Finite Group Databasebeta

← C22×#19099211 #35195208

Subgroups — C22×#19099211 #35195208

Order 20224.

12230 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11929624C211yesmaximal, characteristic, complemented
2C23×#11929623C211yesmaximal, characteristic, complemented
3C2×#19099211C2148yesmaximal, direct product factor
4C22×#14579160C211yesmaximal, characteristic, complemented
5C22×#14579146C211yesmaximal, characteristic, complemented
6C22×#14579145C211yesmaximal, characteristic, complemented
7C22×#14579143C211yesmaximal, characteristic, complemented
8C22×#14579139C211yesmaximal, characteristic, complemented
9C22×#14579138C211yesmaximal, characteristic, complemented
10C22×#14579134C211yesmaximal, characteristic, complemented
11C22×#14579133C211yesmaximal, characteristic, complemented
12C22×(C22⋊D79)⋊C4C211yesmaximal, characteristic, complemented
13C22×(C22⋊D79)⋊C4C211yesmaximal, characteristic, complemented
14C23×Dic79⋊C4C211yesmaximal, characteristic, complemented
15C22×C4⋊C4×D79C211yesmaximal, characteristic, complemented
16C22×#123×C79C211yesmaximal, characteristic, complemented
17C22×#11929624—216no—
18C22×#11929624C22124yescomplemented
19C22×#11929623—216no—
20C22×#11929623C22124yescomplemented
21C23×Dic158C2211yescharacteristic
22C23×Dic158C2211yescharacteristic
23C23×D316C2211yescharacteristic
24C23×C22⋊D79C2211yescharacteristic
25C23×C22⋊D79C2211yescharacteristic
26C23×C22⋊D79C2211yescharacteristic
27C23×C22⋊D79C2211yescharacteristic
28C24×Dic79C2211yescharacteristic
29C24×Dic79C2211yescharacteristic
30C24×Dic79C2211yescharacteristic
31C23×C4×D79C2211yescharacteristic
32C23×C4×D79C2211yescharacteristic
33C23×C4×D79C2211yescharacteristic
34C23×C4×D79C2211yescharacteristic
35#19099211C221256yesdirect product factor
36C2×#14579160C22124yescomplemented
37C2×#14579146C22124yescomplemented
38C2×#14579145C22124yescomplemented
39C2×#14579143C22124yescomplemented
40C2×#14579139C22124yescomplemented
41C2×#14579138C22124yescomplemented
42C2×#14579134C22124yescomplemented
43C2×#14579133C22124yescomplemented
44C2×(C22⋊D79)⋊C4C22124yescomplemented
45C2×(C22⋊D79)⋊C4C22124yescomplemented
46C22×C4⋊Dic79C2211yescharacteristic
47C22×C4⋊Dic79C2211yescharacteristic
48C22×Dic79⋊C4C2211yescharacteristic
49C22×Dic79⋊C4C2211yescharacteristic
50C22×Dic79⋊C4C2211yescharacteristic
51C22×Dic79⋊C4C2211yescharacteristic
52C22×Dic79⋊C4C2211yescharacteristic
53C22×Dic79⋊C4C2211yescharacteristic
54C22×Dic79⋊C4C22124yescomplemented
55C2×C4⋊C4×D79C22124yescomplemented
56C22×C22⋊Dic79C2211yescharacteristic
57C22×(C2×D79)⋊C4C2211yescharacteristic
58C22×(C2×D79)⋊C4C2211yescharacteristic
