Finite Group Databasebeta

← #31997034

Subgroups — #31997034

Order 18176.

1590 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D71C211yesmaximal, characteristic
2C2×#17986040C211yesmaximal, characteristic, complemented
3C2×#17986038C211yesmaximal, characteristic, complemented
4#22590722C211yesmaximal, characteristic
5#380×D71C211yesmaximal, characteristic
6#22588373C211yesmaximal, characteristic, complemented
7#22588371C211yesmaximal, characteristic, complemented
8#22588371C211yesmaximal, characteristic, complemented
9#22588368C211yesmaximal, characteristic, complemented
10#22588366C211yesmaximal, characteristic, complemented
11#22588364C211yesmaximal, characteristic, complemented
12#22588362C211yesmaximal, characteristic, complemented
13#22588058C211yesmaximal, characteristic, complemented
14#22588058C211yesmaximal, characteristic, complemented
15C71×#1809C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C22×#11765849C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×#11765848C2211yescharacteristic
20C2×M16×D71—24no—
21C2×M16×D71—24no—
22C2×M16×D71C418yescomplemented
23C22×C8×D71C2211yescharacteristic
24C22×C8×D71C2211yescharacteristic
25C2×#14556086C2211yescharacteristic
26C2×#14556086C2211yescharacteristic
27C2×C4⋊C4×D71C2211yescharacteristic
28C2×C4⋊C4×D71C2211yescharacteristic
29C2×C22⋊C4×D71—21no—
30#17986040—24no—
31#17986038—24no—
32C2×#14556062C2211yescharacteristic, complemented
33C2×#14556061C2211yescharacteristic, complemented
34C2×#14556061C2211yescharacteristic, complemented
35C2×#14556060C2211yescharacteristic, complemented
36C2×#14556059C2211yescharacteristic, complemented
37C2×#14556059C2211yescharacteristic, complemented
38#17985861—21no—
39#17985859C2211yescharacteristic
40#17985859C2211yescharacteristic
41#17985858—21no—
42#17985857—21no—
43#17985856C2211yescharacteristic
44#17985856C2211yescharacteristic
45#17985856C2211yescharacteristic
46#17985856C2211yescharacteristic
47#17985854—21no—
48C22⋊C4×Dic71—21no—
49#17985846—21no—
50#95×D71—21no—
51#17985762C2211yescharacteristic, complemented
52#17985762C2211yescharacteristic, complemented
53#17985761C2211yescharacteristic, complemented
54#17985761C2211yescharacteristic, complemented
55#17985761C2211yescharacteristic, complemented
56#17985761C2211yescharacteristic, complemented
57C22×M16×C71C2211yescharacteristic
58C2×#107×C71C2211yescharacteristic, complemented
59C2×#106×C71C2211yescharacteristic, complemented
60#380×C71C2211yescharacteristic
61#380×C71C2211yescharacteristic
62#340×C71C2211yescharacteristic, complemented
63#340×C71C2211yescharacteristic, complemented
64C24×D71D411yescharacteristic
65C23×Dic71D411yescharacteristic
66C22×C4×D71—22no—
67C22×C4×D71—22no—
68C22×C4×D71—22no—
69C22×C4×D71—22no—
70C22×C4×D71—21no—
71C22×C4×D71—21no—
72C22×C4×D71C2×C414yes—
73C22×C4×D71D411yescharacteristic
74C22×C4×D71D411yescharacteristic
75C22×C4×D71Q814yes—
76C22×C4×D71C2311yescharacteristic
77C22×C4×D71C2311yescharacteristic
78C2×#11765849—22no—
79C2×#11765849—22no—
80C2×#11765849C2×C414yescomplemented
81C2×#11765848—22no—
82C2×#11765848—22no—
