Finite Group Databasebeta

← C2×#23777303 #35196638

Subgroups — C2×#23777303 #35196638

Order 20224.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777303C2132yesmaximal, direct product factor
2C2×#19099281C212yesmaximal, complemented
3C2×#19099276C212yesmaximal, complemented
4C2×#19099268C212yesmaximal, complemented
5C2×#19099262C214yesmaximal, complemented
6C2×#19099222C214yesmaximal, complemented
7C2×#19099214C212yesmaximal, complemented
8C2×#19099185C212yesmaximal, complemented
9C2×#19099178C212yesmaximal, complemented
10C2×#19099144C211yesmaximal, characteristic, complemented
11C2×#19099141C211yesmaximal, characteristic, complemented
12C2×#19099117C212yesmaximal, complemented
13C2×#19099110C212yesmaximal, complemented
14C2×#19099109C211yesmaximal, characteristic, complemented
15C22×#14579160C211yesmaximal, characteristic, complemented
16C2×#19099043C211yesmaximal, characteristic, complemented
17C2×#19099031C211yesmaximal, characteristic, complemented
18C2×#520×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2211yescharacteristic
20C22×#11929624C2211yescharacteristic
21C22×#11929624C2214yes—
22C23×Dic158C2212yes—
23#19099281C22132yescomplemented
24#19099276C22132yescomplemented
25#19099268C22132yescomplemented
26#19099262C22164yescomplemented
27#19099222C22164yescomplemented
28#19099214C22132yescomplemented
29#19099185C22132yescomplemented
30#19099178C22132yescomplemented
31#19099144C22116yescomplemented
32#19099141C22116yescomplemented
33#19099117C22132yescomplemented
34#19099110C22132yescomplemented
35#19099109C22116yescomplemented
36C2×#14579160C2212yes—
37C2×#14579160C2212yes—
38C2×#14579160C2212yes—
39C2×#14579160C2212yes—
40C2×#14579160C22116yescomplemented
41C2×#14579159C2211yescharacteristic
42C2×#14579157C2211yescharacteristic
43C2×#14579155C2214yes—
44C2×#14579154C2214yes—
45C2×#14579151C2214yes—
46C2×#14579150C2211yescharacteristic
47C2×#14579149C2214yes—
48C2×#14579148C2211yescharacteristic
49C2×#14579147C2214yes—
50C2×#14579147C2214yes—
51C2×#14579146C2214yes—
52C2×#14579144C2214yes—
53C2×#14579141C2212yes—
54C2×#14579141C2212yes—
55C2×#14579140C2214yes—
56C2×#14579140C2212yes—
57C2×#14579139C2214yes—
58C2×#14579139C2214yes—
59C2×#14579137C2212yes—
60C2×#14579136C2212yes—
61C2×#14579136C2212yes—
62C2×#14579135C2212yes—
63C2×#14579135C2214yes—
64C2×#14579134C2214yes—
65C2×#14579133C2212yes—
66C2×#14579133C2214yes—
67C2×#14579133C2212yes—
68C2×#14579132C2212yes—
69#19099043C22116yescomplemented
70#19099031C22116yescomplemented
71C2×C4×Dic158C2212yes—
72C2×C4×Dic158C2214yes—
73C2×#14579126C2211yescharacteristic
74C2×#14579126C2211yescharacteristic
75C2×C4×D316C2212yes—
76C2×#14579123C2211yescharacteristic
77C2×#14579123C2211yescharacteristic
