Finite Group Databasebeta

← C2×#22571055 #31726478

Subgroups — C2×#22571055 #31726478

Order 17152.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863960C211yesmaximal, characteristic, complemented
2#22571055C2116yesmaximal, direct product factor
3C2×#16863714C211yesmaximal, characteristic, complemented
4C2×#16863734C211yesmaximal, characteristic, complemented
5C2×#16863717C211yesmaximal, characteristic, complemented
6C2×#16863709C211yesmaximal, characteristic, complemented
7C2×#16863647C211yesmaximal, characteristic, complemented
8C2×#16863644C211yesmaximal, characteristic, complemented
9C2×#16863630C211yesmaximal, characteristic, complemented
10C2×#16863627C211yesmaximal, characteristic, complemented
11C2×#16863541C211yesmaximal, characteristic, complemented
12C2×#16863541C211yesmaximal, characteristic, complemented
13C2×#16863546C211yesmaximal, characteristic, complemented
14C2×#16863529C211yesmaximal, characteristic, complemented
15C2×#16863363C211yesmaximal, characteristic, complemented
16C2×#537×C67C211yesmaximal, characteristic, complemented
17C23×D268C2211yescharacteristic
18C22×#11761615C2211yescharacteristic
19C22×#11761615C2211yescharacteristic
20C22×#11761613C2211yescharacteristic
21C22×#11761613C2211yescharacteristic
22C22×#11761612C2211yescharacteristic, complemented
23C23×C67⋊C8C2211yescharacteristic, complemented
24#16863960—24no—
25#16863960C2218yescomplemented
26C2×#14524039—21no—
27C2×#14524032—21no—
28C2×#14524017C2211yescharacteristic
29C2×#14524017C2211yescharacteristic
30C2×#14524017C2211yescharacteristic
31C2×#14524017C2211yescharacteristic
32C2×#14524011—21no—
33C2×#14524011—21no—
34C2×#14524002C2211yescharacteristic
35#16863734C2218yescomplemented
36#16863717C2218yescomplemented
37#16863714C2218yescomplemented
38#16863709C2218yescomplemented
39#16863647C2218yescomplemented
40#16863644C2218yescomplemented
41#16863630C2218yescomplemented
42#16863627C2218yescomplemented
43#16863546C2218yescomplemented
44#16863541C2218yescomplemented
45#16863541C2218yescomplemented
46#16863529C2218yescomplemented
47C2×#14523976C2211yescharacteristic, complemented
48C2×#14523976C2211yescharacteristic, complemented
49C2×#14523974C2211yescharacteristic, complemented
50C2×#14523974C2211yescharacteristic, complemented
51C2×#14523967C2211yescharacteristic, complemented
52C2×#14523967C2211yescharacteristic, complemented
53C2×#14523964C2211yescharacteristic, complemented
54C2×#14523964C2211yescharacteristic, complemented
55C2×#14523963C2211yescharacteristic
56C2×#14523963C2211yescharacteristic
57C2×#14523963C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59#16863363C2218yescomplemented
60C2×C22⋊(C67⋊C8)C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic, complemented
63C2×C22⋊(C67⋊C8)C2211yescharacteristic, complemented
64C22×#41×C67C2211yescharacteristic
65C22×#41×C67C2211yescharacteristic, complemented
66#537×C67—24no—
67#537×C67C2218yescomplemented
68C2×C22⋊Q8×C67—21no—
69C2×C22⋊Q8×C67C2211yescharacteristic