59C22×(C2×D79)⋊C4C2211yescharacteristic
60C22×(C2×D79)⋊C4C2211yescharacteristic
61C22×C4×Dic79C2211yescharacteristic
62C23×D4×C79C2211yescharacteristic
63C24×C4×C79C2211yescharacteristic
64C2×#123×C79C22124yescomplemented
65C22×C4⋊C4×C79C2211yescharacteristic
66C22×C4⋊C4×C79C2211yescharacteristic
67C22×C22⋊C4×C79C2211yescharacteristic
68C22×C22⋊C4×C79C2211yescharacteristic
69C22×C22⋊C4×C79C2211yescharacteristic
70C24×D79C2311yescharacteristic
71C24×D79C2311yescharacteristic
72C2×#11929624—2192no—
73C2×#11929624C23164yescomplemented
74C2×#11929623—2192no—
75C2×#11929623C23164yescomplemented
76C22×Dic158—28no—
77C22×Dic158—28no—
78C22×Dic158C23112yes—
79C22×Dic158C23112yes—
80C22×D316—28no—
81C22×D316C23112yes—
82C22×C22⋊D79—28no—
83C22×C22⋊D79—28no—
84C22×C22⋊D79—28no—
85C22×C22⋊D79D4116yescomplemented
86C22×C22⋊D79C23112yes—
87C22×C22⋊D79C23112yes—
88C22×C22⋊D79C23112yes—
89C22×C22⋊D79C23112yes—
90C23×Dic79—28no—
91C23×Dic79—28no—
92C23×Dic79—28no—
93C23×Dic79C2311yescharacteristic
94C23×Dic79C2311yescharacteristic
95C23×Dic79C2311yescharacteristic
96C23×Dic79C2311yescharacteristic
97C23×Dic79C23112yes—
98C23×Dic79C23112yes—
99C23×Dic79C23112yes—
100C23×Dic79C2311yescharacteristic
101C23×Dic79C2311yescharacteristic
102C22×C4×D79—28no—
103C22×C4×D79—28no—
104C22×C4×D79—28no—
105C22×C4×D79—28no—
106C22×C4×D79C23112yes—
107C22×C4×D79C23112yes—
108C22×C4×D79C23112yes—
109C22×C4×D79C23112yes—
110#14579160C23164yescomplemented
111#14579146C23164yescomplemented
112#14579145C23164yescomplemented
113#14579143C23164yescomplemented
114#14579139C23164yescomplemented
115#14579138C23164yescomplemented
116#14579134C23164yescomplemented
117#14579133C23164yescomplemented
118(C22⋊D79)⋊C4C23164yescomplemented
119(C22⋊D79)⋊C4C23164yescomplemented
120C2×C4⋊Dic79C23112yes—
121C2×C4⋊Dic79C23112yes—
122C2×Dic79⋊C4C23112yes—
123C2×Dic79⋊C4C23112yes—
124C2×Dic79⋊C4C23112yes—
125C2×Dic79⋊C4C23112yes—
126C2×Dic79⋊C4C23112yes—
127C2×Dic79⋊C4C23112yes—
128C2×Dic79⋊C4C23164yescomplemented
129C4⋊C4×D79C23164yescomplemented
130C2×C22⋊Dic79C23112yes—
131C2×(C2×D79)⋊C4C23112yes—
132C2×(C2×D79)⋊C4C23112yes—
133C2×(C2×D79)⋊C4C23112yes—
134C2×(C2×D79)⋊C4C23112yes—
135C2×C4×Dic79C23112yes—
136C25×C79C2311yescharacteristic
137C25×C79C2311yescharacteristic
138C22×D4×C79—28no—
139C22×D4×C79C23112yes—
140C23×C4×C79—28no—
141C23×C4×C79C2311yescharacteristic
142C23×C4×C79C2311yescharacteristic
143C23×C4×C79C2311yescharacteristic
144C23×C4×C79C2311yescharacteristic
145C23×C4×C79C2311yescharacteristic
146C23×C4×C79C23112yes—
147#123×C79C23164yescomplemented
148C2×C4⋊C4×C79C23112yes—
149C2×C4⋊C4×C79C23112yes—