78C2×C4×C22⋊D79C2212yes—
79C2×C4×C22⋊D79C2214yes—
80C2×C4×C22⋊D79C2212yes—
81C2×(C22⋊D79)⋊C4C2212yes—
82C2×(C22⋊D79)⋊C4C2212yes—
83C2×(C22⋊D79)⋊C4C2214yes—
84C2×#14579119C2212yes—
85C2×#14579118C2212yes—
86C2×#14579118C2214yes—
87C22×C4⋊Dic79C2211yescharacteristic
88C22×Dic79⋊C4C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C22×C4×Dic79C2211yescharacteristic
91C2×C42×D79C2212yes—
92C22×#41×C79C2211yescharacteristic
93#520×C79C22116yescomplemented
94C2×C4×Q8×C79C2212yes—
95C2×C4×D4×C79C2212yes—
96C2×C4×D4×C79C2214yes—
97C2×#117×C79C2211yescharacteristic
98C2×#117×C79C2212yes—
99C22×C4⋊C4×C79C2212yes—
100C22×C4⋊C4×C79C2211yescharacteristic
101C2×#11929624—28no—
102C2×#11929624—28no—
103C2×#11929624—416no—
104C2×#11929624C2318yes—
105C2×#11929624C2318yes—
106C2×#11929624C23132yes—
107C22×Dic158—48no—
108C22×Dic158C2311yescharacteristic
109C22×Dic158C2311yescharacteristic
110C22×Dic158C2314yes—
111C22×Dic158C23116yes—
112C22×Dic158C2314yes—
113C22×D316C2311yescharacteristic
114C22×D316C2311yescharacteristic
115C22×D316C2314yes—
116C22×C22⋊D79C2312yes—
117C22×C22⋊D79C2312yes—
118C22×C22⋊D79C2312yes—
119C22×C22⋊D79C2312yes—
120C22×C22⋊D79C2314yes—
121C23×Dic79C2311yescharacteristic
122C23×Dic79C2311yescharacteristic
123C23×Dic79C2312yes—
124C22×C4×D79C2312yes—
125C22×C4×D79C2312yes—
126C22×C4×D79C2312yes—
127C22×C4×D79C2312yes—
128C22×C4×D79C2314yes—
129#14579160C23116yes—
130#14579160C23116yes—
131#14579160C23116yes—
132#14579160C23116yes—
133#14579159C2318yes—
134#14579157C2318yes—
135#14579155C23132yes—
136#14579154C23132yes—
137#14579151C23132yes—
138#14579150C2318yes—
139#14579149C23132yes—
140#14579148C2318yes—
141#14579147C23132yes—
142#14579147C23132yes—
143#14579146C23132yes—
144#14579144C23132yes—
145#14579141C23116yes—
146#14579141C23116yes—
147#14579140C23116yes—
148#14579140C23132yes—
149#14579139C23132yes—
150#14579139C23132yes—
151#14579137C23116yes—
152#14579136C23116yes—
153#14579136C23116yes—
154#14579135C23116yes—
155#14579135C23132yes—
156#14579134C23132yes—
157#14579133C23132yes—
158#14579133C23116yes—
159#14579133C23116yes—
160#14579132C23116yes—
161C4×Dic158C23116yes—
162C4×Dic158C23132yes—
163#14579126C2318yes—
164#14579126C2318yes—
165C4×D316C23116yes—
166#14579123C2318yes—
167#14579123C2318yes—
168C4×C22⋊D79C23116yes—
169C4×C22⋊D79C23132yes—
170C4×C22⋊D79C23116yes—
171(C22⋊D79)⋊C4C23116yes—
172(C22⋊D79)⋊C4C23132yes—
173(C22⋊D79)⋊C4C23116yes—
174#14579119C23116yes—
175#14579118C23116yes—
176#14579118C23132yes—
177C2×C4⋊Dic79C2318yes—
178C2×C4⋊Dic79C2312yes—
179C2×C4⋊Dic79C2312yes—
180C2×C4⋊Dic79C2314yes—
181C2×Dic79⋊C4C23116yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2312yes—
188C2×Dic79⋊C4C2312yes—
189C2×Dic79⋊C4C2314yes—