70C2×C22⋊Q8×C67C2211yescharacteristic, complemented
71C2×#121×C67—21no—
72C2×#121×C67—21no—
73C2×#121×C67—21no—
74C2×#121×C67C2211yescharacteristic
75C2×#121×C67C2211yescharacteristic, complemented
76C22×C4⋊C4×C67C2211yescharacteristic, complemented
77C24×D67—21no—
78C22×D268—21no—
79C22×D268—22no—
80C22×D268—42no—
81C22×D268—42no—
82C22×D268C2311yescharacteristic
83C22×D268C2311yescharacteristic
84C22×D268C2314yes—
85C22×C22⋊D67—21no—
86C22×C22⋊D67—21no—
87C22×C22⋊D67—21no—
88C22×C22⋊D67—21no—
89C2×#11761615—42no—
90C2×#11761615—42no—
91C2×#11761615C2314yes—
92C2×#11761615C2314yes—
93C2×#11761613—42no—
94C2×#11761613—42no—
95C2×#11761613C2314yes—
96C2×#11761613C2314yes—
97C2×#11761612—42no—
98C2×#11761612C2314yescomplemented
99C22×C67⋊C8—42no—
100C22×C67⋊C8C2311yescharacteristic
101C22×C67⋊C8C2311yescharacteristic
102C22×C67⋊C8C2311yescharacteristic
103C22×C67⋊C8C2311yescharacteristic
104C22×C67⋊C8C2314yescomplemented
105#14524039—28no—
106#14524032—28no—
107#14524017—22no—
108#14524017—22no—
109#14524017—22no—
110#14524017—22no—
111#14524017C2314yes—
112#14524017C2314yes—
113#14524017C2314yes—
114#14524017C2314yes—
115#14524011—28no—
116#14524011—28no—
117#14524002—22no—
118#14524002C2314yes—
119C2×C4⋊Dic67C2311yescharacteristic
120C2×C4⋊Dic67C2311yescharacteristic
121C2×C22⋊Dic67—21no—
122C2×(C2×D67)⋊C4—21no—
123C2×(C2×D67)⋊C4—21no—
124C2×(C2×D67)⋊C4—21no—
125C2×(C2×D67)⋊C4—21no—
126C2×C4×Dic67—21no—
127#14523976C2314yescomplemented
128#14523976C2314yescomplemented
129#14523974C2314yescomplemented
130#14523974C2314yescomplemented
131#14523967C2314yescomplemented
132#14523967C2314yescomplemented
133#14523964C2314yescomplemented
134#14523964C2314yescomplemented
135#14523963C2314yes—
136#14523963C2314yes—
137#14523963C2314yes—
138#14523963C2314yes—
139C22⋊(C67⋊C8)C2314yes—
140C22⋊(C67⋊C8)C2314yes—
141C22⋊(C67⋊C8)C2314yescomplemented
142C22⋊(C67⋊C8)C2314yescomplemented
143C2×#41×C67—22no—
144C2×#41×C67—42no—
145C2×#41×C67—42no—
146C2×#41×C67—42no—
147C2×#41×C67—42no—
148C2×#41×C67D414yes—
149C2×#41×C67C2314yes—
150C2×#41×C67C2314yescomplemented
151C22×Q8×C67D411yescharacteristic
152C22×Q8×C67C2311yescharacteristic
153C22×D4×C67—21no—
154C22×D4×C67—21no—
155C22×D4×C67—21no—
156C22×D4×C67D411yescharacteristic
157C22×D4×C67D411yescharacteristic
158C22×D4×C67D411yescharacteristic
159C22×D4×C67C2311yescharacteristic
160C23×C4×C67—21no—
161C23×C4×C67—21no—
162C23×C4×C67C2311yescharacteristic
163C23×C4×C67C2311yescharacteristic
164C23×C4×C67C2311yescharacteristic
165C22⋊Q8×C67—28no—
166C22⋊Q8×C67—22no—
167C22⋊Q8×C67—22no—
168C22⋊Q8×C67C2314yes—
169C22⋊Q8×C67C2314yescomplemented
170#121×C67—28no—
171#121×C67—28no—
172#121×C67—28no—
173#121×C67—22no—
174#121×C67—22no—
175#121×C67C2314yes—
176#121×C67C2314yescomplemented
177C2×C4⋊C4×C67—21no—
178C2×C4⋊C4×C67—22no—
179C2×C4⋊C4×C67—21no—
180C2×C4⋊C4×C67—21no—
181C2×C4⋊C4×C67C2311yescharacteristic
182C2×C4⋊C4×C67C2311yescharacteristic
183C2×C4⋊C4×C67C2314yescomplemented
184C2×C22⋊C4×C67—21no—
