Finite Group Databasebeta

← #31726402

Subgroups — #31726402

Order 17152.

2394 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863907C211yesmaximal, characteristic, complemented
2#22570997C214yesmaximal, complemented
3#22570990C212yesmaximal, complemented
4#22570986C212yesmaximal, complemented
5#22570981C211yesmaximal, characteristic, complemented
6#22570974C212yesmaximal, complemented
7#22570970C212yesmaximal, complemented
8#22570966C211yesmaximal, characteristic, complemented
9#22570962C211yesmaximal, characteristic, complemented
10#22570957C211yesmaximal, characteristic, complemented
11#22570122C212yesmaximal, complemented
12#22570118C212yesmaximal, complemented
13#22569787C214yesmaximal, complemented
14#22569427C212yesmaximal, complemented
15#22569425C212yesmaximal, complemented
16C22×C22⋊(C67⋊C8)C211yesmaximal, characteristic, complemented
17C2×#525×C67C211yesmaximal, characteristic, complemented
18C22×#11761628C2211yescharacteristic, complemented
19C2×#14524063C2214yescomplemented
20C23×C67⋊C8C2212yescomplemented
21#16863907—21no—
22#16863907—21no—
23#16863907—21no—
24#16863907—21no—
25#16863907C2212yes—
26#16863907C2212yes—
27#16863907C2212yescomplemented
28#16863907C2212yescomplemented
29C2×#14524026—21no—
30C2×#14524022C2211yescharacteristic
31C2×#14524022C2211yescharacteristic, complemented
32C2×#14524017C2211yescharacteristic
33C2×#14524017C2211yescharacteristic, complemented
34C2×#14524012—21no—
35C2×C4×C22⋊D67—21no—
36C2×C4×C22⋊D67—21no—
37C2×#14524002C2211yescharacteristic, complemented
38#16863737C2214yescomplemented
39#16863734C2214yescomplemented
40#16863731C2212yescomplemented
41#16863729C2212yescomplemented
42#16863726C2212yescomplemented
43#16863724C2212yescomplemented
44#16863720C2214yescomplemented
45#16863717C2214yescomplemented
46#16863714C2212yescomplemented
47#16863712C2212yescomplemented
48#16863709C2212yescomplemented
49#16863707C2212yescomplemented
50#16863635C2214yescomplemented
51#16863635C2214yescomplemented
52#16863630C2214yescomplemented
53#16863630C2214yescomplemented
54#16863627C2214yescomplemented
55#16863627C2214yescomplemented
56#16863623C2214yescomplemented
57#16863623C2214yescomplemented
58#16863558C2214yescomplemented
59#16863556C2214yescomplemented
60#16863552C2212yescomplemented
61#16863551C2212yescomplemented
62#16863547C2212yescomplemented
63#16863546C2212yescomplemented
64#16863541C2214yescomplemented
65#16863539C2214yescomplemented
66#16863535C2212yescomplemented
67#16863534C2212yescomplemented
68#16863530C2212yescomplemented
69#16863529C2212yescomplemented
70#16863432C2214yescomplemented
71#16863392C2214yescomplemented
72#16863390C2214yescomplemented
73C2×C22⋊(C67⋊C8)C2211yescharacteristic
74C2×C22⋊(C67⋊C8)C2211yescharacteristic
75C2×C22⋊(C67⋊C8)C2212yescomplemented
76C2×C22⋊(C67⋊C8)C2212yescomplemented
77C2×C22⋊(C67⋊C8)C2212yescomplemented
78C2×C22⋊(C67⋊C8)C2212yescomplemented
79C2×C22⋊(C67⋊C8)C2212yescomplemented
80C22×#41×C67C2211yescharacteristic, complemented
81C24×C4×C67C2211yescharacteristic
82#525×C67—21no—
83#525×C67—21no—
84#525×C67—21no—
85#525×C67—21no—
86#525×C67C2212yes—
87#525×C67C2212yes—
88#525×C67C2212yescomplemented
89#525×C67C2212yescomplemented
90C2×#123×C67—21no—
91C2×C22⋊Q8×C67C2211yescharacteristic
92C2×C22⋊Q8×C67C2211yescharacteristic, complemented
93C2×#121×C67C2211yescharacteristic
94C2×#121×C67C2211yescharacteristic, complemented
95C2×#120×C67—21no—
96C2×C4×D4×C67—21no—
