Finite Group Databasebeta

← C2×#23774693 #35160501

Subgroups — C2×#23774693 #35160501

Order 20224.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099190C211yesmaximal, characteristic, complemented
2C2×#19099182C211yesmaximal, characteristic
3#23774693C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098959C211yesmaximal, characteristic, complemented
6C2×#19098917C211yesmaximal, characteristic, complemented
7C2×#19098880C211yesmaximal, characteristic
8C2×#19098903C211yesmaximal, characteristic, complemented
9C2×#19098885C211yesmaximal, characteristic
10C2×#19098892C211yesmaximal, characteristic, complemented
11C2×#19098872C211yesmaximal, characteristic, complemented
12C2×#19098846C211yesmaximal, characteristic, complemented
13C2×#19098861C211yesmaximal, characteristic, complemented
14C2×#19098851C211yesmaximal, characteristic, complemented
15C2×#19098625C211yesmaximal, characteristic, complemented
16C2×#489×C79C211yesmaximal, characteristic, complemented
17#19099190—24no—
18#19099190C2218yescomplemented
19#19099182—24no—
20#19099182C2218yes—
21C2×#14579161C2211yescharacteristic
22C2×#14579160C2211yescharacteristic
23C2×#14579159—21no—
24C2×#14579154—21no—
25C2×#14579153C2211yescharacteristic
26C2×#14579152C2211yescharacteristic
27C2×#14579151—21no—
28C2×#14579147—21no—
29C2×#14579145—21no—
30C2×#14579139—21no—
31C2×#14579138—21no—
32C2×#14579137—21no—
33C2×#14579137C2211yescharacteristic
34C2×#14579132C2211yescharacteristic
35C2×Q8×Dic79C2211yescharacteristic
36C2×D4×Dic79C2211yescharacteristic
37C2×#14579119C2211yescharacteristic
38C2×#14579118C2211yescharacteristic
39C2×C4⋊C4×D79C2211yescharacteristic
40#19098972C2218yescomplemented
41#19098959C2218yescomplemented
42#19098917C2218yescomplemented
43#19098903C2218yescomplemented
44#19098892C2218yescomplemented
45#19098885C2218yes—
46#19098880C2218yes—
47#19098872C2218yescomplemented
48#19098861C2218yescomplemented
49#19098851C2218yescomplemented
50#19098846C2218yescomplemented
51#19098625C2218yescomplemented
52C2×#14579095C2211yescharacteristic
53C2×#14579095C2211yescharacteristic
54C2×#14579093C2211yescharacteristic
55C2×#14579093C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C4×C79⋊C8C2211yescharacteristic
69C2×C4⋊Q8×C79C2211yescharacteristic
70C2×#124×C79C2211yescharacteristic
71#489×C79C2218yescomplemented
72C2×#103×C79C2211yescharacteristic
73C2×#103×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×C22⋊D79—21no—
80C23×Dic79—21no—
81C22×C4×D79—21no—
82C22×C4×D79C2311yescharacteristic
83C22×C79⋊C8C2311yescharacteristic
84C22×C79⋊C8C2311yescharacteristic
85#14579161—22no—
86#14579161C2314yes—
87#14579160—22no—
88#14579160C2314yes—
89#14579159—28no—
90#14579154—28no—
91#14579153—22no—
92#14579153C2314yes—
93#14579152—22no—
94#14579152C2314yes—
95#14579151—28no—
96#14579147—28no—
97#14579145—28no—
98#14579139—28no—
99#14579138—28no—
100#14579137—22no—
101#14579137—28no—
102#14579137C2314yes—
103#14579132—22no—
104#14579132C2314yes—
105Q8×Dic79—22no—
106Q8×Dic79C2314yes—
107D4×Dic79—22no—
108D4×Dic79C2314yes—
109#14579119—22no—
110#14579119C2314yes—
111#14579118D414yes—
112#14579118C2314yes—
113C2×C4⋊Dic79—21no—
114C2×C4⋊Dic79—21no—
115C2×C4⋊Dic79—21no—
