Finite Group Databasebeta

← #31920849

Subgroups — #31920849

Order 18176.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D284C211yesmaximal, characteristic
2C2×#17985901C211yesmaximal, characteristic
3C2×#17985901C211yesmaximal, characteristic
4C2×#17985897C211yesmaximal, characteristic, complemented
5C2×#17985870C212yesmaximal, complemented
6#22586584C212yesmaximal, complemented
7#22586582C212yesmaximal, complemented
8#22586570C211yesmaximal, characteristic, complemented
9#22586570C211yesmaximal, characteristic, complemented
10(C2×D71)⋊#95C212yesmaximal, complemented
11C2×C4×C4⋊C4×C71C211yesmaximal, characteristic, complemented
12C23×D284C2211yescharacteristic
13C23×C4×D71C2212yes—
14C2×C4×D284—24no—
15C2×C4×D284—24no—
16C2×C4×D284—24no—
17C22×C4⋊Dic71C2211yescharacteristic
18C22×C4⋊Dic71C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20C22×Dic71⋊C4C2212yes—
21C22×(C2×D71)⋊C4C2212yes—
22C22×(C2×D71)⋊C4C2212yes—
23C22×(C2×D71)⋊C4C2212yes—
24C22×(C2×D71)⋊C4C2212yes—
25C22×(C2×D71)⋊C4C2212yes—
26#17985901—24no—
27#17985901C418yescomplemented
28#17985897—24no—
29#17985870—28no—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C22×C4⋊C4×C71C2211yescharacteristic
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C42×C71C2211yescharacteristic
38C22×C42×C71C2211yescharacteristic
39C22×C42×C71C2211yescharacteristic
40C4×C4⋊C4×C71—24no—
41C2×#95×C71C2211yescharacteristic
42C2×#95×C71C2211yescharacteristic
43C24×D71C2312yes—
44C22×D284—22no—
45C22×D284—22no—
46C22×D284—22no—
47C22×D284—22no—
48C22×D284C2×C414yes—
49C22×D284D414yes—
50C22×D284Q814yes—
51C23×Dic71C2312yes—
52C23×Dic71C2312yes—
53C23×Dic71C2312yes—
54C22×C4×D71—24no—
55C22×C4×D71—24no—
56C22×C4×D71—24no—
57C22×C4×D71—24no—
58C22×C4×D71—24no—
59C22×C4×D71—42no—
60C22×C4×D71—42no—
61C4×D284—232no—
62C2×C4⋊Dic71—22no—
63C2×C4⋊Dic71—22no—
64C2×C4⋊Dic71—22no—
65C2×C4⋊Dic71—22no—
66C2×C4⋊Dic71—22no—
67C2×C4⋊Dic71—22no—
68C2×C4⋊Dic71—22no—
69C2×C4⋊Dic71C2×C414yescomplemented
70C2×C4⋊Dic71D414yes—
71C2×Dic71⋊C4—24no—
72C2×Dic71⋊C4—24no—
73C2×Dic71⋊C4—42no—
74C2×(C2×D71)⋊C4—24no—
75C2×(C2×D71)⋊C4—24no—
76C2×(C2×D71)⋊C4—24no—
77C2×(C2×D71)⋊C4—24no—
78C2×(C2×D71)⋊C4—24no—
79C2×(C2×D71)⋊C4—24no—
80C2×(C2×D71)⋊C4—24no—
81C2×(C2×D71)⋊C4—24no—
82C2×(C2×D71)⋊C4—24no—
83C2×(C2×D71)⋊C4—42no—
84C2×(C2×D71)⋊C4—42no—
85C2×(C2×D71)⋊C4—42no—
86C2×(C2×D71)⋊C4—42no—
87C2×(C2×D71)⋊C4C2×C418yescomplemented
88C2×(C2×D71)⋊C4C2×C418yescomplemented
89C71⋊#95—24no—
90C71⋊#95—24no—
91C71⋊#95—24no—
92C71⋊#95—42no—
93C71⋊#95—42no—
94C23×C4×C71C2311yescharacteristic
95C23×C4×C71C2311yescharacteristic
96C23×C4×C71C2311yescharacteristic
97C23×C4×C71C2311yescharacteristic
98C23×C4×C71C2311yescharacteristic
99C23×C4×C71C2311yescharacteristic
100C23×C4×C71C2311yescharacteristic
101C2×C4⋊C4×C71—22no—
102C2×C4⋊C4×C71—22no—
103C2×C4⋊C4×C71—22no—
104C2×C4⋊C4×C71—22no—
105C2×C4⋊C4×C71—22no—
106C2×C4⋊C4×C71D414yescomplemented
107C2×C42×C71—22no—
108C2×C42×C71—22no—
109C2×C42×C71—22no—
110C2×C42×C71—22no—
111C2×C42×C71—22no—
