Finite Group Databasebeta

← C2×#23776021 #35167014

Subgroups — C2×#23776021 #35167014

Order 20224.

1930 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099277C211yesmaximal, characteristic
2C2×#19099271C211yesmaximal, characteristic, complemented
3#23776021C2116yesmaximal, direct product factor
4C2×#19098967C211yesmaximal, characteristic, complemented
5C2×#19098902C211yesmaximal, characteristic, complemented
6C2×#19098901C211yesmaximal, characteristic, complemented
7C2×#19098875C211yesmaximal, characteristic, complemented
8C2×#19098874C211yesmaximal, characteristic, complemented
9C2×#19098856C211yesmaximal, characteristic, complemented
10C2×#19098851C211yesmaximal, characteristic, complemented
11C2×#19098806C211yesmaximal, characteristic, complemented
12C2×SD16×Dic79C211yesmaximal, characteristic, complemented
13C2×#19098639C211yesmaximal, characteristic, complemented
14C2×#19098605C211yesmaximal, characteristic, complemented
15C2×#19098604C211yesmaximal, characteristic, complemented
16C2×#468×C79C211yesmaximal, characteristic, complemented
17C22×#11929607C2211yescharacteristic
18#19099277—24no—
19#19099277C2218yes—
20#19099271—24no—
21#19099271C2218yescomplemented
22C2×#14579160C2211yescharacteristic
23C2×#14579160C2211yescharacteristic
24C2×#14579151—21no—
25C2×#14579148—21no—
26C2×#14579147—21no—
27C2×#14579141—21no—
28C2×#14579138—21no—
29C2×#14579137C2211yescharacteristic
30C2×#14579133—21no—
31C2×#14579132C2211yescharacteristic
32C2×Q8×Dic79C2211yescharacteristic
33C2×D4×Dic79C2211yescharacteristic
34C2×C4×C22⋊D79C2211yescharacteristic
35C2×(C22⋊D79)⋊C4—21no—
36C2×#14579120C2211yescharacteristic
37C2×#14579119C2211yescharacteristic
38C2×#14579117—21no—
39C22×C4⋊Dic79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41#19098967C2218yescomplemented
42#19098902C2218yescomplemented
43#19098901C2218yescomplemented
44#19098875C2218yescomplemented
45#19098874C2218yescomplemented
46#19098856C2218yescomplemented
47#19098851C2218yescomplemented
48#19098806C2218yescomplemented
49SD16×Dic79C2218yescomplemented
50#19098639C2218yescomplemented
51#19098605C2218yescomplemented
52#19098604C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579093C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C22×M16×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73#468×C79C2218yescomplemented
74C2×#107×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×C22⋊D79—21no—
80C22×C22⋊D79D411yescharacteristic
81C23×Dic79—21no—
82C23×Dic79—21no—
83C22×C4×D79—21no—
84C22×C4×D79C2311yescharacteristic
85C2×#11929607—24no—
86C2×#11929607C2314yes—
87C22×C79⋊C8C2311yescharacteristic
88C22×C79⋊C8C2311yescharacteristic
89#14579160—22no—
90#14579160—22no—
91#14579160C2314yes—
92#14579160C2314yes—
93#14579151—28no—
94#14579148—28no—
95#14579147—28no—
96#14579141—28no—
97#14579138—28no—
98#14579137—22no—
99#14579137C2314yes—
100#14579133—28no—
101#14579132—22no—
102#14579132C2314yes—
103Q8×Dic79—22no—
104Q8×Dic79C2314yes—
105D4×Dic79—22no—
106D4×Dic79C2314yes—
107C4×C22⋊D79D414yes—
108C4×C22⋊D79C2314yes—
109(C22⋊D79)⋊C4—28no—
110#14579120—22no—
111#14579120C2314yes—
112#14579119—22no—
113#14579119C2314yes—
114#14579117—28no—
115C2×C4⋊Dic79—22no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79C2311yescharacteristic
