Finite Group Databasebeta

← #31726574

Subgroups — #31726574

Order 17152.

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×#16863907C211yesmaximal, characteristic, complemented
2#22571023C214yesmaximal, complemented
3#22571015C212yesmaximal, complemented
4#22571006C212yesmaximal, complemented
5#22570974C214yesmaximal, complemented
6#22570966C212yesmaximal, complemented
7#22570957C212yesmaximal, complemented
8#22570145C212yesmaximal, complemented
9#22570132C212yesmaximal, complemented
10#22569824C214yesmaximal, complemented
11#22569459C212yesmaximal, complemented
12#22569436C212yesmaximal, complemented
13C2×#16863360C211yesmaximal, characteristic, complemented
14C22×#121×C67C211yesmaximal, characteristic, complemented
15C22×#11761628C2211yescharacteristic, complemented
16C2×#14524069C2214yescomplemented
17C22×#11761612C2212yescomplemented
18#16863907—21no—
19#16863907—21no—
20#16863907—21no—
21#16863907—21no—
22#16863907C2212yes—
23#16863907C2212yescomplemented
24#16863907C2212yescomplemented
25#16863907C2212yescomplemented
26C2×#14524026—21no—
27C2×#14524022C2211yescharacteristic, complemented
28C2×#14524022C2211yescharacteristic, complemented
29C2×#14524017C2211yescharacteristic, complemented
30C2×#14524017C2211yescharacteristic, complemented
31C2×#14524012—21no—
32C2×C4×C22⋊D67—21no—
33C2×C4×C22⋊D67—21no—
34C2×#14524002C2211yescharacteristic, complemented
35#16863731C2214yescomplemented
36#16863726C2214yescomplemented
37#16863717C2218yescomplemented
38#16863714C2214yescomplemented
39#16863712C2214yescomplemented
40#16863709C2214yescomplemented
41#16863707C2214yescomplemented
42#16863647C2218yescomplemented
43#16863640C2218yescomplemented
44#16863630C2218yescomplemented
45#16863623C2218yescomplemented
46#16863547C2214yescomplemented
47#16863547C2214yescomplemented
48#16863539C2218yescomplemented
49#16863534C2214yescomplemented
50#16863530C2214yescomplemented
51#16863530C2214yescomplemented
52#16863529C2214yescomplemented
53#16863436C2214yescomplemented
54#16863401C2214yescomplemented
55#16863395C2214yescomplemented
56#16863360C2212yescomplemented
57#16863360C2212yescomplemented
58#16863360C2212yescomplemented
59#16863360C2212yescomplemented
60C2×C22⋊(C67⋊C8)C2212yescomplemented
61C2×C22⋊(C67⋊C8)C2212yescomplemented
62C23×D4×C67—21no—
63C23×D4×C67C2211yescharacteristic, complemented
64C24×C4×C67C2211yescharacteristic
65C2×#121×C67—21no—
66C2×#121×C67—21no—
67C2×#121×C67—21no—
68C2×#121×C67—21no—
69C2×#121×C67—21no—
70C2×#121×C67—21no—
71C2×#121×C67C2212yes—
72C2×#121×C67C2212yes—
73C2×#121×C67C2212yes—
74C2×#121×C67C2212yescomplemented
75C2×#121×C67C2212yescomplemented
76C2×#121×C67C2212yescomplemented
77C22×C4⋊C4×C67C2211yescharacteristic, complemented
78C22×C22⋊C4×C67—21no—
79C2×#11761628—21no—
80C2×#11761628—21no—
81C2×#11761628—44no—
82C2×#11761628C2312yes—
83C2×#11761628C2312yescomplemented
84C22×Dic134C2311yescharacteristic, complemented
85C22×D268C2311yescharacteristic, complemented
86C22×C22⋊D67—21no—