97C2×C4×D4×C67—21no—
98C2×#117×C67C2211yescharacteristic, complemented
99C2×#11761628—21no—
100C2×#11761628—21no—
101C2×#11761628—44no—
102C2×#11761628C2312yes—
103C2×#11761628C2312yes—
104C22×Dic134C2311yescharacteristic
105C22×D268C2311yescharacteristic
106C22×C22⋊D67—21no—
107C22×C22⋊D67—21no—
108C22×C22⋊D67—21no—
109C22×C4×D67—21no—
110#14524063—48no—
111C2×#11761618C2314yescomplemented
112C2×#11761616C2314yescomplemented
113C2×#11761615C2314yescomplemented
114C2×#11761613C2314yescomplemented
115C22×C67⋊C8—44no—
116C22×C67⋊C8C2314yes—
117C22×C67⋊C8C2312yes—
118C22×C67⋊C8C2312yes—
119C22×C67⋊C8C2314yes—
120#14524026—22no—
121#14524026—22no—
122#14524026—22no—
123#14524026—22no—
124#14524022—21no—
125#14524022—21no—
126#14524022—21no—
127#14524022—21no—
128#14524022C2312yes—
129#14524022C2312yes—
130#14524022C2312yes—
131#14524022C2312yes—
132#14524017—21no—
133#14524017—21no—
134#14524017—21no—
135#14524017—21no—
136#14524017C2312yes—
137#14524017C2312yes—
138#14524017C2312yes—
139#14524017C2312yes—
140#14524012—22no—
141#14524012—22no—
142#14524012—22no—
143#14524012—22no—
144C4×C22⋊D67—22no—
145C4×C22⋊D67—22no—
146C4×C22⋊D67—22no—
147C4×C22⋊D67—22no—
148C4×C22⋊D67—22no—
149C4×C22⋊D67—22no—
150C4×C22⋊D67—22no—
151C4×C22⋊D67—22no—
152#14524002—21no—
153#14524002—21no—
154#14524002C2312yes—
155#14524002C2312yes—
156C2×C4⋊Dic67C2311yescharacteristic
157C2×C4⋊Dic67C2311yescharacteristic
158C2×Dic67⋊C4—21no—
159C2×Dic67⋊C4—21no—
160C2×C22⋊Dic67—21no—
161C2×C22⋊Dic67—21no—
162C2×C22⋊Dic67—21no—
163C2×(C2×D67)⋊C4—21no—
164C2×(C2×D67)⋊C4—21no—
165C2×C4×Dic67—21no—
166#14523976C2314yescomplemented
167#14523976C2314yescomplemented
168#14523974C2314yescomplemented
169#14523974C2314yescomplemented
170#14523967C2314yescomplemented
171#14523967C2314yescomplemented
172#14523966C2314yescomplemented
173#14523966C2314yescomplemented
174#14523964C2314yescomplemented
175#14523964C2314yescomplemented
176#14523963C2314yescomplemented
177#14523963C2314yescomplemented
178C22⋊(C67⋊C8)C2312yes—
179C22⋊(C67⋊C8)C2312yes—
180C22⋊(C67⋊C8)C2312yes—
181C22⋊(C67⋊C8)C2312yes—
182C22⋊(C67⋊C8)C2314yes—
183C22⋊(C67⋊C8)C2314yes—
184C25×C67D411yescharacteristic
185C2×#41×C67—21no—
186C2×#41×C67—21no—
187C2×#41×C67—44no—
188C2×#41×C67C2312yes—
189C2×#41×C67C2312yes—
190C22×Q8×C67C2311yescharacteristic
191C22×D4×C67—21no—
192C22×D4×C67—21no—
193C22×D4×C67—21no—
194C22×D4×C67C2311yescharacteristic
195C23×C4×C67—21no—
196C23×C4×C67—44no—
197C23×C4×C67D411yescharacteristic
198C23×C4×C67D411yescharacteristic
199C23×C4×C67D411yescharacteristic
200C23×C4×C67D411yescharacteristic
201C23×C4×C67D411yescharacteristic
202C23×C4×C67D411yescharacteristic
203C23×C4×C67D411yescharacteristic
204C23×C4×C67C2311yescharacteristic
205C23×C4×C67C2311yescharacteristic
206C23×C4×C67C2311yescharacteristic
207C23×C4×C67C2311yescharacteristic
208C23×C4×C67C2311yescharacteristic
209C23×C4×C67C2311yescharacteristic
210C23×C4×C67C2311yescharacteristic
211#123×C67—22no—
212#123×C67—22no—
213#123×C67—22no—
214#123×C67—22no—
215C22⋊Q8×C67—21no—
216C22⋊Q8×C67—21no—
217C22⋊Q8×C67—21no—
218C22⋊Q8×C67—21no—
219C22⋊Q8×C67C2312yes—
220C22⋊Q8×C67C2312yes—
221C22⋊Q8×C67C2312yes—
222C22⋊Q8×C67C2312yes—
223#121×C67—21no—
224#121×C67—21no—
225#121×C67—21no—
226#121×C67—21no—
227#121×C67C2312yes—
228#121×C67C2312yes—
229#121×C67C2312yes—
230#121×C67C2312yes—
231#120×C67—22no—
232#120×C67—22no—
233#120×C67—22no—
234#120×C67—22no—