116C2×C4⋊Dic79C2311yescharacteristic
117C2×C4⋊Dic79C2311yescharacteristic
118C2×C4⋊Dic79C2311yescharacteristic
119C2×C4⋊Dic79C2311yescharacteristic
120C2×Dic79⋊C4—21no—
121C2×Dic79⋊C4—21no—
122C2×Dic79⋊C4—21no—
123C2×Dic79⋊C4—21no—
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4D411yescharacteristic
127C2×Dic79⋊C4D411yescharacteristic
128C4⋊C4×D79—22no—
129C4⋊C4×D79C2314yes—
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79—21no—
132C2×(C2×D79)⋊C4—21no—
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4D411yescharacteristic
135C2×(C2×D79)⋊C4D411yescharacteristic
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79C2311yescharacteristic
139#14579095C2314yes—
140#14579095C2314yes—
141#14579093C2314yes—
142#14579093C2314yes—
143#14579092C2314yes—
144#14579092C2314yes—
145#14579092C2314yes—
146#14579092C2314yes—
147Dic79⋊C8C2314yes—
148Dic79⋊C8C2314yes—
149#14579085C2314yes—
150#14579085C2314yes—
151#14579082C2314yes—
152#14579082C2314yes—
153(C2×D79)⋊C8C2314yes—
154(C2×D79)⋊C8C2314yes—
155C4×C79⋊C8C2314yes—
156C22×Q8×C79—21no—
157C22×Q8×C79C2311yescharacteristic
158C22×D4×C79C2311yescharacteristic
159C22×C8×C79C2311yescharacteristic
160C22×C8×C79C2311yescharacteristic
161C4⋊Q8×C79—22no—
162C4⋊Q8×C79C2314yes—
163#124×C79—22no—
164#124×C79C2314yes—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79C2311yescharacteristic
167C2×C4⋊C4×C79C2311yescharacteristic
168C2×C22⋊C4×C79—21no—
169C2×C22⋊C4×C79—21no—
170C2×C42×C79C2311yescharacteristic
171#103×C79C2314yes—
172#103×C79C2314yes—
173#102×C79C2314yes—
174#102×C79C2314yes—
175#97×C79C2314yes—
176C23×D79C2×D411yescharacteristic
177C2×Dic158—24no—
178C2×Dic158—24no—
179C2×Dic158—82no—
180C2×Dic158—82no—
181C2×C22⋊D79—24no—
182C2×C22⋊D79—82no—
183C22×Dic79—24no—
184C22×Dic79—21no—
185C22×Dic79—21no—
186C22×Dic79—21no—
187C22×Dic79—21no—
188C22×Dic79—82no—
189C22×Dic79C2×D411yescharacteristic
190C22×Dic79C2×D411yescharacteristic
191C22×Dic79C2×D411yescharacteristic
192C2×C4×D79—24no—
193C2×C4×D79—22no—
194C2×C4×D79—22no—
195C2×C4×D79—82no—
196C2×C4×D79C2×D412yes—
197C2×C4×D79C2412yes—
198C2×C79⋊C8—22no—
199C2×C79⋊C8—22no—
200C2×C79⋊C8C2412yes—
201C2×C79⋊C8C2412yes—
202C4⋊Dic79—24no—
203C4⋊Dic79—24no—
204C4⋊Dic79—21no—
205C4⋊Dic79—24no—
206C4⋊Dic79—21no—
207C4⋊Dic79—21no—
208C4⋊Dic79—21no—
209C4⋊Dic79C2412yes—
210C4⋊Dic79C2412yes—
211C4⋊Dic79C2412yes—
212C4⋊Dic79C2412yes—
213Dic79⋊C4—24no—
214Dic79⋊C4—24no—
215Dic79⋊C4—24no—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4C2×D414yes—
220Dic79⋊C4C2×D414yes—
221C22⋊Dic79—24no—
222C22⋊Dic79—24no—
223(C2×D79)⋊C4—24no—
224(C2×D79)⋊C4—24no—
225(C2×D79)⋊C4C2×D414yes—
226(C2×D79)⋊C4C2×D414yes—
227C4×Dic79—24no—
228C4×Dic79—24no—
229C4×Dic79C2×D412yes—
230C4×Dic79C2412yes—
231C24×C79—21no—
232C2×Q8×C79—21no—
233C2×Q8×C79—24no—
234C2×Q8×C79—22no—
235C2×Q8×C79—22no—
236C2×Q8×C79—82no—
237C2×Q8×C79C2412yes—
238C2×D4×C79—21no—
239C2×D4×C79—22no—
240C2×D4×C79—22no—
241C2×D4×C79C2412yes—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79C2×D411yescharacteristic
246C22×C4×C79C2×D411yescharacteristic
247C22×C4×C79C2411yescharacteristic
248C2×C8×C79—22no—
249C2×C8×C79—22no—
250C2×C8×C79C2412yes—
251C2×C8×C79C2412yes—
252C4⋊C4×C79—24no—
253C4⋊C4×C79—21no—