119C2×C4⋊Dic79C2314yes—
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×Dic79⋊C4—21no—
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4D411yescharacteristic
128C4⋊C4×D79—22no—
129C4⋊C4×D79C2314yes—
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79—21no—
133C2×C22⋊Dic79D411yescharacteristic
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4D411yescharacteristic
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79C2311yescharacteristic
141#14579095C2314yes—
142#14579095C2314yes—
143#14579094C2314yes—
144#14579094C2314yes—
145#14579094C2314yes—
146#14579093C2314yes—
147#14579093C2314yes—
148#14579092C2314yes—
149Dic79⋊C8C2314yes—
150#14579085C2314yes—
151#14579085C2314yes—
152#14579082C2314yes—
153#14579082C2314yes—
154C22⋊(C79⋊C8)C2314yes—
155(C2×D79)⋊C8C2314yes—
156C8×Dic79C2314yes—
157C22×Q8×C79C2311yescharacteristic
158C22×D4×C79—21no—
159C22×D4×C79C2311yescharacteristic
160C23×C4×C79C2311yescharacteristic
161C2×SD16×C79—24no—
162C2×SD16×C79C2314yes—
163C2×M16×C79—24no—
164C2×M16×C79C2314yes—
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C22⋊Q8×C79—22no—
168C22⋊Q8×C79C2314yes—
169#121×C79—22no—
170#121×C79C2314yes—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176#107×C79C2314yes—
177#103×C79C2314yes—
178#102×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C2×Dic158—24no—
181C2×Dic158—24no—
182C2×Dic158—82no—
183C2×Dic158—82no—
184C2×C22⋊D79—24no—
185C2×C22⋊D79—24no—
186C2×C22⋊D79—82no—
187C2×C22⋊D79C2×D414yes—
188C22×Dic79—24no—
189C22×Dic79—21no—
190C22×Dic79—21no—
191C22×Dic79—21no—
192C22×Dic79—21no—
193C22×Dic79—24no—
194C22×Dic79—44no—
195C22×Dic79—82no—
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C2×C4×D79—24no—
200C2×C4×D79—22no—
201C2×C4×D79—22no—
202C2×C4×D79—82no—
203C2×C4×D79C2×D412yes—
204C2×C4×D79C2412yes—
205#11929607—28no—
206C2×C79⋊C8—22no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8C2412yes—
209C2×C79⋊C8C2412yes—
210C4⋊Dic79—24no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79—24no—
214C4⋊Dic79—21no—
215C4⋊Dic79—21no—
216C4⋊Dic79C2412yes—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219C4⋊Dic79C2412yes—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4C2×D414yes—
225C22⋊Dic79—24no—
226C22⋊Dic79—24no—
227C22⋊Dic79—24no—
228C22⋊Dic79C2×D414yes—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4C2×D414yes—
232C4×Dic79—24no—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79C2×D412yes—
236C4×Dic79C2412yes—
237C24×C79—21no—
238C24×C79C2×D411yescharacteristic
239C2×Q8×C79—21no—
240C2×Q8×C79—22no—
241C2×Q8×C79—22no—
242C2×Q8×C79C2412yes—
243C2×D4×C79—24no—
244C2×D4×C79—21no—
245C2×D4×C79—22no—
246C2×D4×C79—22no—
247C2×D4×C79—82no—
248C2×D4×C79C2412yes—
249C22×C4×C79—22no—
250C22×C4×C79—22no—
251C22×C4×C79—21no—
252C22×C4×C79—21no—
253C22×C4×C79—21no—
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D412yes—
256C22×C4×C79C2412yes—
257C22×C4×C79C2411yescharacteristic
258SD16×C79—28no—
259M16×C79—28no—
260C2×C8×C79—22no—
261C2×C8×C79#4114yes—
262C2×C8×C79C2412yes—
263C2×C8×C79C2412yes—
264C4⋊C4×C79—24no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79—21no—
267C4⋊C4×C79C2412yes—
268C4⋊C4×C79C2412yes—
269C22⋊C4×C79—24no—
270C22⋊C4×C79—24no—