235C4×D4×C67—22no—
236C4×D4×C67—22no—
237C4×D4×C67—22no—
238C4×D4×C67—22no—
239C4×D4×C67—22no—
240C4×D4×C67—22no—
241C4×D4×C67—22no—
242C4×D4×C67—22no—
243#117×C67—21no—
244#117×C67—21no—
245#117×C67C2312yes—
246#117×C67C2312yes—
247C2×C4⋊C4×C67—21no—
248C2×C4⋊C4×C67—21no—
249C2×C4⋊C4×C67C2311yescharacteristic
250C2×C4⋊C4×C67C2311yescharacteristic
251C2×C22⋊C4×C67—21no—
252C2×C22⋊C4×C67—21no—
253C2×C22⋊C4×C67—21no—
254C2×C22⋊C4×C67—21no—
255C2×C22⋊C4×C67—21no—
256C2×C42×C67—21no—
257C23×D67—21no—
258#11761628—28no—
259#11761628—44no—
260#11761628—44no—
261#11761628—44no—
262C2×Dic134—21no—
263C2×Dic134—42no—
264C2×Dic134C2412yes—
265C2×D268—21no—
266C2×D268—42no—
267C2×D268C2412yes—
268C2×C22⋊D67—22no—
269C2×C22⋊D67—22no—
270C2×C22⋊D67—22no—
271C2×C22⋊D67—22no—
272C2×C22⋊D67—22no—
273C2×C22⋊D67—22no—
274C2×C22⋊D67—44no—
275C2×C22⋊D67—44no—
276C2×C22⋊D67—44no—
277C22×Dic67—21no—
278C22×Dic67—21no—
279C22×Dic67—21no—
280C2×C4×D67—22no—
281C2×C4×D67—22no—
282C2×C4×D67—44no—
283#11761618—44no—
284#11761616—44no—
285#11761615—44no—
286#11761613—44no—
287C2×C67⋊C8—28no—
288C2×C67⋊C8—42no—
289C2×C67⋊C8—44no—
290C2×C67⋊C8—42no—
291C2×C67⋊C8C2414yes—
292C2×C67⋊C8C2414yes—
293C4⋊Dic67—21no—
294C4⋊Dic67—21no—
295C4⋊Dic67C2412yes—
296C4⋊Dic67C2412yes—
297Dic67⋊C4—22no—
298Dic67⋊C4—22no—
299Dic67⋊C4—22no—
300Dic67⋊C4—22no—
301C22⋊Dic67—22no—
302C22⋊Dic67—22no—
303C22⋊Dic67—22no—
304C22⋊Dic67—22no—
305C22⋊Dic67—22no—
306C22⋊Dic67—22no—
307(C2×D67)⋊C4—22no—
308(C2×D67)⋊C4—22no—
309(C2×D67)⋊C4—22no—
310(C2×D67)⋊C4—22no—
311C4×Dic67—22no—
312C4×Dic67—22no—
313C24×C67—24no—
314C24×C67—21no—
315C24×C67—42no—
316C24×C67—42no—
317C24×C67C2×D411yescharacteristic
318C24×C67C2×D411yescharacteristic
319C24×C67C2×D411yescharacteristic
320C24×C67C2×D411yescharacteristic
321C24×C67C2×D411yescharacteristic
322C24×C67C2×D411yescharacteristic
323C24×C67C2×D411yescharacteristic
324#41×C67—28no—
325#41×C67—44no—
326#41×C67—44no—
327#41×C67—44no—
328C2×Q8×C67—21no—
329C2×Q8×C67—42no—
330C2×Q8×C67C2412yes—
331C2×D4×C67—22no—
332C2×D4×C67—22no—
333C2×D4×C67—22no—
334C2×D4×C67—22no—
335C2×D4×C67—22no—
336C2×D4×C67—22no—
337C2×D4×C67—21no—
338C2×D4×C67—42no—
339C2×D4×C67—44no—
340C2×D4×C67—44no—
341C2×D4×C67—44no—
342C2×D4×C67C2412yes—
343C22×C4×C67—24no—
344C22×C4×C67—24no—
345C22×C4×C67—24no—
346C22×C4×C67—21no—
347C22×C4×C67—21no—
348C22×C4×C67—21no—
349C22×C4×C67—22no—
350C22×C4×C67—22no—
351C22×C4×C67—42no—
352C22×C4×C67—42no—
353C22×C4×C67—42no—
354C22×C4×C67—42no—
355C22×C4×C67—42no—
356C22×C4×C67—42no—
357C22×C4×C67—42no—
358C22×C4×C67—42no—
359C22×C4×C67—42no—
360C22×C4×C67—42no—
361C22×C4×C67—42no—
362C22×C4×C67—44no—
363C22×C4×C67C2×D411yescharacteristic
364C22×C4×C67C2×D411yescharacteristic
365C22×C4×C67C2×D411yescharacteristic
366C22×C4×C67C2×D411yescharacteristic
367C22×C4×C67C2×D411yescharacteristic
368C22×C4×C67C2×D411yescharacteristic
369C22×C4×C67C2×D411yescharacteristic
370C22×C4×C67C2×D411yescharacteristic
371C22×C4×C67C2×D411yescharacteristic
372C22×C4×C67C2×D411yescharacteristic
373C22×C4×C67C2×D411yescharacteristic
374C22×C4×C67C2×D411yescharacteristic
375C22×C4×C67C2×D411yescharacteristic
376C22×C4×C67C2×D411yescharacteristic
377C22×C4×C67C2×D411yescharacteristic
378C22×C4×C67C2×D411yescharacteristic
379C22×C4×C67C2×D411yescharacteristic
380C22×C4×C67C2×D411yescharacteristic
381C22×C4×C67C2×D411yescharacteristic
382C22×C4×C67C2×D411yescharacteristic
