Finite Group Databasebeta

← #32868197

Subgroups — #32868197

Order 18176.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986510C211yesmaximal, characteristic, complemented
2C22×#14556102C211yesmaximal, characteristic, complemented
3#22599156C214yesmaximal, complemented
4#22599147C212yesmaximal, complemented
5#22599140C212yesmaximal, complemented
6#22599107C214yesmaximal, complemented
7#22599098C212yesmaximal, complemented
8#22599091C212yesmaximal, complemented
9#22598281C212yesmaximal, complemented
10#22598265C212yesmaximal, complemented
11#22597959C214yesmaximal, complemented
12#22597594C212yesmaximal, complemented
13#22597570C212yesmaximal, complemented
14C2×#407×C71C211yesmaximal, characteristic, complemented
15C22×#11765865C2211yescharacteristic, complemented
16C23×D284C2211yescharacteristic, complemented
17C23×C22⋊D71—21no—
18C2×#14556156C2214yescomplemented
19#17986510—21no—
20#17986510—21no—
21#17986510—21no—
22#17986510—21no—
23#17986510C2212yes—
24#17986510C2212yescomplemented
25#17986510C2212yescomplemented
26#17986510C2212yescomplemented
27C2×#14556111—21no—
28C2×#14556107C2211yescharacteristic, complemented
29C2×#14556107C2211yescharacteristic, complemented
30C2×#14556102—21no—
31C2×#14556102—21no—
32C2×#14556102—21no—
33C2×#14556102—21no—
34C2×#14556102—21no—
35C2×#14556102—21no—
36C2×#14556102C2212yes—
37C2×#14556102C2212yes—
38C2×#14556102C2212yes—
39C2×#14556102C2212yescomplemented
40C2×#14556102C2212yescomplemented
41C2×#14556102C2212yescomplemented
42C2×#14556102C2211yescharacteristic, complemented
43C2×#14556102C2211yescharacteristic, complemented
44C2×#14556097—21no—
45C2×C4×C22⋊D71—21no—
46C2×C4×C22⋊D71—21no—
47C2×#14556087C2211yescharacteristic, complemented
48C22×C4⋊Dic71C2211yescharacteristic, complemented
49C22×(C2×D71)⋊C4—21no—
50#17986335C2214yescomplemented
51#17986330C2214yescomplemented
52#17986324C2218yescomplemented
53#17986318C2214yescomplemented
54#17986318C2214yescomplemented
55#17986313C2214yescomplemented
56#17986313C2214yescomplemented
57#17986252C2218yescomplemented
58#17986245C2218yescomplemented
59#17986235C2218yescomplemented
60#17986228C2218yescomplemented
61#17986152C2214yescomplemented
62#17986152C2214yescomplemented
63#17986146C2218yescomplemented
64#17986140C2214yescomplemented
65#17986135C2214yescomplemented
66#17986135C2214yescomplemented
67#17986135C2214yescomplemented
68#17986041C2214yescomplemented
69#17986005C2214yescomplemented
70#17986001C2214yescomplemented
71C24×C4×C71C2211yescharacteristic
72C22×M16×C71C2212yescomplemented
73#407×C71C2212yescomplemented
74#407×C71C2212yescomplemented
75#407×C71C2212yescomplemented
76#407×C71C2212yescomplemented
77C2×C22⋊C8×C71C2212yescomplemented
78C2×C22⋊C8×C71C2212yescomplemented
79C24×D71—21no—
80C2×#11765865—21no—
81C2×#11765865—21no—
82C2×#11765865—44no—
83C2×#11765865C2312yes—
84C2×#11765865C2312yescomplemented
85C22×Dic142C2311yescharacteristic, complemented
86C22×D284—21no—
87C22×D284—21no—
88C22×D284—21no—
89C22×D284—44no—
90C22×D284C2312yes—
91C22×D284C2312yes—
92C22×D284C2312yes—
93C22×D284C2311yescharacteristic, complemented
94C22×C22⋊D71—22no—
95C22×C22⋊D71—22no—
