Finite Group Databasebeta

← #31726568

Subgroups — #31726568

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
1C22×#14524017C211yesmaximal, characteristic, complemented
2#22571019C214yesmaximal, complemented
3#22571011C212yesmaximal, complemented
4#22571006C212yesmaximal, complemented
5#22570970C214yesmaximal, complemented
6#22570962C212yesmaximal, complemented
7#22570957C212yesmaximal, complemented
8#22570149C212yesmaximal, complemented
9#22570129C212yesmaximal, complemented
10#22569830C214yesmaximal, complemented
11#22569461C212yesmaximal, complemented
12#22569435C212yesmaximal, complemented
13C2×#16863360C211yesmaximal, characteristic, complemented
14C2×#525×C67C211yesmaximal, characteristic, complemented
15C23×D268C2211yescharacteristic, complemented
16C23×C22⋊D67—21no—
17C2×#14524068C2214yescomplemented
18C22×#11761612C2212yescomplemented
19C2×#14524017—21no—
20C2×#14524017—21no—
21C2×#14524017—21no—
22C2×#14524017—21no—
23C2×#14524017—21no—
24C2×#14524017—21no—
25C2×#14524017C2212yes—
26C2×#14524017C2212yes—
27C2×#14524017C2212yes—
28C2×#14524017C2212yescomplemented
29C2×#14524017C2212yescomplemented
30C2×#14524017C2212yescomplemented
31C22×C4⋊Dic67C2211yescharacteristic, complemented
32C22×(C2×D67)⋊C4—21no—
33#16863729C2214yescomplemented
34#16863724C2214yescomplemented
35#16863720C2218yescomplemented
36#16863714C2214yescomplemented
37#16863712C2214yescomplemented
38#16863709C2214yescomplemented
39#16863707C2214yescomplemented
40#16863647C2218yescomplemented
41#16863644C2218yescomplemented
42#16863630C2218yescomplemented
43#16863627C2218yescomplemented
44#16863546C2214yescomplemented
45#16863546C2214yescomplemented
46#16863541C2218yescomplemented
47#16863535C2214yescomplemented
48#16863530C2214yescomplemented
49#16863529C2214yescomplemented
50#16863529C2214yescomplemented
51#16863439C2214yescomplemented
52#16863400C2214yescomplemented
53#16863397C2214yescomplemented
54#16863360C2212yescomplemented
55#16863360C2212yescomplemented
56#16863360C2212yescomplemented
57#16863360C2212yescomplemented
58C2×C22⋊(C67⋊C8)C2212yescomplemented
59C2×C22⋊(C67⋊C8)C2212yescomplemented
60C22×#41×C67C2211yescharacteristic, complemented
61C24×C4×C67C2211yescharacteristic
62#525×C67—21no—
63#525×C67—21no—
64#525×C67—21no—
65#525×C67—21no—
66#525×C67C2212yes—
67#525×C67C2212yescomplemented
68#525×C67C2212yescomplemented
69#525×C67C2212yescomplemented
70C2×#123×C67—21no—
71C2×C22⋊Q8×C67C2211yescharacteristic, complemented
72C2×C22⋊Q8×C67C2211yescharacteristic, complemented
73C2×#121×C67C2211yescharacteristic, complemented
74C2×#121×C67C2211yescharacteristic, complemented
75C2×#120×C67—21no—
76C2×C4×D4×C67—21no—
77C2×C4×D4×C67—21no—
78C2×#117×C67C2211yescharacteristic, complemented
79C24×D67—21no—
80C22×D268—21no—
81C22×D268—21no—
82C22×D268—21no—
83C22×D268—44no—
84C22×D268C2312yes—
85C22×D268C2312yes—
86C22×D268C2312yes—
87C22×C22⋊D67—22no—
88C22×C22⋊D67—22no—
89C22×C22⋊D67—22no—
90C22×C22⋊D67—22no—
91C22×C22⋊D67—22no—
92C22×C22⋊D67—22no—