83C2×#11765848C2×C414yes—
84C2×#11765848C2×C414yes—
85C2×#11765848D414yes—
86C2×#11765848D414yes—
87M16×D71—232no—
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C2×C8×D71—22no—
91C2×C8×D71—22no—
92C2×C8×D71—22no—
93C2×C8×D71—22no—
94C2×C8×D71C2×C414yescomplemented
95C2×C8×D71C2×C414yescomplemented
96#14556086—22no—
97#14556086—22no—
98#14556086—22no—
99#14556086—22no—
100C2×C4⋊Dic71C2311yescharacteristic
101C2×C4⋊Dic71C2311yescharacteristic
102C2×C4⋊Dic71C2311yescharacteristic
103C2×C4⋊Dic71C2311yescharacteristic
104C2×Dic71⋊C4—21no—
105C2×Dic71⋊C4—21no—
106C4⋊C4×D71—22no—
107C4⋊C4×D71—22no—
108C4⋊C4×D71—22no—
109C4⋊C4×D71—22no—
110C2×C22⋊Dic71—21no—
111C2×C22⋊Dic71—21no—
112C2×(C2×D71)⋊C4—21no—
113C2×(C2×D71)⋊C4—21no—
114C2×(C2×D71)⋊C4—21no—
115C2×(C2×D71)⋊C4—21no—
116C2×(C2×D71)⋊C4—21no—
117C2×(C2×D71)⋊C4—21no—
118C22⋊C4×D71—44no—
119C2×C4×Dic71—21no—
120C2×C4×Dic71—21no—
121#14556062—22no—
122#14556061—22no—
123#14556061—22no—
124#14556060—22no—
125#14556059—22no—
126#14556059—22no—
127C71⋊#95—21no—
128C71⋊#95—21no—
129C71⋊#95—21no—
130C71⋊#95—21no—
131C71⋊#95—21no—
132C71⋊#95—21no—
133C23×C4×C71C2311yescharacteristic
134C2×M16×C71—22no—
135C2×M16×C71—22no—
136C2×M16×C71C2×C414yescomplemented
137C22×C8×C71C2311yescharacteristic
138C22×C8×C71C2311yescharacteristic
139C2×C4⋊C4×C71C2311yescharacteristic
140C2×C4⋊C4×C71C2311yescharacteristic
141C2×C4⋊C4×C71C2311yescharacteristic
142C2×C4⋊C4×C71C2311yescharacteristic
143C2×C22⋊C4×C71—21no—
144C2×C22⋊C4×C71—21no—
145#107×C71—22no—
146#106×C71—22no—
147#95×C71—21no—
148#95×C71—21no—
149C23×D71—22no—
150C23×D71—22no—
151C23×D71—22no—
152C23×D71—22no—
153C23×D71—41no—
154C23×D71—41no—
155C23×D71C4⋊C414yes—
156C23×D71C2×D411yescharacteristic
157C23×D71C2×D411yescharacteristic
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—21no—
161C22×Dic71—21no—
162C22×Dic71—21no—
163C22×Dic71—21no—
164C22×Dic71C4⋊C414yes—
165C22×Dic71C2×D411yescharacteristic
166C22×Dic71C2×D411yescharacteristic
167C2×C4×D71—22no—
168C2×C4×D71—22no—
169C2×C4×D71—21no—
170C2×C4×D71—21no—
171C2×C4×D71—21no—
172C2×C4×D71—21no—
173C2×C4×D71—22no—
174C2×C4×D71—22no—
175C2×C4×D71—28no—
176C2×C4×D71—28no—
177C2×C4×D71—28no—
178C2×C4×D71—28no—
179C2×C4×D71—42no—
180C2×C4×D71—42no—
181C2×C4×D71—42no—
182C2×C4×D71—42no—
183C2×C4×D71—42no—
184C2×C4×D71—42no—
185C2×C4×D71C4⋊C414yes—
186C2×C4×D71C4⋊C414yes—
187C2×C4×D71C22×C412yes—
188C2×C4×D71C22×C412yes—
189C2×C4×D71C2×D412yes—
190C2×C4×D71C2×D412yes—
191C2×C4×D71C2×Q812yes—
192C2×C4×D71C2×Q812yes—
193C2×C4×D71#4112yes—
194C2×C4×D71#4112yes—
195#11765849—28no—
196#11765848—28no—
197#11765848C22⋊C4116yescomplemented
198C2×C71⋊C8—21no—
199C2×C71⋊C8—21no—
200C2×C71⋊C8C22×C412yes—
201C2×C71⋊C8C22×C412yes—
202C2×C71⋊C8C2×D412yes—
203C2×C71⋊C8C2×D412yes—
204C8×D71—28no—
205C8×D71—28no—
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71—21no—
211C4⋊Dic71—21no—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214Dic71⋊C4—42no—
215Dic71⋊C4—42no—
216C22⋊Dic71—42no—
217C22⋊Dic71—42no—
218(C2×D71)⋊C4—42no—
219(C2×D71)⋊C4—42no—
220(C2×D71)⋊C4—42no—
