Finite Group Databasebeta

← #32016146

Subgroups — #32016146

Order 18176.

970 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986071C211yesmaximal, characteristic
2#22591269C211yesmaximal, characteristic
3#22589108C211yesmaximal, characteristic, complemented
4#22589101C211yesmaximal, characteristic, complemented
5#22588537C211yesmaximal, characteristic, complemented
6#22588533C211yesmaximal, characteristic, complemented
7#22588533C211yesmaximal, characteristic, complemented
8#22588527C211yesmaximal, characteristic, complemented
9#22588475C211yesmaximal, characteristic, complemented
10#22588371C211yesmaximal, characteristic, complemented
11#22588363C211yesmaximal, characteristic, complemented
12#22588238C211yesmaximal, characteristic, complemented
13#22588059C211yesmaximal, characteristic, complemented
14C2×#17985761C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C71C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×#14556087C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20#17986071C418yescomplemented
21C2×#14556061C2211yescharacteristic
22C2×#14556061C2211yescharacteristic
23C2×#14556059C2211yescharacteristic
24C2×#14556059C2211yescharacteristic
25C2×#14556059C2211yescharacteristic
26C2×#14556059C2211yescharacteristic
27C2×C4⋊(C71⋊C8)C2211yescharacteristic
28C2×C22⋊(C71⋊C8)C2211yescharacteristic
29C2×C22⋊(C71⋊C8)C2211yescharacteristic
30C2×#14556039C2211yescharacteristic
31#17985892—21no—
32#17985885—21no—
33#17985879—21no—
34#17985865C2211yescharacteristic
35#17985859C2211yescharacteristic
36#17985859C2211yescharacteristic
37C4×C4⋊Dic71C2211yescharacteristic
38C22⋊C4×Dic71—21no—
39#17985761C2211yescharacteristic
40#17985761C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49C2×C4×D4×C71—21no—
50C2×C4×D4×C71C2211yescharacteristic
51C22×C4⋊C4×C71C2211yescharacteristic
52C22×C4⋊C4×C71C2211yescharacteristic
53#389×C71—21no—
54#385×C71—21no—
55#385×C71—21no—
56#384×C71C2211yescharacteristic
57#380×C71C2211yescharacteristic
58#380×C71C2211yescharacteristic
59C4×C4⋊C4×C71C2211yescharacteristic
60C23×Dic71—21no—
61C2×#11765849—41no—
62C2×#11765849—41no—
63C2×#11765849C2×C414yescomplemented
64C22×C71⋊C8—41no—
65C22×C71⋊C8—41no—
66C22×C71⋊C8C2×C414yescomplemented
67C22×C71⋊C8C2311yescharacteristic
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71#14556087—22no—
72#14556087—41no—
73C2×C4⋊Dic71—22no—
74C2×C4⋊Dic71—21no—
75C2×C4⋊Dic71—41no—
76C2×C4⋊Dic71C2311yescharacteristic
77C2×C4⋊Dic71C2311yescharacteristic
78C2×C4⋊Dic71C2311yescharacteristic
79C2×C4⋊Dic71C2311yescharacteristic
80C2×C22⋊Dic71—21no—
81C2×C22⋊Dic71—21no—
82C2×C22⋊Dic71—21no—
83C2×C4×Dic71—21no—
84C2×C4×Dic71—21no—
85#14556061—22no—
86#14556061—41no—
87#14556059—22no—
88#14556059—41no—
89#14556059—41no—
90#14556059—41no—
91C4⋊(C71⋊C8)C2×C414yescomplemented
92C22⋊(C71⋊C8)C2×C414yescomplemented
93C22⋊(C71⋊C8)C2×C414yescomplemented
94#14556039C2×C414yescomplemented
95C71⋊#95—21no—
96C71⋊#95—21no—