96C22×C22⋊D71—22no—
97C22×C22⋊D71—22no—
98C22×C22⋊D71—22no—
99C22×C22⋊D71—22no—
100C22×C22⋊D71—21no—
101C22×C22⋊D71—21no—
102C22×C22⋊D71—21no—
103C22×C22⋊D71—48no—
104C23×Dic71—21no—
105C22×C4×D71—21no—
106#14556156—48no—
107C2×#11765854C2318yescomplemented
108C2×D568C2318yescomplemented
109#14556111—22no—
110#14556111—22no—
111#14556111—22no—
112#14556111—22no—
113#14556107—21no—
114#14556107—21no—
115#14556107—21no—
116#14556107—21no—
117#14556107C2312yes—
118#14556107C2312yes—
119#14556107C2312yescomplemented
120#14556107C2312yescomplemented
121#14556102—22no—
122#14556102—22no—
123#14556102—22no—
124#14556102—22no—
125#14556102—22no—
126#14556102—22no—
127#14556102—22no—
128#14556102—22no—
129#14556102—22no—
130#14556102—22no—
131#14556102—22no—
132#14556102—22no—
133#14556102—21no—
134#14556102—21no—
135#14556102—21no—
136#14556102—21no—
137#14556102C2312yes—
138#14556102C2314yes—
139#14556102C2312yes—
140#14556102C2314yes—
141#14556102C2314yes—
142#14556102C2314yes—
143#14556102C2312yescomplemented
144#14556102C2312yescomplemented
145#14556097—22no—
146#14556097—22no—
147#14556097—22no—
148#14556097—22no—
149C4×C22⋊D71—22no—
150C4×C22⋊D71—22no—
151C4×C22⋊D71—22no—
152C4×C22⋊D71—22no—
153C4×C22⋊D71—22no—
154C4×C22⋊D71—22no—
155C4×C22⋊D71—22no—
156C4×C22⋊D71—22no—
157#14556087—21no—
158#14556087—21no—
159#14556087C2312yes—
160#14556087C2312yescomplemented
161C2×C4⋊Dic71—21no—
162C2×C4⋊Dic71—21no—
163C2×C4⋊Dic71—21no—
164C2×C4⋊Dic71C2312yes—
165C2×C4⋊Dic71C2312yes—
166C2×C4⋊Dic71C2312yes—
167C2×C4⋊Dic71C2311yescharacteristic, complemented
168C2×C4⋊Dic71C2311yescharacteristic, complemented
169C2×Dic71⋊C4—21no—
170C2×Dic71⋊C4—21no—
171C2×C22⋊Dic71—21no—
172C2×C22⋊Dic71—21no—
173C2×C22⋊Dic71—21no—
174C2×(C2×D71)⋊C4—22no—
175C2×(C2×D71)⋊C4—22no—
176C2×(C2×D71)⋊C4—22no—
177C2×(C2×D71)⋊C4—22no—
178C2×(C2×D71)⋊C4—22no—
179C2×(C2×D71)⋊C4—22no—
180C2×(C2×D71)⋊C4—21no—
181C2×(C2×D71)⋊C4—21no—
182C2×C4×Dic71—21no—
183#14556062C2318yescomplemented
184#14556060C2318yescomplemented
185#14556053C2318yescomplemented
186#14556050C2318yescomplemented
187#14556050C2318yescomplemented
188#14556050C2318yescomplemented
189C25×C71D411yescharacteristic
190C23×C4×C71—44no—
191C23×C4×C71D411yescharacteristic
192C23×C4×C71D411yescharacteristic
193C23×C4×C71D411yescharacteristic
194C23×C4×C71D411yescharacteristic
195C23×C4×C71D411yescharacteristic
196C23×C4×C71D411yescharacteristic
197C23×C4×C71D411yescharacteristic
198C23×C4×C71C2311yescharacteristic
199C23×C4×C71C2311yescharacteristic
200C23×C4×C71C2311yescharacteristic
201C23×C4×C71C2311yescharacteristic
202C23×C4×C71C2311yescharacteristic
203C23×C4×C71C2311yescharacteristic
204C23×C4×C71C2311yescharacteristic
205C2×M16×C71—44no—
206C2×M16×C71C2314yes—
207C2×M16×C71C2314yescomplemented
208C22×C8×C71C2314yescomplemented
209C22⋊C8×C71C2314yes—
210C22⋊C8×C71C2314yes—
211C22⋊C8×C71C2314yescomplemented
212C22⋊C8×C71C2314yescomplemented
213C23×D71—21no—
214C23×D71—22no—
215C23×D71—22no—
216C23×D71—22no—
217C23×D71—44no—
218C23×D71—44no—
219C23×D71—44no—
220#11765865—28no—
221#11765865—44no—
222#11765865—44no—
223#11765865—44no—
224C2×Dic142—21no—