221(C2×D71)⋊C4—42no—
222(C2×D71)⋊C4—42no—
223(C2×D71)⋊C4—42no—
224C4×Dic71—42no—
225C4×Dic71—42no—
226C24×C71C2×D411yescharacteristic
227C22×C4×C71—21no—
228C22×C4×C71—21no—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71C22×C412yes—
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2×Q812yes—
238C22×C4×C71C2411yescharacteristic
239M16×C71—28no—
240C2×C8×C71—21no—
241C2×C8×C71—21no—
242C2×C8×C71C22×C412yes—
243C2×C8×C71C22×C412yes—
244C2×C8×C71C2×D412yes—
245C2×C8×C71C2×D412yes—
246C4⋊C4×C71—21no—
247C4⋊C4×C71—21no—
248C4⋊C4×C71—21no—
249C4⋊C4×C71—21no—
250C4⋊C4×C71—21no—
251C4⋊C4×C71—21no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71—21no—
254C22⋊C4×C71—42no—
255C22⋊C4×C71—42no—
256C23×C71—21no—
257C23×C71—21no—
258C23×C71—21no—
259C23×C71—21no—
260C23×C71—21no—
261C23×C71—21no—
262C23×C71C2×C4⋊C412yes—
263C23×C71C22×D411yescharacteristic
264C22×D71—21no—
265C22×D71—21no—
266C22×D71—21no—
267C22×D71—21no—
268C22×D71—21no—
269C22×D71—21no—
270C22×D71—21no—
271C22×D71—21no—
272C22×D71—28no—
273C22×D71—28no—
274C22×D71—44no—
275C22×D71—44no—
276C22×D71—44no—
277C22×D71—44no—
278C22×D71—44no—
279C22×D71C2×C4⋊C412yes—
280C22×D71C2×C4⋊C412yes—
281C22×D71#12112yes—
282C22×D71#12112yes—
283C22×D71AGL(1,ℤ/8)12yes—
284C22×D71#13712yes—
285C2×C4×C71—21no—
286C2×C4×C71—21no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—41no—
292C2×C4×C71—41no—
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×C71C2×C4⋊C412yes—
304C2×C4×C71C23×C411yescharacteristic
305C2×C4×C71C22×D411yescharacteristic
306C2×C4×C71C22×D411yescharacteristic
307C2×C4×C71C22×Q811yescharacteristic
308C2×C4×C71C2×#4111yescharacteristic
309C2×C4×C71C2×#4111yescharacteristic
310C2×Dic71—21no—
311C2×Dic71—21no—
312C2×Dic71—28no—
313C2×Dic71—41no—
314C2×Dic71—41no—
315C2×Dic71—41no—
316C2×Dic71—41no—
317C2×Dic71—41no—
318C2×Dic71—41no—
319C2×Dic71—41no—
320C2×Dic71—41no—
321C2×Dic71—41no—
322C2×Dic71—41no—
323C2×Dic71—41no—
324C2×Dic71—41no—
325C2×Dic71C2×C4⋊C412yes—
326C2×Dic71C2×C4⋊C412yes—
327C2×Dic71#12112yes—
328C2×Dic71#12112yes—
329C4×D71—28no—
330C4×D71—22no—
331C4×D71—22no—
332C4×D71—22no—
333C4×D71—22no—
334C4×D71—28no—
335C4×D71—84no—
336C4×D71—84no—
337C4×D71C2×C22⋊C414yes—
338C4×D71#11714yes—
339C4×D71C22⋊Q814yes—
340C4×D71C22⋊Q814yes—
341C8×C71—22no—
342C8×C71C2×C22⋊C414yescomplemented
343C71⋊C8—22no—
344C71⋊C8C2×C22⋊C414yescomplemented
345C22×C71—22no—
346C22×C71—22no—
347C22×C71—22no—
348C22×C71—41no—
349C22×C71—41no—
350C22×C71—41no—
351C22×C71—41no—
352C22×C71C22×C4⋊C411yescharacteristic
353C22×C71C2×#12111yescharacteristic
354C22×C71C2×#12111yescharacteristic
355C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C71C2×#13711yescharacteristic
357C22×C71#57511yescharacteristic
358C22×C71#57511yescharacteristic
359C2×D71—22no—
360C2×D71—22no—
361C2×D71—22no—
362C2×D71—22no—
363C2×D71—22no—
364C2×D71—22no—
365C2×D71—22no—
366C2×D71—22no—
367C2×D71—22no—
368C2×D71—22no—
369C2×D71—22no—
370C2×D71—22no—
371C2×D71—416no—
372C2×D71#38014yes—
373C2×D71#42814yescomplemented
374C4×C71—22no—
375C4×C71—81no—
376C4×C71—81no—
377C4×C71—81no—