97C71⋊#95—21no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C22×D4×C71D411yescharacteristic
101C23×C4×C71—21no—
102C23×C4×C71—21no—
103C23×C4×C71C2311yescharacteristic
104C23×C4×C71C2311yescharacteristic
105C4×D4×C71—44no—
106C4×D4×C71C2×C414yes—
107C4×D4×C71Q814yes—
108C2×C4⋊C4×C71—22no—
109C2×C4⋊C4×C71—22no—
110C2×C4⋊C4×C71—21no—
111C2×C4⋊C4×C71—21no—
112C2×C4⋊C4×C71—21no—
113C2×C4⋊C4×C71—21no—
114C2×C4⋊C4×C71—41no—
115C2×C4⋊C4×C71—41no—
116C2×C4⋊C4×C71D411yescharacteristic
117C2×C4⋊C4×C71C2311yescharacteristic
118C2×C4⋊C4×C71C2311yescharacteristic
119C2×C4⋊C4×C71C2311yescharacteristic
120C2×C4⋊C4×C71C2311yescharacteristic
121C2×C22⋊C4×C71—21no—
122C2×C22⋊C4×C71—21no—
123C2×C22⋊C4×C71D411yescharacteristic
124C2×C22⋊C4×C71D411yescharacteristic
125C2×C42×C71—21no—
126C2×C42×C71C2311yescharacteristic
127#95×C71—21no—
128#95×C71—21no—
129#95×C71—21no—
130C22×Dic71—21no—
131C22×Dic71—21no—
132C22×Dic71—21no—
133C22×Dic71—21no—
134C22×Dic71—42no—
135C22×Dic71—42no—
136C22×Dic71—81no—
137#11765849—44no—
138C2×C71⋊C8—21no—
139C2×C71⋊C8—21no—
140C2×C71⋊C8—21no—
141C2×C71⋊C8—21no—
142C2×C71⋊C8—21no—
143C2×C71⋊C8—21no—
144C2×C71⋊C8—21no—
145C2×C71⋊C8—21no—
146C2×C71⋊C8—44no—
147C2×C71⋊C8C22×C412yes—
148C2×C71⋊C8C22×C412yes—
149C2×C71⋊C8C22×C412yes—
150C2×C71⋊C8C22×C412yes—
151C4⋊Dic71—21no—
152C4⋊Dic71—21no—
153C4⋊Dic71—21no—
154C4⋊Dic71—21no—
155C4⋊Dic71—21no—
156C4⋊Dic71—21no—
157C4⋊Dic71—21no—
158C4⋊Dic71—42no—
159C4⋊Dic71#4112yes—
160C22⋊Dic71—42no—
161C22⋊Dic71—42no—
162C22⋊Dic71—81no—
163C4×Dic71—42no—
164C4×Dic71—81no—
165C24×C71C2×D411yescharacteristic
166C24×C71C2×D411yescharacteristic
167C2×D4×C71—22no—
168C2×D4×C71—22no—
169C2×D4×C71C4⋊C414yes—
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—42no—
183C22×C4×C71—42no—
184C22×C4×C71—42no—
185C22×C4×C71—42no—
186C22×C4×C71—81no—
187C22×C4×C71—81no—
188C22×C4×C71C22×C412yes—
189C22×C4×C71C22×C412yes—
190C22×C4×C71C2×D411yescharacteristic
191C22×C4×C71C2×D411yescharacteristic
192C22×C4×C71C2×D411yescharacteristic
193C22×C4×C71C2×D411yescharacteristic
194C22×C4×C71C2×Q812yes—
195C22×C4×C71C2×Q812yes—
196C22×C4×C71C2411yescharacteristic
197C4⋊C4×C71—21no—
198C4⋊C4×C71—21no—
199C4⋊C4×C71—21no—
200C4⋊C4×C71—21no—
201C4⋊C4×C71—21no—
202C4⋊C4×C71—21no—
203C4⋊C4×C71—21no—
204C4⋊C4×C71—42no—
205C4⋊C4×C71—42no—
206C4⋊C4×C71—42no—
207C4⋊C4×C71—81no—
208C4⋊C4×C71C4⋊C414yes—
209C4⋊C4×C71#4112yes—
210C22⋊C4×C71—42no—
211C22⋊C4×C71—42no—
212C22⋊C4×C71C4⋊C414yes—
213C22⋊C4×C71C4⋊C414yes—
214C42×C71—42no—
215C42×C71C22×C412yes—
216C42×C71C2×Q812yes—
217C23×C71—21no—
218C23×C71—21no—
219C23×C71—21no—
220C23×C71—21no—
221C23×C71—21no—
222C23×C71—21no—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71—21no—
227C23×C71C2×C4⋊C412yes—
228C23×C71C2×C4⋊C412yes—
229C23×C71AGL(1,ℤ/8)12yes—
230C23×C71#13712yes—
231C23×C71C22×D411yescharacteristic
232D4×C71—28no—
233C2×C4×C71—21no—
234C2×C4×C71—21no—
235C2×C4×C71—21no—
236C2×C4×C71—21no—