225C2×Dic142—42no—
226C2×Dic142C2412yes—
227C2×D284—28no—
228C2×D284—22no—
229C2×D284—22no—
230C2×D284—22no—
231C2×D284—21no—
232C2×D284—44no—
233C2×D284—44no—
234C2×D284—42no—
235C2×D284—44no—
236C2×D284—44no—
237C2×D284—44no—
238C2×D284C2414yes—
239C2×D284C2412yes—
240C2×C22⋊D71—24no—
241C2×C22⋊D71—24no—
242C2×C22⋊D71—24no—
243C2×C22⋊D71—24no—
244C2×C22⋊D71—22no—
245C2×C22⋊D71—22no—
246C2×C22⋊D71—22no—
247C2×C22⋊D71—22no—
248C2×C22⋊D71—22no—
249C2×C22⋊D71—22no—
250C2×C22⋊D71—44no—
251C2×C22⋊D71—48no—
252C2×C22⋊D71—48no—
253C2×C22⋊D71—48no—
254C2×C22⋊D71—48no—
255C2×C22⋊D71—48no—
256C2×C22⋊D71—44no—
257C2×C22⋊D71—44no—
258C2×C22⋊D71—48no—
259C22×Dic71—21no—
260C22×Dic71—22no—
261C22×Dic71—22no—
262C22×Dic71—22no—
263C22×Dic71—21no—
264C22×Dic71—21no—
265C22×Dic71—44no—
266C2×C4×D71—22no—
267C2×C4×D71—22no—
268C2×C4×D71—44no—
269#11765854—48no—
270D568—48no—
271C4⋊Dic71—22no—
272C4⋊Dic71—22no—
273C4⋊Dic71—22no—
274C4⋊Dic71—21no—
275C4⋊Dic71—21no—
276C4⋊Dic71C2412yes—
277C4⋊Dic71C2412yes—
278C4⋊Dic71C2414yes—
279Dic71⋊C4—22no—
280Dic71⋊C4—22no—
281Dic71⋊C4—22no—
282Dic71⋊C4—22no—
283C22⋊Dic71—22no—
284C22⋊Dic71—22no—
285C22⋊Dic71—22no—
286C22⋊Dic71—22no—
287C22⋊Dic71—22no—
288C22⋊Dic71—22no—
289(C2×D71)⋊C4—24no—
290(C2×D71)⋊C4—24no—
291(C2×D71)⋊C4—24no—
292(C2×D71)⋊C4—24no—
293(C2×D71)⋊C4—22no—
294(C2×D71)⋊C4—22no—
295(C2×D71)⋊C4—22no—
296(C2×D71)⋊C4—22no—
297C4×Dic71—22no—
298C4×Dic71—22no—
299C24×C71—24no—
300C24×C71—42no—
301C24×C71—42no—
302C24×C71C2×D411yescharacteristic
303C24×C71C2×D411yescharacteristic
304C24×C71C2×D411yescharacteristic
305C24×C71C2×D411yescharacteristic
306C24×C71C2×D411yescharacteristic
307C24×C71C2×D411yescharacteristic
308C24×C71C2×D411yescharacteristic
309C22×C4×C71—24no—
310C22×C4×C71—24no—
311C22×C4×C71—24no—
312C22×C4×C71—42no—
313C22×C4×C71—42no—
314C22×C4×C71—42no—
315C22×C4×C71—42no—
316C22×C4×C71—42no—
317C22×C4×C71—42no—
318C22×C4×C71—42no—
319C22×C4×C71—42no—
320C22×C4×C71—42no—
321C22×C4×C71—42no—
322C22×C4×C71—42no—
323C22×C4×C71C2×D411yescharacteristic
324C22×C4×C71C2×D411yescharacteristic
325C22×C4×C71C2×D411yescharacteristic
326C22×C4×C71C2×D411yescharacteristic
327C22×C4×C71C2×D411yescharacteristic
328C22×C4×C71C2×D411yescharacteristic
329C22×C4×C71C2×D411yescharacteristic
330C22×C4×C71C2×D411yescharacteristic
331C22×C4×C71C2×D411yescharacteristic
332C22×C4×C71C2×D411yescharacteristic
333C22×C4×C71C2×D411yescharacteristic
334C22×C4×C71C2×D411yescharacteristic
335C22×C4×C71C2×D411yescharacteristic
336C22×C4×C71C2×D411yescharacteristic
337C22×C4×C71C2×D411yescharacteristic
338C22×C4×C71C2×D411yescharacteristic
339C22×C4×C71C2×D411yescharacteristic
340C22×C4×C71C2×D411yescharacteristic
341C22×C4×C71C2×D411yescharacteristic
342C22×C4×C71C2×D411yescharacteristic
343C22×C4×C71C2×D411yescharacteristic
344C22×C4×C71C2411yescharacteristic
345C22×C4×C71C2411yescharacteristic
346C22×C4×C71C2411yescharacteristic
347C22×C4×C71C2411yescharacteristic
348C22×C4×C71C2411yescharacteristic
349C22×C4×C71C2411yescharacteristic
350C22×C4×C71C2411yescharacteristic
351M16×C71—28no—
352M16×C71—44no—
353C2×C8×C71—44no—
354C2×C8×C71C2418yes—