93C22×C22⋊D67—48no—
94C23×Dic67—21no—
95#14524068—48no—
96C2×#11761615C2318yescomplemented
97C2×#11761613C2318yescomplemented
98C2×#11761612—44no—
99C2×#11761612C2314yes—
100C2×#11761612C2314yescomplemented
101C22×C67⋊C8C2314yescomplemented
102#14524017—22no—
103#14524017—22no—
104#14524017—22no—
105#14524017—22no—
106#14524017—22no—
107#14524017—22no—
108#14524017—22no—
109#14524017—22no—
110#14524017—22no—
111#14524017—22no—
112#14524017—22no—
113#14524017—22no—
114#14524017C2314yes—
115#14524017C2314yes—
116#14524017C2314yes—
117#14524017C2314yes—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67C2312yes—
122C2×C4⋊Dic67C2312yes—
123C2×C4⋊Dic67C2312yes—
124C2×(C2×D67)⋊C4—22no—
125C2×(C2×D67)⋊C4—22no—
126C2×(C2×D67)⋊C4—22no—
127C2×(C2×D67)⋊C4—22no—
128C2×(C2×D67)⋊C4—22no—
129C2×(C2×D67)⋊C4—22no—
130#14523976C2318yescomplemented
131#14523974C2318yescomplemented
132#14523967C2318yescomplemented
133#14523964C2318yescomplemented
134#14523963C2318yescomplemented
135#14523963C2318yescomplemented
136C22⋊(C67⋊C8)C2314yes—
137C22⋊(C67⋊C8)C2314yes—
138C22⋊(C67⋊C8)C2314yescomplemented
139C22⋊(C67⋊C8)C2314yescomplemented
140C25×C67D411yescharacteristic
141C2×#41×C67—21no—
142C2×#41×C67—21no—
143C2×#41×C67—44no—
144C2×#41×C67C2312yes—
145C2×#41×C67C2312yescomplemented
146C22×Q8×C67C2311yescharacteristic, complemented
147C22×D4×C67—21no—
148C22×D4×C67—21no—
149C22×D4×C67—21no—
150C22×D4×C67C2311yescharacteristic, complemented
151C23×C4×C67—21no—
152C23×C4×C67—44no—
153C23×C4×C67D411yescharacteristic
154C23×C4×C67D411yescharacteristic
155C23×C4×C67D411yescharacteristic
156C23×C4×C67D411yescharacteristic
157C23×C4×C67D411yescharacteristic
158C23×C4×C67D411yescharacteristic
159C23×C4×C67D411yescharacteristic
160C23×C4×C67C2311yescharacteristic
161C23×C4×C67C2311yescharacteristic
162C23×C4×C67C2311yescharacteristic
163C23×C4×C67C2311yescharacteristic
164C23×C4×C67C2311yescharacteristic
165C23×C4×C67C2311yescharacteristic
166C23×C4×C67C2311yescharacteristic
167#123×C67—22no—
168#123×C67—22no—
169#123×C67—22no—
170#123×C67—22no—
171C22⋊Q8×C67—21no—
172C22⋊Q8×C67—21no—
173C22⋊Q8×C67—21no—
174C22⋊Q8×C67—21no—
175C22⋊Q8×C67C2312yes—
176C22⋊Q8×C67C2312yes—
177C22⋊Q8×C67C2312yescomplemented
178C22⋊Q8×C67C2312yescomplemented
179#121×C67—21no—
180#121×C67—21no—
181#121×C67—21no—
182#121×C67—21no—
183#121×C67C2312yes—
184#121×C67C2312yes—
185#121×C67C2312yescomplemented
186#121×C67C2312yescomplemented
187#120×C67—22no—
188#120×C67—22no—
189#120×C67—22no—
190#120×C67—22no—
191C4×D4×C67—22no—
192C4×D4×C67—22no—
193C4×D4×C67—22no—
194C4×D4×C67—22no—
195C4×D4×C67—22no—
196C4×D4×C67—22no—
197C4×D4×C67—22no—
198C4×D4×C67—22no—
199#117×C67—21no—
200#117×C67—21no—
201#117×C67C2312yes—
202#117×C67C2312yescomplemented
203C2×C4⋊C4×C67—21no—
204C2×C4⋊C4×C67—21no—
205C2×C4⋊C4×C67C2311yescharacteristic, complemented
206C2×C4⋊C4×C67C2311yescharacteristic, complemented
207C2×C22⋊C4×C67—21no—
208C2×C22⋊C4×C67—21no—
209C2×C22⋊C4×C67—21no—
210C2×C22⋊C4×C67—21no—