378C4×C71—81no—
379C4×C71C22×C22⋊C411yescharacteristic
380C4×C71C2×#11711yescharacteristic
381C4×C71C2×C22⋊Q811yescharacteristic
382C4×C71C2×C22⋊Q811yescharacteristic
383Dic71—22no—
384Dic71—81no—
385Dic71—81no—
386Dic71—81no—
387Dic71—81no—
388Dic71#38014yes—
389#20661—711nomaximal, Sylow
390C2×C71—42no—
391C2×C71C2×#38011yescharacteristic
392C2×C71C2×#42811yescharacteristic
393C2×C71#291111yescharacteristic
394C2×C71#305511yescharacteristic
395C2×C71#305511yescharacteristic
396C2×C71#305611yescharacteristic
397C2×C71#305611yescharacteristic
398D71—24no—
399D71—24no—
400C23×M16—711no—
401C2×#428—711no—
402C2×#428—711no—
403#2280—711no—
404C2×#380—711no—
405#1809—711no—
406#1809—711no—
407#1809—711no—
408#1809D7111yescharacteristic, complemented
409#1808—711no—
410#1808—711no—
411#1807—711no—
412#1807—711no—
413#1736—711no—
414#1736—711no—
415C71#2066111yescharacteristic, complemented, Sylow
416C24×C4—711no—
417C22×M16—711no—
418C22×M16—718no—
419C22×M16—711no—
420C22×M16—711no—
421C22×M16—1424no—
422C22×M16—1424no—
423C22×M16C2×D7111yescharacteristic
424C23×C8—711no—
425C23×C8—711no—
426C2×#117—711no—
427C2×#117—711no—
428C22×C4⋊C4—711no—
429C22×C4⋊C4—711no—
430C22×C22⋊C4—1421no—
431#428—1424no—
432#428—1424no—
433C2×#107—711no—
434C2×#107—711no—
435C2×#107—711no—
436C2×#107C2×D7111yescharacteristic, complemented
437C2×#106—711no—
438C2×#106—711no—
439C2×#106—711no—
440C2×#106C2×D7111yescharacteristic, complemented
441#381—1421no—
442#380—711no—
443#380—711no—
444#380—711no—
445#380—711no—
446#380—711no—
447#380—711no—
448#380—1421no—
449#380—1421no—
450#380C2×D7111yescharacteristic
451#380C2×D7111yescharacteristic
452#379—1421no—
453C4×C22⋊C4—1421no—
454C4×C22⋊C4—1421no—
455C2×#95—1421no—
456#340—711no—
457#340—711no—
458#340—711no—
459#340—711no—
460#340—711no—
461#340—711no—
462#340C2×D7111yescharacteristic, complemented
463#340C2×D7111yescharacteristic, complemented
464C25—711no—
465C23×C4—711no—
466C23×C4—711no—
467C23×C4—714no—
468C23×C4—711no—
469C23×C4—711no—
470C23×C4—714no—
471C23×C4—711no—
472C23×C4—1421no—
473C23×C4—1421no—
474C23×C4—1422no—
475C23×C4—1422no—
476C23×C4—1422no—
477C23×C4—1422no—
478C23×C4C22×D7111yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—714no—
482C2×M16—714no—
483C2×M16—714no—
484C2×M16—714no—
485C2×M16—714no—
486C2×M16—1422no—
487C2×M16—1422no—
488C2×M16—1422no—
489C2×M16—1422no—
490C2×M16—14232no—
491C2×M16C4×D7114yescomplemented
492C22×C8—711no—
493C22×C8—711no—
494C22×C8—714no—
495C22×C8—714no—
496C22×C8—1422no—
497C22×C8—1422no—
498C22×C8—1422no—
499C22×C8—1422no—
500C22×C8C22×D7111yescharacteristic
501C22×C8C22×D7111yescharacteristic
502#117—1422no—
503#117—1422no—
504#117—1422no—
505#117—1422no—
506C2×C4⋊C4—711no—
507C2×C4⋊C4—711no—
508C2×C4⋊C4—711no—
509C2×C4⋊C4—711no—
510C2×C4⋊C4—1422no—
511C2×C4⋊C4—1422no—
512C2×C4⋊C4—1422no—
513C2×C4⋊C4—1422no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4C22×D7111yescharacteristic
517C2×C4⋊C4C22×D7111yescharacteristic
518C2×C4⋊C4C22×D7111yescharacteristic
519C2×C4⋊C4C22×D7111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—2844no—