112C2×C42×C71—22no—
113C2×C42×C71—22no—
114C2×C42×C71C2×C414yescomplemented
115C2×C42×C71D414yes—
116#95×C71—22no—
117#95×C71—22no—
118C23×D71—22no—
119C23×D71—22no—
120C23×D71—22no—
121C23×D71—22no—
122C23×D71—22no—
123C23×D71—22no—
124C23×D71—22no—
125C23×D71—22no—
126C23×D71—22no—
127C23×D71—22no—
128C23×D71—22no—
129C23×D71—22no—
130C23×D71C22×C414yes—
131C23×D71C2×D414yes—
132C23×D71C2×Q814yes—
133C2×D284—28no—
134C2×D284—28no—
135C2×D284—28no—
136C2×D284—28no—
137C2×D284—28no—
138C2×D284—28no—
139C2×D284C4⋊C4116yescomplemented
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×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71C22×C414yes—
160C22×Dic71C2×D414yes—
161C2×C4×D71—216no—
162C2×C4×D71—48no—
163C2×C4×D71—48no—
164C2×C4×D71—48no—
165C2×C4×D71—48no—
166C2×C4×D71—48no—
167C2×C4×D71—48no—
168C4⋊Dic71—28no—
169C4⋊Dic71—28no—
170C4⋊Dic71—44no—
171Dic71⋊C4—48no—
172(C2×D71)⋊C4—216no—
173(C2×D71)⋊C4—216no—
174(C2×D71)⋊C4—48no—
175(C2×D71)⋊C4—48no—
176(C2×D71)⋊C4—48no—
177C24×C71C2411yescharacteristic
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×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—21no—
207C22×C4×C71—21no—
208C22×C4×C71—21no—
209C22×C4×C71—21no—
210C22×C4×C71C22×C412yes—
211C22×C4×C71C22×C412yes—
212C22×C4×C71C22×C412yes—
213C22×C4×C71C2×D412yes—
214C22×C4×C71C2×D412yes—
215C22×C4×C71C2×D412yes—
216C22×C4×C71C2×D412yes—
217C22×C4×C71C2×D412yes—
218C22×C4×C71C2×D412yes—
219C22×C4×C71C2×D412yes—
220C22×C4×C71C2×D412yes—
221C22×C4×C71C2×Q812yes—
222C22×C4×C71#4112yes—
223C22×C4×C71#4112yes—
224C22×C4×C71#4112yes—
225C22×C4×C71#4112yes—
226C22×C4×C71#4112yes—
227C4⋊C4×C71—28no—
228C4⋊C4×C71—28no—
229C42×C71—28no—
230C42×C71—28no—
231C42×C71—44no—
232C23×C71C23×C411yescharacteristic
233C23×C71C22×D411yescharacteristic
234C23×C71C22×D411yescharacteristic
235C23×C71C22×D411yescharacteristic
236C23×C71C22×D411yescharacteristic
237C23×C71C22×Q811yescharacteristic
238C23×C71C2×#4111yescharacteristic
239C23×C71C2×#4111yescharacteristic
240C23×C71C2×#4111yescharacteristic
241C23×C71C2×#4111yescharacteristic
242C23×C71C2×#4111yescharacteristic
243C23×C71H(5,𝔽2)11yescharacteristic
244C23×C71H(5,𝔽2)11yescharacteristic
245C23×C71H(5,𝔽2)11yescharacteristic
246C23×C712−1+411yescharacteristic
247C22×D71—24no—
248C22×D71—24no—
249C22×D71—24no—
250C22×D71—24no—
251C22×D71—24no—
252C22×D71—24no—
253C22×D71—24no—
254C22×D71—24no—
255C22×D71—24no—
256C22×D71—24no—
257C22×D71—24no—
258C22×D71—24no—
259C22×D71—24no—
260C22×D71—24no—
261C22×D71—24no—
262C22×D71—24no—
263C22×D71—24no—
264C22×D71—24no—
265C22×D71—42no—
266C22×D71—42no—
267C22×D71—42no—
268C22×D71—42no—
269C22×D71—42no—
270C22×D71—42no—
271C22×D71—42no—
272C22×D71—42no—
273C22×D71—42no—
274C22×D71—42no—
275C22×D71—42no—
276C22×D71—42no—
277C22×D71—42no—
278C22×D71—42no—
279C22×D71—42no—
280C22×D71—42no—
281C22×D71C2×C4⋊C418yes—
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—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—41no—
307C2×C4×C71—41no—
308C2×C4×C71—41no—