185C2×C22⋊C4×C67—21no—
186C2×C22⋊C4×C67—21no—
187C2×C22⋊C4×C67—21no—
188C23×D67—21no—
189C23×D67—21no—
190C23×D67—24no—
191C23×D67—44no—
192C23×D67—82no—
193C23×D67—82no—
194C2×D268—22no—
195C2×D268—22no—
196C2×D268—22no—
197C2×D268—22no—
198C2×D268—21no—
199C2×D268—21no—
200C2×D268—24no—
201C2×D268—44no—
202C2×D268—44no—
203C2×D268—44no—
204C2×D268—48no—
205C2×D268C2412yes—
206C2×D268C2412yes—
207C2×C22⋊D67—24no—
208C2×C22⋊D67—24no—
209C2×C22⋊D67—24no—
210C2×C22⋊D67—24no—
211C2×C22⋊D67—82no—
212C2×C22⋊D67—82no—
213C2×C22⋊D67—82no—
214C2×C22⋊D67—82no—
215C22×Dic67—21no—
216C22×Dic67—21no—
217#11761615—44no—
218#11761615—44no—
219#11761613—44no—
220#11761613—44no—
221#11761612—44no—
222C2×C67⋊C8—22no—
223C2×C67⋊C8—22no—
224C2×C67⋊C8—22no—
225C2×C67⋊C8—22no—
226C2×C67⋊C8—44no—
227C2×C67⋊C8C2412yes—
228C2×C67⋊C8C2412yes—
229C2×C67⋊C8C2412yes—
230C2×C67⋊C8C2412yes—
231C4⋊Dic67—21no—
232C4⋊Dic67—21no—
233C4⋊Dic67C2412yes—
234C4⋊Dic67C2412yes—
235C22⋊Dic67—24no—
236(C2×D67)⋊C4—24no—
237(C2×D67)⋊C4—24no—
238(C2×D67)⋊C4—24no—
239(C2×D67)⋊C4—24no—
240C4×Dic67—24no—
241C24×C67—21no—
242C24×C67C2×D411yescharacteristic
243C24×C67C2×D411yescharacteristic
244C24×C67C2×D411yescharacteristic
245#41×C67—48no—
246#41×C67—44no—
247#41×C67—44no—
248#41×C67—44no—
249#41×C67—44no—
250#41×C67—48no—
251C2×Q8×C67—21no—
252C2×Q8×C67—22no—
253C2×Q8×C67—22no—
254C2×Q8×C67—42no—
255C2×Q8×C67C2×D414yes—
256C2×Q8×C67C2412yes—
257C2×D4×C67—24no—
258C2×D4×C67—24no—
259C2×D4×C67—24no—
260C2×D4×C67—21no—
261C2×D4×C67—22no—
262C2×D4×C67—22no—
263C2×D4×C67—42no—
264C2×D4×C67—42no—
265C2×D4×C67—42no—
266C2×D4×C67—44no—
267C2×D4×C67—82no—
268C2×D4×C67—82no—
269C2×D4×C67C2×D414yes—
270C2×D4×C67C2×D414yes—
271C2×D4×C67C2×D414yes—
272C2×D4×C67C2412yes—
273C22×C4×C67—22no—
274C22×C4×C67—22no—
275C22×C4×C67—22no—
276C22×C4×C67—22no—
277C22×C4×C67—22no—
278C22×C4×C67—22no—
279C22×C4×C67—21no—
280C22×C4×C67—21no—
281C22×C4×C67—21no—
282C22×C4×C67—24no—
283C22×C4×C67—24no—
284C22×C4×C67—44no—
285C22×C4×C67—82no—
286C22×C4×C67C2×D411yescharacteristic
287C22×C4×C67C2×D411yescharacteristic
288C22×C4×C67C2×D411yescharacteristic
289C22×C4×C67C2×D412yes—
290C22×C4×C67C2×D412yes—
291C22×C4×C67C2×D412yes—
292C22×C4×C67C2412yes—
293C22×C4×C67C2412yes—
294C22×C4×C67C2412yes—
295C22×C4×C67C2411yescharacteristic
296C4⋊C4×C67—21no—
297C4⋊C4×C67—21no—
298C4⋊C4×C67—24no—
299C4⋊C4×C67—24no—
300C4⋊C4×C67—24no—
301C4⋊C4×C67C2412yes—
302C4⋊C4×C67C2412yes—
303C22⋊C4×C67—24no—
304C22⋊C4×C67—24no—
305C22⋊C4×C67—24no—
306C22⋊C4×C67—24no—
307C23×C67—22no—
308C23×C67—22no—
309C23×C67—22no—
310C23×C67—22no—
311C23×C67—22no—
312C23×C67—22no—
313C23×C67—22no—
314C23×C67—22no—
315C23×C67—22no—
316C23×C67—22no—
317C23×C67—42no—
318C23×C67—42no—
319C23×C67—42no—
320C23×C67C22×D412yes—
321C23×C67C22×D412yes—
322C23×C67C22×D412yes—
323C23×C67C22×D411yescharacteristic
324C22×D67—22no—
325C22×D67—22no—
326C22×D67—48no—
327C22×D67—42no—
328C22×D67—42no—
329C22×D67—42no—
330C22×D67—42no—
331C22×D67—42no—
332C22×D67—42no—