150C2×C22⋊C4×C79C23112yes—
151C2×C22⋊C4×C79C23112yes—
152C2×C22⋊C4×C79C23112yes—
153C23×D79—24no—
154C23×D79—24no—
155C23×D79—24no—
156C23×D79—24no—
157C23×D79—24no—
158C23×D79C2×D418yes—
159C23×D79C2416yes—
160C23×D79C2416yes—
161#11929624—2256no—
162#11929623—2256no—
163C2×Dic158—248no—
164C2×Dic158—248no—
165C2×Dic158C24116yes—
166C2×Dic158C24116yes—
167C2×D316—248no—
168C2×D316C24116yes—
169C2×C22⋊D79—248no—
170C2×C22⋊D79—248no—
171C2×C22⋊D79—248no—
172C2×C22⋊D79C2×D4196yescomplemented
173C2×C22⋊D79C24116yes—
174C2×C22⋊D79C24116yes—
175C2×C22⋊D79C24116yes—
176C2×C22⋊D79C24116yes—
177C22×Dic79—248no—
178C22×Dic79—248no—
179C22×Dic79—24no—
180C22×Dic79—24no—
181C22×Dic79—248no—
182C22×Dic79—24no—
183C22×Dic79—24no—
184C22×Dic79C2×D418yes—
185C22×Dic79#4118yescomplemented
186C22×Dic79C2416yes—
187C22×Dic79C2416yes—
188C22×Dic79C24116yes—
189C22×Dic79C24116yes—
190C22×Dic79C2416yes—
191C22×Dic79C2416yes—
192C22×Dic79C24116yes—
193C22×Dic79C2416yes—
194C22×Dic79C2416yes—
195C2×C4×D79—248no—
196C2×C4×D79—248no—
197C2×C4×D79—248no—
198C2×C4×D79—248no—
199C2×C4×D79C24116yes—
200C2×C4×D79C24116yes—
201C2×C4×D79C24116yes—
202C2×C4×D79C24116yes—
203C4⋊Dic79C24116yes—
204C4⋊Dic79C24116yes—
205Dic79⋊C4C24116yes—
206Dic79⋊C4C24116yes—
207Dic79⋊C4C24116yes—
208Dic79⋊C4C24116yes—
209Dic79⋊C4C24116yes—
210Dic79⋊C4C24116yes—
211C22⋊Dic79C24116yes—
212(C2×D79)⋊C4C24116yes—
213(C2×D79)⋊C4C24116yes—
214(C2×D79)⋊C4C24116yes—
215(C2×D79)⋊C4C24116yes—
216C4×Dic79C24116yes—
217C24×C79—24no—
218C24×C79—24no—
219C24×C79—24no—
220C24×C79—24no—
221C24×C79—24no—
222C24×C79C2×D418yes—
223C24×C79C2416yes—
224C24×C79C2416yes—
225C24×C79C2411yescharacteristic
226C2×D4×C79—248no—
227C2×D4×C79C24116yes—
228C22×C4×C79—24no—
229C22×C4×C79—24no—
230C22×C4×C79—248no—
231C22×C4×C79—24no—
232C22×C4×C79—24no—
233C22×C4×C79—24no—
234C22×C4×C79C2416yes—
235C22×C4×C79C2416yes—
236C22×C4×C79C24116yes—
237C22×C4×C79C2416yes—
238C22×C4×C79C2416yes—
239C22×C4×C79C2416yes—
240C4⋊C4×C79C24116yes—
241C4⋊C4×C79C24116yes—
242C22⋊C4×C79C24116yes—
243C22⋊C4×C79C24116yes—
244C22⋊C4×C79C24116yes—
245C23×C79—232no—
246C23×C79—212no—
247C23×C79—212no—
248C23×C79—212no—
249C23×C79—212no—
250C23×C79—212no—
251C23×C79—416no—
252C23×C79C22×D4124yes—
253C23×C79C22×D414yes—
254C23×C79C2×#4114yes—
255C23×C792−1+414yes—
256C23×C79C2514yes—
257C23×C79C2514yes—
258C23×C79C2513yes—
259C22×D79—232no—
260C22×D79—212no—
261C22×D79—212no—
262C22×D79—212no—
263C22×D79—212no—
264C22×D79—212no—
265C22×D79—416no—
266C22×D79C22×D4124yes—
267C22×D79C2514yes—
268C22×D79C2514yes—
269D4×C79—232no—
270C2×C4×C79—212no—
271C2×C4×C79—212no—