271C23×C79—22no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—42no—
276C23×C79—42no—
277C23×C79—42no—
278C23×C79C22×D412yes—
279C23×C79C22×D411yescharacteristic
280C22×D79—22no—
281C22×D79—22no—
282C22×D79—22no—
283C22×D79C22×D412yes—
284Q8×C79—22no—
285Q8×C79—22no—
286Q8×C79—42no—
287D4×C79—22no—
288D4×C79—22no—
289D4×C79—42no—
290D4×C79—84no—
291C2×C4×C79—22no—
292C2×C4×C79—24no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—42no—
299C2×C4×C79—42no—
300C2×C4×C79—42no—
301C2×C4×C79C22×D412yes—
302C2×C4×C79C22×D411yescharacteristic
303C2×C4×C79C2×#4112yes—
304C2×C4×C792−1+412yes—
305C2×C4×C79C2511yescharacteristic
306C22⋊D79—28no—
307C22⋊D79—84no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—42no—
315C2×Dic79—42no—
316C2×Dic79—42no—
317C2×Dic79—42no—
318C2×Dic79—48no—
319C2×Dic79—84no—
320C2×Dic79#13714yes—
321C2×Dic79C22×D412yes—
322C2×Dic79C22×D412yes—
323C2×Dic79C22×D412yes—
324C4×D79—24no—
325C4×D79—22no—
326C4×D79—22no—
327C4×D79—84no—
328Dic158—84no—
329Dic158—84no—
330C8×C79—22no—
331C8×C79C2×#4114yes—
332C79⋊C8—22no—
333C79⋊C8—22no—
334C22×C79—22no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79—44no—
338C22×C79—42no—
339C22×C79—42no—
340C22×C79—42no—
341C22×C79—84no—
342C22×C79#54712yes—
343C22×C79C2×#13712yes—
344C22×C79#57612yes—
345C22×C79C23×D411yescharacteristic
346C2×D79—22no—
347C2×D79—22no—
348C2×D79—22no—
349C2×D79—44no—
350C4×C79—22no—
351C4×C79—42no—
352C4×C79—42no—
353C4×C79—42no—
354C4×C79#54712yes—
355C4×C79C22×#4111yescharacteristic
356C4×C79C2×2−1+411yescharacteristic
357Dic79—22no—
358Dic79—22no—
359Dic79—42no—
360Dic79—42no—
361Dic79—42no—
362Dic79—42no—
363Dic79C2×#13714yes—
364C2×#3357—791nomaximal, Sylow
365C2×C79—42no—
366C2×C79—82no—
367C2×C79#335714yescomplemented
368C2×C79C2×#54711yescharacteristic
369C2×C79C22×#13711yescharacteristic
370C2×C79C2×#57611yescharacteristic
371D79—42no—
372C2×#555—791no—
373C2×#554—791no—
374#3357—7916no—
375C2×#500—791no—
376C2×#485—791no—
377C2×#485—791no—
378C2×#480—791no—
379C2×#480—791no—
380C2×#477—791no—
381C2×#476—791no—
382C2×#468—791no—
383C2×#468D7911yescharacteristic, complemented
384C2×C4×SD16—791no—
385C2×#436—791no—
386C2×#428—791no—
387C2×#428—791no—
388C79C2×#335711yescharacteristic, complemented, Sylow
389C22×SD16C2×D7911yescharacteristic
390C22×M16—791no—
391C22×M16C2×D7911yescharacteristic
392#555—798no—
393#555—1584no—
394#554—798no—
395#554—1584no—
396C2×C4⋊Q8—791no—
397C2×C4⋊Q8—791no—
398C2×#125—1581no—
399C2×#124—1581no—
400C2×#124—1581no—
401C2×C22⋊Q8—791no—
402C2×C22⋊Q8—1581no—
403C2×C22⋊Q8—1581no—
404C2×C22⋊Q8C2×D7911yescharacteristic
405C2×#121—791no—
406C2×#121—1581no—
407C2×#121C2×D7911yescharacteristic
408C2×C4×Q8—791no—
409C2×C4×D4—791no—
410C2×C4×D4—791no—
411C2×C4×D4—1581no—
412C2×#117—791no—
413C2×#117—791no—
414C2×#117—1581no—
415C22×C4⋊C4—791no—
416C22×C4⋊C4—791no—
417#500—798no—
418#485—798no—
419#485—798no—
420#480—798no—
421#480—798no—
422#477—798no—
423#476—798no—
424#468—798no—
425#468C2×D7918yescomplemented
426C4×SD16—798no—
427#436—798no—
428#428—798no—
429#428—798no—
430C2×#107—791no—
431C2×#107—791no—
432C2×#107—791no—
433C2×#107—791no—
434C2×#107—791no—
435C2×#107C2×D7911yescharacteristic
436C2×#106—791no—
437C2×#106—791no—