333C22×D67—84no—
334C22×D67—84no—
335C22×D67—816no—
336Q8×C67—22no—
337Q8×C67—22no—
338Q8×C67—44no—
339Q8×C67—42no—
340D4×C67—22no—
341D4×C67—22no—
342D4×C67—44no—
343D4×C67—44no—
344D4×C67—44no—
345D4×C67—48no—
346D4×C67—42no—
347D4×C67—84no—
348D4×C67—84no—
349C2×C4×C67—22no—
350C2×C4×C67—22no—
351C2×C4×C67—22no—
352C2×C4×C67—24no—
353C2×C4×C67—24no—
354C2×C4×C67—24no—
355C2×C4×C67—22no—
356C2×C4×C67—22no—
357C2×C4×C67—22no—
358C2×C4×C67—22no—
359C2×C4×C67—22no—
360C2×C4×C67—22no—
361C2×C4×C67—22no—
362C2×C4×C67—22no—
363C2×C4×C67—22no—
364C2×C4×C67—48no—
365C2×C4×C67—42no—
366C2×C4×C67—42no—
367C2×C4×C67—42no—
368C2×C4×C67—84no—
369C2×C4×C67C22×D412yes—
370C2×C4×C67C22×D412yes—
371C2×C4×C67C22×D412yes—
372C2×C4×C67C22×D411yescharacteristic
373C2×C4×C67H(5,𝔽2)12yes—
374C2×C4×C67H(5,𝔽2)12yes—
375C2×C4×C67C2511yescharacteristic
376C22⋊D67—84no—
377C22⋊D67—84no—
378C22⋊D67—84no—
379C22⋊D67—84no—
380C2×Dic67—22no—
381C2×Dic67—22no—
382C2×Dic67—42no—
383C2×Dic67—42no—
384D268—22no—
385D268—22no—
386D268—22no—
387D268—22no—
388D268—48no—
389D268—42no—
390D268—42no—
391C67⋊C8—22no—
392C67⋊C8—22no—
393C67⋊C8—22no—
394C67⋊C8—22no—
395C22×C67—22no—
396C22×C67—22no—
397C22×C67—22no—
398C22×C67—22no—
399C22×C67—22no—
400C22×C67—22no—
401C22×C67—22no—
402C22×C67—22no—
403C22×C67—22no—
404C22×C67—44no—
405C22×C67—44no—
406C22×C67—44no—
407C22×C67—42no—
408C22×C67—42no—
409C22×C67—42no—
410C22×C67—84no—
411C22×C67#53412yes—
412C22×C67#57612yes—
413C22×C67#57712yes—
414C22×C67C23×D411yescharacteristic
415C2×D67—42no—
416C2×D67—42no—
417C2×D67—42no—
418C2×D67—42no—
419C2×D67—42no—
420C2×D67—42no—
421C2×D67—816no—
422C2×D67—84no—
423C2×D67—84no—
424C4×C67—22no—
425C4×C67—22no—
426C4×C67—22no—
427C4×C67—42no—
428C4×C67—42no—
429C4×C67—42no—
430C4×C67#53412yes—
431C4×C67C2×H(5,𝔽2)11yescharacteristic
432C4×C67C2×H(5,𝔽2)11yescharacteristic
433Dic67—42no—
434Dic67—42no—
435C2×#3198—671nomaximal, Sylow
436C2×C67—42no—
437C2×C67—42no—
438C2×C67—42no—
439C2×C67—82no—
440C2×C67#319814yescomplemented
441C2×C67C2×#53411yescharacteristic
442C2×C67C2×#57611yescharacteristic
443C2×C67C2×#57711yescharacteristic
444D67—82no—
445D67—82no—
446C2×#537D6711yescharacteristic, complemented
447C2×#535—671no—
448#3198—6716no—
449C2×#481—671no—
450C2×#485—671no—
451C2×#482—671no—
452C2×#480—671no—
453C2×#469—671no—
454C2×#468—671no—
455C2×#466—671no—
456C2×#465—671no—
457C2×#449—671no—
458C2×#449—671no—
459C2×#450—671no—
460C2×#447—671no—
461C2×#408—671no—
462C67C2×#319811yescharacteristic, complemented, Sylow
463C22×#41C2×D6711yescharacteristic
464C22×#41C2×D6711yescharacteristic, complemented
465C23×D4—671no—
466C22×SD16—671no—
467C22×SD16—671no—
468C22×D8—671no—
469C22×D8—671no—
470C22×M16—671no—
471C23×C8—671no—
472#537—24no—
473#537C2×D6718yescomplemented
474#535—678no—
475#535—1344no—
476C2×#127—1341no—
477C2×#124—1341no—
478C2×C22⋊Q8—21no—
479C2×C22⋊Q8C2×D6711yescharacteristic
480C2×C22⋊Q8C2×D6711yescharacteristic, complemented
481C2×#121—21no—
482C2×#121—21no—
483C2×#121—21no—