309C2×C4×C71—41no—
310C2×C4×C71—41no—
311C2×C4×C71—41no—
312C2×C4×C71—41no—
313C2×C4×C71—41no—
314C2×C4×C71—41no—
315C2×C4×C71—41no—
316C2×C4×C71—41no—
317C2×C4×C71—41no—
318C2×C4×C71—41no—
319C2×C4×C71—41no—
320C2×C4×C71—41no—
321C2×C4×C71—41no—
322C2×C4×C71C2×C4⋊C414yes—
323C2×C4×C71C4×D414yes—
324C2×C4×C71C4×D414yes—
325C2×C4×C71C4×D414yescomplemented
326C2×C4×C71#12014yes—
327C2×C4×C71#12114yes—
328C2×C4×C71C22⋊Q814yes—
329C2×C4×C71C22⋊Q814yes—
330C2×C4×C71#12314yes—
331C2×Dic71—24no—
332C2×Dic71—24no—
333C2×Dic71—24no—
334C2×Dic71—24no—
335C2×Dic71—24no—
336C2×Dic71—24no—
337C2×Dic71—42no—
338C2×Dic71—42no—
339C2×Dic71—42no—
340C2×Dic71—42no—
341C2×Dic71—42no—
342C2×Dic71—42no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345C2×Dic71—42no—
346C2×Dic71—42no—
347C2×Dic71—42no—
348C2×Dic71—42no—
349C2×Dic71—42no—
350C2×Dic71—42no—
351C2×Dic71—42no—
352D284—232no—
353C4×D71—432no—
354C22×C71C22×C4⋊C411yescharacteristic
355C22×C71C2×C4×D411yescharacteristic
356C22×C71C2×C4×D411yescharacteristic
357C22×C71C2×C4×D411yescharacteristic
358C22×C71C4×#4111yescharacteristic
359C22×C71#51811yescharacteristic
360C22×C71#52011yescharacteristic
361C22×C71C2×#12011yescharacteristic
362C22×C71C2×#12111yescharacteristic
363C22×C71C2×C22⋊Q811yescharacteristic
364C22×C71C2×C22⋊Q811yescharacteristic
365C22×C71C2×#12311yescharacteristic
366C22×C71#52511yescharacteristic
367C22×C71#52911yescharacteristic
368C22×C71#53211yescharacteristic
369C22×C71#53511yescharacteristic
370C22×C71#53711yescharacteristic
371C22×C71#54011yescharacteristic
372C22×C71#54211yescharacteristic
373C22×C71D4211yescharacteristic
374C22×C71D4211yescharacteristic
375C22×C71#54611yescharacteristic
376C22×C71#54611yescharacteristic
377C22×C71#54611yescharacteristic
378C22×C71#54711yescharacteristic
379C22×C71#54811yescharacteristic
380C22×C71D4×Q811yescharacteristic
381C22×C71#55011yescharacteristic
382C22×C71#55011yescharacteristic
383C22×C71#55411yescharacteristic
384C22×C71#55411yescharacteristic
385C22×C71#55411yescharacteristic
386C22×C71#55611yescharacteristic
387C22×C71#55911yescharacteristic
388C22×C71#55911yescharacteristic
389C2×D71—28no—
390C2×D71—28no—
391C2×D71—28no—
392C2×D71—44no—
393C2×D71—44no—
394C2×D71—44no—
395C2×D71—44no—
396C2×D71—44no—
397C2×D71—44no—
398C2×D71—44no—
399C2×D71—44no—
400C2×D71—44no—
401C2×D71—44no—
402C2×D71—44no—
403C2×D71—44no—
404C4×C71—24no—
405C4×C71—24no—
406C4×C71—42no—
407C4×C71—42no—
408C4×C71—42no—
409C4×C71—42no—
410C4×C71#38518yescomplemented
411Dic71—44no—
412Dic71—44no—
413Dic71—82no—
414#14018—711nomaximal, Sylow
415C2×C71C2×#38511yescharacteristic
416C2×C71C4×#12111yescharacteristic
417C2×C71#232411yescharacteristic
418C2×C71D4×C4⋊C411yescharacteristic
419C2×C71#234911yescharacteristic
420C2×C71#236611yescharacteristic
421C2×C71#236711yescharacteristic
422C2×C71#240711yescharacteristic
423C2×C71#240811yescharacteristic
424C2×C71#244511yescharacteristic
425C2×C71#244711yescharacteristic
426C2×C71#245211yescharacteristic
