Finite Group Databasebeta

← #32868195

Subgroups — #32868195

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
2#22599154C214yesmaximal, complemented
3#22599146C212yesmaximal, complemented
4#22599137C212yesmaximal, complemented
5#22599105C214yesmaximal, complemented
6#22599097C212yesmaximal, complemented
7#22599088C212yesmaximal, complemented
8#22598276C212yesmaximal, complemented
9#22598263C212yesmaximal, complemented
10#22597955C214yesmaximal, complemented
11#22597590C212yesmaximal, complemented
12#22597567C212yesmaximal, complemented
13C2×#17985963C211yesmaximal, characteristic, complemented
14C22×#121×C71C211yesmaximal, characteristic, complemented
15C22×#11765865C2211yescharacteristic, complemented
16C2×#14556154C2214yescomplemented
17C22×#11765849C2212yescomplemented
18#17986510—21no—
19#17986510—21no—
20#17986510—21no—
21#17986510—21no—
22#17986510C2212yes—
23#17986510C2212yescomplemented
24#17986510C2212yescomplemented
25#17986510C2212yescomplemented
26C2×#14556111—21no—
27C2×#14556107C2211yescharacteristic, complemented
28C2×#14556107C2211yescharacteristic, complemented
29C2×#14556102C2211yescharacteristic, complemented
30C2×#14556102C2211yescharacteristic, complemented
31C2×#14556097—21no—
32C2×C4×C22⋊D71—21no—
33C2×C4×C22⋊D71—21no—
34C2×#14556087C2211yescharacteristic, complemented
35#17986334C2214yescomplemented
36#17986329C2214yescomplemented
37#17986320C2218yescomplemented
38#17986317C2214yescomplemented
39#17986315C2214yescomplemented
40#17986312C2214yescomplemented
41#17986310C2214yescomplemented
42#17986250C2218yescomplemented
43#17986243C2218yescomplemented
44#17986233C2218yescomplemented
45#17986226C2218yescomplemented
46#17986150C2214yescomplemented
47#17986150C2214yescomplemented
48#17986142C2218yescomplemented
49#17986137C2214yescomplemented
50#17986133C2214yescomplemented
51#17986133C2214yescomplemented
52#17986132C2214yescomplemented
53#17986039C2214yescomplemented
54#17986004C2214yescomplemented
55#17985998C2214yescomplemented
56#17985963C2212yescomplemented
57#17985963C2212yescomplemented
58#17985963C2212yescomplemented
59#17985963C2212yescomplemented
60C2×C22⋊(C71⋊C8)C2212yescomplemented
61C2×C22⋊(C71⋊C8)C2212yescomplemented
62C23×D4×C71—21no—
63C23×D4×C71C2211yescharacteristic, complemented
64C24×C4×C71C2211yescharacteristic
65C2×#121×C71—21no—
66C2×#121×C71—21no—
67C2×#121×C71—21no—
68C2×#121×C71—21no—
69C2×#121×C71—21no—
70C2×#121×C71—21no—
71C2×#121×C71C2212yes—
72C2×#121×C71C2212yes—
73C2×#121×C71C2212yes—
74C2×#121×C71C2212yescomplemented
75C2×#121×C71C2212yescomplemented
76C2×#121×C71C2212yescomplemented
77C22×C4⋊C4×C71C2211yescharacteristic, complemented
78C22×C22⋊C4×C71—21no—
79C2×#11765865—21no—
80C2×#11765865—21no—
81C2×#11765865—44no—
82C2×#11765865C2312yes—
83C2×#11765865C2312yescomplemented
84C22×Dic142C2311yescharacteristic, complemented
85C22×D284C2311yescharacteristic, complemented
86C22×C22⋊D71—21no—
87C22×C22⋊D71—21no—
88C22×C22⋊D71—21no—
89C22×C4×D71—21no—
90#14556154—48no—
91C2×#11765853C2318yescomplemented