484C2×#121—671no—
485C2×#121—671no—
486C2×#121—671no—
487C2×#121—671no—
488C2×#121C2×D6711yescharacteristic
489C2×#121C2×D6711yescharacteristic, complemented
490C2×#120—1341no—
491C2×#120—1341no—
492C2×#117—671no—
493C22×C4⋊C4C2×D6711yescharacteristic, complemented
494#485—678no—
495#482—678no—
496#481—678no—
497#480—678no—
498#469—678no—
499#468—678no—
500#466—678no—
501#465—678no—
502#450—678no—
503#449—678no—
504#449—678no—
505#447—678no—
506C2×#107—671no—
507C2×#107—671no—
508C2×#106—671no—
509C2×#106—671no—
510C2×#103—671no—
511C2×#103—671no—
512C2×#102—671no—
513C2×#102—671no—
514C2×#102—671no—
515C2×#102—671no—
516C2×#102—671no—
517C2×#102—671no—
518#408—678no—
519C2×C22⋊C8—671no—
520C2×C22⋊C8—671no—
521C2×C22⋊C8—671no—
522C2×C22⋊C8—671no—
523C25—1341no—
524C2×#41—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41C22⋊D6714yes—
530C2×#41C22×D6714yes—
531C2×#41C22×D6714yescomplemented
532C22×Q8C22⋊D6711yescharacteristic
533C22×Q8C22×D6711yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—2682no—
538C22×D4—2682no—
539C22×D4—674no—
540C22×D4—671no—
541C22×D4—671no—
542C22×D4—1341no—
543C22×D4—1341no—
544C22×D4—1341no—
545C22×D4—1341no—
546C22×D4—1341no—
547C22×D4—1342no—
548C22×D4C22⋊D6711yescharacteristic
549C22×D4C22⋊D6711yescharacteristic
550C22×D4C22⋊D6711yescharacteristic
551C22×D4C22×D6711yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C22×D6711yescharacteristic
555C23×C4C22×D6711yescharacteristic
556C23×C4C22×D6711yescharacteristic
557C2×SD16—2682no—
558C2×SD16—2682no—
559C2×SD16—674no—
560C2×SD16—674no—
561C2×D8—2682no—
562C2×D8—2682no—
563C2×D8—674no—
564C2×D8—674no—
565C2×M16—2682no—
566C2×M16—674no—
567C22×C8—2682no—
568C22×C8—674no—
569C22×C8—671no—
570C22×C8—671no—
571C22×C8—671no—
572C22×C8—671no—
573#127—1348no—
574#124—1348no—
575C22⋊Q8—28no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8C22×D6714yes—
579C22⋊Q8C22×D6714yescomplemented
580#121—28no—
581#121—28no—
582#121—28no—
583#121—22no—
584#121—22no—
585#121—674no—
586#121—674no—
587#121—674no—
588#121—674no—
589#121—1342no—
590#121—1342no—
591#121—1342no—
592#121—1342no—
593#121C22×D6714yes—
594#121C22×D6714yescomplemented
595#120—1348no—
596#120—1348no—
597#117—674no—
598#117—1342no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—671no—
604C2×C4⋊C4—671no—
605C2×C4⋊C4C22×D6711yescharacteristic
606C2×C4⋊C4C22×D6711yescharacteristic
607C2×C4⋊C4C22×D6714yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—1341no—
613C2×C22⋊C4—1341no—
614C2×C22⋊C4—1341no—
615C2×C22⋊C4—1341no—
616C2×C22⋊C4—1341no—
617C2×C42—1341no—
618#107—674no—
619#107—674no—
620#106—674no—
621#106—674no—
622#103—674no—
623#103—674no—
624#102—674no—
625#102—674no—
626#102—674no—
627#102—674no—
628#102—674no—
629#102—674no—
630C22⋊C8—674no—
631C22⋊C8—674no—
632C22⋊C8—674no—
633C22⋊C8—674no—
634C24—21no—
635C24—2684no—
636C24—5362no—
637C24—5362no—
638C24—1341no—
639C24—1341no—
640C24—1344no—
641C24C2×C22⋊D6711yescharacteristic
642C24C2×C22⋊D6711yescharacteristic