523C2×C22⋊C4—1421no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C22⋊C4—1421no—
530C2×C22⋊C4—1421no—
531C2×C42—1421no—
532C2×C42—1421no—
533#107—22no—
534#107—1422no—
535#107—1422no—
536#107—1422no—
537#106—22no—
538#106—1422no—
539#106—1422no—
540#106—1422no—
541#95—21no—
542#95—21no—
543#95—1421no—
544#95—1421no—
545#95—1421no—
546#95—1421no—
547#95—1421no—
548#95—1421no—
549C24—2841no—
550C24—2841no—
551C24—714no—
552C24—711no—
553C24—711no—
554C24—1422no—
555C24—1422no—
556C24—1422no—
557C24—1422no—
558C24D4×D7111yescharacteristic
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—2842no—
568C22×C4—2842no—
569C22×C4—2842no—
570C22×C4—2842no—
571C22×C4—2842no—
572C22×C4—2842no—
573C22×C4—711no—
574C22×C4—712no—
575C22×C4—712no—
576C22×C4—712no—
577C22×C4—712no—
578C22×C4—712no—
579C22×C4—712no—
580C22×C4—711no—
581C22×C4—714no—
582C22×C4—712no—
583C22×C4—712no—
584C22×C4—714no—
585C22×C4—714no—
586C22×C4—1428no—
587C22×C4—1422no—
588C22×C4—1422no—
589C22×C4—1428no—
590C22×C4—1428no—
591C22×C4—1428no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1421no—
595C22×C4—1421no—
596C22×C4—1421no—
597C22×C4—1421no—
598C22×C4—1422no—
599C22×C4—1422no—
600C22×C4—1421no—
601C22×C4—1421no—
602C22×C4—1421no—
603C22×C4—1421no—
604C22×C4C2×C4×D7112yes—
605C22×C4D4×D7111yescharacteristic
606C22×C4Q8×D7112yes—
607C22×C4C23×D7111yescharacteristic
608M16—28no—
609M16—7116no—
610M16—1428no—
611M16—1428no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—712no—
615C2×C8—712no—
616C2×C8—712no—
617C2×C8—712no—
618C2×C8—1428no—
619C2×C8—1421no—
620C2×C8—1421no—
621C2×C8—1428no—
622C2×C8C2×C4×D7112yes—
623C2×C8C2×C4×D7112yes—
624C2×C8D4×D7112yes—
625C2×C8D4×D7112yes—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—2842no—
635C4⋊C4—2842no—
636C4⋊C4—1421no—
637C4⋊C4—1421no—
638C4⋊C4—1421no—
639C4⋊C4—1421no—
640C4⋊C4—1421no—
641C4⋊C4—1421no—
642C4⋊C4—1421no—
643C4⋊C4—1421no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—2842no—
647C22⋊C4—2842no—
648C22⋊C4—2842no—
649C22⋊C4—2842no—
650C22⋊C4—2842no—
651C22⋊C4—2842no—
652C22⋊C4—2842no—
653C22⋊C4—2842no—
654C42—2842no—
655C42—2842no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—2844no—
663C23—2844no—
664C23—2844no—
665C23—2844no—
666C23—2844no—
667C23—712no—
668C23—712no—
669C23—712no—
670C23—712no—
671C23—712no—
672C23—712no—
673C23—1428no—
674C23—1428no—
675C23—1421no—
676C23—1421no—
677C23—1421no—
678C23—1421no—
679C23—1421no—
680C23—1421no—
681C23—1421no—
682C23—1421no—
683C23C4⋊C4×D7112yes—
684C23C2×D4×D7111yescharacteristic
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—2841no—
704C2×C4—2841no—
705C2×C4—2841no—
706C2×C4—2841no—
707C2×C4—2841no—
708C2×C4—2841no—
709C2×C4—2841no—
710C2×C4—2841no—
711C2×C4—2841no—
712C2×C4—2841no—
713C2×C4—2841no—
714C2×C4—2841no—
715C2×C4—5684no—
716C2×C4—5684no—
717C2×C4—712no—
718C2×C4—712no—
719C2×C4—712no—
720C2×C4—714no—
721C2×C4—714no—
722C2×C4—714no—
723C2×C4—714no—
724C2×C4—712no—
725C2×C4—1428no—
726C2×C4—1428no—
727C2×C4—1428no—
728C2×C4—1421no—