92C2×#11765850C2318yescomplemented
93C2×#11765849—44no—
94C2×#11765849C2314yes—
95C2×#11765849C2314yescomplemented
96C22×C71⋊C8C2314yescomplemented
97#14556111—22no—
98#14556111—22no—
99#14556111—22no—
100#14556111—22no—
101#14556107—21no—
102#14556107—21no—
103#14556107—21no—
104#14556107—21no—
105#14556107C2312yes—
106#14556107C2312yes—
107#14556107C2312yescomplemented
108#14556107C2312yescomplemented
109#14556102—21no—
110#14556102—21no—
111#14556102—21no—
112#14556102—21no—
113#14556102C2312yes—
114#14556102C2312yes—
115#14556102C2312yescomplemented
116#14556102C2312yescomplemented
117#14556097—22no—
118#14556097—22no—
119#14556097—22no—
120#14556097—22no—
121C4×C22⋊D71—22no—
122C4×C22⋊D71—22no—
123C4×C22⋊D71—22no—
124C4×C22⋊D71—22no—
125C4×C22⋊D71—22no—
126C4×C22⋊D71—22no—
127C4×C22⋊D71—22no—
128C4×C22⋊D71—22no—
129#14556087—21no—
130#14556087—21no—
131#14556087C2312yes—
132#14556087C2312yescomplemented
133C2×C4⋊Dic71C2311yescharacteristic, complemented
134C2×C4⋊Dic71C2311yescharacteristic, complemented
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C2×C22⋊Dic71—21no—
138C2×C22⋊Dic71—21no—
139C2×C22⋊Dic71—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×C4×Dic71—21no—
143#14556061C2318yescomplemented
144#14556059C2318yescomplemented
145#14556051C2318yescomplemented
146#14556049C2318yescomplemented
147#14556049C2318yescomplemented
148#14556048C2318yescomplemented
149C22⋊(C71⋊C8)C2314yes—
150C22⋊(C71⋊C8)C2314yes—
151C22⋊(C71⋊C8)C2314yescomplemented
152C22⋊(C71⋊C8)C2314yescomplemented
153C25×C71—21no—
154C25×C71D411yescharacteristic
155C22×D4×C71—22no—
156C22×D4×C71—22no—
157C22×D4×C71—22no—
158C22×D4×C71—22no—
159C22×D4×C71—22no—
160C22×D4×C71—22no—
161C22×D4×C71—21no—
162C22×D4×C71—21no—
163C22×D4×C71—21no—
164C22×D4×C71—44no—
165C22×D4×C71—48no—
166C22×D4×C71C2312yes—
167C22×D4×C71C2312yes—
168C22×D4×C71C2312yes—
169C23×C4×C71—21no—
170C23×C4×C71—44no—
171C23×C4×C71D411yescharacteristic
172C23×C4×C71D411yescharacteristic
173C23×C4×C71D411yescharacteristic
174C23×C4×C71D411yescharacteristic
175C23×C4×C71D411yescharacteristic
176C23×C4×C71D411yescharacteristic
177C23×C4×C71D411yescharacteristic
178C23×C4×C71C2311yescharacteristic
179C23×C4×C71C2311yescharacteristic
180C23×C4×C71C2311yescharacteristic
181C23×C4×C71C2311yescharacteristic
182C23×C4×C71C2311yescharacteristic
183C23×C4×C71C2311yescharacteristic
184C23×C4×C71C2311yescharacteristic
185#121×C71—22no—
186#121×C71—22no—
187#121×C71—22no—
188#121×C71—22no—
189#121×C71—22no—
190#121×C71—22no—
191#121×C71—22no—
192#121×C71—22no—
193#121×C71—22no—
194#121×C71—22no—
195#121×C71—22no—
196#121×C71—22no—
197#121×C71C2314yes—
198#121×C71C2314yes—
199#121×C71C2314yes—
200#121×C71C2314yes—
201C2×C4⋊C4×C71—21no—
202C2×C4⋊C4×C71—21no—
203C2×C4⋊C4×C71—21no—
204C2×C4⋊C4×C71C2312yes—
205C2×C4⋊C4×C71C2312yes—
206C2×C4⋊C4×C71C2312yes—
207C2×C22⋊C4×C71—22no—
208C2×C22⋊C4×C71—22no—
209C2×C22⋊C4×C71—22no—
210C2×C22⋊C4×C71—22no—
211C2×C22⋊C4×C71—22no—
212C2×C22⋊C4×C71—22no—
213C23×D71—21no—
214#11765865—28no—
215#11765865—44no—