355C23×C71—22no—
356C23×C71—22no—
357C23×C71—22no—
358C23×C71—22no—
359C23×C71—22no—
360C23×C71—22no—
361C23×C71—22no—
362C23×C71—22no—
363C23×C71—22no—
364C23×C71—22no—
365C23×C71—22no—
366C23×C71—22no—
367C23×C71—41no—
368C23×C71—41no—
369C23×C71—41no—
370C23×C71—41no—
371C23×C71—41no—
372C23×C71—41no—
373C23×C71—41no—
374C23×C71—41no—
375C23×C71—416no—
376C23×C71AGL(1,ℤ/8)14yescomplemented
377C23×C71C22×D411yescharacteristic
378C23×C71C22×D411yescharacteristic
379C23×C71C22×D411yescharacteristic
380C23×C71C22×D411yescharacteristic
381C23×C71C22×D411yescharacteristic
382C23×C71C22×D411yescharacteristic
383C23×C71C22×D411yescharacteristic
384C22×D71—22no—
385C22×D71—24no—
386C22×D71—42no—
387C22×D71—44no—
388C22×D71—44no—
389C22×D71—42no—
390C22×D71—44no—
391C22×D71—44no—
392C22×D71—44no—
393C22×D71—44no—
394C22×D71—44no—
395C22×D71—44no—
396C22×D71—42no—
397C22×D71—44no—
398C22×D71—816no—
399C2×C4×C71—22no—
400C2×C4×C71—22no—
401C2×C4×C71—22no—
402C2×C4×C71—22no—
403C2×C4×C71—22no—
404C2×C4×C71—22no—
405C2×C4×C71—22no—
406C2×C4×C71—22no—
407C2×C4×C71—22no—
408C2×C4×C71—22no—
409C2×C4×C71—22no—
410C2×C4×C71—22no—
411C2×C4×C71—22no—
412C2×C4×C71—22no—
413C2×C4×C71—22no—
414C2×C4×C71—41no—
415C2×C4×C71—41no—
416C2×C4×C71—41no—
417C2×C4×C71—41no—
418C2×C4×C71—41no—
419C2×C4×C71—41no—
420C2×C4×C71—41no—
421C2×C4×C71—41no—
422C2×C4×C71—41no—
423C2×C4×C71—41no—
424C2×C4×C71—41no—
425C2×C4×C71—41no—
426C2×C4×C71C22×D411yescharacteristic
427C2×C4×C71C22×D411yescharacteristic
428C2×C4×C71C22×D411yescharacteristic
429C2×C4×C71C22×D411yescharacteristic
430C2×C4×C71C22×D411yescharacteristic
431C2×C4×C71C22×D411yescharacteristic
432C2×C4×C71C22×D411yescharacteristic
433C2×C4×C71H(5,𝔽2)14yes—
434C2×C4×C71C2511yescharacteristic
435C22⋊D71—44no—
436C22⋊D71—48no—
437C22⋊D71—48no—
438C22⋊D71—44no—
439C22⋊D71—44no—
440C22⋊D71—44no—
441C22⋊D71—44no—
442C22⋊D71—48no—
443C22⋊D71—48no—
444C22⋊D71—44no—
445C2×Dic71—22no—
446C2×Dic71—22no—
447C2×Dic71—24no—
448C2×Dic71—22no—
449C2×Dic71—42no—
450C2×Dic71—44no—
451C2×Dic71—44no—
452C2×Dic71—42no—
453C2×Dic71—44no—
454C2×Dic71—42no—
455D284—24no—
456D284—28no—
457D284—44no—
458D284—44no—
459D284—42no—
460D284—44no—
461C4×D71—44no—
462C4×D71—44no—
463Dic142—24no—
464Dic142—42no—
465C8×C71—28no—
466C22×C71—28no—
467C22×C71—21no—
468C22×C71—21no—
469C22×C71—21no—
470C22×C71—21no—
471C22×C71—21no—
472C22×C71—21no—
473C22×C71—21no—
474C22×C71—21no—
475C22×C71—21no—
476C22×C71—21no—
477C22×C71—21no—
478C22×C71—21no—
479C22×C71—21no—
480C22×C71—21no—
481C22×C71—21no—
482C22×C71—21no—
483C22×C71—44no—
484C22×C71—44no—
485C22×C71—44no—
486C22×C71—44no—
487C22×C71—44no—
488C22×C71—44no—
489C22×C71#53412yes—
490C22×C71C2×AGL(1,ℤ/8)12yes—
491C22×C71C2×AGL(1,ℤ/8)12yes—
492C22×C71C2×AGL(1,ℤ/8)12yes—
493C22×C71#57512yes—
494C22×C71C23×D411yescharacteristic
495C2×D71—42no—
496C2×D71—44no—
497C2×D71—44no—
498C2×D71—42no—
499C2×D71—42no—
500C2×D71—44no—
501C2×D71—84no—
502C2×D71—88no—
503C2×D71—88no—
504C2×D71—88no—
505C4×C71—21no—
506C4×C71—21no—
507C4×C71—21no—
508C4×C71—21no—
509C4×C71—21no—
510C4×C71—21no—
511C4×C71#53412yes—
512C4×C71C2×H(5,𝔽2)12yes—
513Dic71—42no—