237C2×C4×C71—21no—
238C2×C4×C71—21no—
239C2×C4×C71—21no—
240C2×C4×C71—21no—
241C2×C4×C71—22no—
242C2×C4×C71—22no—
243C2×C4×C71—22no—
244C2×C4×C71—22no—
245C2×C4×C71—22no—
246C2×C4×C71—22no—
247C2×C4×C71—22no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—41no—
251C2×C4×C71—41no—
252C2×C4×C71—41no—
253C2×C4×C71—41no—
254C2×C4×C71—41no—
255C2×C4×C71—41no—
256C2×C4×C71—41no—
257C2×C4×C71—41no—
258C2×C4×C71—41no—
259C2×C4×C71—41no—
260C2×C4×C71—41no—
261C2×C4×C71—84no—
262C2×C4×C71—84no—
263C2×C4×C71C2×C4⋊C412yes—
264C2×C4×C71C2×C4⋊C412yes—
265C2×C4×C71C2×C4⋊C412yes—
266C2×C4×C71C2×C4⋊C412yes—
267C2×C4×C71C23×C411yescharacteristic
268C2×C4×C71C22×Q811yescharacteristic
269C2×C4×C71C2×#4111yescharacteristic
270C2×C4×C71C2×#4111yescharacteristic
271C2×C4×C71H(5,𝔽2)11yescharacteristic
272C2×C4×C71H(5,𝔽2)11yescharacteristic
273C2×Dic71—22no—
274C2×Dic71—41no—
275C2×Dic71—41no—
276C2×Dic71—41no—
277C2×Dic71—41no—
278C2×Dic71—41no—
279C2×Dic71—41no—
280C2×Dic71—41no—
281C2×Dic71—41no—
282C2×Dic71—41no—
283C2×Dic71—41no—
284C2×Dic71—41no—
285C2×Dic71—84no—
286C71⋊C8—22no—
287C71⋊C8—22no—
288C71⋊C8—22no—
289C71⋊C8—22no—
290C22×C71—22no—
291C22×C71—22no—
292C22×C71—22no—
293C22×C71—22no—
294C22×C71—22no—
295C22×C71—22no—
296C22×C71—22no—
297C22×C71—22no—
298C22×C71—22no—
299C22×C71—41no—
300C22×C71—41no—
301C22×C71—41no—
302C22×C71—41no—
303C22×C71#42814yes—
304C22×C71C22×C4⋊C411yescharacteristic
305C22×C71#54611yescharacteristic
306C22×C71#54611yescharacteristic
307C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C71C2×#13711yescharacteristic
309C22×C71#57711yescharacteristic
310C22×C71#57711yescharacteristic
311C4×C71—22no—
312C4×C71—22no—
313C4×C71—22no—
314C4×C71—22no—
315C4×C71—42no—
316C4×C71—81no—
317C4×C71—81no—
318C4×C71—81no—
319C4×C71C4×#4111yescharacteristic
320C4×C71#51811yescharacteristic
321C4×C71#55411yescharacteristic
322C4×C71#55411yescharacteristic
323Dic71—42no—
324Dic71—81no—
325Dic71—81no—
326Dic71—81no—
327#22711—711nomaximal, Sylow
328C2×C71—24no—
329C2×C71—42no—
330C2×C71#234911yescharacteristic
331C2×C71C2×#42811yescharacteristic
332C2×C71#291211yescharacteristic
333C2×C71#330611yescharacteristic
334C2×C71#331011yescharacteristic
335C2×C71#331611yescharacteristic
336C2×C71#332011yescharacteristic
337C2×#435—711no—
338#2352—711no—
339D4×C4⋊C4D7111yescharacteristic
340#1949—711no—
341#1948—711no—
342#1854—711no—
343#1853—711no—
344#1853—711no—
345#1852—711no—
346#1836—711no—
347#1809—711no—
348#1807—711no—
349#1776—711no—
350#1736—711no—
351C2×#340—711no—
352C71#2271111yescharacteristic, complemented, Sylow
353C22×M16—711no—
354C23×C8—711no—
355C2×C4×D4—21no—
356C2×C4×D4C2×D7111yescharacteristic
357C2×#117—711no—
358C22×C4⋊C4—711no—
359C22×C4⋊C4C2×D7111yescharacteristic
360C22×C4⋊C4C2×D7111yescharacteristic
361#435—718no—
362C2×#107—711no—
363C2×#107—711no—
364C2×#106—711no—
365C2×#106—711no—
366C2×#106—711no—
367C2×#106—711no—
368C2×C4⋊C8—711no—