216#11765865—44no—
217#11765865—44no—
218C2×Dic142—21no—
219C2×Dic142—42no—
220C2×Dic142C2412yes—
221C2×D284—21no—
222C2×D284—42no—
223C2×D284C2412yes—
224C2×C22⋊D71—22no—
225C2×C22⋊D71—22no—
226C2×C22⋊D71—22no—
227C2×C22⋊D71—22no—
228C2×C22⋊D71—22no—
229C2×C22⋊D71—22no—
230C2×C22⋊D71—44no—
231C2×C22⋊D71—44no—
232C2×C22⋊D71—44no—
233C22×Dic71—21no—
234C22×Dic71—21no—
235C22×Dic71—21no—
236C2×C4×D71—22no—
237C2×C4×D71—22no—
238C2×C4×D71—44no—
239#11765853—48no—
240#11765850—48no—
241#11765849—28no—
242#11765849—44no—
243C2×C71⋊C8—44no—
244C2×C71⋊C8C2418yes—
245C4⋊Dic71—21no—
246C4⋊Dic71—21no—
247C4⋊Dic71C2412yes—
248C4⋊Dic71C2412yes—
249Dic71⋊C4—22no—
250Dic71⋊C4—22no—
251Dic71⋊C4—22no—
252Dic71⋊C4—22no—
253C22⋊Dic71—22no—
254C22⋊Dic71—22no—
255C22⋊Dic71—22no—
256C22⋊Dic71—22no—
257C22⋊Dic71—22no—
258C22⋊Dic71—22no—
259(C2×D71)⋊C4—22no—
260(C2×D71)⋊C4—22no—
261(C2×D71)⋊C4—22no—
262(C2×D71)⋊C4—22no—
263C4×Dic71—22no—
264C4×Dic71—22no—
265C24×C71—24no—
266C24×C71—22no—
267C24×C71—22no—
268C24×C71—22no—
269C24×C71—42no—
270C24×C71—42no—
271C24×C71—44no—
272C24×C71—44no—
273C24×C71—44no—
274C24×C71C2×D411yescharacteristic
275C24×C71C2×D411yescharacteristic
276C24×C71C2×D411yescharacteristic
277C24×C71C2×D411yescharacteristic
278C24×C71C2×D411yescharacteristic
279C24×C71C2×D411yescharacteristic
280C24×C71C2×D411yescharacteristic
281C2×D4×C71—24no—
282C2×D4×C71—24no—
283C2×D4×C71—24no—
284C2×D4×C71—24no—
285C2×D4×C71—22no—
286C2×D4×C71—22no—
287C2×D4×C71—22no—
288C2×D4×C71—28no—
289C2×D4×C71—44no—
290C2×D4×C71—44no—
291C2×D4×C71—44no—
292C2×D4×C71—44no—
293C2×D4×C71—44no—
294C2×D4×C71—48no—
295C2×D4×C71—48no—
296C2×D4×C71—48no—
297C2×D4×C71—48no—
298C2×D4×C71—48no—
299C2×D4×C71—48no—
300C2×D4×C71C2414yes—
301C22×C4×C71—24no—
302C22×C4×C71—24no—
303C22×C4×C71—24no—
304C22×C4×C71—22no—
305C22×C4×C71—22no—
306C22×C4×C71—22no—
307C22×C4×C71—42no—
308C22×C4×C71—42no—
309C22×C4×C71—42no—
310C22×C4×C71—42no—
311C22×C4×C71—42no—
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—44no—
319C22×C4×C71C2×D411yescharacteristic
320C22×C4×C71C2×D411yescharacteristic
321C22×C4×C71C2×D411yescharacteristic
322C22×C4×C71C2×D411yescharacteristic
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×C71C2411yescharacteristic
341C22×C4×C71C2411yescharacteristic
342C22×C4×C71C2411yescharacteristic
343C22×C4×C71C2411yescharacteristic
344C22×C4×C71C2411yescharacteristic
345C22×C4×C71C2411yescharacteristic
346C22×C4×C71C2411yescharacteristic
347C4⋊C4×C71—22no—
348C4⋊C4×C71—22no—
349C4⋊C4×C71—22no—
350C4⋊C4×C71C2414yes—
351C22⋊C4×C71—24no—
352C22⋊C4×C71—24no—
353C22⋊C4×C71—24no—
354C22⋊C4×C71—24no—
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—24no—
368C23×C71—41no—
369C23×C71—41no—
370C23×C71—41no—
371C23×C71—41no—
372C23×C71—41no—
373C23×C71—41no—
374C23×C71—41no—
375C23×C71—41no—
376C23×C71—416no—
377C23×C71—44no—
378C23×C71—44no—
379C23×C71—44no—
380C23×C71—44no—
381C23×C71—44no—
382C23×C71—44no—
383C23×C71—44no—
384C23×C71—44no—
385C23×C71—44no—
386C23×C71—816no—
387C23×C71AGL(1,ℤ/8)14yescomplemented