729C2×C4—1421no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4C4⋊C4×D7112yes—
735C2×C4C22×C4×D7111yescharacteristic
736C2×C4C2×D4×D7111yescharacteristic
737C2×C4C2×D4×D7111yescharacteristic
738C2×C4C2×Q8×D7111yescharacteristic
739C2×C4#41×D7111yescharacteristic
740C2×C4#41×D7111yescharacteristic
741C8—22no—
742C8—714no—
743C8—1422no—
744C8C22⋊C4×D7114yescomplemented
745C22—22no—
746C22—22no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—28416no—
753C22—714no—
754C22—714no—
755C22—1422no—
756C22—1422no—
757C22—1422no—
758C22—1422no—
759C22—1422no—
760C22—1422no—
761C22—1422no—
762C22—1422no—
763C22—1422no—
764C22—1422no—
765C22—1422no—
766C22—1422no—
767C22C2×C4⋊C4×D7111yescharacteristic
768C22#121×D7111yescharacteristic
769C22#121×D7111yescharacteristic
770C22AGL(1,ℤ/8)×D7111yescharacteristic
771C22#137×D7111yescharacteristic
772C22#1798679511yescharacteristic
773C22#1798679811yescharacteristic
774C4—22no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—5681no—
780C4—5681no—
781C4—5681no—
782C4—5681no—
783C4—714no—
784C4—1422no—
785C4C2×C22⋊C4×D7111yescharacteristic
786C4#117×D7111yescharacteristic
787C4C22⋊Q8×D7111yescharacteristic
788C4C22⋊Q8×D7111yescharacteristic
789C2—42no—
790C2—1424no—
791C2—1424no—
792C2#380×D7111yescharacteristic
793C2#428×D7111yescharacteristic
794C2#2259692711yescharacteristic
795C2#2259795411yescharacteristic
796C2#2259795811yescharacteristic
797C2#2259796511yescharacteristic
798C2#2259796911yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#1809C2
socleC23×C71C22×D4
prime radicalC24×D71D4
cosocleC22×C4×C71C24
hypercenter#1809D71
hypocenterC71#20661
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#17986040C2semidirect
3. C2×#17986038C2semidirect
6. #22588373C2semidirect
7. #22588371C2semidirect
8. #22588371C2semidirect
9. #22588368C2semidirect
10. #22588366C2semidirect
11. #22588364C2semidirect
12. #22588362C2semidirect
13. #22588058C2semidirect
14. #22588058C2semidirect
15. C71×#1809C2semidirect
22. C2×M16×D71C4semidirect
32. C2×#14556062C22semidirect
33. C2×#14556061C22semidirect
34. C2×#14556061C22semidirect
35. C2×#14556060C22semidirect
36. C2×#14556059C22semidirect
37. C2×#14556059C22semidirect
51. #17985762C22semidirect
52. #17985762C22semidirect
53. #17985761C22semidirect
54. #17985761C22semidirect
55. #17985761C22semidirect
56. #17985761C22semidirect
58. C2×#107×C71C22semidirect
59. C2×#106×C71C22semidirect
62. #340×C71C22semidirect
63. #340×C71C22semidirect
80. C2×#11765849C2×C4semidirect
94. C2×C8×D71C2×C4semidirect
95. C2×C8×D71C2×C4semidirect
136. C2×M16×C71C2×C4semidirect
197. #11765848C22⋊C4semidirect
342. C8×C71C2×C22⋊C4semidirect
344. C71⋊C8C2×C22⋊C4semidirect
373. C2×D71#428semidirect
408. #1809D71semidirect
415. C71#20661semidirect
436. C2×#107C2×D71semidirect
440. C2×#106C2×D71semidirect
462. #340C2×D71semidirect
463. #340C2×D71semidirect
491. C2×M16C4×D71semidirect
744. C8C22⋊C4×D71semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D712
C2×#179860402
C2×#179860382
#225907222
#380×D712
#225883732
#225883712
#225883682
#225883662
#225883642
#225883622
#225880582
C71×#18092
#2066171