369C2×C22⋊C8—711no—
370C2×C22⋊C8—711no—
371C2×#97—711no—
372#389—21no—
373#388—1421no—
374#387—1421no—
375#386—1421no—
376#385—21no—
377#385—21no—
378#384C2×D7111yescharacteristic
379#382—711no—
380#380—711no—
381#380—711no—
382#380C2×D7111yescharacteristic
383#380C2×D7111yescharacteristic
384C4×C4⋊C4—711no—
385C4×C4⋊C4C2×D7111yescharacteristic
386C4×C22⋊C4—1421no—
387#340—711no—
388#340—711no—
389#340—711no—
390#340—711no—
391#340—711no—
392#340—711no—
393#340—711no—
394#340—711no—
395#340—711no—
396#340—711no—
397C22×D4C22⋊D7111yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—1421no—
401C23×C4C22×D7111yescharacteristic
402C23×C4C22×D7111yescharacteristic
403C2×M16—2841no—
404C2×M16—2841no—
405C2×M16—714no—
406C22×C8—2841no—
407C22×C8—2841no—
408C22×C8—714no—
409C22×C8—711no—
410C22×C8—711no—
411C22×C8—711no—
412C22×C8—711no—
413C4×D4—44no—
414C4×D4Dic14214yes—
415C4×D4C4×D7114yes—
416#117—2841no—
417#117—1422no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4—2841no—
427C2×C4⋊C4—711no—
428C2×C4⋊C4—711no—
429C2×C4⋊C4—711no—
430C2×C4⋊C4—711no—
431C2×C4⋊C4—1421no—
432C2×C4⋊C4—1422no—
433C2×C4⋊C4C22⋊D7111yescharacteristic
434C2×C4⋊C4C22×D7111yescharacteristic
435C2×C4⋊C4C22×D7111yescharacteristic
436C2×C4⋊C4C22×D7111yescharacteristic
437C2×C4⋊C4C22×D7111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—1421no—
441C2×C22⋊C4—1421no—
442C2×C22⋊C4—1421no—
443C2×C22⋊C4C22⋊D7111yescharacteristic
444C2×C22⋊C4C22⋊D7111yescharacteristic
445C2×C42—21no—
446C2×C42—1421no—
447C2×C42—1421no—
448C2×C42C22×D7111yescharacteristic
449#107—2841no—
450#107—1422no—
451#106—2841no—
452#106—2841no—
453#106—2841no—
454#106—1422no—
455C4⋊C8—714no—
456C22⋊C8—714no—
457C22⋊C8—714no—
458#97—714no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—1421no—
463#95—1421no—
464#95—1421no—
465#95—1421no—
466#95—1421no—
467C24C2×C22⋊D7111yescharacteristic
468C24C2×C22⋊D7111yescharacteristic
469C2×D4—22no—
470C2×D4—22no—
471C2×D4Dic71⋊C414yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4—2842no—
491C22×C4—2842no—
492C22×C4—5681no—
493C22×C4—1421no—
494C22×C4—1421no—
495C22×C4—1421no—
496C22×C4—1421no—
497C22×C4C2×C4×D7112yes—
498C22×C4C2×C4×D7112yes—
499C22×C4C2×C22⋊D7111yescharacteristic
500C22×C4C2×C22⋊D7111yescharacteristic
501C22×C4C2×C22⋊D7111yescharacteristic
502C22×C4C2×C22⋊D7111yescharacteristic
503C22×C4C2×Dic14212yes—
504C22×C4C2×Dic14212yes—
505C22×C4C23×D7111yescharacteristic
506M16—2844no—
507C2×C8—2844no—
508C2×C8—712no—
509C2×C8—712no—
510C2×C8—712no—
511C2×C8—712no—
512C2×C8—1421no—
513C2×C8—1421no—
514C2×C8—1421no—
515C2×C8—1421no—
516C2×C8—1421no—
517C2×C8—1421no—
518C2×C8—1421no—
519C2×C8—1421no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—81no—
531C4⋊C4—2842no—
532C4⋊C4—712no—
533C4⋊C4—1421no—
534C4⋊C4—1421no—
535C4⋊C4—1421no—
536C4⋊C4—1421no—
537C4⋊C4—1421no—
538C4⋊C4—1421no—
539C4⋊C4—1421no—
540C4⋊C4Dic71⋊C414yes—
541C4⋊C4#1176586412yes—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—2842no—