272C2×C4×C79—212no—
273C2×C4×C79—232no—
274C2×C4×C79—212no—
275C2×C4×C79—212no—
276C2×C4×C79C2514yes—
277C2×C4×C79C2514yes—
278C2×C4×C79C2514yes—
279C2×C4×C79C2514yes—
280C2×C4×C79C2514yes—
281C22⋊D79—232no—
282C22⋊D79—232no—
283C22⋊D79—232no—
284C22⋊D79C22×D4164yescomplemented
285C2×Dic79—212no—
286C2×Dic79—212no—
287C2×Dic79—212no—
288C2×Dic79—232no—
289C2×Dic79—212no—
290C2×Dic79—232no—
291C2×Dic79—232no—
292C2×Dic79C22×D4124yes—
293C2×Dic79C2×#41124yescomplemented
294C2×Dic79C2514yes—
295C2×Dic79C2514yes—
296C2×Dic79C2514yes—
297C2×Dic79C2514yes—
298C2×Dic79C2514yes—
299C2×Dic79C2514yes—
300D316—232no—
301C4×D79—232no—
302C4×D79—232no—
303C4×D79—232no—
304C4×D79—232no—
305Dic158—232no—
306Dic158—232no—
307C22×C79—24no—
308C22×C79—24no—
309C22×C79—248no—
310C22×C79—24no—
311C22×C79—24no—
312C22×C79—24no—
313C22×C79—424no—
314C22×C79#547116yescomplemented
315C22×C79C23×D418yes—
316C22×C79C23×D416yes—
317C22×C79C22×#4116yes—
318C22×C79C2×2−1+416yes—
319C22×C79C2611yescharacteristic
320C2×D79—24no—
321C2×D79—24no—
322C2×D79—248no—
323C2×D79—24no—
324C2×D79—24no—
325C2×D79—24no—
326C2×D79—424no—
327C2×D79C23×D418yes—
328C4×C79—24no—
329C4×C79—24no—
330C4×C79—24no—
331C4×C79—24no—
332C4×C79—24no—
333Dic79—24no—
334Dic79—24no—
335Dic79—24no—
336Dic79—24no—
337Dic79C23×D418yes—
338Dic79C22×#4118yescomplemented
339C22×#547—791nomaximal, Sylow
340C2×C79—28no—
341C2×C79—44no—
342C2×C79C2×#547112yescomplemented
343C2×C79C24×D411yescharacteristic
344C2×C79C23×#4111yescharacteristic
345C2×C79C22×2−1+411yescharacteristic
346D79—28no—
347D79—44no—
348C23×#41—791no—
349C23×#41—791no—
350C2×#547—7948no—
351C22×C4⋊Q8—791no—
352C22×#123—791no—
353C22×#123—791no—
354C22×#123—791no—
355C22×#123D7911yescharacteristic, complemented
356C22×C22⋊Q8—791no—
357C22×C22⋊Q8—791no—
358C22×#121—791no—
359C22×#121—791no—
360C22×C4×D4—791no—
361C22×C4×D4—791no—
362C23×C4⋊C4—791no—
363C23×C4⋊C4—791no—
364C79C22×#54711yescharacteristic, complemented, Sylow
365C22×#41—7924no—
366C22×#41—7924no—
367C22×#41—15816no—
368C22×#41—15816no—
369C23×Q8—791no—
370C23×Q8—791no—
371C23×D4—791no—
372C23×D4—791no—
373C23×D4—791no—
374C23×D4—791no—
375C23×D4—791no—
376C23×D4C2×D7911yescharacteristic
377C24×C4—791no—
378C24×C4—791no—
379C24×C4—791no—
380C24×C4—791no—
381C24×C4—791no—
382C24×C4—791no—
383C24×C4—791no—
384C24×C4C2×D7911yescharacteristic
385#547—79256no—
386C2×C4⋊Q8—7924no—
387C2×#123—7924no—
388C2×#123—7924no—
389C2×#123—7924no—
390C2×#123C2×D79124yescomplemented
391C2×C22⋊Q8—7924no—
392C2×C22⋊Q8—7924no—
393C2×#121—7924no—
394C2×#121—7924no—
395C2×C4×D4—7924no—
396C2×C4×D4—7924no—
397C22×C4⋊C4—791no—