388C23×C71C22×D411yescharacteristic
389C23×C71C22×D411yescharacteristic
390C23×C71C22×D411yescharacteristic
391C23×C71C22×D411yescharacteristic
392C23×C71C22×D411yescharacteristic
393C23×C71C22×D411yescharacteristic
394C23×C71C22×D411yescharacteristic
395C22×D71—22no—
396C22×D71—42no—
397C22×D71—42no—
398C22×D71—42no—
399D4×C71—28no—
400D4×C71—44no—
401D4×C71—44no—
402D4×C71—48no—
403D4×C71—48no—
404D4×C71—48no—
405D4×C71—48no—
406D4×C71—44no—
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—22no—
415C2×C4×C71—22no—
416C2×C4×C71—22no—
417C2×C4×C71—22no—
418C2×C4×C71—22no—
419C2×C4×C71—22no—
420C2×C4×C71—22no—
421C2×C4×C71—22no—
422C2×C4×C71—24no—
423C2×C4×C71—41no—
424C2×C4×C71—41no—
425C2×C4×C71—41no—
426C2×C4×C71—41no—
427C2×C4×C71—41no—
428C2×C4×C71—41no—
429C2×C4×C71—41no—
430C2×C4×C71—41no—
431C2×C4×C71—41no—
432C2×C4×C71—41no—
433C2×C4×C71—41no—
434C2×C4×C71—41no—
435C2×C4×C71—44no—
436C2×C4×C71—44no—
437C2×C4×C71—44no—
438C2×C4×C71C22×D411yescharacteristic
439C2×C4×C71C22×D411yescharacteristic
440C2×C4×C71C22×D411yescharacteristic
441C2×C4×C71C22×D411yescharacteristic
442C2×C4×C71C22×D411yescharacteristic
443C2×C4×C71C22×D411yescharacteristic
444C2×C4×C71C22×D411yescharacteristic
445C2×C4×C71H(5,𝔽2)14yes—
446C2×C4×C71C2511yescharacteristic
447C22⋊D71—44no—
448C22⋊D71—44no—
449C22⋊D71—44no—
450C22⋊D71—44no—
451C22⋊D71—44no—
452C22⋊D71—44no—
453C2×Dic71—22no—
454C2×Dic71—22no—
455C2×Dic71—22no—
456C2×Dic71—42no—
457C2×Dic71—42no—
458C2×Dic71—42no—
459D284—24no—
460D284—42no—
461C4×D71—44no—
462C4×D71—44no—
463Dic142—24no—
464Dic142—42no—
465C71⋊C8—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—44no—
490C22×C71—44no—
491C22×C71—44no—
492C22×C71—88no—
493C22×C71—88no—
494C22×C71—88no—
495C22×C71#53412yes—
496C22×C71C2×AGL(1,ℤ/8)12yes—
497C22×C71C2×AGL(1,ℤ/8)12yes—
498C22×C71C2×AGL(1,ℤ/8)12yes—
499C22×C71#57512yes—
500C22×C71C23×D411yescharacteristic
501C2×D71—42no—
502C2×D71—42no—
503C2×D71—42no—
504C2×D71—84no—
505C4×C71—21no—
506C4×C71—21no—
507C4×C71—21no—
508C4×C71—21no—
509C4×C71—21no—
510C4×C71—21no—
511C4×C71—44no—
512C4×C71#53412yes—
513C4×C71C2×H(5,𝔽2)12yes—
514Dic71—42no—
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×C71—84no—
526C2×C71C2×#53411yescharacteristic
527C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
528C2×C71C2×#57511yescharacteristic
529D71—82no—
530C2×#525—711no—
531C22×#121D7111yescharacteristic, complemented
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×#407—711no—
544C71#6075011yescharacteristic, complemented, Sylow
545C22×#41—711no—
546C23×D4—21no—
547C23×D4C2×D7111yescharacteristic, complemented
548C24×C4C2×D7111yescharacteristic
549C2×AGL(1,ℤ/8)—714no—
550C22×M16—712no—
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—21no—
563C2×#121—21no—
564C2×#121—21no—
565C2×#121—21no—
566C2×#121—21no—
567C2×#121—21no—
568C2×#121—711no—
569C2×#121—711no—
570C2×#121C2×D7112yes—
571C2×#121C2×D7112yes—
572C2×#121C2×D7112yes—
573C2×#121C2×D7112yescomplemented
574C2×#121C2×D7112yescomplemented