545C22⋊C4—2842no—
546C22⋊C4—5681no—
547C22⋊C4Dic71⋊C414yes—
548C22⋊C4Dic71⋊C414yes—
549C42—42no—
550C42—2842no—
551C42—5681no—
552C42C2×C4×D7112yes—
553C42C2×Dic14212yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23C2×Dic71⋊C412yes—
565C23C2×Dic71⋊C412yes—
566C23#1455615412yes—
567C23#1455615912yes—
568C23C22×C22⋊D7111yescharacteristic
569D4—28no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4—2841no—
601C2×C4—2841no—
602C2×C4—2841no—
603C2×C4—2841no—
604C2×C4—2841no—
605C2×C4—2841no—
606C2×C4—2841no—
607C2×C4—2841no—
608C2×C4—2841no—
609C2×C4—2841no—
610C2×C4—2841no—
611C2×C4—5684no—
612C2×C4—1422no—
613C2×C4C2×Dic71⋊C412yes—
614C2×C4C2×Dic71⋊C412yes—
615C2×C4C2×Dic71⋊C412yes—
616C2×C4C2×Dic71⋊C412yes—
617C2×C4C22×C4×D7111yescharacteristic
618C2×C4C22×Dic14211yescharacteristic
619C2×C4#41×D7111yescharacteristic
620C2×C4C2×#1176586411yescharacteristic
621C2×C4#1455617311yescharacteristic
622C2×C4#1455617411yescharacteristic
623C8—1422no—
624C8—1422no—
625C8—1422no—
626C8—1422no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22#1798603914yes—
641C22C22×Dic71⋊C411yescharacteristic
642C22#1798663711yescharacteristic
643C22#1798664311yescharacteristic
644C22C2×#1455615411yescharacteristic
645C22C2×#1455615911yescharacteristic
646C22#1798680711yescharacteristic
647C22#1798681011yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—22no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—2842no—
657C4—5681no—
658C4—5681no—
659C4—5681no—
660C4C4×#1176586411yescharacteristic
661C4#1798647111yescharacteristic
662C4#1798670611yescharacteristic
663C4#1798670811yescharacteristic
664C2—24no—
665C2—42no—
666C2#2259124511yescharacteristic
667C2C2×#1798603911yescharacteristic
668C2#2259693311yescharacteristic
669C2#2260029511yescharacteristic
670C2#2260036111yescharacteristic
671C2#2260044511yescharacteristic
672C2#2260051111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingD4×C4⋊C4×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
cosocleC22×C4×C71C24
hypercenterD4×C4⋊C4D71
hypocenterC71#22711
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22589108C2semidirect
4. #22589101C2semidirect
5. #22588537C2semidirect
6. #22588533C2semidirect
7. #22588533C2semidirect
8. #22588527C2semidirect
9. #22588475C2semidirect
10. #22588371C2semidirect
11. #22588363C2semidirect
12. #22588238C2semidirect
13. #22588059C2semidirect
14. C2×#17985761C2semidirect
20. #17986071C4semidirect
63. C2×#11765849C2×C4semidirect
66. C22×C71⋊C8C2×C4semidirect
91. C4⋊(C71⋊C8)C2×C4semidirect
92. C22⋊(C71⋊C8)C2×C4semidirect
93. C22⋊(C71⋊C8)C2×C4semidirect
94. #14556039C2×C4semidirect
352. C71#22711semidirect

Maximal subgroups

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

subgroupindex
C2×#179860712
#225912692
#225891082
#225891012
#225885372
#225885332
#225885272
#225884752
#225883712
#225883632
#225882382
#225880592
C2×#179857612
D4×C4⋊C4×C712
#2271171