514Dic71—44no—
515Dic71—42no—
516Dic71—42no—
517#60750—711nomaximal, Sylow
518C2×C71—22no—
519C2×C71—22no—
520C2×C71—22no—
521C2×C71—22no—
522C2×C71—22no—
523C2×C71—41no—
524C2×C71—41no—
525C2×C71C2×#53411yescharacteristic
526C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
527C2×C71C2×#57511yescharacteristic
528D71—82no—
529D71—84no—
530C2×#525—711no—
531C22×#121—711no—
532#3194—714no—
533#3193—712no—
534#3192—712no—
535#3188—714no—
536#3187—712no—
537#3186—712no—
538#3094—712no—
539#3092—712no—
540#3055—714no—
541#3006—712no—
542#3003—712no—
543C2×#407D7111yescharacteristic, complemented
544C71#6075011yescharacteristic, complemented, Sylow
545C22×#41—711no—
546C23×D4—711no—
547C23×D4—1421no—
548C24×C4C2×D7111yescharacteristic
549C2×AGL(1,ℤ/8)—714no—
550C22×M16C2×D7112yescomplemented
551#525—712no—
552#525—712no—
553#525—712no—
554#525—712no—
555#525—1421no—
556#525—1421no—
557#525—1421no—
558#525—1421no—
559C2×#123—1421no—
560C2×C22⋊Q8—711no—
561C2×C22⋊Q8—711no—
562C2×#121—712no—
563C2×#121—712no—
564C2×#121—712no—
565C2×#121—712no—
566C2×#121—712no—
567C2×#121—712no—
568C2×#121—711no—
569C2×#121—711no—
570C2×#121—1421no—
571C2×#121—1421no—
572C2×#121—1421no—
573C2×#121—1421no—
574C2×#121—1421no—
575C2×#121—1421no—
576C2×#120—1421no—
577C2×C4×D4—1421no—
578C2×C4×D4—1421no—
579C2×#117—711no—
580C22×C4⋊C4—711no—
581C22×C22⋊C4—1421no—
582#484—714no—
583#483—714no—
584#482—718no—
585#481—714no—
586#481—714no—
587#480—714no—
588#480—714no—
589#469—718no—
590#468—718no—
591#466—718no—
592#465—718no—
593#450—714no—
594#450—714no—
595#449—718no—
596#448—714no—
597#447—714no—
598#447—714no—
599#447—714no—
600#428—714no—
601#418—714no—
602#417—714no—
603#407C2×D7112yescomplemented
604#407C2×D7112yescomplemented
605#407C2×D7112yescomplemented
606#407C2×D7112yescomplemented
607C2×C22⋊C8C2×D7112yescomplemented
608C2×C22⋊C8C2×D7112yescomplemented
609C25—1421no—
610C25D28411yescharacteristic
611C2×#41—2844no—
612C2×#41—712no—
613C2×#41—712no—
614C2×#41—1421no—
615C2×#41—1421no—
616C22×Q8—711no—
617C22×D4—2844no—
618C22×D4—2848no—
619C22×D4—712no—
620C22×D4—712no—
621C22×D4—711no—
622C22×D4—712no—
623C22×D4—1421no—
624C22×D4—1421no—
625C22×D4—1421no—
626C22×D4—1422no—
627C22×D4—1422no—
628C22×D4—1422no—
629C22×D4—1422no—
630C22×D4—1422no—
631C22×D4—1422no—
632C22×D4—1421no—
633C22×D4—1421no—
634C22×D4—1421no—
635C23×C4—44no—
636C23×C4—1421no—
637C23×C4—1421no—
638C23×C4D28411yescharacteristic
639C23×C4D28411yescharacteristic
640C23×C4D28411yescharacteristic
641C23×C4D28411yescharacteristic
642C23×C4D28411yescharacteristic
643C23×C4D28411yescharacteristic
644C23×C4D28411yescharacteristic
645C23×C4C22×D7111yescharacteristic
646C23×C4C22×D7111yescharacteristic
647C23×C4C22×D7111yescharacteristic
648C23×C4C22×D7111yescharacteristic
649C23×C4C22×D7111yescharacteristic
650C23×C4C22×D7111yescharacteristic
651C23×C4C22×D7111yescharacteristic
652AGL(1,ℤ/8)—2848no—
653C2×SD16—718no—
654C2×D8—718no—
655C2×M16—44no—
656C2×M16C22×D7114yes—
657C2×M16C22×D7114yescomplemented
658C22×C8C22×D7114yescomplemented
659#123—1422no—
660#123—1422no—
661#123—1422no—
662#123—1422no—
663C22⋊Q8—712no—