87C22×C22⋊D67—21no—
88C22×C22⋊D67—21no—
89C22×C4×D67—21no—
90#14524069—48no—
91C2×#11761616C2318yescomplemented
92C2×#11761613C2318yescomplemented
93C2×#11761612—44no—
94C2×#11761612C2314yes—
95C2×#11761612C2314yescomplemented
96C22×C67⋊C8C2314yescomplemented
97#14524026—22no—
98#14524026—22no—
99#14524026—22no—
100#14524026—22no—
101#14524022—21no—
102#14524022—21no—
103#14524022—21no—
104#14524022—21no—
105#14524022C2312yes—
106#14524022C2312yes—
107#14524022C2312yescomplemented
108#14524022C2312yescomplemented
109#14524017—21no—
110#14524017—21no—
111#14524017—21no—
112#14524017—21no—
113#14524017C2312yes—
114#14524017C2312yes—
115#14524017C2312yescomplemented
116#14524017C2312yescomplemented
117#14524012—22no—
118#14524012—22no—
119#14524012—22no—
120#14524012—22no—
121C4×C22⋊D67—22no—
122C4×C22⋊D67—22no—
123C4×C22⋊D67—22no—
124C4×C22⋊D67—22no—
125C4×C22⋊D67—22no—
126C4×C22⋊D67—22no—
127C4×C22⋊D67—22no—
128C4×C22⋊D67—22no—
129#14524002—21no—
130#14524002—21no—
131#14524002C2312yes—
132#14524002C2312yescomplemented
133C2×C4⋊Dic67C2311yescharacteristic, complemented
134C2×C4⋊Dic67C2311yescharacteristic, complemented
135C2×Dic67⋊C4—21no—
136C2×Dic67⋊C4—21no—
137C2×C22⋊Dic67—21no—
138C2×C22⋊Dic67—21no—
139C2×C22⋊Dic67—21no—
140C2×(C2×D67)⋊C4—21no—
141C2×(C2×D67)⋊C4—21no—
142C2×C4×Dic67—21no—
143#14523976C2318yescomplemented
144#14523974C2318yescomplemented
145#14523966C2318yescomplemented
146#14523964C2318yescomplemented
147#14523964C2318yescomplemented
148#14523963C2318yescomplemented
149C22⋊(C67⋊C8)C2314yes—
150C22⋊(C67⋊C8)C2314yes—
151C22⋊(C67⋊C8)C2314yescomplemented
152C22⋊(C67⋊C8)C2314yescomplemented
153C25×C67—21no—
154C25×C67D411yescharacteristic
155C22×D4×C67—22no—
156C22×D4×C67—22no—
157C22×D4×C67—22no—
158C22×D4×C67—22no—
159C22×D4×C67—22no—
160C22×D4×C67—22no—
161C22×D4×C67—21no—
162C22×D4×C67—21no—
163C22×D4×C67—21no—
164C22×D4×C67—44no—
165C22×D4×C67—48no—
166C22×D4×C67C2312yes—
167C22×D4×C67C2312yes—
168C22×D4×C67C2312yes—
169C23×C4×C67—21no—
170C23×C4×C67—44no—
171C23×C4×C67D411yescharacteristic
172C23×C4×C67D411yescharacteristic
173C23×C4×C67D411yescharacteristic
174C23×C4×C67D411yescharacteristic
175C23×C4×C67D411yescharacteristic
176C23×C4×C67D411yescharacteristic
177C23×C4×C67D411yescharacteristic
178C23×C4×C67C2311yescharacteristic
179C23×C4×C67C2311yescharacteristic
180C23×C4×C67C2311yescharacteristic
181C23×C4×C67C2311yescharacteristic
182C23×C4×C67C2311yescharacteristic
183C23×C4×C67C2311yescharacteristic
184C23×C4×C67C2311yescharacteristic
185#121×C67—22no—
186#121×C67—22no—
187#121×C67—22no—
188#121×C67—22no—
189#121×C67—22no—
190#121×C67—22no—
191#121×C67—22no—
192#121×C67—22no—
193#121×C67—22no—
194#121×C67—22no—
195#121×C67—22no—
196#121×C67—22no—
197#121×C67C2314yes—
198#121×C67C2314yes—
199#121×C67C2314yes—
200#121×C67C2314yes—
201C2×C4⋊C4×C67—21no—
202C2×C4⋊C4×C67—21no—
203C2×C4⋊C4×C67—21no—
204C2×C4⋊C4×C67C2312yes—
205C2×C4⋊C4×C67C2312yes—
206C2×C4⋊C4×C67C2312yes—
207C2×C22⋊C4×C67—22no—
