Finite Group Databasebeta

← C2×#23777142 #35196692

Subgroups — C2×#23777142 #35196692

Order 20224.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777142C2132yesmaximal, direct product factor
2C2×#19099286C212yesmaximal, complemented
3C2×#19099273C212yesmaximal, complemented
4C2×#19099254C212yesmaximal, complemented
5C2×#19099254C212yesmaximal, complemented
6C2×#19099246C214yesmaximal, complemented
7C2×#19099237C214yesmaximal, complemented
8C2×#19099191C211yesmaximal, characteristic, complemented
9C2×#19099185C212yesmaximal, complemented
10C2×#19099171C212yesmaximal, complemented
11C2×#19099137C211yesmaximal, characteristic, complemented
12C2×#19099117C212yesmaximal, complemented
13C2×#19099100C212yesmaximal, complemented
14C2×#19099075C211yesmaximal, characteristic
15C22×#14579137C211yesmaximal, characteristic, complemented
16C2×#19099043C211yesmaximal, characteristic, complemented
17C2×#117×D79C211yesmaximal, characteristic, complemented
18C2×#519×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2211yescharacteristic
20C23×C4×D79C2211yescharacteristic
21#19099286C22132yescomplemented
22#19099273C22132yescomplemented
23#19099254C22132yescomplemented
24#19099254C22132yescomplemented
25#19099246C22164yescomplemented
26#19099237C22164yescomplemented
27#19099191C22116yescomplemented
28#19099185C22132yescomplemented
29#19099171C22132yescomplemented
30#19099137C22116yescomplemented
31#19099117C22132yescomplemented
32C2×#14579161C2212yescomplemented
33C2×#14579160C2212yescomplemented
34C2×#14579159C2212yescomplemented
35#19099100C22132yescomplemented
36C2×#14579156C2214yes—
37C2×#14579156C2214yescomplemented
38C2×#14579155C2214yes—
39C2×#14579155C2214yescomplemented
40C2×#14579153C2212yescomplemented
41C2×#14579153C2214yescomplemented
42C2×#14579152C2212yescomplemented
43C2×#14579151C2214yescomplemented
44C2×#14579151C2214yescomplemented
45C2×#14579150C2212yescomplemented
46C2×#14579149C2214yes—
47#19099075C22116yes—
48C2×#14579146C2214yes—
49C2×#14579146C2214yes—
50C2×#14579145C2212yes—
51C2×#14579144C2214yes—
52C2×#14579141C2211yescharacteristic
53C2×#14579141C2211yescharacteristic
54C2×#14579139C2214yes—
55C2×#14579139C2214yescomplemented
56C2×#14579138C2214yes—
57C2×#14579137C2212yes—
58C2×#14579137C2212yes—
59C2×#14579137C2212yes—
60C2×#14579137C2212yes—
61C2×#14579137C22116yescomplemented
62C2×#14579137C2212yescomplemented
63C2×#14579137C2212yescomplemented
64C2×#14579136C2211yescharacteristic
65C2×#14579136C2211yescharacteristic
66C2×#14579131C2212yes—
67#19099043C22116yescomplemented
68C2×C4×Dic158C2212yescomplemented
69C2×C4×Dic158C2214yescomplemented
70C2×C4×D316C2214yes—
71C2×C4×D316C2212yes—
72C2×C4×D316C2212yes—
73C2×C4×D316C2212yescomplemented
74C2×(C22⋊D79)⋊C4C2214yes—
75C2×#14579120C2211yescharacteristic
76C2×#14579119C2211yescharacteristic
77C2×#14579119C2211yescharacteristic
78C2×#14579119C2212yescomplemented