211C2×C22⋊C4×C67—21no—
212C2×C42×C67—21no—
213C23×D67—22no—
214C23×D67—22no—
215C23×D67—22no—
216C23×D67—44no—
217C23×D67—44no—
218C23×D67—44no—
219C2×D268—28no—
220C2×D268—22no—
221C2×D268—22no—
222C2×D268—22no—
223C2×D268—44no—
224C2×D268—44no—
225C2×D268—44no—
226C2×D268—44no—
227C2×D268—44no—
228C2×D268C2414yes—
229C2×C22⋊D67—24no—
230C2×C22⋊D67—24no—
231C2×C22⋊D67—24no—
232C2×C22⋊D67—24no—
233C2×C22⋊D67—48no—
234C2×C22⋊D67—48no—
235C2×C22⋊D67—48no—
236C2×C22⋊D67—48no—
237C2×C22⋊D67—48no—
238C2×C22⋊D67—48no—
239C22×Dic67—22no—
240C22×Dic67—22no—
241C22×Dic67—22no—
242C22×Dic67—44no—
243#11761615—48no—
244#11761613—48no—
245#11761612—28no—
246#11761612—44no—
247C2×C67⋊C8—44no—
248C2×C67⋊C8C2418yes—
249C4⋊Dic67—22no—
250C4⋊Dic67—22no—
251C4⋊Dic67—22no—
252C4⋊Dic67C2414yes—
253(C2×D67)⋊C4—24no—
254(C2×D67)⋊C4—24no—
255(C2×D67)⋊C4—24no—
256(C2×D67)⋊C4—24no—
257C24×C67—24no—
258C24×C67—21no—
259C24×C67—42no—
260C24×C67—42no—
261C24×C67C2×D411yescharacteristic
262C24×C67C2×D411yescharacteristic
263C24×C67C2×D411yescharacteristic
264C24×C67C2×D411yescharacteristic
265C24×C67C2×D411yescharacteristic
266C24×C67C2×D411yescharacteristic
267C24×C67C2×D411yescharacteristic
268#41×C67—28no—
269#41×C67—44no—
270#41×C67—44no—
271#41×C67—44no—
272C2×Q8×C67—21no—
273C2×Q8×C67—42no—
274C2×Q8×C67C2412yes—
275C2×D4×C67—22no—
276C2×D4×C67—22no—
277C2×D4×C67—22no—
278C2×D4×C67—22no—
279C2×D4×C67—22no—
280C2×D4×C67—22no—
281C2×D4×C67—21no—
282C2×D4×C67—42no—
283C2×D4×C67—44no—
284C2×D4×C67—44no—
285C2×D4×C67—44no—
286C2×D4×C67C2412yes—
287C22×C4×C67—24no—
288C22×C4×C67—24no—
289C22×C4×C67—24no—
290C22×C4×C67—21no—
291C22×C4×C67—21no—
292C22×C4×C67—21no—
293C22×C4×C67—22no—
294C22×C4×C67—22no—
295C22×C4×C67—42no—
296C22×C4×C67—42no—
297C22×C4×C67—42no—
298C22×C4×C67—42no—
299C22×C4×C67—42no—
300C22×C4×C67—42no—
301C22×C4×C67—42no—
302C22×C4×C67—42no—
303C22×C4×C67—42no—
304C22×C4×C67—42no—
305C22×C4×C67—42no—
306C22×C4×C67—44no—
307C22×C4×C67C2×D411yescharacteristic
308C22×C4×C67C2×D411yescharacteristic
309C22×C4×C67C2×D411yescharacteristic
310C22×C4×C67C2×D411yescharacteristic
311C22×C4×C67C2×D411yescharacteristic
312C22×C4×C67C2×D411yescharacteristic
313C22×C4×C67C2×D411yescharacteristic
314C22×C4×C67C2×D411yescharacteristic
315C22×C4×C67C2×D411yescharacteristic
316C22×C4×C67C2×D411yescharacteristic
317C22×C4×C67C2×D411yescharacteristic
318C22×C4×C67C2×D411yescharacteristic
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×C67C2411yescharacteristic
329C22×C4×C67C2411yescharacteristic
330C22×C4×C67C2411yescharacteristic
331C22×C4×C67C2411yescharacteristic
332C22×C4×C67C2411yescharacteristic
333C22×C4×C67C2411yescharacteristic
334C22×C4×C67C2411yescharacteristic
335C4⋊C4×C67—22no—
336C4⋊C4×C67—22no—
337C4⋊C4×C67—22no—
338C4⋊C4×C67—22no—
339C4⋊C4×C67—21no—
340C4⋊C4×C67—21no—
341C4⋊C4×C67C2412yes—
342C4⋊C4×C67C2412yes—
343C22⋊C4×C67—22no—
344C22⋊C4×C67—22no—
345C22⋊C4×C67—22no—
346C22⋊C4×C67—22no—
347C22⋊C4×C67—22no—
348C22⋊C4×C67—22no—