208C2×C22⋊C4×C67—22no—
209C2×C22⋊C4×C67—22no—
210C2×C22⋊C4×C67—22no—
211C2×C22⋊C4×C67—22no—
212C2×C22⋊C4×C67—22no—
213C23×D67—21no—
214#11761628—28no—
215#11761628—44no—
216#11761628—44no—
217#11761628—44no—
218C2×Dic134—21no—
219C2×Dic134—42no—
220C2×Dic134C2412yes—
221C2×D268—21no—
222C2×D268—42no—
223C2×D268C2412yes—
224C2×C22⋊D67—22no—
225C2×C22⋊D67—22no—
226C2×C22⋊D67—22no—
227C2×C22⋊D67—22no—
228C2×C22⋊D67—22no—
229C2×C22⋊D67—22no—
230C2×C22⋊D67—44no—
231C2×C22⋊D67—44no—
232C2×C22⋊D67—44no—
233C22×Dic67—21no—
234C22×Dic67—21no—
235C22×Dic67—21no—
236C2×C4×D67—22no—
237C2×C4×D67—22no—
238C2×C4×D67—44no—
239#11761616—48no—
240#11761613—48no—
241#11761612—28no—
242#11761612—44no—
243C2×C67⋊C8—44no—
244C2×C67⋊C8C2418yes—
245C4⋊Dic67—21no—
246C4⋊Dic67—21no—
247C4⋊Dic67C2412yes—
248C4⋊Dic67C2412yes—
249Dic67⋊C4—22no—
250Dic67⋊C4—22no—
251Dic67⋊C4—22no—
252Dic67⋊C4—22no—
253C22⋊Dic67—22no—
254C22⋊Dic67—22no—
255C22⋊Dic67—22no—
256C22⋊Dic67—22no—
257C22⋊Dic67—22no—
258C22⋊Dic67—22no—
259(C2×D67)⋊C4—22no—
260(C2×D67)⋊C4—22no—
261(C2×D67)⋊C4—22no—
262(C2×D67)⋊C4—22no—
263C4×Dic67—22no—
264C4×Dic67—22no—
265C24×C67—24no—
266C24×C67—22no—
267C24×C67—22no—
268C24×C67—22no—
269C24×C67—42no—
270C24×C67—42no—
271C24×C67—44no—
272C24×C67—44no—
273C24×C67—44no—
274C24×C67C2×D411yescharacteristic
275C24×C67C2×D411yescharacteristic
276C24×C67C2×D411yescharacteristic
277C24×C67C2×D411yescharacteristic
278C24×C67C2×D411yescharacteristic
279C24×C67C2×D411yescharacteristic
280C24×C67C2×D411yescharacteristic
281C2×D4×C67—24no—
282C2×D4×C67—24no—
283C2×D4×C67—24no—
284C2×D4×C67—24no—
285C2×D4×C67—22no—
286C2×D4×C67—22no—
287C2×D4×C67—22no—
288C2×D4×C67—28no—
289C2×D4×C67—44no—
290C2×D4×C67—44no—
291C2×D4×C67—44no—
292C2×D4×C67—44no—
293C2×D4×C67—44no—
294C2×D4×C67—48no—
295C2×D4×C67—48no—
296C2×D4×C67—48no—
297C2×D4×C67—48no—
298C2×D4×C67—48no—
299C2×D4×C67—48no—
300C2×D4×C67C2414yes—
301C22×C4×C67—24no—
302C22×C4×C67—24no—
303C22×C4×C67—24no—
304C22×C4×C67—22no—
305C22×C4×C67—22no—
306C22×C4×C67—22no—
307C22×C4×C67—42no—
308C22×C4×C67—42no—
309C22×C4×C67—42no—
310C22×C4×C67—42no—
311C22×C4×C67—42no—
312C22×C4×C67—42no—
313C22×C4×C67—42no—
314C22×C4×C67—42no—
315C22×C4×C67—42no—
316C22×C4×C67—42no—
317C22×C4×C67—42no—
318C22×C4×C67—44no—
319C22×C4×C67C2×D411yescharacteristic
320C22×C4×C67C2×D411yescharacteristic
321C22×C4×C67C2×D411yescharacteristic
322C22×C4×C67C2×D411yescharacteristic
323C22×C4×C67C2×D411yescharacteristic
324C22×C4×C67C2×D411yescharacteristic
325C22×C4×C67C2×D411yescharacteristic
326C22×C4×C67C2×D411yescharacteristic
327C22×C4×C67C2×D411yescharacteristic
328C22×C4×C67C2×D411yescharacteristic
329C22×C4×C67C2×D411yescharacteristic
330C22×C4×C67C2×D411yescharacteristic
331C22×C4×C67C2×D411yescharacteristic
332C22×C4×C67C2×D411yescharacteristic
333C22×C4×C67C2×D411yescharacteristic
334C22×C4×C67C2×D411yescharacteristic
335C22×C4×C67C2×D411yescharacteristic
336C22×C4×C67C2×D411yescharacteristic
337C22×C4×C67C2×D411yescharacteristic