79C2×#14579118C2212yes—
80C2×#14579118C2214yes—
81C2×#14579118C2214yescomplemented
82C2×#14579117C2212yes—
83#117×D79C22116yescomplemented
84C22×C4⋊Dic79C2211yescharacteristic
85C22×Dic79⋊C4C2212yes—
86C2×C4⋊C4×D79C2211yescharacteristic
87C2×C4⋊C4×D79C2211yescharacteristic
88C2×C4⋊C4×D79C2212yescomplemented
89C22×(C2×D79)⋊C4C2212yes—
90C2×C22⋊C4×D79C2212yes—
91C2×C42×D79C2212yes—
92C23×Q8×C79C2211yescharacteristic
93#519×C79C22116yescomplemented
94C2×C4×Q8×C79C2212yescomplemented
95C2×C4×Q8×C79C2212yescomplemented
96C2×C4×Q8×C79C2212yescomplemented
97C2×C4×Q8×C79C2212yescomplemented
98C2×#117×C79C2211yescharacteristic
99C2×#117×C79C2211yescharacteristic
100C2×#117×C79C2214yes—
101C24×D79C2311yescharacteristic
102C2×#11929624—28no—
103C2×#11929624C2318yes—
104C22×Dic158C2311yescharacteristic
105C22×Dic158C2314yes—
106C22×D316C2312yes—
107C22×D316C2311yescharacteristic
108C22×D316C2312yes—
109C22×C22⋊D79C2312yes—
110C23×Dic79C2311yescharacteristic
111C23×Dic79C2312yes—
112C22×C4×D79—28no—
113C22×C4×D79C2311yescharacteristic
114C22×C4×D79C2312yes—
115C22×C4×D79C2311yescharacteristic
116C22×C4×D79C2312yes—
117C22×C4×D79C2318yes—
118C22×C4×D79C2311yescharacteristic
119C22×C4×D79C2311yescharacteristic
120C22×C4×D79C2312yes—
121C22×C4×D79C2314yes—
122#14579161C23116yescomplemented
123#14579160C23116yescomplemented
124#14579159C23116yescomplemented
125#14579156C23132yes—
126#14579156C23132yescomplemented
127#14579155C23132yes—
128#14579155C23132yescomplemented
129#14579153C23132yescomplemented
130#14579153C23116yescomplemented
131#14579152C23116yescomplemented
132#14579151C23132yescomplemented
133#14579151C23132yescomplemented
134#14579150C23116yescomplemented
135#14579149C23132yes—
136#14579146C23132yes—
137#14579146C23132yes—
138#14579145C23116yes—
139#14579144C23132yes—
140#14579141C2318yes—
141#14579141C2318yes—
142#14579139C23132yes—
143#14579139C23132yescomplemented
144#14579138C23132yes—
145#14579137C23116yes—
146#14579137C23116yes—
147#14579137C23116yes—
148#14579137C23116yes—
149#14579137C23116yescomplemented
150#14579137C23116yescomplemented
151#14579136C2318yes—
152#14579136C2318yes—
153#14579131C23116yes—
154C4×Dic158C23116yescomplemented
155C4×Dic158C23132yescomplemented
156C4×D316C23132yes—
157C4×D316C23116yes—
158C4×D316C23116yes—
159C4×D316C23116yescomplemented
160(C22⋊D79)⋊C4C23132yes—
161#14579120C2318yes—
162#14579119C2318yes—
163#14579119C2318yes—
164#14579119C23116yescomplemented
165#14579118C23116yes—
166#14579118C23132yes—
167#14579118C23132yescomplemented
168#14579117C23116yes—
169C2×C4⋊Dic79C2318yes—
170C2×C4⋊Dic79C2311yescharacteristic
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2312yes—
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2314yes—
176C2×C4⋊Dic79C2312yes—
177C2×Dic79⋊C4C23116yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2314yes—
186C2×Dic79⋊C4C2314yes—
187C4⋊C4×D79C2318yes—
188C4⋊C4×D79C2318yes—