349C22⋊C4×C67—22no—
350C22⋊C4×C67—22no—
351C22⋊C4×C67—22no—
352C22⋊C4×C67—22no—
353C42×C67—22no—
354C42×C67—22no—
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—22no—
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—42no—
378C23×C67—42no—
379C23×C67—42no—
380C23×C67AGL(1,ℤ/8)14yescomplemented
381C23×C67C22×D411yescharacteristic
382C23×C67C22×D411yescharacteristic
383C23×C67C22×D411yescharacteristic
384C23×C67C22×D411yescharacteristic
385C23×C67C22×D411yescharacteristic
386C23×C67C22×D411yescharacteristic
387C23×C67C22×D411yescharacteristic
388C22×D67—24no—
389C22×D67—44no—
390C22×D67—44no—
391C22×D67—44no—
392C22×D67—44no—
393C22×D67—44no—
394C22×D67—44no—
395C22×D67—44no—
396C22×D67—44no—
397C22×D67—44no—
398C22×D67—816no—
399Q8×C67—24no—
400Q8×C67—42no—
401D4×C67—24no—
402D4×C67—42no—
403D4×C67—44no—
404D4×C67—44no—
405D4×C67—44no—
406D4×C67—44no—
407D4×C67—44no—
408D4×C67—44no—
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—22no—
423C2×C4×C67—22no—
424C2×C4×C67—22no—
425C2×C4×C67—22no—
426C2×C4×C67—22no—
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—41no—
436C2×C4×C67—41no—
437C2×C4×C67—41no—
438C2×C4×C67—41no—
439C2×C4×C67—44no—
440C2×C4×C67—42no—
441C2×C4×C67—42no—
442C2×C4×C67—42no—
443C2×C4×C67—44no—
444C2×C4×C67C22×D411yescharacteristic
445C2×C4×C67C22×D411yescharacteristic
446C2×C4×C67C22×D411yescharacteristic
447C2×C4×C67C22×D411yescharacteristic
448C2×C4×C67C22×D411yescharacteristic
449C2×C4×C67C22×D411yescharacteristic
450C2×C4×C67C22×D411yescharacteristic
451C2×C4×C67H(5,𝔽2)14yes—
452C2×C4×C67C2511yescharacteristic
453C22⋊D67—48no—
454C22⋊D67—48no—
455C22⋊D67—48no—
456C22⋊D67—48no—
457C2×Dic67—24no—
458C2×Dic67—44no—
459C2×Dic67—44no—
460C2×Dic67—44no—
461D268—28no—
462D268—44no—
463D268—44no—
464D268—44no—
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—42no—
490C22×C67—42no—
491C22×C67—42no—
492C22×C67—84no—
493C22×C67#53412yes—
494C22×C67C2×AGL(1,ℤ/8)12yes—
495C22×C67C2×AGL(1,ℤ/8)12yes—
496C22×C67C2×AGL(1,ℤ/8)12yes—
497C22×C67#57512yes—
498C22×C67C23×D411yescharacteristic
499C2×D67—44no—
500C2×D67—44no—
501C2×D67—44no—
502C2×D67—88no—
503C2×D67—88no—
504C2×D67—88no—
505C4×C67—21no—
506C4×C67—21no—
507C4×C67—21no—
508C4×C67—21no—
509C4×C67—21no—
510C4×C67—21no—
511C4×C67—42no—
512C4×C67—42no—
513C4×C67—42no—
514C4×C67#53412yes—
515C4×C67C2×H(5,𝔽2)12yes—
516Dic67—44no—
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—82no—
526C2×C67C2×#53411yescharacteristic
527C2×C67C22×AGL(1,ℤ/8)11yescharacteristic
528C2×C67C2×#57511yescharacteristic
529D67—84no—
530C2×#525D6711yescharacteristic, complemented
531C22×#121—671no—
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×#41C2×D6711yescharacteristic, complemented
546C23×D4—671no—
547C23×D4—1341no—
548C24×C4C2×D6711yescharacteristic
549C2×AGL(1,ℤ/8)—674no—
550C22×M16—672no—
551#525—21no—
552#525—21no—
553#525—21no—
554#525—21no—
555#525C2×D6712yes—
556#525C2×D6712yescomplemented
557#525C2×D6712yescomplemented