338C22×C4×C67C2×D411yescharacteristic
339C22×C4×C67C2×D411yescharacteristic
340C22×C4×C67C2411yescharacteristic
341C22×C4×C67C2411yescharacteristic
342C22×C4×C67C2411yescharacteristic
343C22×C4×C67C2411yescharacteristic
344C22×C4×C67C2411yescharacteristic
345C22×C4×C67C2411yescharacteristic
346C22×C4×C67C2411yescharacteristic
347C4⋊C4×C67—22no—
348C4⋊C4×C67—22no—
349C4⋊C4×C67—22no—
350C4⋊C4×C67C2414yes—
351C22⋊C4×C67—24no—
352C22⋊C4×C67—24no—
353C22⋊C4×C67—24no—
354C22⋊C4×C67—24no—
355C23×C67—22no—
356C23×C67—22no—
357C23×C67—22no—
358C23×C67—22no—
359C23×C67—22no—
360C23×C67—22no—
361C23×C67—22no—
362C23×C67—22no—
363C23×C67—22no—
364C23×C67—22no—
365C23×C67—22no—
366C23×C67—22no—
367C23×C67—24no—
368C23×C67—41no—
369C23×C67—41no—
370C23×C67—41no—
371C23×C67—41no—
372C23×C67—41no—
373C23×C67—41no—
374C23×C67—41no—
375C23×C67—41no—
376C23×C67—416no—
377C23×C67—44no—
378C23×C67—44no—
379C23×C67—44no—
380C23×C67—44no—
381C23×C67—44no—
382C23×C67—44no—
383C23×C67—44no—
384C23×C67—44no—
385C23×C67—44no—
386C23×C67—816no—
387C23×C67AGL(1,ℤ/8)14yescomplemented
388C23×C67C22×D411yescharacteristic
389C23×C67C22×D411yescharacteristic
390C23×C67C22×D411yescharacteristic
391C23×C67C22×D411yescharacteristic
392C23×C67C22×D411yescharacteristic
393C23×C67C22×D411yescharacteristic
394C23×C67C22×D411yescharacteristic
395C22×D67—22no—
396C22×D67—42no—
397C22×D67—42no—
398C22×D67—42no—
399D4×C67—28no—
400D4×C67—44no—
401D4×C67—44no—
402D4×C67—48no—
403D4×C67—48no—
404D4×C67—48no—
405D4×C67—48no—
406D4×C67—44no—
407C2×C4×C67—22no—
408C2×C4×C67—22no—
409C2×C4×C67—22no—
410C2×C4×C67—22no—
411C2×C4×C67—22no—
412C2×C4×C67—22no—
413C2×C4×C67—22no—
414C2×C4×C67—22no—
415C2×C4×C67—22no—
416C2×C4×C67—22no—
417C2×C4×C67—22no—
418C2×C4×C67—22no—
419C2×C4×C67—22no—
420C2×C4×C67—22no—
421C2×C4×C67—22no—
422C2×C4×C67—24no—
423C2×C4×C67—41no—
424C2×C4×C67—41no—
425C2×C4×C67—41no—
426C2×C4×C67—41no—
427C2×C4×C67—41no—
428C2×C4×C67—41no—
429C2×C4×C67—41no—
430C2×C4×C67—41no—
431C2×C4×C67—41no—
432C2×C4×C67—41no—
433C2×C4×C67—41no—
434C2×C4×C67—41no—
435C2×C4×C67—44no—
436C2×C4×C67—44no—
437C2×C4×C67—44no—
438C2×C4×C67C22×D411yescharacteristic
439C2×C4×C67C22×D411yescharacteristic
440C2×C4×C67C22×D411yescharacteristic
441C2×C4×C67C22×D411yescharacteristic
442C2×C4×C67C22×D411yescharacteristic
443C2×C4×C67C22×D411yescharacteristic
444C2×C4×C67C22×D411yescharacteristic
445C2×C4×C67H(5,𝔽2)14yes—
446C2×C4×C67C2511yescharacteristic
447C22⋊D67—44no—
448C22⋊D67—44no—
449C22⋊D67—44no—
450C22⋊D67—44no—
451C22⋊D67—44no—
452C22⋊D67—44no—
453C2×Dic67—22no—
454C2×Dic67—22no—
455C2×Dic67—22no—
456C2×Dic67—42no—
457C2×Dic67—42no—
458C2×Dic67—42no—
459D268—24no—
460D268—42no—
461C4×D67—44no—
462C4×D67—44no—
463Dic134—24no—
464Dic134—42no—
465C67⋊C8—28no—
466C22×C67—28no—
467C22×C67—21no—
468C22×C67—21no—
469C22×C67—21no—
470C22×C67—21no—
471C22×C67—21no—
472C22×C67—21no—
473C22×C67—21no—
474C22×C67—21no—
475C22×C67—21no—
476C22×C67—21no—
477C22×C67—21no—
478C22×C67—21no—