383C22×C4×C67C2×D411yescharacteristic
384C22×C4×C67C2411yescharacteristic
385C22×C4×C67C2411yescharacteristic
386C22×C4×C67C2411yescharacteristic
387C22×C4×C67C2411yescharacteristic
388C22×C4×C67C2411yescharacteristic
389C22×C4×C67C2411yescharacteristic
390C22×C4×C67C2411yescharacteristic
391C4⋊C4×C67—22no—
392C4⋊C4×C67—22no—
393C4⋊C4×C67—22no—
394C4⋊C4×C67—22no—
395C4⋊C4×C67—21no—
396C4⋊C4×C67—21no—
397C4⋊C4×C67C2412yes—
398C4⋊C4×C67C2412yes—
399C22⋊C4×C67—22no—
400C22⋊C4×C67—22no—
401C22⋊C4×C67—22no—
402C22⋊C4×C67—22no—
403C22⋊C4×C67—22no—
404C22⋊C4×C67—22no—
405C22⋊C4×C67—22no—
406C22⋊C4×C67—22no—
407C22⋊C4×C67—22no—
408C22⋊C4×C67—22no—
409C42×C67—22no—
410C42×C67—22no—
411C23×C67—22no—
412C23×C67—22no—
413C23×C67—22no—
414C23×C67—22no—
415C23×C67—22no—
416C23×C67—22no—
417C23×C67—22no—
418C23×C67—22no—
419C23×C67—22no—
420C23×C67—22no—
421C23×C67—22no—
422C23×C67—22no—
423C23×C67—22no—
424C23×C67—41no—
425C23×C67—41no—
426C23×C67—41no—
427C23×C67—41no—
428C23×C67—41no—
429C23×C67—41no—
430C23×C67—41no—
431C23×C67—41no—
432C23×C67—416no—
433C23×C67—42no—
434C23×C67—42no—
435C23×C67—42no—
436C23×C67#13514yescomplemented
437C23×C67C22×D411yescharacteristic
438C23×C67C22×D411yescharacteristic
439C23×C67C22×D411yescharacteristic
440C23×C67C22×D411yescharacteristic
441C23×C67C22×D411yescharacteristic
442C23×C67C22×D411yescharacteristic
443C23×C67C22×D411yescharacteristic
444C22×D67—22no—
445C22×D67—42no—
446C22×D67—42no—
447C22×D67—42no—
448Q8×C67—24no—
449Q8×C67—42no—
450D4×C67—24no—
451D4×C67—42no—
452D4×C67—44no—
453D4×C67—44no—
454D4×C67—44no—
455D4×C67—44no—
456D4×C67—44no—
457D4×C67—44no—
458C2×C4×C67—22no—
459C2×C4×C67—22no—
460C2×C4×C67—22no—
461C2×C4×C67—22no—
462C2×C4×C67—22no—
463C2×C4×C67—22no—
464C2×C4×C67—22no—
465C2×C4×C67—22no—
466C2×C4×C67—22no—
467C2×C4×C67—22no—
468C2×C4×C67—22no—
469C2×C4×C67—22no—
470C2×C4×C67—22no—
471C2×C4×C67—22no—
472C2×C4×C67—22no—
473C2×C4×C67—22no—
474C2×C4×C67—22no—
475C2×C4×C67—22no—
476C2×C4×C67—41no—
477C2×C4×C67—41no—
478C2×C4×C67—41no—
479C2×C4×C67—41no—
480C2×C4×C67—41no—
481C2×C4×C67—41no—
482C2×C4×C67—41no—
483C2×C4×C67—41no—
484C2×C4×C67—41no—
485C2×C4×C67—41no—
486C2×C4×C67—41no—
487C2×C4×C67—41no—
488C2×C4×C67—44no—
489C2×C4×C67—42no—
490C2×C4×C67—42no—
491C2×C4×C67—42no—
492C2×C4×C67—44no—
493C2×C4×C67C22×D411yescharacteristic
494C2×C4×C67C22×D411yescharacteristic
495C2×C4×C67C22×D411yescharacteristic
496C2×C4×C67C22×D411yescharacteristic
497C2×C4×C67C22×D411yescharacteristic
498C2×C4×C67C22×D411yescharacteristic
499C2×C4×C67C22×D411yescharacteristic
500C2×C4×C67H(5,𝔽2)14yes—
501C2×C4×C67C2511yescharacteristic
502C22⋊D67—44no—
503C22⋊D67—44no—
504C22⋊D67—44no—
505C22⋊D67—44no—
506C22⋊D67—44no—
507C22⋊D67—44no—
508C2×Dic67—22no—
509C2×Dic67—22no—
510C2×Dic67—22no—
511C2×Dic67—42no—
512C2×Dic67—42no—
513C2×Dic67—42no—
514D268—24no—
515D268—42no—
516C4×D67—44no—
517C4×D67—44no—
518Dic134—24no—
519Dic134—42no—
520C67⋊C8—24no—
521C67⋊C8—24no—
522C22×C67—28no—
523C22×C67—21no—
524C22×C67—21no—
525C22×C67—21no—
526C22×C67—21no—
527C22×C67—21no—
528C22×C67—21no—
529C22×C67—21no—
530C22×C67—21no—
531C22×C67—21no—
532C22×C67—21no—
533C22×C67—21no—
534C22×C67—21no—
535C22×C67—21no—
536C22×C67—21no—
537C22×C67—21no—
538C22×C67—21no—
539C22×C67—44no—
540C22×C67—44no—
541C22×C67—44no—
542C22×C67—44no—
543C22×C67—44no—
544C22×C67—44no—
545C22×C67—42no—
546C22×C67—42no—
547C22×C67—42no—
548C22×C67—84no—
549C22×C67#53412yes—