558#525C2×D6712yescomplemented
559C2×#123—21no—
560C2×C22⋊Q8C2×D6711yescharacteristic, complemented
561C2×C22⋊Q8C2×D6711yescharacteristic, complemented
562C2×#121—672no—
563C2×#121—672no—
564C2×#121—672no—
565C2×#121—672no—
566C2×#121—672no—
567C2×#121—672no—
568C2×#121—1341no—
569C2×#121—1341no—
570C2×#121—1341no—
571C2×#121—1341no—
572C2×#121—1341no—
573C2×#121—1341no—
574C2×#121C2×D6711yescharacteristic, complemented
575C2×#121C2×D6711yescharacteristic, complemented
576C2×#120—21no—
577C2×C4×D4—21no—
578C2×C4×D4—21no—
579C2×#117C2×D6711yescharacteristic, complemented
580C22×C4⋊C4—671no—
581C22×C22⋊C4—1341no—
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—1341no—
610C25C22⋊D6711yescharacteristic
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—44no—
614C2×#41C22×D6712yes—
615C2×#41C22×D6712yescomplemented
616C22×Q8C22×D6711yescharacteristic, complemented
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4—2684no—
621C22×D4—2688no—
622C22×D4—672no—
623C22×D4—672no—
624C22×D4—672no—
625C22×D4—1342no—
626C22×D4—1342no—
627C22×D4—1342no—
628C22×D4—1342no—
629C22×D4—1342no—
630C22×D4—1342no—
631C22×D4—1341no—
632C22×D4—1341no—
633C22×D4—1341no—
634C22×D4C22×D6711yescharacteristic, complemented
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—22no—
660#123—22no—
661#123—22no—
662#123—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8C22×D6712yes—
668C22⋊Q8C22×D6712yes—
669C22⋊Q8C22×D6712yescomplemented
670C22⋊Q8C22×D6712yescomplemented
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—674no—
676#121—674no—
677#121—674no—
678#121—674no—
679#121—1342no—
680#121—1342no—
681#121—1342no—
682#121—1342no—
683#121—1342no—
684#121—1342no—
685#121—1342no—
686#121—1342no—
687#121—1342no—
688#121—1342no—
689#121—1342no—
690#121—1342no—
691#121C22×D6712yes—
692#121C22×D6712yes—
693#121C22×D6712yescomplemented
694#121C22×D6712yescomplemented
695#120—22no—
696#120—22no—
697#120—22no—
698#120—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—22no—
707#117—21no—
708#117—21no—
709#117C22×D6712yes—
710#117C22×D6712yescomplemented
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—672no—
714C2×C4⋊C4—672no—
715C2×C4⋊C4—672no—
716C2×C4⋊C4—1341no—
717C2×C4⋊C4—1341no—
718C2×C4⋊C4—1341no—
719C2×C4⋊C4C22×D6711yescharacteristic, complemented
720C2×C4⋊C4C22×D6711yescharacteristic, complemented
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—1342no—
727C2×C22⋊C4—1342no—
728C2×C22⋊C4—1342no—
729C2×C22⋊C4—1342no—
730C2×C22⋊C4—1342no—
731C2×C22⋊C4—1342no—
732C2×C42—21no—
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—21no—
745C24—42no—
746C24—42no—
747C24—2684no—
748C24—2684no—
749C24—2684no—
750C24—1342no—
751C24—1342no—
752C24—1342no—
753C24C2×C22⋊D6711yescharacteristic
754C24C2×C22⋊D6711yescharacteristic
755C24C2×C22⋊D6711yescharacteristic
756C24C2×C22⋊D6711yescharacteristic
757C24C2×C22⋊D6711yescharacteristic
758C24C2×C22⋊D6711yescharacteristic
759C24C2×C22⋊D6711yescharacteristic
760#41—28no—
761#41—44no—
762#41—44no—