479C22×C67—21no—
480C22×C67—21no—
481C22×C67—21no—
482C22×C67—21no—
483C22×C67—44no—
484C22×C67—44no—
485C22×C67—44no—
486C22×C67—44no—
487C22×C67—44no—
488C22×C67—44no—
489C22×C67—44no—
490C22×C67—44no—
491C22×C67—44no—
492C22×C67—88no—
493C22×C67—88no—
494C22×C67—88no—
495C22×C67#53412yes—
496C22×C67C2×AGL(1,ℤ/8)12yes—
497C22×C67C2×AGL(1,ℤ/8)12yes—
498C22×C67C2×AGL(1,ℤ/8)12yes—
499C22×C67#57512yes—
500C22×C67C23×D411yescharacteristic
501C2×D67—42no—
502C2×D67—42no—
503C2×D67—42no—
504C2×D67—84no—
505C4×C67—21no—
506C4×C67—21no—
507C4×C67—21no—
508C4×C67—21no—
509C4×C67—21no—
510C4×C67—21no—
511C4×C67—44no—
512C4×C67#53412yes—
513C4×C67C2×H(5,𝔽2)12yes—
514Dic67—42no—
515Dic67—42no—
516Dic67—42no—
517#60750—671nomaximal, Sylow
518C2×C67—22no—
519C2×C67—22no—
520C2×C67—22no—
521C2×C67—22no—
522C2×C67—22no—
523C2×C67—41no—
524C2×C67—41no—
525C2×C67—84no—
526C2×C67C2×#53411yescharacteristic
527C2×C67C22×AGL(1,ℤ/8)11yescharacteristic
528C2×C67C2×#57511yescharacteristic
529D67—82no—
530C2×#525—671no—
531C22×#121D6711yescharacteristic, complemented
532#3194—674no—
533#3193—672no—
534#3192—672no—
535#3188—674no—
536#3187—672no—
537#3186—672no—
538#3094—672no—
539#3092—672no—
540#3055—674no—
541#3006—672no—
542#3003—672no—
543C2×#407—671no—
544C67#6075011yescharacteristic, complemented, Sylow
545C22×#41—671no—
546C23×D4—21no—
547C23×D4C2×D6711yescharacteristic, complemented
548C24×C4C2×D6711yescharacteristic
549C2×AGL(1,ℤ/8)—674no—
550C22×M16—672no—
551#525—672no—
552#525—672no—
553#525—672no—
554#525—672no—
555#525—1341no—
556#525—1341no—
557#525—1341no—
558#525—1341no—
559C2×#123—1341no—
560C2×C22⋊Q8—671no—
561C2×C22⋊Q8—671no—
562C2×#121—21no—
563C2×#121—21no—
564C2×#121—21no—
565C2×#121—21no—
566C2×#121—21no—
567C2×#121—21no—
568C2×#121—671no—
569C2×#121—671no—
570C2×#121C2×D6712yes—
571C2×#121C2×D6712yes—
572C2×#121C2×D6712yes—
573C2×#121C2×D6712yescomplemented
574C2×#121C2×D6712yescomplemented
575C2×#121C2×D6712yescomplemented
576C2×#120—1341no—
577C2×C4×D4—1341no—
578C2×C4×D4—1341no—
579C2×#117—671no—
580C22×C4⋊C4C2×D6711yescharacteristic, complemented
581C22×C22⋊C4—21no—
582#484—674no—
583#483—674no—
584#482—678no—
585#481—674no—
586#481—674no—
587#480—674no—
588#480—674no—
589#469—678no—
590#468—678no—
591#466—678no—
592#465—678no—
593#450—674no—
594#450—674no—
595#449—678no—
596#448—674no—
597#447—674no—
598#447—674no—
599#447—674no—
600#428—674no—
601#418—674no—
602#417—674no—
603#407—672no—
604#407—672no—
605#407—672no—
606#407—672no—
607C2×C22⋊C8—672no—
608C2×C22⋊C8—672no—
609C25—21no—
610C25C22⋊D6711yescharacteristic
611C2×#41—2684no—
612C2×#41—672no—
613C2×#41—672no—
614C2×#41—1341no—
615C2×#41—1341no—
616C22×Q8—671no—
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—671no—
629C22×D4—1341no—
630C22×D4—1341no—
631C22×D4—1341no—
632C22×D4C22×D6712yes—
633C22×D4C22×D6712yes—
634C22×D4C22×D6712yes—
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1341no—
638C23×C4C22⋊D6711yescharacteristic