189C4⋊C4×D79C23116yescomplemented
190C2×C22⋊Dic79C2312yes—
191C2×(C2×D79)⋊C4C23116yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2312yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2314yes—
199C2×(C2×D79)⋊C4C2314yes—
200C2×(C2×D79)⋊C4C2312yes—
201C2×(C2×D79)⋊C4C2312yes—
202C2×(C2×D79)⋊C4C2314yes—
203C22⋊C4×D79C23116yes—
204C2×C4×Dic79C2312yes—
205C2×C4×Dic79C2312yes—
206C2×C4×Dic79C2312yes—
207C2×C4×Dic79C2314yes—
208C42×D79C23116yes—
209C22×Q8×C79—28no—
210C22×Q8×C79C2318yes—
211C22×Q8×C79C2312yes—
212C22×Q8×C79C2312yes—
213C23×C4×C79C2312yes—
214C23×C4×C79C2311yescharacteristic
215C4×Q8×C79C23116yescomplemented
216C4×Q8×C79C23116yescomplemented
217C4×Q8×C79C23116yescomplemented
218C4×Q8×C79C23116yescomplemented
219#117×C79C2318yes—
220#117×C79C23132yes—
221#117×C79C2318yes—
222C2×C4⋊C4×C79C2311yescharacteristic
223C2×C4⋊C4×C79C2311yescharacteristic
224C2×C4⋊C4×C79C2311yescharacteristic
225C2×C4⋊C4×C79C2311yescharacteristic
226C2×C4⋊C4×C79C2314yes—
227C2×C4⋊C4×C79C2314yes—
228C2×C22⋊C4×C79C2312yes—
229C2×C22⋊C4×C79C2312yes—
230C2×C42×C79C2312yes—
231C2×C42×C79C2314yes—
232C2×C42×C79C2314yes—
233C2×C42×C79C2312yes—
234C23×D79—24no—
235C23×D79—24no—
236C23×D79—42no—
237C23×D79C2411yescharacteristic
238C23×D79C2412yes—
239C23×D79C2414yes—
240C23×D79C2411yescharacteristic
241#11929624—232no—
242C2×Dic158—24no—
243C2×Dic158—48no—
244C2×Dic158C2414yes—
245C2×Dic158C24116yes—
246C2×D316—28no—
247C2×D316—24no—
248C2×D316—44no—
249C2×D316C2414yes—
250C2×D316C2418yes—
251C2×D316C2418yes—
252C2×C22⋊D79—28no—
253C2×C22⋊D79C2418yes—
254C22×Dic79—24no—
255C22×Dic79—44no—
256C22×Dic79C2412yes—
257C22×Dic79C2412yes—
258C22×Dic79C2414yes—
259C22×Dic79C2411yescharacteristic
260C22×Dic79C2412yes—
261C22×Dic79C2411yescharacteristic
262C22×Dic79C2414yes—
263C22×Dic79C2418yes—
264C2×C4×D79—28no—
265C2×C4×D79—28no—
266C2×C4×D79—24no—
267C2×C4×D79—24no—
268C2×C4×D79—24no—
269C2×C4×D79—24no—
270C2×C4×D79—232no—
271C2×C4×D79—44no—
272C2×C4×D79—48no—
273C2×C4×D79C2418yes—
274C2×C4×D79C2414yes—
275C2×C4×D79C2418yes—
276C2×C4×D79C2414yes—
277C2×C4×D79C2414yes—
278C2×C4×D79C2414yes—
279C2×C4×D79C2418yes—
280C2×C4×D79C24116yes—
281C4⋊Dic79C2414yes—
282C4⋊Dic79C2414yes—
283C4⋊Dic79C2418yes—
284C4⋊Dic79C2418yes—
285C4⋊Dic79C2418yes—
286C4⋊Dic79C24116yes—
287C4⋊Dic79C2418yes—
288Dic79⋊C4C2418yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C24116yes—
291Dic79⋊C4C24116yes—
292Dic79⋊C4C24116yes—
293Dic79⋊C4C24116yes—
294Dic79⋊C4C24116yes—
295Dic79⋊C4C24116yes—
296Dic79⋊C4C24116yes—
297C22⋊Dic79C2418yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C2418yes—
300(C2×D79)⋊C4C24116yes—
301(C2×D79)⋊C4C24116yes—
302(C2×D79)⋊C4C2418yes—
303(C2×D79)⋊C4C2418yes—
304(C2×D79)⋊C4C24116yes—
305(C2×D79)⋊C4C24116yes—
306(C2×D79)⋊C4C2418yes—
307(C2×D79)⋊C4C2418yes—
308(C2×D79)⋊C4C24116yes—
309C4×Dic79C2418yes—
310C4×Dic79C2418yes—
311C4×Dic79C2418yes—
312C4×Dic79C24116yes—
