C22⋊C4—2848no—
627C22⋊C4—2848no—
628C22⋊C4—2848no—
629C22⋊C4—2848no—
630C22⋊C4—2848no—
631C22⋊C4—14216no—
632C42—28no—
633C42—28no—
634C42—44no—
635C42—2848no—
636C23—2842no—
637C23—2842no—
638C23—2842no—
639C23—2842no—
640C23—2842no—
641C23—2842no—
642C23—2842no—
643C23—2842no—
644C23—2842no—
645C23—2842no—
646C23—2842no—
647C23—2842no—
648C23—2842no—
649C23—2842no—
650C23—2842no—
651C23—2842no—
652C23—2842no—
653C23—2842no—
654C23—2842no—
655C23—2842no—
656C23—2842no—
657C23—2842no—
658C23—2842no—
659C23—2842no—
660C23—2842no—
661C23—2842no—
662C23—2842no—
663C23—2842no—
664C23—1424no—
665C23—1424no—
666C23—1424no—
667C23—1424no—
668C23—1424no—
669C23—1424no—
670C23—1424no—
671C23C22×C4×D7111yescharacteristic
672C23C2×D4×D7111yescharacteristic
673C23C22×C22⋊D7111yescharacteristic
674C23C22×D28411yescharacteristic
675C23C2×#1176586411yescharacteristic
676C23C2×#1176586511yescharacteristic
677C23C2×#1176586511yescharacteristic
678C23C2×#1176586511yescharacteristic
679C23C2×#1176586511yescharacteristic
680C23C2×#1176586611yescharacteristic
681C23C2×#1176586611yescharacteristic
682C23#1455617411yescharacteristic
683C23#1455617411yescharacteristic
684C23#1455617411yescharacteristic
685C23#1455617511yescharacteristic
686D4—28416no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—2842no—
728C2×C4—2842no—
729C2×C4—2842no—
730C2×C4—2842no—
731C2×C4—2842no—
732C2×C4—2842no—
733C2×C4—2842no—
734C2×C4—2842no—
735C2×C4—2842no—
736C2×C4—2842no—
737C2×C4—2842no—
738C2×C4—2842no—
739C2×C4—2842no—
740C2×C4—2842no—
741C2×C4—2842no—
742C2×C4—1424no—
743C2×C4—1424no—
744C2×C4—1424no—
745C2×C4—1424no—
746C2×C4—1424no—
747C2×C4—1424no—
748C2×C4#1455608614yes—
749C2×C4C4×C22⋊D7114yes—
750C2×C4#1455609014yes—
751C2×C4C4×D28414yes—
752C2×C4#1455610014yes—
753C2×C4#1455610214yes—
754C2×C4#1455611314yes—
755C2×C4#1455611714yes—
756C2×C4#1455612314yes—
757C22—2844no—
758C22—2844no—
759C22—2844no—
760C22—2844no—
761C22—2844no—
762C22—2844no—
763C22—2844no—
764C22—5682no—
765C22—5682no—
766C22—5682no—
767C22—5682no—
768C22—5682no—
769C22—5682no—
770C22—5682no—
771C22—5682no—
772C22C2×#1455608611yescharacteristic
773C22C2×C4×C22⋊D7111yescharacteristic
774C22C2×#1455609011yescharacteristic
775C22C2×C4×D28411yescharacteristic
776C22C4×#1176586511yescharacteristic
777C22#1798647311yescharacteristic
778C22#1798647911yescharacteristic
779C22C2×#1455610011yescharacteristic
780C22C2×#1455610211yescharacteristic
781C22C2×#1455611311yescharacteristic
782C22#1798651011yescharacteristic
783C22C2×#1455611711yescharacteristic
784C22C2×#1455612311yescharacteristic
785C22#1798653311yescharacteristic
786C22#1798654911yescharacteristic
787C22#1798656311yescharacteristic
788C22#1798657711yescharacteristic
789C22#1798660411yescharacteristic
790C22#1798662011yescharacteristic
791C22D4×D28411yescharacteristic
792C22#1798664511yescharacteristic
793C22#1798665311yescharacteristic
794C22#1798665811yescharacteristic
795C22#1798667011yescharacteristic
796C22#1798667111yescharacteristic
797C22#1798667111yescharacteristic
798C22#1798669511yescharacteristic
799C22#1798669511yescharacteristic
800C22#1798671411yescharacteristic
801C22#1798672211yescharacteristic
802C22#1798672211yescharacteristic
803C22#1798673411yescharacteristic
804C22#1798673411yescharacteristic
805C22#1798673411yescharacteristic
806C22#1798673411yescharacteristic
807C4—24no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—2844no—
814C4—2844no—
815C4—5682no—
816C4#1798588918yescomplemented
817C2—5684no—
818C2C2×#1798588911yescharacteristic
819C2C4×#1455610211yescharacteristic
820C2#2259103311yescharacteristic
821C2#2259128711yescharacteristic
822C2#2259131111yescharacteristic
823C2#2259140411yescharacteristic
824C2#2259140911yescharacteristic
825C2#2259175811yescharacteristic
826C2#2259178011yescharacteristic
827C2#2259210511yescharacteristic
828C2#2259213811yescharacteristic
829C2#2259292611yescharacteristic
830C2#2259293711yescharacteristic
831C2#2259333911yescharacteristic
832C2#2259382811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×C4×C4⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×C4×C4⋊C4D71
hypocenterC71#14022
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#17985889C2semidirect
5. C2×C4×C4⋊Dic71C2semidirect
6. #22586588C2semidirect
7. #22586582C2semidirect
8. #22586576C2semidirect
9. #22586570C2semidirect
10. #22586570C2semidirect
11. C2×C4×C4⋊C4×C71C2semidirect
25. #17985901C4semidirect
99. C2×C4⋊C4×C71D4semidirect
396. C4×C71#388semidirect
422. C2×C4×C4⋊C4D71semidirect
428. C71#14022semidirect
490. C2×C4⋊C4D284semidirect
816. C4#17985889semidirect

Maximal subgroups

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

subgroupindex
C2×#179859012
C2×#179858892
C2×C4×C4⋊Dic712
#225865882
#225865822
#225865762
#225865702
C2×C4×C4⋊C4×C712
#1402271