190C4⋊C4×D79C23116yes—
191C2×C22⋊Dic79C2314yes—
192C2×C22⋊Dic79C2312yes—
193C2×C22⋊Dic79C2312yes—
194C2×(C2×D79)⋊C4C2312yes—
195C2×(C2×D79)⋊C4C2312yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2314yes—
198C2×(C2×D79)⋊C4C2314yes—
199C2×(C2×D79)⋊C4C2312yes—
200C2×(C2×D79)⋊C4C2312yes—
201C2×(C2×D79)⋊C4C2314yes—
202C2×C4×Dic79C2311yescharacteristic
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2312yes—
205C2×C4×Dic79C2311yescharacteristic
206C2×C4×Dic79C2311yescharacteristic
207C2×C4×Dic79C2311yescharacteristic
208C2×C4×Dic79C2318yes—
209C2×C4×Dic79C2314yes—
210C42×D79C23116yes—
211C2×#41×C79—28no—
212C2×#41×C79C2318yes—
213C22×Q8×C79C2311yescharacteristic
214C22×D4×C79C2311yescharacteristic
215C22×D4×C79C2312yes—
216C23×C4×C79C2312yes—
217C23×C4×C79C2312yes—
218C23×C4×C79C2314yes—
219C23×C4×C79C2311yescharacteristic
220C4×Q8×C79C23116yes—
221C4×D4×C79C23116yes—
222C4×D4×C79C23132yes—
223#117×C79C23116yes—
224#117×C79C2318yes—
225C2×C4⋊C4×C79C2318yes—
226C2×C4⋊C4×C79C23116yes—
227C2×C4⋊C4×C79C2311yescharacteristic
228C2×C4⋊C4×C79C2312yes—
229C2×C4⋊C4×C79C2312yes—
230C2×C4⋊C4×C79C2314yes—
231C2×C4⋊C4×C79C2311yescharacteristic
232C2×C22⋊C4×C79C2312yes—
233C2×C22⋊C4×C79C2314yes—
234C2×C42×C79C2312yes—
235C2×C42×C79C2314yes—
236C23×D79C2412yes—
237C23×D79C2412yes—
238#11929624—232no—
239#11929624—232no—
240#11929624—464no—
241C2×Dic158—216no—
242C2×Dic158—24no—
243C2×Dic158—24no—
244C2×Dic158—48no—
245C2×Dic158—432no—
246C2×Dic158C24116yes—
247C2×Dic158C2414yes—
248C2×Dic158C2414yes—
249C2×Dic158C24116yes—
250C2×D316—24no—
251C2×D316—24no—
252C2×D316—48no—
253C2×D316C2414yes—
254C2×D316C2414yes—
255C2×D316C24116yes—
256C2×C22⋊D79—28no—
257C2×C22⋊D79—28no—
258C2×C22⋊D79—28no—
259C2×C22⋊D79—28no—
260C2×C22⋊D79—48no—
261C2×C22⋊D79C2418yes—
262C2×C22⋊D79C2418yes—
263C2×C22⋊D79C2418yes—
264C2×C22⋊D79C2418yes—
265C2×C22⋊D79C24116yes—
266C22×Dic79—24no—
267C22×Dic79—24no—
268C22×Dic79—44no—
269C22×Dic79C2411yescharacteristic
270C22×Dic79C2414yes—
271C22×Dic79C2414yes—
272C22×Dic79C2412yes—
273C22×Dic79C2412yes—
274C22×Dic79C2411yescharacteristic
275C22×Dic79C2414yes—
276C22×Dic79C2418yes—
277C22×Dic79C2411yescharacteristic
278C22×Dic79C2411yescharacteristic
279C2×C4×D79—28no—
280C2×C4×D79—28no—
281C2×C4×D79—28no—
282C2×C4×D79—28no—
283C2×C4×D79—48no—
284C2×C4×D79C2418yes—
285C2×C4×D79C2418yes—
286C2×C4×D79C2418yes—
287C2×C4×D79C2418yes—
288C2×C4×D79C24116yes—
289C4⋊Dic79C2418yes—
290C4⋊Dic79C2418yes—
291C4⋊Dic79C24116yes—
292Dic79⋊C4C24116yes—
293Dic79⋊C4C24116yes—
294Dic79⋊C4C24116yes—
295Dic79⋊C4C2418yes—
296Dic79⋊C4C2418yes—
297Dic79⋊C4C2418yes—
298Dic79⋊C4C2418yes—
299Dic79⋊C4C24116yes—
300C22⋊Dic79C24116yes—
301C22⋊Dic79C2418yes—
302C22⋊Dic79C2418yes—