550C22×C67C2×#13512yes—
551C22×C67C2×#13512yes—
552C22×C67C2×#13512yes—
553C22×C67#57512yes—
554C22×C67C23×D411yescharacteristic
555C2×D67—42no—
556C2×D67—42no—
557C2×D67—42no—
558C2×D67—84no—
559C4×C67—21no—
560C4×C67—21no—
561C4×C67—21no—
562C4×C67—21no—
563C4×C67—21no—
564C4×C67—21no—
565C4×C67—42no—
566C4×C67—42no—
567C4×C67—42no—
568C4×C67#53412yes—
569C4×C67C2×H(5,𝔽2)12yes—
570Dic67—42no—
571Dic67—42no—
572Dic67—42no—
573#60734—671nomaximal, Sylow
574C2×C67—22no—
575C2×C67—22no—
576C2×C67—22no—
577C2×C67—22no—
578C2×C67—22no—
579C2×C67—41no—
580C2×C67—41no—
581C2×C67—82no—
582C2×C67C2×#53411yescharacteristic
583C2×C67C22×#13511yescharacteristic
584C2×C67C2×#57511yescharacteristic
585D67—82no—
586C2×#525—671no—
587C2×#525D6711yescharacteristic, complemented
588#3191—674no—
589#3190—672no—
590#3190—672no—
591#3189—671no—
592#3188—672no—
593#3188—672no—
594#3187—671no—
595#3187—671no—
596#3186—671no—
597#3091—672no—
598#3091—672no—
599#3050—674no—
600#3002—672no—
601#3002—672no—
602C22×C22⋊C8—671no—
603C67#6073411yescharacteristic, complemented, Sylow
604C22×#41—671no—
605C22×#41C2×D6711yescharacteristic, complemented
606C24×C4C2×D6711yescharacteristic
607C2×#135—674no—
608C23×C8—672no—
609#525—21no—
610#525—21no—
611#525—21no—
612#525—21no—
613#525—672no—
614#525—672no—
615#525—672no—
616#525—672no—
617#525—1341no—
618#525—1341no—
619#525—1341no—
620#525—1341no—
621#525C2×D6712yes—
622#525C2×D6712yes—
623#525C2×D6712yescomplemented
624#525C2×D6712yescomplemented
625C2×#123—21no—
626C2×#123—1341no—
627C2×C22⋊Q8—671no—
628C2×C22⋊Q8—671no—
629C2×C22⋊Q8C2×D6711yescharacteristic
630C2×C22⋊Q8C2×D6711yescharacteristic, complemented
631C2×#121—671no—
632C2×#121—671no—
633C2×#121C2×D6711yescharacteristic
634C2×#121C2×D6711yescharacteristic, complemented
635C2×#120—21no—
636C2×#120—1341no—
637C2×C4×D4—21no—
638C2×C4×D4—21no—
639C2×C4×D4—1341no—
640C2×C4×D4—1341no—
641C2×#117—671no—
642C2×#117C2×D6711yescharacteristic, complemented
643#485—674no—
644#485—674no—
645#484—672no—
646#484—672no—
647#483—672no—
648#483—672no—
649#482—674no—
650#482—674no—
651#481—672no—
652#481—672no—
653#480—672no—
654#480—672no—
655#467—674no—
656#467—674no—
657#466—674no—
658#466—674no—
659#465—674no—
660#465—674no—
661#465—674no—
662#465—674no—
663#452—674no—
664#452—674no—
665#451—672no—
666#451—672no—
667#450—672no—
668#450—672no—
669#449—674no—
670#449—674no—
671#448—672no—
672#448—672no—
673#447—672no—
674#447—672no—
675#427—674no—
676#416—674no—
677#416—674no—
678C2×C22⋊C8—672no—
679C2×C22⋊C8—672no—
680C2×C22⋊C8—671no—
681C2×C22⋊C8—671no—
682C2×C22⋊C8—672no—
683C2×C22⋊C8—672no—
684C2×C22⋊C8—672no—
685C25C22⋊D6711yescharacteristic
686C2×#41—21no—
687C2×#41—21no—
688C2×#41—44no—
689C2×#41—2684no—
690C2×#41—672no—
691C2×#41—672no—
692C2×#41—1341no—
693C2×#41—1341no—
694C2×#41C22×D6712yes—
695C2×#41C22×D6712yes—
696C22×Q8—671no—
697C22×Q8C22×D6711yescharacteristic
698C22×D4—21no—
699C22×D4—21no—
700C22×D4—21no—
701C22×D4—671no—
702C22×D4—1341no—
703C22×D4—1341no—
704C22×D4—1341no—
705C22×D4C22×D6711yescharacteristic
706C23×C4—21no—
707C23×C4—44no—
708C23×C4—1341no—
709C23×C4C22⋊D6711yescharacteristic
710C23×C4C22⋊D6711yescharacteristic
711C23×C4C22⋊D6711yescharacteristic
712C23×C4C22⋊D6711yescharacteristic
713C23×C4C22⋊D6711yescharacteristic
714C23×C4C22⋊D6711yescharacteristic
715C23×C4C22⋊D6711yescharacteristic
716C23×C4C22×D6711yescharacteristic
717C23×C4C22×D6711yescharacteristic