763#41—44no—
764C2×Q8—21no—
765C2×Q8—42no—
766C2×Q8C23×D6712yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—2684no—
779C2×D4—2684no—
780C2×D4—2684no—
781C2×D4—2684no—
782C2×D4—2684no—
783C2×D4—2688no—
784C2×D4—2688no—
785C2×D4—2688no—
786C2×D4—2688no—
787C2×D4—2688no—
788C2×D4—2688no—
789C2×D4—674no—
790C2×D4—1344no—
791C2×D4—1344no—
792C2×D4—1344no—
793C2×D4—1344no—
794C2×D4—1342no—
795C2×D4—1342no—
796C2×D4—1342no—
797C2×D4—1348no—
798C2×D4C23×D6712yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
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—42no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—2684no—
820C22×C4—1342no—
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—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—674no—
864C4⋊C4—1342no—
865C4⋊C4—1342no—
866C4⋊C4—1342no—
867C4⋊C4C23×D6712yes—
868C4⋊C4C23×D6712yes—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—1344no—
880C22⋊C4—1344no—
881C22⋊C4—1344no—
882C22⋊C4—1344no—
883C42—22no—
884C42—22no—
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—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—2684no—
911C23—2684no—
912C23—2684no—
913C23—2684no—
914C23—2684no—
915C23—2684no—
916C23—2684no—
917C23—2684no—
918C23—2684no—
919C23—53616no—
920C23—1344no—
921C23#1452406814yescomplemented
922C23C22×C22⋊D6711yescharacteristic
923C23C22×C22⋊D6711yescharacteristic
924C23C22×C22⋊D6711yescharacteristic
925C23C22×C22⋊D6711yescharacteristic
926C23C22×C22⋊D6711yescharacteristic
927C23C22×C22⋊D6711yescharacteristic
928C23C22×C22⋊D6711yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—42no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—2684no—
940D4—2684no—
941D4—2688no—
942D4—2688no—
943D4—2688no—
944D4—2688no—
945D4—2684no—
946D4—1348no—
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—22no—
963C2×C4—22no—
964C2×C4—22no—
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—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—44no—
982C2×C4—2684no—
983C2×C4—2684no—
984C2×C4—2684no—
985C2×C4—1344no—
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—42no—
1020C22—42no—
1021C22—42no—
1022C22—84no—
1023C22—2684no—
1024C22—2684no—
1025C22—2684no—
1026C22—5368no—
1027C22—5368no—
1028C22—5368no—
1029C22#1686395512yes—
1030C22C2×#1452406812yes—
1031C22C2×#1452406812yes—
1032C22C2×#1452406812yes—
1033C22#1686419412yes—
1034C22C23×C22⋊D6711yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—2684no—
1045C4#1686395512yes—
1046C4C2×#1452408812yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—82no—
1055C2—5364no—
1056C2C2×#1686395511yescharacteristic
1057C2C22×#1452406811yescharacteristic
1058C2C2×#1686419411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#525×C67C2
socleC22×C67C23×D4
hypercenterC2×#525D67
hypocenterC67#60750
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#14524017C2semidirect
2. #22571019C2semidirect
3. #22571011C2semidirect
4. #22571006C2semidirect
5. #22570970C2semidirect
6. #22570962C2semidirect