398C22×C4⋊C4—791no—
399C22×C4⋊C4—791no—
400C22×C4⋊C4—791no—
401C22×C4⋊C4—791no—
402C22×C4⋊C4—791no—
403C22×C4⋊C4—7924no—
404C22×C4⋊C4—791no—
405C22×C4⋊C4—791no—
406C22×C4⋊C4—7924no—
407C22×C4⋊C4C2×D7911yescharacteristic
408C22×C4⋊C4C2×D7911yescharacteristic
409C22×C22⋊C4—791no—
410C22×C22⋊C4—791no—
411C22×C22⋊C4—791no—
412C22×C22⋊C4—791no—
413C22×C22⋊C4—791no—
414C22×C22⋊C4C2×D7911yescharacteristic
415C22×C22⋊C4C2×D7911yescharacteristic
416C22×C22⋊C4C2×D7911yescharacteristic
417C22×C42—791no—
418C25—791no—
419C25—791no—
420C25C22×D7911yescharacteristic
421C25C22×D7911yescharacteristic
422C2×#41—7964no—
423C2×#41—7964no—
424C2×#41—158192no—
425C2×#41—158192no—
426C22×Q8—7912no—
427C22×Q8—7912no—
428C22×Q8—1588no—
429C22×Q8—1588no—
430C22×D4—28no—
431C22×D4—7916no—
432C22×D4—7912no—
433C22×D4—7912no—
434C22×D4—7912no—
435C22×D4—7912no—
436C22×D4—7912no—
437C22×D4—1588no—
438C22×D4—1588no—
439C22×D4—1588no—
440C22×D4—1588no—
441C22×D4C22×D79112yes—
442C23×C4—28no—
443C23×C4—791no—
444C23×C4—791no—
445C23×C4—7912no—
446C23×C4—7912no—
447C23×C4—7912no—
448C23×C4—791no—
449C23×C4—791no—
450C23×C4—791no—
451C23×C4—791no—
452C23×C4—7912no—
453C23×C4—7912no—
454C23×C4—7912no—
455C23×C4—7912no—
456C23×C4—1588no—
457C23×C4—1588no—
458C23×C4—1588no—
459C23×C4—1588no—
460C23×C4—1588no—
461C23×C4—1588no—
462C23×C4—1588no—
463C23×C4C22×D79112yes—
464C23×C4C22×D7911yescharacteristic
465C23×C4C22×D7911yescharacteristic
466C23×C4C22×D7911yescharacteristic
467C23×C4C22×D7911yescharacteristic
468C23×C4C22×D7911yescharacteristic
469C4⋊Q8—7964no—
470#123—7964no—
471#123—7964no—
472#123—7964no—
473#123C22×D79164yescomplemented
474C22⋊Q8—7964no—
475C22⋊Q8—7964no—
476#121—7964no—
477#121—7964no—
478C4×D4—7964no—
479C4×D4—7964no—
480C2×C4⋊C4—7912no—
481C2×C4⋊C4—7912no—
482C2×C4⋊C4—7912no—
483C2×C4⋊C4—7912no—
484C2×C4⋊C4—7912no—
485C2×C4⋊C4—7912no—
486C2×C4⋊C4—7964no—
487C2×C4⋊C4—7912no—
488C2×C4⋊C4—7912no—
489C2×C4⋊C4—7964no—
490C2×C4⋊C4C22×D79112yes—
491C2×C4⋊C4C22×D79112yes—
492C2×C22⋊C4—7912no—
493C2×C22⋊C4—7912no—
494C2×C22⋊C4—7912no—
495C2×C22⋊C4—7912no—
496C2×C22⋊C4—7912no—
497C2×C22⋊C4C22×D79112yes—
498C2×C22⋊C4C22×D79112yes—
499C2×C22⋊C4C22×D79112yes—
500C2×C42—7912no—
501C24—24no—
502C24—24no—
503C24—24no—
504C24—24no—
505C24—24no—
506C24—796no—
507C24—798no—
508C24—796no—
509C24—1584no—
510C24—1584no—
511C24—1584no—
512C24—1584no—
513C24—1584no—
514C24D4×D7918yes—
515C24C23×D7916yes—
516C24C23×D7916yes—
517C24C23×D7911yescharacteristic
518#41—158256no—
519#41—158256no—
520C2×Q8—7916no—
521C2×Q8—7916no—
522C2×Q8—15848no—
523C2×Q8—15848no—
524C2×D4—248no—
525C2×D4—7916no—
526C2×D4—7996no—