718C23×C4C22×D6711yescharacteristic
719C23×C4C22×D6711yescharacteristic
720C23×C4C22×D6711yescharacteristic
721C23×C4C22×D6711yescharacteristic
722C23×C4C22×D6711yescharacteristic
723#135—2688no—
724C2×Q16—674no—
725C2×SD16—674no—
726C2×SD16—674no—
727C2×D8—674no—
728C22×C8—2684no—
729C22×C8—672no—
730C22×C8—674no—
731C22×C8—672no—
732C22×C8—674no—
733#123—22no—
734#123—22no—
735#123—22no—
736#123—22no—
737#123—1342no—
738#123—1342no—
739#123—1342no—
740#123—1342no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—21no—
745C22⋊Q8—672no—
746C22⋊Q8—672no—
747C22⋊Q8—672no—
748C22⋊Q8—672no—
749C22⋊Q8—1341no—
750C22⋊Q8—1341no—
751C22⋊Q8—1341no—
752C22⋊Q8—1341no—
753C22⋊Q8C22×D6712yes—
754C22⋊Q8C22×D6712yes—
755C22⋊Q8C22×D6712yes—
756C22⋊Q8C22×D6712yes—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—21no—
761#121—672no—
762#121—672no—
763#121—672no—
764#121—672no—
765#121—1341no—
766#121—1341no—
767#121—1341no—
768#121—1341no—
769#121C22×D6712yes—
770#121C22×D6712yes—
771#121C22×D6712yes—
772#121C22×D6712yes—
773#120—22no—
774#120—22no—
775#120—22no—
776#120—22no—
777#120—1342no—
778#120—1342no—
779#120—1342no—
780#120—1342no—
781C4×D4—22no—
782C4×D4—22no—
783C4×D4—22no—
784C4×D4—22no—
785C4×D4—22no—
786C4×D4—22no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—1342no—
790C4×D4—1342no—
791C4×D4—1342no—
792C4×D4—1342no—
793C4×D4—1342no—
794C4×D4—1342no—
795C4×D4—1342no—
796C4×D4—1342no—
797#117—21no—
798#117—21no—
799#117—672no—
800#117—672no—
801#117—1341no—
802#117—1341no—
803#117C22×D6712yes—
804#117C22×D6712yes—
805C2×C4⋊C4—21no—
806C2×C4⋊C4—21no—
807C2×C4⋊C4—671no—
808C2×C4⋊C4—671no—
809C2×C4⋊C4—1341no—
810C2×C4⋊C4—1341no—
811C2×C4⋊C4C22×D6711yescharacteristic
812C2×C4⋊C4C22×D6711yescharacteristic
813C2×C22⋊C4—21no—
814C2×C22⋊C4—21no—
815C2×C22⋊C4—21no—
816C2×C22⋊C4—21no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—1341no—
819C2×C22⋊C4—1341no—
820C2×C22⋊C4—1341no—
821C2×C22⋊C4—1341no—
822C2×C22⋊C4—1341no—
823C2×C42—21no—
824C2×C42—1341no—
825#107—674no—
826#107—674no—
827#106—674no—
828#106—674no—
829#103—674no—
830#103—674no—
831#103—674no—
832#103—674no—
833#102—674no—
834#102—674no—
835#102—674no—
836#102—674no—
837C22⋊C8—672no—
838C22⋊C8—672no—
839C22⋊C8—672no—
840C22⋊C8—672no—
841C22⋊C8—674no—
842C22⋊C8—674no—
843C24—24no—
844C24—21no—
845C24—42no—
846C24—42no—
847C24—1341no—
848C24C2×C22⋊D6711yescharacteristic
849C24C2×C22⋊D6711yescharacteristic
850C24C2×C22⋊D6711yescharacteristic
851C24C2×C22⋊D6711yescharacteristic
852C24C2×C22⋊D6711yescharacteristic
853C24C2×C22⋊D6711yescharacteristic
854C24C2×C22⋊D6711yescharacteristic
855#41—28no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—2684no—
860#41—2684no—
861#41—2684no—
862#41—1348no—
863C2×Q8—21no—
864C2×Q8—42no—
865C2×Q8—2682no—
866C2×Q8—672no—
867C2×Q8—1341no—
868C2×Q8C23×D6712yes—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—21no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—2682no—
881C2×D4—2684no—
882C2×D4—2684no—
883C2×D4—2684no—
884C2×D4—672no—
885C2×D4—1342no—
886C2×D4—1342no—
887C2×D4—1342no—
888C2×D4—1342no—
889C2×D4—1342no—
890C2×D4—1342no—
891C2×D4—1341no—
892C2×D4C23×D6712yes—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—2684no—
914C22×C4—1341no—
915C22×C4—1341no—
916C22×C4—1341no—
917C22×C4—1342no—
918C22×C4—1342no—
919C22×C4C2×C22⋊D6711yescharacteristic
920C22×C4C2×C22⋊D6711yescharacteristic
921C22×C4C2×C22⋊D6711yescharacteristic