303(C2×D79)⋊C4C2418yes—
304(C2×D79)⋊C4C2418yes—
305(C2×D79)⋊C4C24116yes—
306(C2×D79)⋊C4C24116yes—
307(C2×D79)⋊C4C24116yes—
308(C2×D79)⋊C4C2418yes—
309(C2×D79)⋊C4C2418yes—
310(C2×D79)⋊C4C24116yes—
311C4×Dic79C2414yes—
312C4×Dic79C2418yes—
313C4×Dic79C2418yes—
314C4×Dic79C2414yes—
315C4×Dic79C2414yes—
316C4×Dic79C2414yes—
317C4×Dic79C24116yes—
318C24×C79C2412yes—
319C24×C79C2411yescharacteristic
320#41×C79—232no—
321C2×Q8×C79—24no—
322C2×Q8×C79C2414yes—
323C2×D4×C79—28no—
324C2×D4×C79—24no—
325C2×D4×C79C2414yes—
326C2×D4×C79C2418yes—
327C22×C4×C79—28no—
328C22×C4×C79—44no—
329C22×C4×C79—48no—
330C22×C4×C79#4118yescomplemented
331C22×C4×C79C2414yes—
332C22×C4×C79C2412yes—
333C22×C4×C79C2412yes—
334C22×C4×C79C2412yes—
335C22×C4×C79C2418yes—
336C22×C4×C79C2418yes—
337C22×C4×C79C24116yes—
338C22×C4×C79C2411yescharacteristic
339C22×C4×C79C2411yescharacteristic
340C22×C4×C79C2414yes—
341C4⋊C4×C79C2414yes—
342C4⋊C4×C79C2418yes—
343C4⋊C4×C79C2418yes—
344C4⋊C4×C79C24116yes—
345C4⋊C4×C79C2414yes—
346C22⋊C4×C79C2418yes—
347C22⋊C4×C79C24116yes—
348C42×C79C2418yes—
349C42×C79C24116yes—
350C23×C79—22no—
351C23×C79—22no—
352C23×C79—24no—
353C23×C79—24no—
354C23×C79—24no—
355C23×C79C2×#4114yes—
356C23×C79C2514yes—
357C23×C79C2512yes—
358C23×C79C2511yescharacteristic
359C22×D79—24no—
360C22×D79—24no—
361C22×D79—24no—
362C22×D79—24no—
363C22×D79—24no—
364C22×D79—24no—
365C22×D79C2514yes—
366C22×D79C2514yes—
367Q8×C79—28no—
368D4×C79—216no—
369D4×C79—28no—
370C2×C4×C79—24no—
371C2×C4×C79—24no—
372C2×C4×C79—28no—
373C2×C4×C79—24no—
374C2×C4×C79—216no—
375C2×C4×C79—48no—
376C2×C4×C79—416no—
377C2×C4×C79C2×#4114yes—
378C2×C4×C79C2×#4114yes—
379C2×C4×C79C2×#41116yescomplemented
380C2×C4×C79C2514yes—
381C2×C4×C79C2514yes—
382C2×C4×C79C2514yes—
383C2×C4×C79C2518yes—
384C2×C4×C79C2512yes—
385C2×C4×C79C2512yes—
386C22⋊D79—216no—
387C22⋊D79—216no—
388C22⋊D79—216no—
389C22⋊D79—216no—
390C22⋊D79—416no—
391C2×Dic79—24no—
392C2×Dic79—24no—
393C2×Dic79—28no—
394C2×Dic79—22no—
395C2×Dic79—22no—
396C2×Dic79—28no—
397C2×Dic79—28no—
398C2×Dic79—48no—
399C2×Dic79H(5,𝔽2)14yes—
400C2×Dic792−1+414yes—
401C2×Dic79C2512yes—
402C2×Dic79C2512yes—
403C2×Dic79C2514yes—
404C2×Dic79C2514yes—
405C2×Dic79C2518yes—
406C2×Dic79C2512yes—
407C2×Dic79C2512yes—
408D316—28no—
409D316—28no—
410D316—416no—
411C4×D79—216no—
412C4×D79—216no—
413C4×D79—216no—
414C4×D79—216no—
415C4×D79—416no—
416Dic158—28no—
417Dic158—28no—
418Dic158—232no—
419Dic158—416no—
420C22×C79—22no—
421C22×C79—22no—
422C22×C79—28no—
423C22×C79—24no—
424C22×C79—24no—
425C22×C79—24no—
426C22×C79—48no—
427C22×C79C22×#4114yes—
428C22×C79C22×#4112yes—
429C22×C79C2×H(5,𝔽2)12yes—
430C22×C79C2×2−1+412yes—
431C22×C79C2611yescharacteristic
432C2×D79—24no—