639C23×C4C22⋊D6711yescharacteristic
640C23×C4C22⋊D6711yescharacteristic
641C23×C4C22⋊D6711yescharacteristic
642C23×C4C22⋊D6711yescharacteristic
643C23×C4C22⋊D6711yescharacteristic
644C23×C4C22⋊D6711yescharacteristic
645C23×C4C22×D6711yescharacteristic
646C23×C4C22×D6711yescharacteristic
647C23×C4C22×D6711yescharacteristic
648C23×C4C22×D6711yescharacteristic
649C23×C4C22×D6711yescharacteristic
650C23×C4C22×D6711yescharacteristic
651C23×C4C22×D6711yescharacteristic
652AGL(1,ℤ/8)—2688no—
653C2×SD16—678no—
654C2×D8—678no—
655C2×M16—2684no—
656C2×M16—674no—
657C2×M16—674no—
658C22×C8—674no—
659#123—1342no—
660#123—1342no—
661#123—1342no—
662#123—1342no—
663C22⋊Q8—672no—
664C22⋊Q8—672no—
665C22⋊Q8—672no—
666C22⋊Q8—672no—
667C22⋊Q8—1341no—
668C22⋊Q8—1341no—
669C22⋊Q8—1341no—
670C22⋊Q8—1341no—
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—672no—
684#121—672no—
685#121—672no—
686#121—672no—
687#121—1341no—
688#121—1341no—
689#121—1341no—
690#121—1341no—
691#121C22×D6714yes—
692#121C22×D6714yes—
693#121C22×D6714yes—
694#121C22×D6714yes—
695#120—1342no—
696#120—1342no—
697#120—1342no—
698#120—1342no—
699C4×D4—1342no—
700C4×D4—1342no—
701C4×D4—1342no—
702C4×D4—1342no—
703C4×D4—1342no—
704C4×D4—1342no—
705C4×D4—1342no—
706C4×D4—1342no—
707#117—672no—
708#117—672no—
709#117—1341no—
710#117—1341no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—671no—
715C2×C4⋊C4—671no—
716C2×C4⋊C4—1341no—
717C2×C4⋊C4—1341no—
718C2×C4⋊C4C22×D6712yes—
719C2×C4⋊C4C22×D6712yes—
720C2×C4⋊C4C22×D6712yes—
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—1341no—
728C2×C22⋊C4—1341no—
729C2×C22⋊C4—1341no—
730C2×C22⋊C4—1341no—
731C2×C22⋊C4—1341no—
732C2×C42—1341no—
733#107—678no—
734#106—678no—
735#103—678no—
736#102—678no—
737#102—678no—
738#102—678no—
739C22⋊C8—674no—
740C22⋊C8—674no—
741C22⋊C8—674no—
742C22⋊C8—674no—
743C24—24no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—42no—
748C24—42no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24—1341no—
753C24C2×C22⋊D6711yescharacteristic
754C24C2×C22⋊D6711yescharacteristic
755C24C2×C22⋊D6711yescharacteristic
756C24C2×C22⋊D6711yescharacteristic
757C24C2×C22⋊D6711yescharacteristic
758C24C2×C22⋊D6711yescharacteristic
759C24C2×C22⋊D6711yescharacteristic
760#41—2684no—
761#41—2684no—
762#41—2684no—
763#41—1348no—
764C2×Q8—2682no—
765C2×Q8—672no—
766C2×Q8—1341no—
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—2682no—
787C2×D4—2684no—
788C2×D4—2684no—
789C2×D4—2684no—
790C2×D4—672no—
791C2×D4—1342no—
792C2×D4—1342no—
793C2×D4—1342no—
794C2×D4—1342no—
795C2×D4—1342no—
796C2×D4—1342no—
797C2×D4—1341no—
798C2×D4C23×D6714yes—
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—2684no—
818C22×C4—1341no—
819C22×C4—1341no—
820C22×C4—1341no—
821C22×C4—1342no—
822C22×C4—1342no—
823C22×C4C2×C22⋊D6711yescharacteristic
824C22×C4C2×C22⋊D6711yescharacteristic
825C22×C4C2×C22⋊D6711yescharacteristic
826C22×C4C2×C22⋊D6711yescharacteristic
827C22×C4C2×C22⋊D6711yescharacteristic
828C22×C4C2×C22⋊D6711yescharacteristic