427C2×C71#245411yescharacteristic
428C2×C71#253811yescharacteristic
429C2×C71#258011yescharacteristic
430D71—48no—
431C22×C4×D4—711no—
432C2×#390—711no—
433C2×#390—711no—
434C2×#389—711no—
435C2×#385—712no—
436C2×C4×C4⋊C4D7111yescharacteristic, complemented
437#1439—712no—
438#1439—712no—
439C4⋊#95—711no—
440C4⋊#95—711no—
441C22⋊#95—712no—
442C71#1401811yescharacteristic, complemented, Sylow
443C23×D4—711no—
444C24×C4—712no—
445C2×C4×D4—1424no—
446C2×C4×D4—1424no—
447C2×C4×D4—1424no—
448C22×C4⋊C4—712no—
449C22×C4⋊C4—711no—
450C22×C4⋊C4—711no—
451C22×C4⋊C4—711no—
452C22×C4⋊C4C2×D7111yescharacteristic
453C22×C4⋊C4C2×D7111yescharacteristic
454C22×C22⋊C4—712no—
455C22×C22⋊C4—712no—
456C22×C22⋊C4—712no—
457C22×C22⋊C4—712no—
458C22×C22⋊C4—712no—
459C22×C42C2×D7111yescharacteristic
460C22×C42C2×D7111yescharacteristic
461C22×C42C2×D7111yescharacteristic
462#390—718no—
463#390—1424no—
464#389—1424no—
465#385—1428no—
466C4×C4⋊C4—24no—
467C2×#95—712no—
468C2×#95—712no—
469C2×#95—712no—
470C2×#95—712no—
471C2×#95—712no—
472C2×#95C2×D7111yescharacteristic
473C2×#95C2×D7111yescharacteristic
474C25—712no—
475C22×D4—714no—
476C22×D4—714no—
477C22×D4—714no—
478C22×D4—1422no—
479C22×D4—1422no—
480C22×D4—1422no—
481C22×D4—1422no—
482C23×C4—2842no—
483C23×C4—2842no—
484C23×C4—712no—
485C23×C4—712no—
486C23×C4—712no—
487C23×C4—1424no—
488C23×C4—1424no—
489C23×C4—1424no—
490C23×C4—1424no—
491C23×C4—1424no—
492C23×C4C22×D7111yescharacteristic
493C23×C4C22×D7111yescharacteristic
494C23×C4C22×D7111yescharacteristic
495C23×C4C22×D7111yescharacteristic
496C23×C4C22×D7111yescharacteristic
497C23×C4C22×D7111yescharacteristic
498C23×C4C22×D7111yescharacteristic
499C4×D4—14232no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—2842no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4—714no—
508C2×C4⋊C4—1424no—
509C2×C4⋊C4—1422no—
510C2×C4⋊C4—1424no—
511C2×C4⋊C4—1422no—
512C2×C4⋊C4—1422no—
513C2×C4⋊C4—1422no—
514C2×C4⋊C4—1422no—
515C2×C4⋊C4—1422no—
516C2×C4⋊C4—1422no—
517C2×C4⋊C4D28414yescomplemented
518C2×C22⋊C4—2842no—
519C2×C22⋊C4—2842no—
520C2×C22⋊C4—2842no—
521C2×C22⋊C4—2842no—
522C2×C22⋊C4—718no—
523C2×C22⋊C4—718no—
524C2×C22⋊C4—1424no—
525C2×C22⋊C4—1424no—
526C2×C22⋊C4—1424no—
527C2×C22⋊C4—1424no—
528C2×C22⋊C4—1424no—
529C2×C22⋊C4—1424no—
530C2×C22⋊C4—1424no—
531C2×C22⋊C4—1424no—
532C2×C22⋊C4—1424no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42C4×D7114yescomplemented
541C2×C42C22⋊D7114yes—
542#95—22no—
543#95—22no—
544#95—2842no—
545#95—2842no—
546#95—1424no—
547#95—1424no—
548#95—1424no—
549C24—714no—
550C24—714no—
551C24—714no—
552C24—1422no—
553C24—1422no—
554C24—1422no—
555C24—1422no—
556C24—1422no—
557C24—1422no—
558C24—1422no—
559C24—1422no—
560C24—1422no—
561C24—1422no—
562C24—1422no—
563C24—1422no—
564C24C23×D7111yescharacteristic
565C2×D4—7116no—
566C2×D4—1428no—
567C2×D4—1428no—
568C2×D4—1428no—
569C2×D4—1428no—
570C2×D4—1428no—
571C2×D4—1428no—
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—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—2848no—