433C2×D79—24no—
434C2×D79—24no—
435C2×D79—24no—
436C2×D79—24no—
437C2×D79—24no—
438C2×D79—48no—
439C2×D79—48no—
440C4×C79—24no—
441C4×C79—28no—
442C4×C79—24no—
443C4×C79—24no—
444C4×C79C22×#4114yes—
445C4×C79C22×#4114yes—
446Dic79—24no—
447Dic79—24no—
448Dic79—28no—
449Dic79—22no—
450Dic79—22no—
451Dic79C2×H(5,𝔽2)14yes—
452Dic79C2×2−1+414yes—
453C2×#3511—791nomaximal, Sylow
454C2×C79—24no—
455C2×C79—44no—
456C2×C79#351114yescomplemented
457C2×C79C23×#4111yescharacteristic
458C2×C79C22×H(5,𝔽2)11yescharacteristic
459C2×C79C22×2−1+411yescharacteristic
460D79—44no—
461D79—44no—
462#3511—7932no—
463C2×#556—792no—
464C2×#555—792no—
465C2×#554—792no—
466C2×#553—794no—
467C2×#548—794no—
468C2×#547—792no—
469C2×#542—792no—
470C2×#542—792no—
471C2×#537—791no—
472C2×#537—791no—
473C2×#533—792no—
474C2×#532—791no—
475C2×#532—792no—
476C22×C4⋊Q8—791no—
477C2×#520—791no—
478C2×#520D7911yescharacteristic, complemented
479C2×C4×#41—791no—
480C79C2×#351111yescharacteristic, complemented, Sylow
481C22×#41—794no—
482C22×#41—791no—
483C22×#41—791no—
484C22×#41C2×D7911yescharacteristic
485C23×Q8—792no—
486#556—7932no—
487#555—7932no—
488#554—7932no—
489#553—7964no—
490#548—7964no—
491#547—7932no—
492#542—7932no—
493#542—7932no—
494#537—7916no—
495#537—7916no—
496#533—7932no—
497#532—7916no—
498#532—7932no—
499C2×C4⋊Q8—791no—
500C2×C4⋊Q8—792no—
501C2×C4⋊Q8—792no—
502C2×C4⋊Q8—792no—
503C2×C4⋊Q8—792no—
504C2×C4⋊Q8—7916no—
505C2×#127—791no—
506C2×#126—794no—
507C2×#126—794no—
508C2×#125—794no—
509C2×#124—791no—
510C2×#124—791no—
511C2×#124—794no—
512C2×#124—794no—
513C2×#124—794no—
514C2×#123—794no—
515C2×#123—794no—
516C2×C22⋊Q8—792no—
517C2×C22⋊Q8—792no—
518C2×C22⋊Q8—794no—
519C2×C22⋊Q8—792no—
520C2×C22⋊Q8—794no—
521C2×C22⋊Q8—792no—
522C2×C22⋊Q8—794no—
523C2×#121—792no—
524C2×#121—792no—
525C2×#121—792no—
526C2×#121—794no—
527C2×#121—792no—
528C2×#121—794no—
529C2×#121—792no—
530C2×#121—792no—
531C2×#121—794no—
532#520—7916no—
533#520C2×D79116yescomplemented
534C4×#41—7916no—
535C2×C4×Q8—791no—
536C2×C4×Q8—791no—
537C2×C4×Q8—792no—
538C2×C4×Q8—794no—
539C2×C4×Q8C2×D7912yes—
540C2×C4×D4—792no—
541C2×C4×D4—794no—
542C2×C4×D4—792no—
543C2×C4×D4—791no—
544C2×C4×D4—791no—
545C2×C4×D4—792no—
546C2×C4×D4—792no—
547C2×C4×D4—794no—
548C2×C4×D4—792no—
549C2×C4×D4C2×D7912yes—
550C2×C4×D4C2×D7914yes—
551C2×#117—792no—
552C2×#117—792no—
553C2×#117—794no—
554C2×#117C2×D7911yescharacteristic
555C2×#117C2×D7912yes—
556C22×C4⋊C4—791no—
557C22×C4⋊C4—792no—
558C22×C4⋊C4—792no—
559C22×C4⋊C4C2×D7911yescharacteristic
560C22×C4⋊C4C2×D7912yes—
561C22×C42—791no—
562C22×C42—792no—
563C2×#41—28no—
564C2×#41—31616no—
565C2×#41—7932no—
566C2×#41—798no—
567C2×#41—798no—
568C2×#41—1588no—
569C2×#41—1588no—
570C2×#41C22×D7918yes—