575C2×#121C2×D7112yescomplemented
576C2×#120—1421no—
577C2×C4×D4—1421no—
578C2×C4×D4—1421no—
579C2×#117—711no—
580C22×C4⋊C4C2×D7111yescharacteristic, complemented
581C22×C22⋊C4—21no—
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#407—712no—
604#407—712no—
605#407—712no—
606#407—712no—
607C2×C22⋊C8—712no—
608C2×C22⋊C8—712no—
609C25—21no—
610C25C22⋊D7111yescharacteristic
611C2×#41—2844no—
612C2×#41—712no—
613C2×#41—712no—
614C2×#41—1421no—
615C2×#41—1421no—
616C22×Q8—711no—
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—21no—
626C22×D4—44no—
627C22×D4—48no—
628C22×D4—711no—
629C22×D4—1421no—
630C22×D4—1421no—
631C22×D4—1421no—
632C22×D4C22×D7112yes—
633C22×D4C22×D7112yes—
634C22×D4C22×D7112yes—
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1421no—
638C23×C4C22⋊D7111yescharacteristic
639C23×C4C22⋊D7111yescharacteristic
640C23×C4C22⋊D7111yescharacteristic
641C23×C4C22⋊D7111yescharacteristic
642C23×C4C22⋊D7111yescharacteristic
643C23×C4C22⋊D7111yescharacteristic
644C23×C4C22⋊D7111yescharacteristic
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—2844no—
656C2×M16—714no—
657C2×M16—714no—
658C22×C8—714no—
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—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—22no—
682#121—22no—
683#121—712no—
684#121—712no—
685#121—712no—
686#121—712no—
687#121—1421no—
688#121—1421no—
689#121—1421no—
690#121—1421no—
691#121C22×D7114yes—
692#121C22×D7114yes—
693#121C22×D7114yes—
694#121C22×D7114yes—
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—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—711no—
715C2×C4⋊C4—711no—
716C2×C4⋊C4—1421no—
717C2×C4⋊C4—1421no—
718C2×C4⋊C4C22×D7112yes—
719C2×C4⋊C4C22×D7112yes—
720C2×C4⋊C4C22×D7112yes—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—1421no—
728C2×C22⋊C4—1421no—
729C2×C22⋊C4—1421no—
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⋊C8—714no—
740C22⋊C8—714no—
741C22⋊C8—714no—
742C22⋊C8—714no—
743C24—24no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—42no—
748C24—42no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24—1421no—
753C24C2×C22⋊D7111yescharacteristic
754C24C2×C22⋊D7111yescharacteristic
755C24C2×C22⋊D7111yescharacteristic
756C24C2×C22⋊D7111yescharacteristic
757C24C2×C22⋊D7111yescharacteristic
758C24C2×C22⋊D7111yescharacteristic
759C24C2×C22⋊D7111yescharacteristic
760#41—2844no—
761#41—2844no—
762#41—2844no—
763#41—1428no—
764C2×Q8—2842no—
765C2×Q8—712no—
766C2×Q8—1421no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—2842no—
787C2×D4—2844no—
788C2×D4—2844no—
789C2×D4—2844no—
790C2×D4—712no—
791C2×D4—1422no—
792C2×D4—1422no—
793C2×D4—1422no—
794C2×D4—1422no—
795C2×D4—1422no—
796C2×D4—1422no—
797C2×D4—1421no—
798C2×D4C23×D7114yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
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—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—2844no—
818C22×C4—1421no—
819C22×C4—1421no—
820C22×C4—1421no—
821C22×C4—1422no—
822C22×C4—1422no—
823C22×C4C2×C22⋊D7111yescharacteristic
824C22×C4C2×C22⋊D7111yescharacteristic