527C2×D4—7916no—
528C2×D4—7916no—
529C2×D4—7916no—
530C2×D4—7916no—
531C2×D4—15848no—
532C2×D4—15848no—
533C2×D4—15848no—
534C2×D4—15848no—
535C2×D4C23×D79116yes—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—248no—
541C22×C4—24no—
542C22×C4—798no—
543C22×C4—796no—
544C22×C4—796no—
545C22×C4—798no—
546C22×C4—796no—
547C22×C4—796no—
548C22×C4—796no—
549C22×C4—796no—
550C22×C4—7916no—
551C22×C4—7916no—
552C22×C4—7916no—
553C22×C4—7916no—
554C22×C4—7916no—
555C22×C4—7916no—
556C22×C4—7916no—
557C22×C4—15848no—
558C22×C4—15848no—
559C22×C4—15848no—
560C22×C4—15848no—
561C22×C4—15848no—
562C22×C4—15848no—
563C22×C4—1584no—
564C22×C4—1584no—
565C22×C4—1584no—
566C22×C4—1584no—
567C22×C4—15848no—
568C22×C4C23×D7916yes—
569C22×C4C23×D7916yes—
570C22×C4C23×D7916yes—
571C22×C4C23×D7916yes—
572C22×C4C23×D7916yes—
573C22×C4C23×D79116yes—
574C4⋊C4—7916no—
575C4⋊C4—7916no—
576C4⋊C4—7916no—
577C4⋊C4—7916no—
578C4⋊C4—7916no—
579C4⋊C4—7916no—
580C4⋊C4—7916no—
581C4⋊C4—7916no—
582C4⋊C4C23×D79116yes—
583C4⋊C4C23×D79116yes—
584C22⋊C4—7916no—
585C22⋊C4—7916no—
586C22⋊C4—7916no—
587C22⋊C4—7916no—
588C22⋊C4—7916no—
589C22⋊C4C23×D79116yes—
590C22⋊C4C23×D79116yes—
591C22⋊C4C23×D79116yes—
592C42—7916no—
593C23—212no—
594C23—232no—
595C23—212no—
596C23—212no—
597C23—212no—
598C23—212no—
599C23—416no—
600C23—31616no—
601C23—794no—
602C23—7924no—
603C23—794no—
604C23—15812no—
605C23—15812no—
606C23—15812no—
607C23—15812no—
608C23—15832no—
609C23—15812no—
610C23C2×D4×D79124yes—
611C23C2×D4×D7914yes—
612C23#41×D7914yes—
613C23#1457920814yes—
614C23C24×D7914yes—
615C23C24×D7914yes—
616C23C24×D7913yes—
617Q8—15832no—
618Q8—15832no—
619D4—232no—
620D4—7964no—
621D4—15832no—
622D4—15832no—
623D4—15832no—
624D4—15832no—
625C2×C4—212no—
626C2×C4—212no—
627C2×C4—212no—
628C2×C4—232no—
629C2×C4—212no—
630C2×C4—212no—
631C2×C4—794no—
632C2×C4—794no—
633C2×C4—7924no—
634C2×C4—7924no—
635C2×C4—794no—
636C2×C4—794no—
637C2×C4—794no—
638C2×C4—794no—
639C2×C4—15832no—
640C2×C4—15832no—
641C2×C4—15832no—
642C2×C4—15832no—
643C2×C4—15832no—
644C2×C4—15832no—
645C2×C4—15812no—
646C2×C4—15812no—
647C2×C4—15812no—
648C2×C4—15832no—
649C2×C4—15812no—
650C2×C4C24×D7914yes—
651C2×C4C24×D7914yes—
652C2×C4C24×D7914yes—
653C2×C4C24×D7914yes—
654C2×C4C24×D7914yes—
655C22—248no—
656C22—24no—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—424no—
662C22—31624no—
663C22—798no—
664C22—1584no—
665C22—1584no—
666C22—1584no—
667C22—15848no—
668C22—1584no—
669C22—1584no—
670C22#19099211116yesdirect product factor
671C22C22×D4×D7918yes—
672C22C22×D4×D7916yes—
673C22C2×#41×D7916yes—
674C22C2×#1457920816yes—