254C4⋊C4×C79—21no—
255C4⋊C4×C79C2412yes—
256C4⋊C4×C79C2412yes—
257C22⋊C4×C79—24no—
258C22⋊C4×C79—24no—
259C42×C79C2×D412yes—
260C42×C79C2412yes—
261C23×C79—22no—
262C23×C79—42no—
263C23×C79—42no—
264C23×C79—42no—
265C23×C79C22×D411yescharacteristic
266C22×D79—22no—
267C22×D79—22no—
268C22×D79—22no—
269C22×D79C22×D412yes—
270Q8×C79—22no—
271Q8×C79—22no—
272Q8×C79—42no—
273Q8×C79—84no—
274D4×C79—22no—
275D4×C79—22no—
276D4×C79—42no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—42no—
283C2×C4×C79—42no—
284C2×C4×C79—42no—
285C2×C4×C79C22×D412yes—
286C2×C4×C79C22×D412yes—
287C2×C4×C79C22×D411yescharacteristic
288C2×C4×C792−1+412yes—
289C2×C4×C792−1+412yes—
290C2×C4×C79C2511yescharacteristic
291C22⋊D79—84no—
292C2×Dic79—22no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—42no—
300C2×Dic79—42no—
301C2×Dic79—42no—
302C2×Dic79—42no—
303C2×Dic79—84no—
304C2×Dic79C22×D412yes—
305C2×Dic79C22×D412yes—
306C2×Dic79C22×D412yes—
307C4×D79—24no—
308C4×D79—22no—
309C4×D79—22no—
310C4×D79—84no—
311Dic158—84no—
312Dic158—84no—
313C8×C79—22no—
314C8×C79—22no—
315C79⋊C8—22no—
316C79⋊C8—22no—
317C22×C79—42no—
318C22×C79—42no—
319C22×C79—42no—
320C22×C79—84no—
321C22×C79#53612yes—
322C22×C79#57712yes—
323C22×C79#57712yes—
324C22×C79C23×D411yescharacteristic
325C2×D79—22no—
326C2×D79—22no—
327C2×D79—22no—
328C2×D79—44no—
329C4×C79—22no—
330C4×C79—22no—
331C4×C79—42no—
332C4×C79—42no—
333C4×C79—42no—
334C4×C79#53612yes—
335C4×C79C2×2−1+411yescharacteristic
336C4×C79C2×2−1+411yescharacteristic
337Dic79—22no—
338Dic79—22no—
339Dic79—22no—
340Dic79—42no—
341Dic79—42no—
342Dic79—42no—
343Dic79—42no—
344C2×#3244—791nomaximal, Sylow
345C2×C79—82no—
346C2×C79#324414yescomplemented
347C2×C79C2×#53611yescharacteristic
348C2×C79C2×#57711yescharacteristic
349C2×C79C2×#57711yescharacteristic
350D79—42no—
351C2×#544—791no—
352C2×#542—791no—
353#3244—7916no—
354C2×#501—791no—
355C2×#498—791no—
356C2×#489D7911yescharacteristic, complemented
357C2×#488—791no—
358C2×#481—791no—
359C2×#485—791no—
360C2×#482—791no—
361C2×#483—791no—
362C2×#479—791no—
363C2×#475—791no—
364C2×#478—791no—
365C2×#476—791no—
366C2×#433—791no—
367C79C2×#324411yescharacteristic, complemented, Sylow
368#544—798no—
369#544—1584no—
370#542—798no—
371#542—1584no—
372C2×C4⋊Q8—791no—
373C2×C4⋊Q8—791no—
374C2×C4⋊Q8—1581no—
375C2×C4⋊Q8C2×D7911yescharacteristic
376C2×#126—1581no—
377C2×#125—791no—
378C2×#125—791no—
379C2×#125—1581no—
380C2×#124—1581no—
381C2×#124C2×D7911yescharacteristic
382C2×#123—1581no—
383C2×C22⋊Q8—791no—
384C2×C22⋊Q8—1581no—
385C2×C22⋊Q8—1581no—
386C2×C22⋊Q8—1581no—
387C2×#121—791no—
388C2×C4×Q8—791no—
389C2×C4×D4—791no—
390C2×#117—791no—
391C2×#117—791no—
392C22×C4⋊C4—791no—
393#501—798no—
394#498—798no—
395#489C2×D7918yescomplemented
396#488—798no—
397#485—798no—
398#483—798no—
399#482—798no—
400#481—798no—
401#479—798no—
402#478—798no—
403#476—798no—
404#475—798no—
405#433—798no—
406C2×#107—791no—
407C2×#107—791no—
408C2×#106—791no—
409C2×#106—791no—
410C2×#106—791no—
411C2×#106—791no—
412C2×#106—791no—
413C2×#106—791no—
414C2×C4⋊C8—791no—
415C2×C4⋊C8—791no—
416C2×#103—791no—
417C2×#103—791no—
418C2×#103C2×D7911yescharacteristic
419C2×#103C2×D7911yescharacteristic
420C2×#102—791no—