825C22×C4C2×C22⋊D7111yescharacteristic
826C22×C4C2×C22⋊D7111yescharacteristic
827C22×C4C2×C22⋊D7111yescharacteristic
828C22×C4C2×C22⋊D7111yescharacteristic
829C22×C4C2×C22⋊D7111yescharacteristic
830C22×C4C2×C22⋊D7111yescharacteristic
831C22×C4C2×C22⋊D7111yescharacteristic
832C22×C4C2×C22⋊D7111yescharacteristic
833C22×C4C2×C22⋊D7111yescharacteristic
834C22×C4C2×C22⋊D7111yescharacteristic
835C22×C4C2×C22⋊D7111yescharacteristic
836C22×C4C2×C22⋊D7111yescharacteristic
837C22×C4C2×C22⋊D7111yescharacteristic
838C22×C4C2×C22⋊D7111yescharacteristic
839C22×C4C2×C22⋊D7111yescharacteristic
840C22×C4C2×C22⋊D7111yescharacteristic
841C22×C4C2×C22⋊D7111yescharacteristic
842C22×C4C2×C22⋊D7111yescharacteristic
843C22×C4C2×C22⋊D7111yescharacteristic
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—2844no—
854M16—1428no—
855C2×C8—2844no—
856C2×C8—718no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—712no—
861C4⋊C4—712no—
862C4⋊C4—1422no—
863C4⋊C4—1422no—
864C4⋊C4—1422no—
865C4⋊C4—1422no—
866C4⋊C4—1421no—
867C4⋊C4—1421no—
868C4⋊C4C23×D7114yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—1422no—
874C22⋊C4—1422no—
875C22⋊C4—1422no—
876C22⋊C4—1422no—
877C22⋊C4—1422no—
878C22⋊C4—1422no—
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—24no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—816no—
917C23—2842no—
918C23—2842no—
919C23—2842no—
920C23—1422no—
921C23#1455615414yescomplemented
922C23C22×C22⋊D7111yescharacteristic
923C23C22×C22⋊D7111yescharacteristic
924C23C22×C22⋊D7111yescharacteristic
925C23C22×C22⋊D7111yescharacteristic
926C23C22×C22⋊D7111yescharacteristic
927C23C22×C22⋊D7111yescharacteristic
928C23C22×C22⋊D7111yescharacteristic
929Q8—2842no—
930Q8—1424no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—2842no—
940D4—2844no—
941D4—2844no—
942D4—2844no—
943D4—2844no—
944D4—2844no—
945D4—2844no—
946D4—1424no—
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—24no—
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—41no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—2844no—
979C2×C4—2842no—
980C2×C4—2842no—
981C2×C4—2842no—
982C2×C4—2844no—
983C2×C4—1422no—
984C2×C4—1422no—
985C2×C4—1422no—
986C2×C4C22×C22⋊D7111yescharacteristic
987C2×C4C22×C22⋊D7111yescharacteristic
988C2×C4C22×C22⋊D7111yescharacteristic
989C2×C4C22×C22⋊D7111yescharacteristic
990C2×C4C22×C22⋊D7111yescharacteristic
991C2×C4C22×C22⋊D7111yescharacteristic
992C2×C4C22×C22⋊D7111yescharacteristic
993C2×C4#1455617314yes—
994C2×C4C24×D7111yescharacteristic
995C8—1428no—
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—44no—
1020C22—44no—
1021C22—44no—
1022C22—88no—
1023C22—88no—
1024C22—88no—
1025C22—2842no—
1026C22—2842no—
1027C22—2842no—
1028C22—5684no—
1029C22#1798655812yes—
1030C22C2×#1455615412yes—
1031C22C2×#1455615412yes—
1032C22C2×#1455615412yes—
1033C22#1798679712yes—
1034C22C23×C22⋊D7111yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—2842no—
1043C4—2842no—
1044C4—2842no—
1045C4#1798655812yes—
1046C4C2×#1455617312yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—5682no—