829C22×C4C2×C22⋊D6711yescharacteristic
830C22×C4C2×C22⋊D6711yescharacteristic
831C22×C4C2×C22⋊D6711yescharacteristic
832C22×C4C2×C22⋊D6711yescharacteristic
833C22×C4C2×C22⋊D6711yescharacteristic
834C22×C4C2×C22⋊D6711yescharacteristic
835C22×C4C2×C22⋊D6711yescharacteristic
836C22×C4C2×C22⋊D6711yescharacteristic
837C22×C4C2×C22⋊D6711yescharacteristic
838C22×C4C2×C22⋊D6711yescharacteristic
839C22×C4C2×C22⋊D6711yescharacteristic
840C22×C4C2×C22⋊D6711yescharacteristic
841C22×C4C2×C22⋊D6711yescharacteristic
842C22×C4C2×C22⋊D6711yescharacteristic
843C22×C4C2×C22⋊D6711yescharacteristic
844C22×C4C23×D6711yescharacteristic
845C22×C4C23×D6711yescharacteristic
846C22×C4C23×D6711yescharacteristic
847C22×C4C23×D6711yescharacteristic
848C22×C4C23×D6711yescharacteristic
849C22×C4C23×D6711yescharacteristic
850C22×C4C23×D6711yescharacteristic
851SD16—2688no—
852D8—2688no—
853M16—2684no—
854M16—1348no—
855C2×C8—2684no—
856C2×C8—678no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—672no—
861C4⋊C4—672no—
862C4⋊C4—1341no—
863C4⋊C4—1341no—
864C4⋊C4—1342no—
865C4⋊C4—1342no—
866C4⋊C4—1342no—
867C4⋊C4—1342no—
868C4⋊C4C23×D6714yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—1342no—
874C22⋊C4—1342no—
875C22⋊C4—1342no—
876C22⋊C4—1342no—
877C22⋊C4—1342no—
878C22⋊C4—1342no—
879C22⋊C4—1342no—
880C22⋊C4—1342no—
881C22⋊C4—1342no—
882C22⋊C4—1342no—
883C42—1342no—
884C42—1342no—
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—2682no—
918C23—2682no—
919C23—2682no—
920C23—1342no—
921C23#1452406914yescomplemented
922C23C22×C22⋊D6711yescharacteristic
923C23C22×C22⋊D6711yescharacteristic
924C23C22×C22⋊D6711yescharacteristic
925C23C22×C22⋊D6711yescharacteristic
926C23C22×C22⋊D6711yescharacteristic
927C23C22×C22⋊D6711yescharacteristic
928C23C22×C22⋊D6711yescharacteristic
929Q8—2682no—
930Q8—1344no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—2682no—
940D4—2684no—
941D4—2684no—
942D4—2684no—
943D4—2684no—
944D4—2684no—
945D4—2684no—
946D4—1344no—
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—2684no—
979C2×C4—2682no—
980C2×C4—2682no—
981C2×C4—2682no—
982C2×C4—2684no—
983C2×C4—1342no—
984C2×C4—1342no—
985C2×C4—1342no—
986C2×C4C22×C22⋊D6711yescharacteristic
987C2×C4C22×C22⋊D6711yescharacteristic
988C2×C4C22×C22⋊D6711yescharacteristic
989C2×C4C22×C22⋊D6711yescharacteristic
990C2×C4C22×C22⋊D6711yescharacteristic
991C2×C4C22×C22⋊D6711yescharacteristic
992C2×C4C22×C22⋊D6711yescharacteristic
993C2×C4#1452408814yes—
994C2×C4C24×D6711yescharacteristic
995C8—1348no—
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—2682no—
1026C22—2682no—
1027C22—2682no—
1028C22—5364no—
1029C22#1686395512yes—
1030C22C2×#1452406912yes—
1031C22C2×#1452406912yes—
1032C22C2×#1452406912yes—
1033C22#1686419412yes—
1034C22C23×C22⋊D6711yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—2682no—
1043C4—2682no—
1044C4—2682no—
1045C4#1686395512yes—
1046C4C2×#1452408812yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—5362no—
1056C2C2×#1686395511yescharacteristic