922C22×C4C2×C22⋊D6711yescharacteristic
923C22×C4C2×C22⋊D6711yescharacteristic
924C22×C4C2×C22⋊D6711yescharacteristic
925C22×C4C2×C22⋊D6711yescharacteristic
926C22×C4C2×C22⋊D6711yescharacteristic
927C22×C4C2×C22⋊D6711yescharacteristic
928C22×C4C2×C22⋊D6711yescharacteristic
929C22×C4C2×C22⋊D6711yescharacteristic
930C22×C4C2×C22⋊D6711yescharacteristic
931C22×C4C2×C22⋊D6711yescharacteristic
932C22×C4C2×C22⋊D6711yescharacteristic
933C22×C4C2×C22⋊D6711yescharacteristic
934C22×C4C2×C22⋊D6711yescharacteristic
935C22×C4C2×C22⋊D6711yescharacteristic
936C22×C4C2×C22⋊D6711yescharacteristic
937C22×C4C2×C22⋊D6711yescharacteristic
938C22×C4C2×C22⋊D6711yescharacteristic
939C22×C4C2×C22⋊D6711yescharacteristic
940C22×C4C23×D6711yescharacteristic
941C22×C4C23×D6711yescharacteristic
942C22×C4C23×D6711yescharacteristic
943C22×C4C23×D6711yescharacteristic
944C22×C4C23×D6711yescharacteristic
945C22×C4C23×D6711yescharacteristic
946C22×C4C23×D6711yescharacteristic
947Q16—2684no—
948SD16—2684no—
949SD16—2684no—
950D8—2684no—
951C2×C8—2682no—
952C2×C8—2684no—
953C2×C8—2682no—
954C2×C8—674no—
955C2×C8—674no—
956C2×C8—1348no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—672no—
964C4⋊C4—672no—
965C4⋊C4—1341no—
966C4⋊C4—1341no—
967C4⋊C4—1342no—
968C4⋊C4—1342no—
969C4⋊C4—1342no—
970C4⋊C4—1342no—
971C4⋊C4C23×D6712yes—
972C4⋊C4C23×D6712yes—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—1342no—
984C22⋊C4—1342no—
985C22⋊C4—1342no—
986C22⋊C4—1342no—
987C22⋊C4—1342no—
988C22⋊C4—1342no—
989C22⋊C4—1342no—
990C22⋊C4—1342no—
991C22⋊C4—1342no—
992C22⋊C4—1342no—
993C42—22no—
994C42—22no—
995C42—1342no—
996C42—1342no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—416no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—2682no—
1023C23—2682no—
1024C23—2682no—
1025C23—1342no—
1026C23#1452406314yescomplemented
1027C23C22×C22⋊D6711yescharacteristic
1028C23C22×C22⋊D6711yescharacteristic
1029C23C22×C22⋊D6711yescharacteristic
1030C23C22×C22⋊D6711yescharacteristic
1031C23C22×C22⋊D6711yescharacteristic
1032C23C22×C22⋊D6711yescharacteristic
1033C23C22×C22⋊D6711yescharacteristic
1034Q8—24no—
1035Q8—42no—
1036Q8—2682no—
1037Q8—1344no—
1038D4—24no—
1039D4—42no—
1040D4—44no—
1041D4—44no—
1042D4—44no—
1043D4—44no—
1044D4—44no—
1045D4—44no—
1046D4—2682no—
1047D4—2684no—
1048D4—2684no—
1049D4—2684no—
1050D4—2684no—
1051D4—2684no—
1052D4—2684no—
1053D4—1344no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—44no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—44no—
1089C2×C4—2684no—
1090C2×C4—2682no—
1091C2×C4—2682no—
1092C2×C4—2682no—
1093C2×C4—2684no—
1094C2×C4—1342no—
1095C2×C4—1342no—
1096C2×C4—1342no—
1097C2×C4C22×C22⋊D6711yescharacteristic
1098C2×C4C22×C22⋊D6711yescharacteristic
1099C2×C4C22×C22⋊D6711yescharacteristic
1100C2×C4C22×C22⋊D6711yescharacteristic
1101C2×C4C22×C22⋊D6711yescharacteristic
1102C2×C4C22×C22⋊D6711yescharacteristic
1103C2×C4C22×C22⋊D6711yescharacteristic
1104C2×C4#1452408814yes—
1105C2×C4C24×D6711yescharacteristic
1106C8—1344no—
1107C8—1344no—
1108C22—28no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—84no—
1135C22—2682no—
1136C22—2682no—
1137C22—2682no—
1138C22—5364no—
1139C22#1686395512yes—
1140C22C2×#1452406312yes—
1141C22C2×#1452406312yes—
1142C22C2×#1452406312yes—
1143C22#1686419412yes—
1144C22C23×C22⋊D6711yescharacteristic
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—2682no—
1155C4—2682no—
1156C4—2682no—
1157C4#1686395512yes—