421C2×#102—791no—
422C2×#102C2×D7911yescharacteristic
423C2×#102C2×D7911yescharacteristic
424C2×C22⋊C8—791no—
425C2×C22⋊C8—791no—
426C2×#97C2×D7911yescharacteristic
427C2×C4×C8—791no—
428C22×Q8—21no—
429C22×Q8—1581no—
430C22×Q8—1581no—
431C22×Q8C22×D7911yescharacteristic
432C22×D4—1581no—
433C22×D4C22×D7911yescharacteristic
434C23×C4—791no—
435C23×C4—1581no—
436C23×C4—1581no—
437C22×C8—791no—
438C22×C8—791no—
439C22×C8C22×D7911yescharacteristic
440C22×C8C22×D7911yescharacteristic
441C4⋊Q8—22no—
442C4⋊Q8—794no—
443C4⋊Q8—794no—
444C4⋊Q8—1582no—
445C4⋊Q8—1588no—
446C4⋊Q8—1582no—
447C4⋊Q8C22×D7914yes—
448#126—1588no—
449#125—794no—
450#125—794no—
451#125—1582no—
452#125—1588no—
453#125—1582no—
454#124—22no—
455#124—1588no—
456#124C22×D7914yes—
457#123—1588no—
458C22⋊Q8—794no—
459C22⋊Q8—1588no—
460C22⋊Q8—1588no—
461C22⋊Q8—1588no—
462C22⋊Q8—1582no—
463#121—794no—
464#121—1582no—
465C4×Q8—794no—
466C4×Q8—1582no—
467C4×D4—794no—
468C4×D4—1582no—
469#117—794no—
470#117—794no—
471#117—794no—
472#117—1582no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—791no—
475C2×C4⋊C4—791no—
476C2×C4⋊C4—791no—
477C2×C4⋊C4—791no—
478C2×C4⋊C4—791no—
479C2×C4⋊C4—791no—
480C2×C4⋊C4—794no—
481C2×C4⋊C4—1582no—
482C2×C4⋊C4—1581no—
483C2×C4⋊C4—1581no—
484C2×C4⋊C4—1581no—
485C2×C4⋊C4—1581no—
486C2×C4⋊C4—1581no—
487C2×C4⋊C4—1581no—
488C2×C4⋊C4—1581no—
489C2×C4⋊C4—1581no—
490C2×C4⋊C4—1581no—
491C2×C4⋊C4C22×D7911yescharacteristic
492C2×C4⋊C4C22×D7911yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—791no—
496C2×C22⋊C4—791no—
497C2×C22⋊C4—1581no—
498C2×C22⋊C4—1581no—
499C2×C22⋊C4—1581no—
500C2×C22⋊C4—1581no—
501C2×C42—791no—
502C2×C42—1581no—
503C2×C42—1581no—
504C2×C42C22×D7911yescharacteristic
505#107—794no—
506#107—794no—
507#106—794no—
508#106—794no—
509#106—794no—
510#106—794no—
511#106—794no—
512#106—794no—
513C4⋊C8—794no—
514C4⋊C8—794no—
515#103—794no—
516#103—794no—
517#103C22×D7914yes—
518#103C22×D7914yes—
519#102—794no—
520#102—794no—
521#102C22×D7914yes—
522#102C22×D7914yes—
523C22⋊C8—794no—
524C22⋊C8—794no—
525#97C22×D7914yes—
526C4×C8—794no—
527C24—21no—
528C24—791no—
529C2×Q8—21no—
530C2×Q8—24no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—82no—
534C2×Q8—6322no—
535C2×Q8—6322no—
536C2×Q8—1584no—
537C2×Q8—1584no—
538C2×Q8C23×D7912yes—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—6322no—
543C2×D4—1584no—
544C2×D4C23×D7912yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—791no—
549C22×C4—791no—
550C22×C4—791no—
551C22×C4—792no—
552C22×C4—792no—
553C22×C4—6322no—
554C22×C4—6322no—
555C22×C4—1584no—
556C22×C4—1581no—
557C22×C4—1581no—
558C22×C4—1581no—
559C22×C4—1581no—
560C22×C4—1584no—
561C22×C4—1582no—
562C22×C4—1582no—
563C22×C4D4×D7911yescharacteristic
564C22×C4D4×D7911yescharacteristic
565C22×C4C23×D7911yescharacteristic
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—792no—
569C2×C8—792no—
570C2×C8—1582no—
571C2×C8—1582no—
572C2×C8C23×D7912yes—
573C2×C8C23×D7912yes—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—794no—
578C4⋊C4—794no—
579C4⋊C4—792no—
580C4⋊C4—792no—
581C4⋊C4—792no—
582C4⋊C4—792no—
583C4⋊C4—1584no—
584C4⋊C4—1584no—
585C4⋊C4—1584no—
586C4⋊C4—1584no—
587C4⋊C4—1584no—
588C4⋊C4—1584no—
589C4⋊C4—1584no—