605C22×C4—2848no—
606C22×C4—2848no—
607C22×C4—2848no—
608C22×C4—2848no—
609C22×C4—2848no—
610C22×C4—714no—
611C22×C4—714no—
612C22×C4—14216no—
613C22×C4—1422no—
614C22×C4—1422no—
615C22×C4—1422no—
616C22×C4—1422no—
617C22×C4—1422no—
618C22×C4—1422no—
619C22×C4—1422no—
620C22×C4—1422no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4—1422no—
624C22×C4—1422no—
625C22×C4—1422no—
626C22×C4—1422no—
627C22×C4—1422no—
628C22×C4—1422no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4C2×C4×D7112yes—
633C22×C4C2×C4×D7112yes—
634C22×C4C2×C4×D7112yes—
635C22×C4D4×D7112yes—
636C22×C4D4×D7112yes—
637C22×C4C2×C22⋊D7112yes—
638C22×C4C2×C22⋊D7112yes—
639C22×C4C2×C22⋊D7112yes—
640C22×C4C2×D28412yes—
641C22×C4C2×D28412yes—
642C22×C4C2×D28412yes—
643C22×C4Q8×D7112yes—
644C22×C4#1176586512yes—
645C22×C4#1176586512yes—
646C22×C4#1176586512yes—
647C22×C4#1176586512yes—
648C22×C4#1176586612yes—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—2848no—
652C4⋊C4—2844no—
653C4⋊C4—1428no—
654C4⋊C4—1428no—
655C22⋊C4—2848no—
656C22⋊C4—2848no—
657C22⋊C4—2848no—
658C22⋊C4—14216no—
659C22⋊C4—14216no—
660C42—28no—
661C42—28no—
662C42—44no—
663C23—2842no—
664C23—2842no—
665C23—2842no—
666C23—2842no—
667C23—2842no—
668C23—2842no—
669C23—2842no—
670C23—2842no—
671C23—2842no—
672C23—2842no—
673C23—2842no—
674C23—2842no—
675C23—2842no—
676C23—2842no—
677C23—2842no—
678C23—2842no—
679C23—718no—
680C23—1424no—
681C23—1424no—
682C23—1424no—
683C23—1424no—
684C23—1424no—
685C23—1424no—
686C23—1424no—
687C23—1424no—
688C23—1424no—
689C23—1424no—
690C23—1424no—
691C23—1424no—
692C23—1424no—
693C23—1424no—
694C23—1424no—
695C23—1424no—
696C23—1424no—
697C23—1424no—
698C23C22×C4×D7111yescharacteristic
699C23C2×D4×D7111yescharacteristic
700C23C2×D4×D7111yescharacteristic
701C23C22×C22⋊D7111yescharacteristic
702C23C22×D28411yescharacteristic
703C23C2×Q8×D7111yescharacteristic
704C23C2×#1176586511yescharacteristic
705C23C2×#1176586511yescharacteristic
706C23C2×#1176586511yescharacteristic
707C23C2×#1176586511yescharacteristic
708C23C2×#1176586611yescharacteristic
709C23#1455617411yescharacteristic
710C23#1455617411yescharacteristic
711C23#1455617411yescharacteristic
712C23#1455617511yescharacteristic
713D4—14232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—28432no—
755C2×C4—2842no—
756C2×C4—2842no—
757C2×C4—2842no—
758C2×C4—2842no—
759C2×C4—2842no—
760C2×C4—2842no—
761C2×C4—2842no—
762C2×C4—2842no—
763C2×C4—2842no—
764C2×C4—2842no—
765C2×C4—2842no—
766C2×C4—2842no—
767C2×C4—2842no—
768C2×C4—2842no—
769C2×C4—2842no—
770C2×C4—1424no—
771C2×C4—1424no—
772C2×C4—1424no—
773C2×C4—1424no—
774C2×C4—1424no—
775C2×C4—1424no—
776C2×C4C4⋊C4×D7114yes—
777C2×C4C4×C22⋊D7114yes—
778C2×C4#1455609014yes—
779C2×C4C4×D28414yescomplemented
780C2×C4#1455609614yes—
781C2×C4#1455610214yes—
782C2×C4#1455610414yes—
783C2×C4#1455610614yes—
784C2×C4#1455611314yes—
785C22—2844no—
786C22—2844no—
787C22—2844no—
788C22—2844no—
789C22—2844no—
790C22—2844no—
791C22—2844no—
792C22—2844no—
793C22—2844no—