313C24×C79C2411yescharacteristic
314C2×Q8×C79—28no—
315C2×Q8×C79—28no—
316C2×Q8×C79—232no—
317C2×Q8×C79C2418yes—
318C2×Q8×C79C2418yes—
319C22×C4×C79—28no—
320C22×C4×C79#4118yes—
321C22×C4×C79C2412yes—
322C22×C4×C79C2412yes—
323C22×C4×C79C2412yes—
324C22×C4×C79C2412yes—
325C22×C4×C79C2414yes—
326C22×C4×C79C2418yes—
327C22×C4×C79C2411yescharacteristic
328C22×C4×C79C2414yes—
329C22×C4×C79C2411yescharacteristic
330C4⋊C4×C79C2414yes—
331C4⋊C4×C79C2414yes—
332C4⋊C4×C79C2414yes—
333C4⋊C4×C79C2414yes—
334C4⋊C4×C79C24116yes—
335C4⋊C4×C79C24116yes—
336C22⋊C4×C79C2418yes—
337C22⋊C4×C79C2418yes—
338C42×C79C2418yes—
339C42×C79C24116yes—
340C42×C79C24116yes—
341C42×C79C2418yes—
342C23×C79—22no—
343C23×C79—22no—
344C23×C79C2×#4114yes—
345C23×C79C2512yes—
346C23×C79C2511yescharacteristic
347C22×D79—22no—
348C22×D79—22no—
349C22×D79—28no—
350C22×D79—22no—
351C22×D79—24no—
352C22×D79—24no—
353C22×D79—22no—
354C22×D79—24no—
355C22×D79—22no—
356C22×D79—28no—
357C22×D79—44no—
358C22×D79—416no—
359C22×D792−1+414yes—
360C22×D79C2512yes—
361C22×D79C2514yes—
362C22×D79C2512yes—
363Q8×C79—216no—
364Q8×C79—216no—
365C2×C4×C79—216no—
366C2×C4×C79—28no—
367C2×C4×C79—24no—
368C2×C4×C79—24no—
369C2×C4×C79—24no—
370C2×C4×C79—24no—
371C2×C4×C79C2×#4114yes—
372C2×C4×C79C2×#4114yes—
373C2×C4×C79C2×#41116yes—
374C2×C4×C79C2514yes—
375C2×C4×C79C2514yes—
376C2×C4×C79C2518yes—
377C2×C4×C79C2514yes—
378C2×C4×C79C2514yes—
379C2×C4×C79C2512yes—
380C2×C4×C79C2512yes—
381C22⋊D79—216no—
382C2×Dic79—28no—
383C2×Dic79—22no—
384C2×Dic79—22no—
385C2×Dic79—24no—
386C2×Dic79—24no—
387C2×Dic79—28no—
388C2×Dic79—24no—
389C2×Dic79—48no—
390C2×Dic79C2512yes—
391C2×Dic79C2514yes—
392C2×Dic79C2514yes—
393C2×Dic79C2514yes—
394C2×Dic79C2518yes—
395C2×Dic79C2512yes—
396D316—216no—
397D316—28no—
398D316—48no—
399C4×D79—216no—
400C4×D79—28no—
401C4×D79—28no—
402C4×D79—28no—
403C4×D79—28no—
404C4×D79—216no—
405C4×D79—48no—
406C4×D79—416no—
407Dic158—28no—
408Dic158—416no—
409C22×C79—22no—
410C22×C79—22no—
411C22×C79—28no—
412C22×C79C22×#4114yes—
413C22×C79C22×#4112yes—
414C22×C79C2×2−1+412yes—
415C22×C79#58512yes—
416C22×C79C2611yescharacteristic
417C2×D79—22no—
418C2×D79—22no—
419C2×D79—28no—
420C2×D79—24no—
421C2×D79—22no—
422C2×D79—22no—
423C2×D79—24no—
424C2×D79—22no—
425C2×D79—24no—
426C2×D79—416no—
427C2×D79—48no—
428C2×D79—44no—
429C2×D79C2×2−1+414yes—
430C4×C79—28no—
431C4×C79—24no—
432C4×C79—24no—
433C4×C79—24no—
434C4×C79—24no—
435C4×C79C22×#4114yes—
436C4×C79C22×#4114yes—
437Dic79—24no—
438Dic79—22no—
439Dic79—22no—
440Dic79—24no—
441Dic79—24no—
442Dic79—28no—
443C2×#3495—791nomaximal, Sylow
444C2×C79—24no—
445C2×C79#349514yescomplemented
446C2×C79C23×#4111yescharacteristic
447C2×C79C22×2−1+411yescharacteristic
448C2×C79C2×#58511yescharacteristic
449D79—24no—
450D79—44no—
451D79—42no—
452#3495—7932no—
453C2×#556—792no—
454C2×#554—792no—
455C2×#552—792no—
456C2×#552—792no—
457C2×#552—794no—
458C2×#551—794no—