643C24C2×C22⋊D6711yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—44no—
649#41—48no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—42no—
654C2×Q8C2×C22⋊D6714yes—
655C2×Q8C23×D6712yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—82no—
667C2×D4—82no—
668C2×D4—2684no—
669C2×D4—2688no—
670C2×D4—2684no—
671C2×D4—2684no—
672C2×D4—5362no—
673C2×D4—5362no—
674C2×D4—5362no—
675C2×D4—5362no—
676C2×D4—672no—
677C2×D4—672no—
678C2×D4—1344no—
679C2×D4—1344no—
680C2×D4—1344no—
681C2×D4—1344no—
682C2×D4—1341no—
683C2×D4—1341no—
684C2×D4—1344no—
685C2×D4—1342no—
686C2×D4—1342no—
687C2×D4—1342no—
688C2×D4—1342no—
689C2×D4C2×C22⋊D6714yes—
690C2×D4C2×C22⋊D6714yes—
691C2×D4C2×C22⋊D6714yes—
692C2×D4C23×D6712yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—44no—
705C22×C4—82no—
706C22×C4—1341no—
707C22×C4—1341no—
708C22×C4C2×C22⋊D6712yes—
709C22×C4C2×C22⋊D6712yes—
710C22×C4C2×C22⋊D6712yes—
711C22×C4C2×C22⋊D6711yescharacteristic
712C22×C4C2×C22⋊D6711yescharacteristic
713C22×C4C2×C22⋊D6711yescharacteristic
714C22×C4C23×D6712yes—
715C22×C4C23×D6712yes—
716C22×C4C23×D6712yes—
717C22×C4C23×D6711yescharacteristic
718SD16—2684no—
719SD16—2684no—
720D8—2684no—
721D8—2684no—
722M16—2684no—
723C2×C8—2684no—
724C2×C8—672no—
725C2×C8—672no—
726C2×C8—672no—
727C2×C8—672no—
728C2×C8—1342no—
729C2×C8—1342no—
730C2×C8—1342no—
731C2×C8—1342no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—672no—
738C4⋊C4—672no—
739C4⋊C4—1341no—
740C4⋊C4—1341no—
741C4⋊C4C23×D6712yes—
742C4⋊C4C23×D6712yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—1344no—
748C22⋊C4—1344no—
749C22⋊C4—1344no—
750C22⋊C4—1344no—
751C22⋊C4—1344no—
752C42—1344no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—2688no—
767C23—2682no—
768C23—2682no—
769C23—2682no—
770C23—2682no—
771C23—2682no—
772C23—2682no—
773C23—5364no—
774C23—5364no—
775C23—53616no—
776C23—1342no—
777C23—1342no—
778C23C22×C22⋊D6712yes—
779C23C22×C22⋊D6712yes—
780C23C22×C22⋊D6712yes—
781C23C22×C22⋊D6711yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—42no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—44no—
790D4—44no—
791D4—48no—
792D4—42no—
793D4—84no—
794D4—84no—
795D4—2688no—
796D4—2682no—
797D4—2682no—
798D4—5364no—
799D4—5364no—
800D4—5364no—
801D4—5364no—
802D4—1342no—
803D4—1342no—
804D4—1342no—
805D4—1342no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—48no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—84no—
826C2×C4—2682no—
827C2×C4—2682no—
828C2×C4—1342no—
829C2×C4—1342no—
830C2×C4C22×C22⋊D6712yes—
831C2×C4C22×C22⋊D6712yes—
832C2×C4C22×C22⋊D6712yes—
833C2×C4C22×C22⋊D6711yescharacteristic
834C2×C4#1452408812yes—
835C2×C4#1452408812yes—
836C2×C4C24×D6711yescharacteristic
837C8—1342no—
838C8—1342no—
839C8—1342no—
840C8—1342no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—2682no—
858C22—2682no—
859C22—2682no—
860C22—2682no—
861C22—2682no—
862C22—2682no—
863C22—53616no—
864C22—5364no—
865C22—5364no—
866C22#1686395512yes—
867C22#1686419912yes—
868C22#1686420412yes—