675C22C25×D7911yescharacteristic
676C4—24no—
677C4—24no—
678C4—24no—
679C4—24no—
680C4—24no—
681C4—798no—
682C4—798no—
683C4—1584no—
684C4—1584no—
685C4—1584no—
686C4—1584no—
687C2—28no—
688C2—44no—
689C2—3164no—
690C2—1588no—
691C2C2×#19099211112yesdirect product factor
692C2C23×D4×D7911yescharacteristic
693C2C22×#41×D7911yescharacteristic
694C2C22×#1457920811yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC22×#123×C79C2
socleC24×C79C24
hypercenterC22×#123D79
hypocenterC79C22×#547
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C23×#11929624C2semidirect
2. C23×#11929623C2semidirect
3. C2×#19099211C2direct (N × H)
4. C22×#14579160C2semidirect
5. C22×#14579146C2semidirect
6. C22×#14579145C2semidirect
7. C22×#14579143C2semidirect
8. C22×#14579139C2semidirect
9. C22×#14579138C2semidirect
10. C22×#14579134C2semidirect
11. C22×#14579133C2semidirect
12. C22×(C22⋊D79)⋊C4C2semidirect
13. C22×(C22⋊D79)⋊C4C2semidirect
14. C23×Dic79⋊C4C2semidirect
15. C22×C4⋊C4×D79C2semidirect
16. C22×#123×C79C2semidirect
18. C22×#11929624C22semidirect
20. C22×#11929623C22semidirect
35. #19099211C22direct (N × H)
36. C2×#14579160C22semidirect
37. C2×#14579146C22semidirect
38. C2×#14579145C22semidirect
39. C2×#14579143C22semidirect
40. C2×#14579139C22semidirect
41. C2×#14579138C22semidirect
42. C2×#14579134C22semidirect
43. C2×#14579133C22semidirect
44. C2×(C22⋊D79)⋊C4C22semidirect
45. C2×(C22⋊D79)⋊C4C22semidirect
54. C22×Dic79⋊C4C22semidirect
55. C2×C4⋊C4×D79C22semidirect
64. C2×#123×C79C22semidirect
73. C2×#11929624C23semidirect
75. C2×#11929623C23semidirect
85. C22×C22⋊D79D4semidirect
110. #14579160C23semidirect
111. #14579146C23semidirect
112. #14579145C23semidirect
113. #14579143C23semidirect
114. #14579139C23semidirect
115. #14579138C23semidirect
116. #14579134C23semidirect
117. #14579133C23semidirect
118. (C22⋊D79)⋊C4C23semidirect
119. (C22⋊D79)⋊C4C23semidirect
128. C2×Dic79⋊C4C23semidirect
129. C4⋊C4×D79C23semidirect
147. #123×C79C23semidirect
172. C2×C22⋊D79C2×D4semidirect
185. C22×Dic79#41semidirect
284. C22⋊D79C22×D4semidirect
293. C2×Dic79C2×#41semidirect
314. C22×C79#547semidirect
338. Dic79C22×#41semidirect
342. C2×C79C2×#547semidirect
355. C22×#123D79semidirect
364. C79C22×#547semidirect
390. C2×#123C2×D79semidirect
473. #123C22×D79semidirect
670. C22#19099211direct (N × H)
691. C2C2×#19099211direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#119296242
C23×#119296232
C2×#190992112
C22×#145791602
C22×#145791462
C22×#145791452
C22×#145791432
C22×#145791392
C22×#145791382
C22×#145791342
C22×#145791332
C22×(C22⋊D79)⋊C42
C23×Dic79⋊C42
C22×C4⋊C4×D792
C22×#123×C792
C22×#54779