459C2×#544—791no—
460C2×#542—792no—
461C2×#541—792no—
462C2×#536—791no—
463C2×#533—792no—
464C2×#529—792no—
465C2×#525—791no—
466C22×C22⋊Q8—791no—
467C2×#520—791no—
468C2×#519D7911yescharacteristic, complemented
469C22×#117—791no—
470C79C2×#349511yescharacteristic, complemented, Sylow
471C22×#41—791no—
472C23×Q8C2×D7911yescharacteristic
473C24×C4—791no—
474#556—7932no—
475#554—7932no—
476#552—7932no—
477#552—7932no—
478#552—7964no—
479#551—7964no—
480#544—7916no—
481#542—7932no—
482#541—7932no—
483#536—7916no—
484#533—7932no—
485C2×C4⋊Q8—792no—
486C2×C4⋊Q8—792no—
487C2×C4⋊Q8—792no—
488#529—7932no—
489C2×#126—794no—
490C2×#126—794no—
491C2×#126—794no—
492C2×#126—794no—
493C2×#125—792no—
494C2×#125—794no—
495C2×#125—794no—
496C2×#125—794no—
497C2×#125—792no—
498C2×#124—792no—
499C2×#124—794no—
500#525—7916no—
501C2×#123—794no—
502C2×#123—794no—
503C2×#123—794no—
504C2×#123—792no—
505C2×C22⋊Q8—792no—
506C2×C22⋊Q8—792no—
507C2×C22⋊Q8—792no—
508C2×C22⋊Q8—792no—
509C2×C22⋊Q8—7916no—
510C2×C22⋊Q8—792no—
511C2×C22⋊Q8—792no—
512C2×C22⋊Q8—791no—
513C2×C22⋊Q8—791no—
514C2×C22⋊Q8—794no—
515C2×C22⋊Q8—794no—
516C2×C22⋊Q8—794no—
517C2×#121—791no—
518C2×#121—791no—
519C2×#120—792no—
520#520—7916no—
521#519C2×D79116yescomplemented
522C2×C4×Q8—792no—
523C2×C4×Q8—794no—
524C2×C4×Q8C2×D7912yescomplemented
525C2×C4×Q8C2×D7912yescomplemented
526C2×C4×Q8C2×D7912yescomplemented
527C2×C4×Q8C2×D7912yescomplemented
528C2×C4×D4—794no—
529C2×C4×D4—792no—
530C2×C4×D4—792no—
531C2×C4×D4—792no—
532C2×C4×D4—794no—
533C2×#117—791no—
534C2×#117—7916no—
535C2×#117—791no—
536C2×#117—791no—
537C2×#117—792no—
538C2×#117—792no—
539C2×#117—792no—
540C2×#117—794no—
541C2×#117—794no—
542C2×#117C2×D7911yescharacteristic
543C2×#117C2×D7911yescharacteristic
544C2×#117C2×D7914yes—
545C22×C4⋊C4—791no—
546C22×C4⋊C4—792no—
547C22×C4⋊C4—791no—
548C22×C4⋊C4—791no—
549C22×C4⋊C4—792no—
550C22×C22⋊C4—792no—
551C22×C22⋊C4—792no—
552C22×C42—792no—
553C25—791no—
554C2×#41—798no—
555C2×#41—1588no—
556C22×Q8—28no—
557C22×Q8—794no—
558C22×Q8—791no—
559C22×Q8C22×D7912yes—
560C22×Q8C22×D7912yes—
561C22×Q8C22×D7918yes—
562C22×D4—792no—
563C22×D4—792no—
564C22×D4—792no—
565C22×D4—791no—
566C23×C4—792no—
567C23×C4—792no—
568C23×C4—794no—
569C23×C4—791no—
570C23×C4—792no—
571C23×C4—791no—
572C23×C4—792no—
573C23×C4—791no—
574C23×C4—791no—
575C23×C4—798no—
576C23×C4—791no—
577C23×C4—1588no—
578C23×C4C22×D7912yes—
579C23×C4C22×D7911yescharacteristic
580C4⋊Q8—7916no—
581C4⋊Q8—7916no—
582C4⋊Q8—7916no—
583#126—7932no—
584#126—7932no—
585#126—7932no—
586#126—7932no—
587#125—7916no—
588#125—7932no—
589#125—7932no—
590#125—7932no—
591#125—7916no—
592#124—7916no—
593#124—7932no—
594#123—7932no—
595#123—7932no—
596#123—7932no—
597#123—7916no—
598C22⋊Q8—7916no—
599C22⋊Q8—7916no—
600C22⋊Q8—7916no—
601C22⋊Q8—7916no—
602C22⋊Q8—7916no—
603C22⋊Q8—7916no—
604C22⋊Q8—798no—
605C22⋊Q8—798no—
606C22⋊Q8—7932no—
607C22⋊Q8—7932no—