7. #22570957C2semidirect
8. #22570149C2semidirect
9. #22570129C2semidirect
10. #22569830C2semidirect
11. #22569461C2semidirect
12. #22569435C2semidirect
13. C2×#16863360C2semidirect
14. C2×#525×C67C2semidirect
15. C23×D268C22semidirect
17. C2×#14524068C22semidirect
18. C22×#11761612C22semidirect
28. C2×#14524017C22semidirect
29. C2×#14524017C22semidirect
30. C2×#14524017C22semidirect
31. C22×C4⋊Dic67C22semidirect
33. #16863729C22semidirect
34. #16863724C22semidirect
35. #16863720C22semidirect
36. #16863714C22semidirect
37. #16863712C22semidirect
38. #16863709C22semidirect
39. #16863707C22semidirect
40. #16863647C22semidirect
41. #16863644C22semidirect
42. #16863630C22semidirect
43. #16863627C22semidirect
44. #16863546C22semidirect
45. #16863546C22semidirect
46. #16863541C22semidirect
47. #16863535C22semidirect
48. #16863530C22semidirect
49. #16863529C22semidirect
50. #16863529C22semidirect
51. #16863439C22semidirect
52. #16863400C22semidirect
53. #16863397C22semidirect
54. #16863360C22semidirect
55. #16863360C22semidirect
56. #16863360C22semidirect
57. #16863360C22semidirect
58. C2×C22⋊(C67⋊C8)C22semidirect
59. C2×C22⋊(C67⋊C8)C22semidirect
60. C22×#41×C67C22semidirect
67. #525×C67C22semidirect
68. #525×C67C22semidirect
69. #525×C67C22semidirect
71. C2×C22⋊Q8×C67C22semidirect
72. C2×C22⋊Q8×C67C22semidirect
73. C2×#121×C67C22semidirect
74. C2×#121×C67C22semidirect
78. C2×#117×C67C22semidirect
96. C2×#11761615C23semidirect
97. C2×#11761613C23semidirect
100. C2×#11761612C23semidirect
101. C22×C67⋊C8C23semidirect
130. #14523976C23semidirect
131. #14523974C23semidirect
132. #14523967C23semidirect
133. #14523964C23semidirect
134. #14523963C23semidirect
135. #14523963C23semidirect
138. C22⋊(C67⋊C8)C23semidirect
139. C22⋊(C67⋊C8)C23semidirect
145. C2×#41×C67C23semidirect
146. C22×Q8×C67C23semidirect
150. C22×D4×C67C23semidirect
177. C22⋊Q8×C67C23semidirect
178. C22⋊Q8×C67C23semidirect
185. #121×C67C23semidirect
186. #121×C67C23semidirect
202. #117×C67C23semidirect
205. C2×C4⋊C4×C67C23semidirect
206. C2×C4⋊C4×C67C23semidirect
380. C23×C67AGL(1,ℤ/8)semidirect
530. C2×#525D67semidirect
544. C67#60750semidirect
545. C22×#41C2×D67semidirect
556. #525C2×D67semidirect
557. #525C2×D67semidirect
558. #525C2×D67semidirect
560. C2×C22⋊Q8C2×D67semidirect
561. C2×C22⋊Q8C2×D67semidirect
574. C2×#121C2×D67semidirect
575. C2×#121C2×D67semidirect
579. C2×#117C2×D67semidirect
615. C2×#41C22×D67semidirect
616. C22×Q8C22×D67semidirect
634. C22×D4C22×D67semidirect
669. C22⋊Q8C22×D67semidirect
670. C22⋊Q8C22×D67semidirect
693. #121C22×D67semidirect
694. #121C22×D67semidirect
710. #117C22×D67semidirect
719. C2×C4⋊C4C22×D67semidirect
720. C2×C4⋊C4C22×D67semidirect
921. C23#14524068semidirect

Maximal subgroups

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

subgroupindex
C22×#145240172
#225710192
#225710112
#225710062
#225709702
#225709622
#225709572
#225701492
#225701292
#225698302
#225694612
#225694352
C2×#168633602
C2×#525×C672
#6075067