571C22×Q8—3168no—
572C22×Q8—794no—
573C22×Q8—7916no—
574C22×Q8—791no—
575C22×Q8—791no—
576C22×Q8—794no—
577C22×Q8C22×D7911yescharacteristic
578C22×D4—794no—
579C22×D4—792no—
580C22×D4—792no—
581C22×D4—792no—
582C22×D4—792no—
583C22×D4—794no—
584C22×D4—791no—
585C22×D4—791no—
586C22×D4C22×D7912yes—
587C22×D4C22×D7911yescharacteristic
588C23×C4—792no—
589C23×C4—794no—
590C23×C4—791no—
591C23×C4—791no—
592C23×C4—792no—
593C23×C4—792no—
594C23×C4—792no—
595C23×C4—792no—
596C23×C4C22×D7912yes—
597C23×C4C22×D7912yes—
598C23×C4C22×D7914yes—
599C23×C4C22×D7911yescharacteristic
600C4⋊Q8—798no—
601C4⋊Q8—7916no—
602C4⋊Q8—7916no—
603C4⋊Q8—7916no—
604C4⋊Q8—7916no—
605#127—798no—
606#126—7932no—
607#126—7932no—
608#125—7932no—
609#124—798no—
610#124—798no—
611#124—7932no—
612#124—7932no—
613#124—7932no—
614#123—7932no—
615#123—7932no—
616C22⋊Q8—7916no—
617C22⋊Q8—7916no—
618C22⋊Q8—7932no—
619C22⋊Q8—7916no—
620C22⋊Q8—7932no—
621C22⋊Q8—7916no—
622C22⋊Q8—7932no—
623#121—7916no—
624#121—7916no—
625#121—7916no—
626#121—7932no—
627#121—7916no—
628#121—7932no—
629#121—7916no—
630#121—7916no—
631#121—7932no—
632C4×Q8—798no—
633C4×Q8—798no—
634C4×Q8—7916no—
635C4×Q8—7932no—
636C4×Q8C22×D79116yes—
637C4×D4—7916no—
638C4×D4—7932no—
639C4×D4—7916no—
640C4×D4—798no—
641C4×D4—798no—
642C4×D4—7916no—
643C4×D4—7916no—
644C4×D4—7932no—
645C4×D4—7916no—
646C4×D4C22×D79116yes—
647C4×D4C22×D79132yes—
648#117—7916no—
649#117—7916no—
650#117—7932no—
651#117C22×D7918yes—
652#117C22×D79116yes—
653C2×C4⋊C4—792no—
654C2×C4⋊C4—794no—
655C2×C4⋊C4—792no—
656C2×C4⋊C4—794no—
657C2×C4⋊C4—798no—
658C2×C4⋊C4—794no—
659C2×C4⋊C4—7916no—
660C2×C4⋊C4—792no—
661C2×C4⋊C4—792no—
662C2×C4⋊C4—792no—
663C2×C4⋊C4—792no—
664C2×C4⋊C4—794no—
665C2×C4⋊C4—794no—
666C2×C4⋊C4—7916no—
667C2×C4⋊C4C22×D7911yescharacteristic
668C2×C4⋊C4C22×D7912yes—
669C2×C4⋊C4C22×D7912yes—
670C2×C4⋊C4C22×D7914yes—
671C2×C4⋊C4C22×D7918yes—
672C2×C4⋊C4C22×D79116yes—
673C2×C4⋊C4C22×D7911yescharacteristic
674C2×C22⋊C4—794no—
675C2×C22⋊C4—792no—
676C2×C22⋊C4—792no—
677C2×C22⋊C4—794no—
678C2×C22⋊C4—792no—
679C2×C22⋊C4—792no—
680C2×C22⋊C4—794no—
681C2×C22⋊C4—794no—
682C2×C22⋊C4—794no—
683C2×C22⋊C4—792no—
684C2×C22⋊C4—792no—
685C2×C22⋊C4C22×D7912yes—
686C2×C22⋊C4C22×D7914yes—
687C2×C42—794no—
688C2×C42—791no—
689C2×C42—792no—
690C2×C42—791no—
691C2×C42—791no—
692C2×C42—792no—
693C2×C42—798no—
694C2×C42—791no—
695C2×C42—7916no—
696C2×C42C22×D7912yes—
697C2×C42C22×D7914yes—
698C24—792no—
699C24—792no—
700C24C23×D7912yes—
701C24C23×D7911yescharacteristic
702#41—232no—
703#41—31664no—
704#41—15832no—
705#41—15832no—
706C2×Q8—24no—
707C2×Q8—3168no—
708C2×Q8—31632no—
709C2×Q8—7916no—
710C2×Q8—794no—
711C2×Q8—794no—
712C2×Q8—7916no—
713C2×Q8—15816no—