794C22—2844no—
795C22—2844no—
796C22—2844no—
797C22—1428no—
798C22—1428no—
799C22—1428no—
800C22C2×C4⋊C4×D7111yescharacteristic
801C22C2×C4×C22⋊D7111yescharacteristic
802C22C2×#1455609011yescharacteristic
803C22C2×C4×D28411yescharacteristic
804C22C4×#1176586511yescharacteristic
805C22#1798647311yescharacteristic
806C22#1798647911yescharacteristic
807C22C2×#1455609611yescharacteristic
808C22C2×#1455610211yescharacteristic
809C22C2×#1455610411yescharacteristic
810C22C2×#1455610611yescharacteristic
811C22C2×#1455611311yescharacteristic
812C22#1798651011yescharacteristic
813C22#1798653311yescharacteristic
814C22#1798654911yescharacteristic
815C22#1798656311yescharacteristic
816C22#1798657711yescharacteristic
817C22#1798660411yescharacteristic
818C22#1798662011yescharacteristic
819C22D4×D28411yescharacteristic
820C22D4×D28411yescharacteristic
821C22#1798664511yescharacteristic
822C22#1798664511yescharacteristic
823C22#1798664511yescharacteristic
824C22#1798665411yescharacteristic
825C22#1798665811yescharacteristic
826C22Q8×D28411yescharacteristic
827C22#1798667011yescharacteristic
828C22#1798667111yescharacteristic
829C22#1798670911yescharacteristic
830C22#1798670911yescharacteristic
831C22#1798670911yescharacteristic
832C22#1798672211yescharacteristic
833C22#1798673411yescharacteristic
834C22#1798673411yescharacteristic
835C4—24no—
836C4—24no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—2844no—
842C4—2844no—
843C4—5682no—
844C4#1798587018yescomplemented
845C2—2848no—
846C2C2×#1798587011yescharacteristic
847C2C4×#1455610211yescharacteristic
848C2#2259103311yescharacteristic
849C2C4⋊C4×D28411yescharacteristic
850C2#2259125111yescharacteristic
851C2#2259140411yescharacteristic
852C2#2259140911yescharacteristic
853C2#2259168511yescharacteristic
854C2#2259169611yescharacteristic
855C2#2259210511yescharacteristic
856C2#2259212711yescharacteristic
857C2#2259219011yescharacteristic
858C2#2259221211yescharacteristic
859C2#2259325811yescharacteristic
860C2#2259369811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×C4×C4⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×C4×C4⋊C4D71
hypocenterC71#14018
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×#17985897C2semidirect
5. C2×#17985870C2semidirect
6. #22586584C2semidirect
7. #22586582C2semidirect
8. #22586570C2semidirect
9. #22586570C2semidirect
10. (C2×D71)⋊#95C2semidirect
11. C2×C4×C4⋊C4×C71C2semidirect
27. #17985901C4semidirect
69. C2×C4⋊Dic71C2×C4semidirect
87. C2×(C2×D71)⋊C4C2×C4semidirect
88. C2×(C2×D71)⋊C4C2×C4semidirect
106. C2×C4⋊C4×C71D4semidirect
114. C2×C42×C71C2×C4semidirect
139. C2×D284C4⋊C4semidirect
325. C2×C4×C71C4×D4semidirect
410. C4×C71#385semidirect
436. C2×C4×C4⋊C4D71semidirect
442. C71#14018semidirect
517. C2×C4⋊C4D284semidirect
540. C2×C42C4×D71semidirect
779. C2×C4C4×D284semidirect
844. C4#17985870semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2842
C2×#179859012
C2×#179858972
C2×#179858702
#225865842
#225865822
#225865702
(C2×D71)⋊#952
C2×C4×C4⋊C4×C712
#1401871