1158C4C2×#1452408812yes—
1159C2—22no—
1160C2—22no—
1161C2—22no—
1162C2—22no—
1163C2—22no—
1164C2—41no—
1165C2—41no—
1166C2—82no—
1167C2—5362no—
1168C2C2×#1686395511yescharacteristic
1169C2C22×#1452406311yescharacteristic
1170C2C2×#1686419411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#525×C67C2
socleC22×C67C23×D4
hypercenterC2×#525D67
hypocenterC67#60734
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16863907C2semidirect
2. #22570997C2semidirect
3. #22570990C2semidirect
4. #22570986C2semidirect
5. #22570981C2semidirect
6. #22570974C2semidirect
7. #22570970C2semidirect
8. #22570966C2semidirect
9. #22570962C2semidirect
10. #22570957C2semidirect
11. #22570122C2semidirect
12. #22570118C2semidirect
13. #22569787C2semidirect
14. #22569427C2semidirect
15. #22569425C2semidirect
16. C22×C22⋊(C67⋊C8)C2semidirect
17. C2×#525×C67C2semidirect
18. C22×#11761628C22semidirect
19. C2×#14524063C22semidirect
20. C23×C67⋊C8C22semidirect
27. #16863907C22semidirect
28. #16863907C22semidirect
31. C2×#14524022C22semidirect
33. C2×#14524017C22semidirect
37. C2×#14524002C22semidirect
38. #16863737C22semidirect
39. #16863734C22semidirect
40. #16863731C22semidirect
41. #16863729C22semidirect
42. #16863726C22semidirect
43. #16863724C22semidirect
44. #16863720C22semidirect
45. #16863717C22semidirect
46. #16863714C22semidirect
47. #16863712C22semidirect
48. #16863709C22semidirect
49. #16863707C22semidirect
50. #16863635C22semidirect
51. #16863635C22semidirect
52. #16863630C22semidirect
53. #16863630C22semidirect
54. #16863627C22semidirect
55. #16863627C22semidirect
56. #16863623C22semidirect
57. #16863623C22semidirect
58. #16863558C22semidirect
59. #16863556C22semidirect
60. #16863552C22semidirect
61. #16863551C22semidirect
62. #16863547C22semidirect
63. #16863546C22semidirect
64. #16863541C22semidirect
65. #16863539C22semidirect
66. #16863535C22semidirect
67. #16863534C22semidirect
68. #16863530C22semidirect
69. #16863529C22semidirect
70. #16863432C22semidirect
71. #16863392C22semidirect
72. #16863390C22semidirect
75. C2×C22⋊(C67⋊C8)C22semidirect
76. C2×C22⋊(C67⋊C8)C22semidirect
77. C2×C22⋊(C67⋊C8)C22semidirect
78. C2×C22⋊(C67⋊C8)C22semidirect
79. C2×C22⋊(C67⋊C8)C22semidirect
80. C22×#41×C67C22semidirect
88. #525×C67C22semidirect
89. #525×C67C22semidirect
92. C2×C22⋊Q8×C67C22semidirect
94. C2×#121×C67C22semidirect
98. C2×#117×C67C22semidirect
111. C2×#11761618C23semidirect
112. C2×#11761616C23semidirect
113. C2×#11761615C23semidirect
114. C2×#11761613C23semidirect
166. #14523976C23semidirect
167. #14523976C23semidirect
168. #14523974C23semidirect
169. #14523974C23semidirect
170. #14523967C23semidirect
171. #14523967C23semidirect
172. #14523966C23semidirect
173. #14523966C23semidirect
174. #14523964C23semidirect
175. #14523964C23semidirect
176. #14523963C23semidirect
177. #14523963C23semidirect
436. C23×C67#135semidirect
587. C2×#525D67semidirect
603. C67#60734semidirect
605. C22×#41C2×D67semidirect
623. #525C2×D67semidirect
624. #525C2×D67semidirect
630. C2×C22⋊Q8C2×D67semidirect
634. C2×#121C2×D67semidirect
642. C2×#117C2×D67semidirect
1026. C23#14524063semidirect

Maximal subgroups

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

subgroupindex
C2×#168639072
#225709972
#225709902
#225709862
#225709812
#225709742
#225709702
#225709662
#225709622
#225709572
#225701222
#225701182
#225697872
#225694272
#225694252
C22×C22⋊(C67⋊C8)2
C2×#525×C672
#6073467