608C22⋊Q8—7932no—
609#121—798no—
610#121—798no—
611#120—7916no—
612C4×Q8—7916no—
613C4×Q8—7932no—
614C4×Q8C22×D79116yescomplemented
615C4×Q8C22×D79116yescomplemented
616C4×Q8C22×D79116yescomplemented
617C4×Q8C22×D79116yescomplemented
618C4×D4—7932no—
619C4×D4—7916no—
620C4×D4—7916no—
621C4×D4—7916no—
622C4×D4—7932no—
623#117—798no—
624#117—798no—
625#117—798no—
626#117—7916no—
627#117—7916no—
628#117—7916no—
629#117—7932no—
630#117—7932no—
631#117C22×D7918yes—
632#117C22×D7918yes—
633#117C22×D79132yes—
634C2×C4⋊C4—792no—
635C2×C4⋊C4—792no—
636C2×C4⋊C4—791no—
637C2×C4⋊C4—791no—
638C2×C4⋊C4—792no—
639C2×C4⋊C4—794no—
640C2×C4⋊C4—792no—
641C2×C4⋊C4—794no—
642C2×C4⋊C4—798no—
643C2×C4⋊C4—794no—
644C2×C4⋊C4—7916no—
645C2×C4⋊C4—794no—
646C2×C4⋊C4—794no—
647C2×C4⋊C4—794no—
648C2×C4⋊C4—792no—
649C2×C4⋊C4—792no—
650C2×C4⋊C4—794no—
651C2×C4⋊C4—794no—
652C2×C4⋊C4—798no—
653C2×C4⋊C4—798no—
654C2×C4⋊C4—7916no—
655C2×C4⋊C4C22×D7911yescharacteristic
656C2×C4⋊C4C22×D7911yescharacteristic
657C2×C4⋊C4C22×D7911yescharacteristic
658C2×C4⋊C4C22×D7911yescharacteristic
659C2×C4⋊C4C22×D7914yes—
660C2×C4⋊C4C22×D7914yes—
661C2×C22⋊C4—792no—
662C2×C22⋊C4—792no—
663C2×C22⋊C4—792no—
664C2×C22⋊C4—794no—
665C2×C22⋊C4—794no—
666C2×C22⋊C4—7916no—
667C2×C22⋊C4—792no—
668C2×C22⋊C4—792no—
669C2×C22⋊C4—794no—
670C2×C22⋊C4—794no—
671C2×C22⋊C4—792no—
672C2×C22⋊C4—792no—
673C2×C22⋊C4—794no—
674C2×C22⋊C4—7916no—
675C2×C22⋊C4C22×D7912yes—
676C2×C22⋊C4C22×D7912yes—
677C2×C42—792no—
678C2×C42—794no—
679C2×C42—792no—
680C2×C42—792no—
681C2×C42—7916no—
682C2×C42C22×D7912yes—
683C2×C42C22×D7914yes—
684C2×C42C22×D7914yes—
685C2×C42C22×D7912yes—
686C24—3162no—
687C24—794no—
688C24—791no—
689C24—791no—
690C24—792no—
691C24—1584no—
692C24—1584no—
693C24C23×D7911yescharacteristic
694#41—15832no—
695C2×Q8—28no—
696C2×Q8—28no—
697C2×Q8—232no—
698C2×Q8—3168no—
699C2×Q8—7916no—
700C2×Q8—794no—
701C2×Q8—1584no—
702C2×Q8C23×D7918yes—
703C2×Q8C23×D7918yes—
704C2×D4—3164no—
705C2×D4—798no—
706C2×D4—798no—
707C2×D4—798no—
708C2×D4—794no—
709C2×D4—1588no—
710C2×D4—1588no—
711C2×D4—1584no—
712C22×C4—28no—
713C22×C4—3168no—
714C22×C4—3164no—
715C22×C4—3164no—
716C22×C4—798no—
717C22×C4—798no—
718C22×C4—7916no—
719C22×C4—794no—
720C22×C4—791no—
721C22×C4—792no—
722C22×C4—792no—
723C22×C4—792no—
724C22×C4—794no—
725C22×C4—791no—
726C22×C4—794no—
727C22×C4—798no—
728C22×C4—794no—
729C22×C4—798no—
730C22×C4—794no—
731C22×C4—794no—
732C22×C4—1588no—
733C22×C4—1584no—
734C22×C4—1584no—
735C22×C4—1584no—
736C22×C4—1584no—
737C22×C4—1584no—
738C22×C4—15832no—
739C22×C4—1588no—
740C22×C4#1192962418yes—
741C22×C4C23×D7918yes—
742C22×C4C23×D7912yes—
743C22×C4C23×D7912yes—
744C22×C4C23×D7912yes—
745C22×C4C23×D7912yes—
746C22×C4C23×D7914yes—
747C22×C4C23×D7914yes—
748C22×C4C23×D7911yescharacteristic
749C22×C4C23×D7911yescharacteristic
750C4⋊C4—798no—
751C4⋊C4—798no—
752C4⋊C4—7916no—
753C4⋊C4—7916no—
754C4⋊C4—7916no—