1057C2C22×#1452406911yescharacteristic
1058C2C2×#1686419411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC22×#121×C67C2
socleC22×C67C23×D4
hypercenterC22×#121D67
hypocenterC67#60750
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16863907C2semidirect
2. #22571023C2semidirect
3. #22571015C2semidirect
4. #22571006C2semidirect
5. #22570974C2semidirect
6. #22570966C2semidirect
7. #22570957C2semidirect
8. #22570145C2semidirect
9. #22570132C2semidirect
10. #22569824C2semidirect
11. #22569459C2semidirect
12. #22569436C2semidirect
13. C2×#16863360C2semidirect
14. C22×#121×C67C2semidirect
15. C22×#11761628C22semidirect
16. C2×#14524069C22semidirect
17. C22×#11761612C22semidirect
23. #16863907C22semidirect
24. #16863907C22semidirect
25. #16863907C22semidirect
27. C2×#14524022C22semidirect
28. C2×#14524022C22semidirect
29. C2×#14524017C22semidirect
30. C2×#14524017C22semidirect
34. C2×#14524002C22semidirect
35. #16863731C22semidirect
36. #16863726C22semidirect
37. #16863717C22semidirect
38. #16863714C22semidirect
39. #16863712C22semidirect
40. #16863709C22semidirect
41. #16863707C22semidirect
42. #16863647C22semidirect
43. #16863640C22semidirect
44. #16863630C22semidirect
45. #16863623C22semidirect
46. #16863547C22semidirect
47. #16863547C22semidirect
48. #16863539C22semidirect
49. #16863534C22semidirect
50. #16863530C22semidirect
51. #16863530C22semidirect
52. #16863529C22semidirect
53. #16863436C22semidirect
54. #16863401C22semidirect
55. #16863395C22semidirect
56. #16863360C22semidirect
57. #16863360C22semidirect
58. #16863360C22semidirect
59. #16863360C22semidirect
60. C2×C22⋊(C67⋊C8)C22semidirect
61. C2×C22⋊(C67⋊C8)C22semidirect
63. C23×D4×C67C22semidirect
74. C2×#121×C67C22semidirect
75. C2×#121×C67C22semidirect
76. C2×#121×C67C22semidirect
77. C22×C4⋊C4×C67C22semidirect
83. C2×#11761628C23semidirect
84. C22×Dic134C23semidirect
85. C22×D268C23semidirect
91. C2×#11761616C23semidirect
92. C2×#11761613C23semidirect
95. C2×#11761612C23semidirect
96. C22×C67⋊C8C23semidirect
107. #14524022C23semidirect
108. #14524022C23semidirect
115. #14524017C23semidirect
116. #14524017C23semidirect
132. #14524002C23semidirect
133. C2×C4⋊Dic67C23semidirect
134. C2×C4⋊Dic67C23semidirect
143. #14523976C23semidirect
144. #14523974C23semidirect
145. #14523966C23semidirect
146. #14523964C23semidirect
147. #14523964C23semidirect
148. #14523963C23semidirect
151. C22⋊(C67⋊C8)C23semidirect
152. C22⋊(C67⋊C8)C23semidirect
387. C23×C67AGL(1,ℤ/8)semidirect
531. C22×#121D67semidirect
544. C67#60750semidirect
547. C23×D4C2×D67semidirect
573. C2×#121C2×D67semidirect
574. C2×#121C2×D67semidirect
575. C2×#121C2×D67semidirect
580. C22×C4⋊C4C2×D67semidirect
921. C23#14524069semidirect

Maximal subgroups

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

subgroupindex
C2×#168639072
#225710232
#225710152
#225710062
#225709742
#225709662
#225709572
#225701452
#225701322
#225698242
#225694592
#225694362
C2×#168633602
C22×#121×C672
#6075067