438C2×#106—791no—
439C2×C4⋊C8—791no—
440C2×#103—791no—
441C2×#103—791no—
442C2×#103C2×D7911yescharacteristic
443C2×#102—791no—
444C2×#102—791no—
445C2×#102C2×D7911yescharacteristic
446C2×C22⋊C8—791no—
447C2×C22⋊C8—791no—
448C2×C4×C8—791no—
449C22×Q8—1581no—
450C22×Q8—1581no—
451C22×Q8C22×D7911yescharacteristic
452C22×D4—21no—
453C22×D4—791no—
454C22×D4—1581no—
455C22×D4C22×D7911yescharacteristic
456C23×C4—791no—
457C23×C4—1581no—
458C23×C4—1581no—
459C23×C4—1581no—
460C23×C4C22×D7911yescharacteristic
461C2×SD16—24no—
462C2×SD16C22×D7914yes—
463C2×M16—24no—
464C2×M16—794no—
465C2×M16—1584no—
466C2×M16C22×D7914yes—
467C22×C8—791no—
468C22×C8—791no—
469C22×C8C22×D7911yescharacteristic
470C22×C8C22×D7911yescharacteristic
471C4⋊Q8—794no—
472C4⋊Q8—794no—
473C4⋊Q8—1582no—
474C4⋊Q8—1582no—
475#125—1588no—
476#124—1588no—
477#124—1588no—
478C22⋊Q8—22no—
479C22⋊Q8—794no—
480C22⋊Q8—1588no—
481C22⋊Q8—1588no—
482C22⋊Q8—1582no—
483C22⋊Q8C22×D7914yes—
484#121—22no—
485#121—794no—
486#121—1582no—
487#121—1588no—
488#121C22×D7914yes—
489C4×Q8—794no—
490C4×Q8—1582no—
491C4×D4—794no—
492C4×D4—794no—
493C4×D4—794no—
494C4×D4—1582no—
495C4×D4—1588no—
496#117—794no—
497#117—794no—
498#117—1588no—
499#117—1582no—
500#117—1582no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—791no—
503C2×C4⋊C4—791no—
504C2×C4⋊C4—791no—
505C2×C4⋊C4—794no—
506C2×C4⋊C4—791no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—794no—
509C2×C4⋊C4—1582no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4—1581no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1582no—
517C2×C4⋊C4C22×D7911yescharacteristic
518C2×C4⋊C4C22×D7911yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—791no—
522C2×C22⋊C4—791no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C42—791no—
529C2×C42—1581no—
530C2×C42—1581no—
531C2×C42—1581no—
532#107—794no—
533#107—794no—
534#107—794no—
535#107—794no—
536#107—794no—
537#107C22×D7914yes—
538#106—794no—
539#106—794no—
540#106—794no—
541C4⋊C8—794no—
542#103—794no—
543#103—794no—
544#103C22×D7914yes—
545#102—794no—
546#102—794no—
547#102C22×D7914yes—
548C22⋊C8—794no—
549C22⋊C8—794no—
550C4×C8—794no—
551C24—21no—
552C24—791no—
553C24D4×D7911yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—6322no—
558C2×Q8—6322no—
559C2×Q8—1584no—
560C2×Q8—1584no—
561C2×Q8C23×D7912yes—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—82no—
567C2×D4—794no—
568C2×D4—6322no—
569C2×D4—1584no—
570C2×D4—1584no—
571C2×D4C23×D7912yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—3164no—
578C22×C4—791no—
579C22×C4—791no—
580C22×C4—791no—
581C22×C4—792no—
582C22×C4—792no—
583C22×C4—6322no—
584C22×C4—6322no—
585C22×C4—1584no—
586C22×C4—1584no—
587C22×C4—1581no—
588C22×C4—1581no—
589C22×C4—1581no—
590C22×C4—1581no—
591C22×C4—1584no—
592C22×C4—1582no—
593C22×C4—1582no—
594C22×C4D4×D7912yes—
595C22×C4D4×D7911yescharacteristic
596C22×C4C23×D7912yes—
597C22×C4C23×D7911yescharacteristic
598SD16—28no—
599M16—28no—
600M16—1588no—
601C2×C8—22no—
602C2×C8—792no—
603C2×C8—792no—
604C2×C8—1582no—
605C2×C8—1582no—
606C2×C8#1192962314yes—
607C2×C8C23×D7912yes—
608C2×C8C23×D7912yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—794no—
613C4⋊C4—792no—
614C4⋊C4—792no—
615C4⋊C4—792no—
616C4⋊C4—792no—