755C4⋊C4—7916no—
756C4⋊C4—7916no—
757C4⋊C4—7916no—
758C4⋊C4—7916no—
759C4⋊C4—798no—
760C4⋊C4—794no—
761C4⋊C4—794no—
762C4⋊C4—798no—
763C4⋊C4—798no—
764C4⋊C4—798no—
765C4⋊C4—7916no—
766C4⋊C4C23×D7914yes—
767C4⋊C4C23×D7914yes—
768C4⋊C4C23×D7914yes—
769C4⋊C4C23×D7914yes—
770C4⋊C4C23×D79116yes—
771C4⋊C4C23×D79116yes—
772C22⋊C4—798no—
773C22⋊C4—798no—
774C22⋊C4—798no—
775C22⋊C4—7916no—
776C22⋊C4—7916no—
777C22⋊C4—798no—
778C22⋊C4—798no—
779C22⋊C4—7916no—
780C22⋊C4—7916no—
781C22⋊C4—798no—
782C22⋊C4—798no—
783C22⋊C4—7916no—
784C22⋊C4C23×D7918yes—
785C22⋊C4C23×D7918yes—
786C42—798no—
787C42—798no—
788C42—798no—
789C42—7916no—
790C42C23×D7918yes—
791C42C23×D79116yes—
792C42C23×D79116yes—
793C42C23×D7918yes—
794C23—22no—
795C23—22no—
796C23—31616no—
797C23—3164no—
798C23—794no—
799C23—792no—
800C23—792no—
801C23—794no—
802C23—1588no—
803C23—1584no—
804C23—1582no—
805C23—1584no—
806C23—1582no—
807C23—1588no—
808C23—1582no—
809C23—1584no—
810C23—1582no—
811C23—1582no—
812C23C2×#1192962414yes—
813C23C24×D7912yes—
814C23C24×D7911yescharacteristic
815Q8—216no—
816Q8—216no—
817Q8—31616no—
818Q8—1588no—
819D4—3168no—
820D4—15816no—
821D4—15816no—
822D4—1588no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—216no—
828C2×C4—28no—
829C2×C4—31616no—
830C2×C4—3168no—
831C2×C4—3168no—
832C2×C4—792no—
833C2×C4—794no—
834C2×C4—794no—
835C2×C4—794no—
836C2×C4—798no—
837C2×C4—792no—
838C2×C4—15816no—
839C2×C4—1584no—
840C2×C4—1588no—
841C2×C4—1584no—
842C2×C4—1588no—
843C2×C4—1582no—
844C2×C4—1582no—
845C2×C4—1584no—
846C2×C4—1588no—
847C2×C4—1588no—
848C2×C4—1588no—
849C2×C4—1588no—
850C2×C4—15816no—
851C2×C4C2×#1192962414yes—
852C2×C4C2×#1192962414yes—
853C2×C4C2×#11929624116yes—
854C2×C4C24×D7914yes—
855C2×C4C24×D7914yes—
856C2×C4C24×D7914yes—
857C2×C4C24×D7914yes—
858C2×C4C24×D7918yes—
859C2×C4C24×D7912yes—
860C2×C4C24×D7912yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—31616no—
865C22—3164no—
866C22—3168no—
867C22—794no—
868C22—1582no—
869C22—1584no—
870C22—1584no—
871C22—1582no—
872C22—1584no—
873C22—1582no—
874C22—1588no—
875C22—1582no—
876C22—1582no—
877C22C22×#1192962414yes—
878C22C22×#1192962412yes—
879C222−1+4×D7912yes—
880C22#1909940012yes—
881C22C25×D7911yescharacteristic
882C4—28no—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—1582no—
888C4—1582no—
889C4—1584no—
890C4—1584no—
891C4—1588no—
892C4—1584no—
893C4C22×#1192962414yes—
894C4C22×#1192962414yes—
895C2—24no—
896C2—3162no—
897C2—3164no—
898C2—1584no—
899C2#2377714214yesdirect product factor
900C2C23×#1192962411yescharacteristic
901C2C2×2−1+4×D7911yescharacteristic
902C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#519×C79C2
socleC23×C79C25
prime radicalC2×#19099075C2
hypercenterC2×#519D79
hypocenterC79C2×#3495
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. #23777142C2direct (N × H)
2. C2×#19099286C2semidirect
3. C2×#19099273C2semidirect
4. C2×#19099254C2semidirect