714C2×Q8—1584no—
715C2×Q8—1584no—
716C2×Q8C23×D7914yes—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—3168no—
720C2×D4—3168no—
721C2×D4—7916no—
722C2×D4—798no—
723C2×D4—798no—
724C2×D4—798no—
725C2×D4—798no—
726C2×D4—7916no—
727C2×D4—794no—
728C2×D4—794no—
729C2×D4—1588no—
730C2×D4—1588no—
731C2×D4—1588no—
732C2×D4—1588no—
733C2×D4—1584no—
734C2×D4—1584no—
735C2×D4C23×D7918yes—
736C2×D4C23×D7914yes—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—48no—
740C22×C4—3168no—
741C22×C4—3164no—
742C22×C4—798no—
743C22×C4—7916no—
744C22×C4—791no—
745C22×C4—791no—
746C22×C4—794no—
747C22×C4—794no—
748C22×C4—791no—
749C22×C4—791no—
750C22×C4—792no—
751C22×C4—792no—
752C22×C4—794no—
753C22×C4—798no—
754C22×C4—798no—
755C22×C4—798no—
756C22×C4—798no—
757C22×C4—1588no—
758C22×C4—1588no—
759C22×C4—1584no—
760C22×C4—1584no—
761C22×C4—1588no—
762C22×C4—1588no—
763C22×C4#1192962418yescomplemented
764C22×C4C23×D7918yes—
765C22×C4C23×D7912yes—
766C22×C4C23×D7912yes—
767C22×C4C23×D7912yes—
768C22×C4C23×D7914yes—
769C22×C4C23×D7918yes—
770C22×C4C23×D79116yes—
771C22×C4C23×D7911yescharacteristic
772C22×C4C23×D7911yescharacteristic
773C22×C4C23×D7914yes—
774C4⋊C4—7916no—
775C4⋊C4—7916no—
776C4⋊C4—7916no—
777C4⋊C4—798no—
778C4⋊C4—798no—
779C4⋊C4—798no—
780C4⋊C4—798no—
781C4⋊C4—7916no—
782C4⋊C4—798no—
783C4⋊C4—798no—
784C4⋊C4—7916no—
785C4⋊C4C23×D7914yes—
786C4⋊C4C23×D7918yes—
787C4⋊C4C23×D7918yes—
788C4⋊C4C23×D79116yes—
789C4⋊C4C23×D7914yes—
790C22⋊C4—7916no—
791C22⋊C4—798no—
792C22⋊C4—798no—
793C22⋊C4—7916no—
794C22⋊C4—798no—
795C22⋊C4—798no—
796C22⋊C4—7916no—
797C22⋊C4—7916no—
798C22⋊C4—7916no—
799C22⋊C4—798no—
800C22⋊C4—798no—
801C22⋊C4C23×D7918yes—
802C22⋊C4C23×D79116yes—
803C42—794no—
804C42—794no—
805C42—798no—
806C42—794no—
807C42—794no—
808C42—798no—
809C42—7916no—
810C42C23×D7918yes—
811C42C23×D79116yes—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—794no—
818C23—794no—
819C23—1584no—
820C23—1584no—
821C23—1584no—
822C23—1584no—
823C23—1584no—
824C23—1584no—
825C23C2×#1192962414yes—
826C23C24×D7914yes—
827C23C24×D7912yes—
828C23C24×D7911yescharacteristic
829Q8—28no—
830Q8—31616no—
831Q8—15832no—
832Q8—1588no—
833Q8—1588no—
834D4—216no—
835D4—28no—
836D4—31616no—
837D4—31616no—
838D4—15816no—
839D4—15816no—
840D4—15816no—
841D4—15816no—
842D4—1588no—
843D4—1588no—
844C2×C4—24no—
845C2×C4—28no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—416no—
851C2×C4—31616no—
852C2×C4—3168no—
853C2×C4—794no—
854C2×C4—794no—
855C2×C4—792no—
856C2×C4—792no—
857C2×C4—792no—
858C2×C4—792no—
859C2×C4—794no—
860C2×C4—794no—
861C2×C4—798no—
862C2×C4—15816no—
863C2×C4—15816no—
864C2×C4—1588no—
865C2×C4—1588no—
866C2×C4—1588no—
867C2×C4—1582no—
868C2×C4—1582no—
869C2×C4—1584no—