617C4⋊C4—1584no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1584no—
621C4⋊C4—1584no—
622C4⋊C4—1581no—
623C4⋊C4—1584no—
624C4⋊C4—1581no—
625C4⋊C4—1581no—
626C4⋊C4—1581no—
627C4⋊C4C23×D7912yes—
628C4⋊C4C23×D7912yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—794no—
632C22⋊C4—794no—
633C22⋊C4—1584no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C42—792no—
639C42—792no—
640C42—1584no—
641C42—1584no—
642C42—1584no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—792no—
651C23—1582no—
652C23—1582no—
653C23—1582no—
654C23C2×D4×D7912yes—
655C23C2×D4×D7911yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—6324no—
660Q8—6324no—
661D4—22no—
662D4—22no—
663D4—42no—
664D4—84no—
665D4—6324no—
666D4—1588no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—3162no—
678C2×C4—3162no—
679C2×C4—3162no—
680C2×C4—3162no—
681C2×C4—3168no—
682C2×C4—794no—
683C2×C4—792no—
684C2×C4—792no—
685C2×C4—792no—
686C2×C4—6324no—
687C2×C4—6324no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1584no—
696C2×C4—1582no—
697C2×C4C2×D4×D7912yes—
698C2×C4C2×D4×D7911yescharacteristic
699C2×C4C2×#1192962312yes—
700C2×C4#1457920812yes—
701C2×C4C24×D7911yescharacteristic
702C8—22no—
703C8—1582no—
704C8—1582no—
705C8C2×#1192962314yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—3164no—
715C22—1582no—
716C22—1582no—
717C22—1582no—
718C22#1909921312yes—
719C22#137×D7912yes—
720C22#1909936712yes—
721C22C22×D4×D7911yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—3162no—
727C4—3162no—
728C4—3162no—
729C4—3162no—
730C4—794no—
731C4—1582no—
732C4—1582no—
733C4#1909921312yes—
734C4C22×#1192962311yescharacteristic
735C4C2×#1457920811yescharacteristic
736C2—42no—
737C2—82no—
738C2—3162no—
739C2#2377602114yesdirect product factor
740C2C2×#1909921311yescharacteristic
741C2C2×#137×D7911yescharacteristic
742C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#468×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099277C2
hypercenterC2×#468D79
hypocenterC79C2×#3357
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#19099271C2semidirect
3. #23776021C2direct (N × H)
4. C2×#19098967C2semidirect
5. C2×#19098902C2semidirect
6. C2×#19098901C2semidirect
7. C2×#19098875C2semidirect
8. C2×#19098874C2semidirect
9. C2×#19098856C2semidirect
10. C2×#19098851C2semidirect
11. C2×#19098806C2semidirect
12. C2×SD16×Dic79C2semidirect
13. C2×#19098639C2semidirect
14. C2×#19098605C2semidirect
15. C2×#19098604C2semidirect
16. C2×#468×C79C2semidirect
21. #19099271C22semidirect
41. #19098967C22semidirect
42. #19098902C22semidirect
43. #19098901C22semidirect
44. #19098875C22semidirect
45. #19098874C22semidirect
46. #19098856C22semidirect
47. #19098851C22semidirect
48. #19098806C22semidirect
49. SD16×Dic79C22semidirect
50. #19098639C22semidirect
51. #19098605C22semidirect
52. #19098604C22semidirect
73. #468×C79C22semidirect
367. C2×C79#3357semidirect
383. C2×#468D79semidirect
388. C79C2×#3357semidirect
425. #468C2×D79semidirect
739. C2#23776021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992772
C2×#190992712
#237760212
C2×#190989672
C2×#190989022
C2×#190989012
C2×#190988752
C2×#190988742
C2×#190988562
C2×#190988512
C2×#190988062
C2×SD16×Dic792
C2×#190986392
C2×#190986052
C2×#190986042
C2×#468×C792
C2×#335779