5. C2×#19099254C2semidirect
6. C2×#19099246C2semidirect
7. C2×#19099237C2semidirect
8. C2×#19099191C2semidirect
9. C2×#19099185C2semidirect
10. C2×#19099171C2semidirect
11. C2×#19099137C2semidirect
12. C2×#19099117C2semidirect
13. C2×#19099100C2semidirect
15. C22×#14579137C2semidirect
16. C2×#19099043C2semidirect
17. C2×#117×D79C2semidirect
18. C2×#519×C79C2semidirect
21. #19099286C22semidirect
22. #19099273C22semidirect
23. #19099254C22semidirect
24. #19099254C22semidirect
25. #19099246C22semidirect
26. #19099237C22semidirect
27. #19099191C22semidirect
28. #19099185C22semidirect
29. #19099171C22semidirect
30. #19099137C22semidirect
31. #19099117C22semidirect
32. C2×#14579161C22semidirect
33. C2×#14579160C22semidirect
34. C2×#14579159C22semidirect
35. #19099100C22semidirect
37. C2×#14579156C22semidirect
39. C2×#14579155C22semidirect
40. C2×#14579153C22semidirect
41. C2×#14579153C22semidirect
42. C2×#14579152C22semidirect
43. C2×#14579151C22semidirect
44. C2×#14579151C22semidirect
45. C2×#14579150C22semidirect
55. C2×#14579139C22semidirect
61. C2×#14579137C22semidirect
62. C2×#14579137C22semidirect
63. C2×#14579137C22semidirect
67. #19099043C22semidirect
68. C2×C4×Dic158C22semidirect
69. C2×C4×Dic158C22semidirect
73. C2×C4×D316C22semidirect
78. C2×#14579119C22semidirect
81. C2×#14579118C22semidirect
83. #117×D79C22semidirect
88. C2×C4⋊C4×D79C22semidirect
93. #519×C79C22semidirect
94. C2×C4×Q8×C79C22semidirect
95. C2×C4×Q8×C79C22semidirect
96. C2×C4×Q8×C79C22semidirect
97. C2×C4×Q8×C79C22semidirect
122. #14579161C23semidirect
123. #14579160C23semidirect
124. #14579159C23semidirect
126. #14579156C23semidirect
128. #14579155C23semidirect
129. #14579153C23semidirect
130. #14579153C23semidirect
131. #14579152C23semidirect
132. #14579151C23semidirect
133. #14579151C23semidirect
134. #14579150C23semidirect
143. #14579139C23semidirect
149. #14579137C23semidirect
150. #14579137C23semidirect
154. C4×Dic158C23semidirect
155. C4×Dic158C23semidirect
159. C4×D316C23semidirect
164. #14579119C23semidirect
167. #14579118C23semidirect
189. C4⋊C4×D79C23semidirect
215. C4×Q8×C79C23semidirect
216. C4×Q8×C79C23semidirect
217. C4×Q8×C79C23semidirect
218. C4×Q8×C79C23semidirect
445. C2×C79#3495semidirect
468. C2×#519D79semidirect
470. C79C2×#3495semidirect
521. #519C2×D79semidirect
524. C2×C4×Q8C2×D79semidirect
525. C2×C4×Q8C2×D79semidirect
526. C2×C4×Q8C2×D79semidirect
527. C2×C4×Q8C2×D79semidirect
614. C4×Q8C22×D79semidirect
615. C4×Q8C22×D79semidirect
616. C4×Q8C22×D79semidirect
617. C4×Q8C22×D79semidirect
899. C2#23777142direct (N × H)

Maximal subgroups

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

subgroupindex
#237771422
C2×#190992862
C2×#190992732
C2×#190992542
C2×#190992462
C2×#190992372
C2×#190991912
C2×#190991852
C2×#190991712
C2×#190991372
C2×#190991172
C2×#190991002
C2×#190990752
C22×#145791372
C2×#190990432
C2×#117×D792
C2×#519×C792
C2×#349579