1056C2C2×#1798655811yescharacteristic
1057C2C22×#1455615411yescharacteristic
1058C2C2×#1798679711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC22×#121×C71C2
socleC22×C71C23×D4
hypercenterC22×#121D71
hypocenterC71#60750
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#17986510C2semidirect
2. #22599154C2semidirect
3. #22599146C2semidirect
4. #22599137C2semidirect
5. #22599105C2semidirect
6. #22599097C2semidirect
7. #22599088C2semidirect
8. #22598276C2semidirect
9. #22598263C2semidirect
10. #22597955C2semidirect
11. #22597590C2semidirect
12. #22597567C2semidirect
13. C2×#17985963C2semidirect
14. C22×#121×C71C2semidirect
15. C22×#11765865C22semidirect
16. C2×#14556154C22semidirect
17. C22×#11765849C22semidirect
23. #17986510C22semidirect
24. #17986510C22semidirect
25. #17986510C22semidirect
27. C2×#14556107C22semidirect
28. C2×#14556107C22semidirect
29. C2×#14556102C22semidirect
30. C2×#14556102C22semidirect
34. C2×#14556087C22semidirect
35. #17986334C22semidirect
36. #17986329C22semidirect
37. #17986320C22semidirect
38. #17986317C22semidirect
39. #17986315C22semidirect
40. #17986312C22semidirect
41. #17986310C22semidirect
42. #17986250C22semidirect
43. #17986243C22semidirect
44. #17986233C22semidirect
45. #17986226C22semidirect
46. #17986150C22semidirect
47. #17986150C22semidirect
48. #17986142C22semidirect
49. #17986137C22semidirect
50. #17986133C22semidirect
51. #17986133C22semidirect
52. #17986132C22semidirect
53. #17986039C22semidirect
54. #17986004C22semidirect
55. #17985998C22semidirect
56. #17985963C22semidirect
57. #17985963C22semidirect
58. #17985963C22semidirect
59. #17985963C22semidirect
60. C2×C22⋊(C71⋊C8)C22semidirect
61. C2×C22⋊(C71⋊C8)C22semidirect
63. C23×D4×C71C22semidirect
74. C2×#121×C71C22semidirect
75. C2×#121×C71C22semidirect
76. C2×#121×C71C22semidirect
77. C22×C4⋊C4×C71C22semidirect
83. C2×#11765865C23semidirect
84. C22×Dic142C23semidirect
85. C22×D284C23semidirect
91. C2×#11765853C23semidirect
92. C2×#11765850C23semidirect
95. C2×#11765849C23semidirect
96. C22×C71⋊C8C23semidirect
107. #14556107C23semidirect
108. #14556107C23semidirect
115. #14556102C23semidirect
116. #14556102C23semidirect
132. #14556087C23semidirect
133. C2×C4⋊Dic71C23semidirect
134. C2×C4⋊Dic71C23semidirect
143. #14556061C23semidirect
144. #14556059C23semidirect
145. #14556051C23semidirect
146. #14556049C23semidirect
147. #14556049C23semidirect
148. #14556048C23semidirect
151. C22⋊(C71⋊C8)C23semidirect
152. C22⋊(C71⋊C8)C23semidirect
387. C23×C71AGL(1,ℤ/8)semidirect
531. C22×#121D71semidirect
544. C71#60750semidirect
547. C23×D4C2×D71semidirect
573. C2×#121C2×D71semidirect
574. C2×#121C2×D71semidirect
575. C2×#121C2×D71semidirect
580. C22×C4⋊C4C2×D71semidirect
921. C23#14556154semidirect

Maximal subgroups

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

subgroupindex
C2×#179865102
#225991542
#225991462
#225991372
#225991052
#225990972
#225990882
#225982762
#225982632
#225979552
#225975902
#225975672
C2×#179859632
C22×#121×C712
#6075071