664C22⋊Q8—712no—
665C22⋊Q8—712no—
666C22⋊Q8—712no—
667C22⋊Q8—1421no—
668C22⋊Q8—1421no—
669C22⋊Q8—1421no—
670C22⋊Q8—1421no—
671#121—714no—
672#121—714no—
673#121—714no—
674#121—714no—
675#121—712no—
676#121—712no—
677#121—712no—
678#121—712no—
679#121—1422no—
680#121—1422no—
681#121—1422no—
682#121—1422no—
683#121—1422no—
684#121—1422no—
685#121—1422no—
686#121—1422no—
687#121—1422no—
688#121—1422no—
689#121—1422no—
690#121—1422no—
691#121—1421no—
692#121—1421no—
693#121—1421no—
694#121—1421no—
695#120—1422no—
696#120—1422no—
697#120—1422no—
698#120—1422no—
699C4×D4—1422no—
700C4×D4—1422no—
701C4×D4—1422no—
702C4×D4—1422no—
703C4×D4—1422no—
704C4×D4—1422no—
705C4×D4—1422no—
706C4×D4—1422no—
707#117—712no—
708#117—712no—
709#117—1421no—
710#117—1421no—
711C2×C4⋊C4—712no—
712C2×C4⋊C4—712no—
713C2×C4⋊C4—712no—
714C2×C4⋊C4—711no—
715C2×C4⋊C4—711no—
716C2×C4⋊C4—1421no—
717C2×C4⋊C4—1421no—
718C2×C4⋊C4—1421no—
719C2×C4⋊C4—1421no—
720C2×C4⋊C4—1421no—
721C2×C22⋊C4—1421no—
722C2×C22⋊C4—1421no—
723C2×C22⋊C4—1421no—
724C2×C22⋊C4—1422no—
725C2×C22⋊C4—1422no—
726C2×C22⋊C4—1422no—
727C2×C22⋊C4—1422no—
728C2×C22⋊C4—1422no—
729C2×C22⋊C4—1422no—
730C2×C22⋊C4—1421no—
731C2×C22⋊C4—1421no—
732C2×C42—1421no—
733#107—718no—
734#106—718no—
735#103—718no—
736#102—718no—
737#102—718no—
738#102—718no—
739C22⋊C8C22×D7114yes—
740C22⋊C8C22×D7114yes—
741C22⋊C8C22×D7114yescomplemented
742C22⋊C8C22×D7114yescomplemented
743C24—24no—
744C24—42no—
745C24—42no—
746C24—2844no—
747C24—2844no—
748C24—2844no—
749C24—1421no—
750C24—1422no—
751C24—1422no—
752C24—1422no—
753C24C2×D28411yescharacteristic
754C24C2×D28411yescharacteristic
755C24C2×D28411yescharacteristic
756C24C2×D28411yescharacteristic
757C24C2×D28411yescharacteristic
758C24C2×D28411yescharacteristic
759C24C2×D28411yescharacteristic
760#41—2844no—
761#41—2844no—
762#41—2844no—
763#41—1428no—
764C2×Q8—2842no—
765C2×Q8—712no—
766C2×Q8—1421no—
767C2×D4—2844no—
768C2×D4—2844no—
769C2×D4—2844no—
770C2×D4—2844no—
771C2×D4—2844no—
772C2×D4—2842no—
773C2×D4—2848no—
774C2×D4—2848no—
775C2×D4—2848no—
776C2×D4—2848no—
777C2×D4—2848no—
778C2×D4—2844no—
779C2×D4—2844no—
780C2×D4—2848no—
781C2×D4—2844no—
782C2×D4—712no—
783C2×D4—714no—
784C2×D4—1422no—
785C2×D4—1422no—
786C2×D4—1422no—
787C2×D4—1422no—
788C2×D4—1422no—
789C2×D4—1422no—
790C2×D4—1424no—
791C2×D4—1424no—
792C2×D4—1424no—
793C2×D4—1424no—
794C2×D4—1422no—
795C2×D4—1422no—
796C2×D4—1422no—
797C2×D4—1421no—
798C2×D4—1428no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—2844no—
814C22×C4—2844no—
815C22×C4—1421no—
816C22×C4—1421no—
817C22×C4—1422no—
818C22×C4—1422no—
819C22×C4—1422no—
820C22×C4—1421no—
821C22×C4—1422no—
822C22×C4—1422no—
823C22×C4C2×D28411yescharacteristic
824C22×C4C2×D28411yescharacteristic
825C22×C4C2×D28411yescharacteristic
826C22×C4C2×D28411yescharacteristic
827C22×C4C2×D28411yescharacteristic
828C22×C4C2×D28411yescharacteristic
829C22×C4C2×D28411yescharacteristic
830C22×C4C2×D28411yescharacteristic
831C22×C4C2×D28411yescharacteristic
832C22×C4C2×D28411yescharacteristic
833C22×C4C2×D28411yescharacteristic
834C22×C4C2×D28411yescharacteristic
835C22×C4C2×D28411yescharacteristic