590C4⋊C4—1584no—
591C4⋊C4—1581no—
592C4⋊C4—1581no—
593C4⋊C4—1581no—
594C4⋊C4—1581no—
595C4⋊C4—1584no—
596C4⋊C4C23×D7912yes—
597C4⋊C4C23×D7912yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—794no—
601C22⋊C4—794no—
602C22⋊C4—1584no—
603C22⋊C4—1584no—
604C22⋊C4—1584no—
605C22⋊C4—1584no—
606C42—792no—
607C42—792no—
608C42—1584no—
609C42—1584no—
610C42D4×D7912yes—
611C42C23×D7912yes—
612C23—22no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—792no—
617C23—1582no—
618C23—1582no—
619C23—1582no—
620C23C2×D4×D7911yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624Q8—84no—
625Q8—6324no—
626Q8—6324no—
627D4—22no—
628D4—22no—
629D4—42no—
630D4—6324no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—3162no—
640C2×C4—3162no—
641C2×C4—3162no—
642C2×C4—3162no—
643C2×C4—792no—
644C2×C4—792no—
645C2×C4—792no—
646C2×C4—6324no—
647C2×C4—6324no—
648C2×C4—1582no—
649C2×C4—1582no—
650C2×C4—1582no—
651C2×C4—1582no—
652C2×C4—1582no—
653C2×C4—1582no—
654C2×C4—1582no—
655C2×C4—1582no—
656C2×C4—1582no—
657C2×C4—1584no—
658C2×C4C2×D4×D7912yes—
659C2×C4C2×D4×D7912yes—
660C2×C4C2×D4×D7911yescharacteristic
661C2×C4#1457920812yes—
662C2×C4#1457920812yes—
663C2×C4C24×D7911yescharacteristic
664C8—22no—
665C8—22no—
666C8—1582no—
667C8—1582no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—84no—
672C22—3164no—
673C22—1582no—
674C22—1582no—
675C22—1582no—
676C22#1909913312yes—
677C22#1909937212yes—
678C22#1909937312yes—
679C22C22×D4×D7911yescharacteristic
680C4—22no—
681C4—22no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—3162no—
686C4—3162no—
687C4—3162no—
688C4—3162no—
689C4—1582no—
690C4—1582no—
691C4—1582no—
692C4#1909913312yes—
693C4C2×#1457920811yescharacteristic
694C4C2×#1457920811yescharacteristic
695C2—82no—
696C2—3162no—
697C2#2377469314yesdirect product factor
698C2C2×#1909913311yescharacteristic
699C2C2×#1909937211yescharacteristic
700C2C2×#1909937311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#489×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579132C22
hypercenterC2×#489D79
hypocenterC79C2×#3244
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#19099190C2semidirect
3. #23774693C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098959C2semidirect
6. C2×#19098917C2semidirect
8. C2×#19098903C2semidirect
10. C2×#19098892C2semidirect
11. C2×#19098872C2semidirect
12. C2×#19098846C2semidirect
13. C2×#19098861C2semidirect
14. C2×#19098851C2semidirect
15. C2×#19098625C2semidirect
16. C2×#489×C79C2semidirect
18. #19099190C22semidirect
40. #19098972C22semidirect
41. #19098959C22semidirect
42. #19098917C22semidirect
43. #19098903C22semidirect
44. #19098892C22semidirect
47. #19098872C22semidirect
48. #19098861C22semidirect
49. #19098851C22semidirect
50. #19098846C22semidirect
51. #19098625C22semidirect
71. #489×C79C22semidirect
346. C2×C79#3244semidirect
356. C2×#489D79semidirect
367. C79C2×#3244semidirect
395. #489C2×D79semidirect
697. C2#23774693direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991902
C2×#190991822
#237746932
C2×#190989722
C2×#190989592
C2×#190989172
C2×#190988802
C2×#190989032
C2×#190988852
C2×#190988922
C2×#190988722
C2×#190988462
C2×#190988612
C2×#190988512
C2×#190986252
C2×#489×C792
C2×#324479