870C2×C4—1584no—
871C2×C4—15816no—
872C2×C4—15816no—
873C2×C4C2×#1192962414yes—
874C2×C4C2×#1192962414yes—
875C2×C4C2×#11929624116yescomplemented
876C2×C4C24×D7914yes—
877C2×C4C24×D7914yes—
878C2×C4C24×D7914yes—
879C2×C4C24×D7918yes—
880C2×C4C24×D7912yes—
881C2×C4C24×D7912yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—48no—
889C22—3168no—
890C22—3168no—
891C22—1584no—
892C22—1584no—
893C22—1584no—
894C22—1584no—
895C22—1584no—
896C22—1584no—
897C22C22×#1192962414yes—
898C22C22×#1192962412yes—
899C22H(5,𝔽2)×D7912yes—
900C222−1+4×D7912yes—
901C22C25×D7911yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—24no—
906C4—794no—
907C4—794no—
908C4—1584no—
909C4—1584no—
910C4—1588no—
911C4—1582no—
912C4—1582no—
913C4C22×#1192962414yes—
914C4C22×#1192962414yes—
915C2—24no—
916C2—44no—
917C2—3164no—
918C2—3164no—
919C2#2377730314yesdirect product factor
920C2C23×#1192962411yescharacteristic
921C2C2×H(5,𝔽2)×D7911yescharacteristic
922C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#520×C79C2
socleC23×C79C25
hypercenterC2×#520D79
hypocenterC79C2×#3511
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #23777303C2direct (N × H)
2. C2×#19099281C2semidirect
3. C2×#19099276C2semidirect
4. C2×#19099268C2semidirect
5. C2×#19099262C2semidirect
6. C2×#19099222C2semidirect
7. C2×#19099214C2semidirect
8. C2×#19099185C2semidirect
9. C2×#19099178C2semidirect
10. C2×#19099144C2semidirect
11. C2×#19099141C2semidirect
12. C2×#19099117C2semidirect
13. C2×#19099110C2semidirect
14. C2×#19099109C2semidirect
15. C22×#14579160C2semidirect
16. C2×#19099043C2semidirect
17. C2×#19099031C2semidirect
18. C2×#520×C79C2semidirect
23. #19099281C22semidirect
24. #19099276C22semidirect
25. #19099268C22semidirect
26. #19099262C22semidirect
27. #19099222C22semidirect
28. #19099214C22semidirect
29. #19099185C22semidirect
30. #19099178C22semidirect
31. #19099144C22semidirect
32. #19099141C22semidirect
33. #19099117C22semidirect
34. #19099110C22semidirect
35. #19099109C22semidirect
40. C2×#14579160C22semidirect
69. #19099043C22semidirect
70. #19099031C22semidirect
93. #520×C79C22semidirect
330. C22×C4×C79#41semidirect
379. C2×C4×C79C2×#41semidirect
456. C2×C79#3511semidirect
478. C2×#520D79semidirect
480. C79C2×#3511semidirect
533. #520C2×D79semidirect
763. C22×C4#11929624semidirect
875. C2×C4C2×#11929624semidirect
919. C2#23777303direct (N × H)

Maximal subgroups

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

subgroupindex
#237773032
C2×#190992812
C2×#190992762
C2×#190992682
C2×#190992622
C2×#190992222
C2×#190992142
C2×#190991852
C2×#190991782
C2×#190991442
C2×#190991412
C2×#190991172
C2×#190991102
C2×#190991092
C22×#145791602
C2×#190990432
C2×#190990312
C2×#520×C792
C2×#351179