836C22×C4C2×D28411yescharacteristic
837C22×C4C2×D28411yescharacteristic
838C22×C4C2×D28411yescharacteristic
839C22×C4C2×D28411yescharacteristic
840C22×C4C2×D28411yescharacteristic
841C22×C4C2×D28411yescharacteristic
842C22×C4C2×D28411yescharacteristic
843C22×C4C2×D28411yescharacteristic
844C22×C4C23×D7111yescharacteristic
845C22×C4C23×D7111yescharacteristic
846C22×C4C23×D7111yescharacteristic
847C22×C4C23×D7111yescharacteristic
848C22×C4C23×D7111yescharacteristic
849C22×C4C23×D7111yescharacteristic
850C22×C4C23×D7111yescharacteristic
851SD16—2848no—
852D8—2848no—
853M16—28no—
854M16—44no—
855C2×C8—44no—
856C2×C8C23×D7118yes—
857C4⋊C4—712no—
858C4⋊C4—712no—
859C4⋊C4—714no—
860C4⋊C4—1422no—
861C4⋊C4—1422no—
862C4⋊C4—1422no—
863C4⋊C4—1422no—
864C4⋊C4—1422no—
865C4⋊C4—1422no—
866C4⋊C4—1422no—
867C4⋊C4—1421no—
868C4⋊C4—1421no—
869C22⋊C4—1422no—
870C22⋊C4—1422no—
871C22⋊C4—1422no—
872C22⋊C4—1422no—
873C22⋊C4—1422no—
874C22⋊C4—1422no—
875C22⋊C4—1424no—
876C22⋊C4—1424no—
877C22⋊C4—1424no—
878C22⋊C4—1424no—
879C22⋊C4—1422no—
880C22⋊C4—1422no—
881C22⋊C4—1422no—
882C22⋊C4—1422no—
883C42—1422no—
884C42—1422no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—416no—
906C23—2842no—
907C23—2844no—
908C23—2844no—
909C23—2844no—
910C23—2844no—
911C23—2842no—
912C23—2844no—
913C23—2844no—
914C23—2844no—
915C23—2844no—
916C23—2842no—
917C23—2844no—
918C23—56816no—
919C23—1422no—
920C23—1424no—
921C23#1455615614yescomplemented
922C23C22×D28411yescharacteristic
923C23C22×D28411yescharacteristic
924C23C22×D28411yescharacteristic
925C23C22×D28411yescharacteristic
926C23C22×D28411yescharacteristic
927C23C22×D28411yescharacteristic
928C23C22×D28411yescharacteristic
929Q8—2842no—
930Q8—1424no—
931D4—2844no—
932D4—2844no—
933D4—2842no—
934D4—2848no—
935D4—2848no—
936D4—2844no—
937D4—2844no—
938D4—2844no—
939D4—2848no—
940D4—2848no—
941D4—2844no—
942D4—2844no—
943D4—2844no—
944D4—2844no—
945D4—1424no—
946D4—1428no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—2844no—
975C2×C4—2844no—
976C2×C4—2844no—
977C2×C4—2842no—
978C2×C4—2842no—
979C2×C4—2844no—
980C2×C4—2842no—
981C2×C4—2844no—
982C2×C4—1422no—
983C2×C4—1422no—
984C2×C4—1424no—
985C2×C4—1422no—
986C2×C4C22×D28411yescharacteristic
987C2×C4C22×D28411yescharacteristic
988C2×C4C22×D28411yescharacteristic
989C2×C4C22×D28411yescharacteristic
990C2×C4C22×D28411yescharacteristic
991C2×C4C22×D28411yescharacteristic
992C2×C4C22×D28411yescharacteristic
993C2×C4#1455617314yes—
994C2×C4C24×D7111yescharacteristic
995C8—28no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—2844no—
1020C22—2842no—
1021C22—2842no—
1022C22—2844no—
1023C22—2842no—
1024C22—2844no—
1025C22—5688no—
1026C22—5688no—
1027C22—5688no—
1028C22—5684no—
1029C22#1798656112yes—
1030C22C2×#1455615612yes—
1031C22C2×#1455615612yes—
1032C22C2×#1455615612yes—
1033C22#1798679912yes—
1034C22C23×D28411yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—2844no—
1042C4—2842no—
1043C4—2842no—
1044C4—2842no—
1045C4#1798656112yes—
1046C4C2×#1455617312yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—5684no—
1055C2—5682no—
1056C2C2×#1798656111yescharacteristic
1057C2C22×#1455615611yescharacteristic