869C22C23×C22⋊D6711yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—2682no—
877C4—2682no—
878C4#1686395512yes—
879C4C2×#1452408811yescharacteristic
880C4C2×#1452408811yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—5362no—
886C2—5362no—
887C2#2257105514yesdirect product factor
888C2C2×#1686395511yescharacteristic
889C2C2×#1686419911yescharacteristic
890C2C2×#1686420411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#537×C67C2
socleC23×C67C22×D4
hypercenterC2×#537D67
hypocenterC67C2×#3198
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16863960C2semidirect
2. #22571055C2direct (N × H)
3. C2×#16863714C2semidirect
4. C2×#16863734C2semidirect
5. C2×#16863717C2semidirect
6. C2×#16863709C2semidirect
7. C2×#16863647C2semidirect
8. C2×#16863644C2semidirect
9. C2×#16863630C2semidirect
10. C2×#16863627C2semidirect
11. C2×#16863541C2semidirect
12. C2×#16863541C2semidirect
13. C2×#16863546C2semidirect
14. C2×#16863529C2semidirect
15. C2×#16863363C2semidirect
16. C2×#537×C67C2semidirect
22. C22×#11761612C22semidirect
23. C23×C67⋊C8C22semidirect
25. #16863960C22semidirect
35. #16863734C22semidirect
36. #16863717C22semidirect
37. #16863714C22semidirect
38. #16863709C22semidirect
39. #16863647C22semidirect
40. #16863644C22semidirect
41. #16863630C22semidirect
42. #16863627C22semidirect
43. #16863546C22semidirect
44. #16863541C22semidirect
45. #16863541C22semidirect
46. #16863529C22semidirect
47. C2×#14523976C22semidirect
48. C2×#14523976C22semidirect
49. C2×#14523974C22semidirect
50. C2×#14523974C22semidirect
51. C2×#14523967C22semidirect
52. C2×#14523967C22semidirect
53. C2×#14523964C22semidirect
54. C2×#14523964C22semidirect
59. #16863363C22semidirect
62. C2×C22⋊(C67⋊C8)C22semidirect
63. C2×C22⋊(C67⋊C8)C22semidirect
65. C22×#41×C67C22semidirect
67. #537×C67C22semidirect
70. C2×C22⋊Q8×C67C22semidirect
75. C2×#121×C67C22semidirect
76. C22×C4⋊C4×C67C22semidirect
98. C2×#11761612C23semidirect
104. C22×C67⋊C8C23semidirect
127. #14523976C23semidirect
128. #14523976C23semidirect
129. #14523974C23semidirect
130. #14523974C23semidirect
131. #14523967C23semidirect
132. #14523967C23semidirect
133. #14523964C23semidirect
134. #14523964C23semidirect
141. C22⋊(C67⋊C8)C23semidirect
142. C22⋊(C67⋊C8)C23semidirect
150. C2×#41×C67C23semidirect
169. C22⋊Q8×C67C23semidirect
176. #121×C67C23semidirect
183. C2×C4⋊C4×C67C23semidirect
440. C2×C67#3198semidirect
446. C2×#537D67semidirect
462. C67C2×#3198semidirect
464. C22×#41C2×D67semidirect
473. #537C2×D67semidirect
480. C2×C22⋊Q8C2×D67semidirect
489. C2×#121C2×D67semidirect
493. C22×C4⋊C4C2×D67semidirect
531. C2×#41C22×D67semidirect
579. C22⋊Q8C22×D67semidirect
594. #121C22×D67semidirect
607. C2×C4⋊C4C22×D67semidirect
887. C2#22571055direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639602
#225710552
C2×#168637142
C2×#168637342
C2×#168637172
C2×#168637092
C2×#168636472
C2×#168636442
C2×#168636302
C2×#168636272
C2×#168635412
C2×#168635462
C2×#168635292
C2×#168633632
C2×#537×C672
C2×#319867