1058C2C2×#1798679911yescharacteristic
subgroupG/H
centerC22C23×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#407×C71C2
socleC22×C71C23×D4
hypercenterC2×#407D71
hypocenterC71#60750
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#17986510C2semidirect
2. C22×#14556102C2semidirect
3. #22599156C2semidirect
4. #22599147C2semidirect
5. #22599140C2semidirect
6. #22599107C2semidirect
7. #22599098C2semidirect
8. #22599091C2semidirect
9. #22598281C2semidirect
10. #22598265C2semidirect
11. #22597959C2semidirect
12. #22597594C2semidirect
13. #22597570C2semidirect
14. C2×#407×C71C2semidirect
15. C22×#11765865C22semidirect
16. C23×D284C22semidirect
18. C2×#14556156C22semidirect
24. #17986510C22semidirect
25. #17986510C22semidirect
26. #17986510C22semidirect
28. C2×#14556107C22semidirect
29. C2×#14556107C22semidirect
39. C2×#14556102C22semidirect
40. C2×#14556102C22semidirect
41. C2×#14556102C22semidirect
42. C2×#14556102C22semidirect
43. C2×#14556102C22semidirect
47. C2×#14556087C22semidirect
48. C22×C4⋊Dic71C22semidirect
50. #17986335C22semidirect
51. #17986330C22semidirect
52. #17986324C22semidirect
53. #17986318C22semidirect
54. #17986318C22semidirect
55. #17986313C22semidirect
56. #17986313C22semidirect
57. #17986252C22semidirect
58. #17986245C22semidirect
59. #17986235C22semidirect
60. #17986228C22semidirect
61. #17986152C22semidirect
62. #17986152C22semidirect
63. #17986146C22semidirect
64. #17986140C22semidirect
65. #17986135C22semidirect
66. #17986135C22semidirect
67. #17986135C22semidirect
68. #17986041C22semidirect
69. #17986005C22semidirect
70. #17986001C22semidirect
72. C22×M16×C71C22semidirect
73. #407×C71C22semidirect
74. #407×C71C22semidirect
75. #407×C71C22semidirect
76. #407×C71C22semidirect
77. C2×C22⋊C8×C71C22semidirect
78. C2×C22⋊C8×C71C22semidirect
84. C2×#11765865C23semidirect
85. C22×Dic142C23semidirect
93. C22×D284C23semidirect
107. C2×#11765854C23semidirect
108. C2×D568C23semidirect
119. #14556107C23semidirect
120. #14556107C23semidirect
143. #14556102C23semidirect
144. #14556102C23semidirect
160. #14556087C23semidirect
167. C2×C4⋊Dic71C23semidirect
168. C2×C4⋊Dic71C23semidirect
183. #14556062C23semidirect
184. #14556060C23semidirect
185. #14556053C23semidirect
186. #14556050C23semidirect
187. #14556050C23semidirect
188. #14556050C23semidirect
207. C2×M16×C71C23semidirect
208. C22×C8×C71C23semidirect
211. C22⋊C8×C71C23semidirect
212. C22⋊C8×C71C23semidirect
376. C23×C71AGL(1,ℤ/8)semidirect
543. C2×#407D71semidirect
544. C71#60750semidirect
550. C22×M16C2×D71semidirect
603. #407C2×D71semidirect
604. #407C2×D71semidirect
605. #407C2×D71semidirect
606. #407C2×D71semidirect
607. C2×C22⋊C8C2×D71semidirect
608. C2×C22⋊C8C2×D71semidirect
657. C2×M16C22×D71semidirect
658. C22×C8C22×D71semidirect
741. C22⋊C8C22×D71semidirect
742. C22⋊C8C22×D71semidirect
921. C23#14556156semidirect

Maximal subgroups

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

subgroupindex
C2×#179865102
C22×#145561022
#225991562
#225991472
#225991402
#225991072
#225990982
#225990912
#225982812
#225982652
#225979592
#225975942
#225975702
C2×#407×C712
#6075071