Finite Group Databasebeta

← C2×#23775441 #35164944

Subgroups — C2×#23775441 #35164944

Order 20224.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099286C211yesmaximal, characteristic, complemented
2C2×#19099208C211yesmaximal, characteristic
3#23775441C2116yesmaximal, direct product factor
4C2×#19098923C211yesmaximal, characteristic, complemented
5C2×#19098906C211yesmaximal, characteristic, complemented
6C2×#19098890C211yesmaximal, characteristic, complemented
7C2×#19098853C211yesmaximal, characteristic, complemented
8C2×#19098820C211yesmaximal, characteristic, complemented
9C2×#19098795C211yesmaximal, characteristic, complemented
10C2×#19098785C211yesmaximal, characteristic, complemented
11C2×#19098722C211yesmaximal, characteristic, complemented
12C2×#19098712C211yesmaximal, characteristic, complemented
13C2×#19098636C211yesmaximal, characteristic, complemented
14C2×#19098566C211yesmaximal, characteristic, complemented
15C2×#19098556C211yesmaximal, characteristic, complemented
16C2×#440×C79C211yesmaximal, characteristic, complemented
17C22×#11929623C2211yescharacteristic
18C22×D4×D79C2211yescharacteristic
19C22×#11929614C2211yescharacteristic, complemented
20C22×#11929611C2211yescharacteristic
21C22×#11929607C2211yescharacteristic
22C22×C8×D79C2211yescharacteristic, complemented
23#19099286—24no—
24#19099286C2218yescomplemented
25#19099208—24no—
26#19099208C2218yes—
27C2×#14579161C2211yescharacteristic, complemented
28C2×#14579156—21no—
29C2×#14579156—21no—
30C2×#14579149—21no—
31C2×#14579149C2211yescharacteristic
32C2×#14579145—21no—
33C2×#14579141C2211yescharacteristic
34C2×#14579137C2211yescharacteristic
35C2×#14579137C2211yescharacteristic, complemented
36C2×#14579136C2211yescharacteristic
37C2×#14579135—21no—
38C2×#14579131—21no—
39C2×C4×Dic158—21no—
40C2×C4×D316C2211yescharacteristic
41C2×#14579119C2211yescharacteristic
42C2×#14579119C2211yescharacteristic, complemented
43C22×(C2×D79)⋊C4—21no—
44#19098923C2218yescomplemented
45#19098906C2218yescomplemented
46#19098890C2218yescomplemented
47#19098853C2218yescomplemented
48#19098820C2218yescomplemented
49#19098795C2218yescomplemented
50#19098785C2218yescomplemented
51#19098722C2218yescomplemented
52#19098712C2218yescomplemented
53#19098636C2218yescomplemented
54C2×#14579092C2211yescharacteristic, complemented
55C2×#14579092C2211yescharacteristic, complemented
56C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
57#19098566C2218yescomplemented
58#19098556C2218yescomplemented
59C2×#14579086C2211yescharacteristic, complemented
60C2×#14579086C2211yescharacteristic, complemented
61C2×#14579084C2211yescharacteristic, complemented
62C2×#14579083C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×(C2×D79)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic, complemented
71C2×C4×D4×C79C2211yescharacteristic
72#440×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic, complemented
74C2×#103×C79C2211yescharacteristic, complemented
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic, complemented
77C24×D79—21no—
78C2×#11929623—24no—
79C2×#11929623—22no—
80C2×#11929623—42no—
81C2×#11929623C2314yes—
82C22×Dic158—21no—
83C22×Dic158C2311yescharacteristic
84C22×D316—21no—
85C22×D316D411yescharacteristic
86C22×D316C2311yescharacteristic
87C22×C22⋊D79—21no—
88C22×C22⋊D79—21no—
89C2×D4×D79—24no—
90C2×D4×D79—22no—
91C2×D4×D79—42no—
92C2×D4×D79C2314yes—
93C23×Dic79—21no—
94C22×C4×D79C2311yescharacteristic
95C22×C4×D79C2311yescharacteristic
96C2×#11929614—42no—
97C2×#11929614C2314yescomplemented
98C2×#11929611—42no—
99C2×#11929611C2314yes—
100C2×#11929607—42no—
101C2×#11929607C2314yes—
102C22×C79⋊C8C2311yescharacteristic
103C22×C79⋊C8C2311yescharacteristic
104C2×C8×D79—42no—
105C2×C8×D79C2314yescomplemented
106#14579161—22no—
107#14579161C2314yescomplemented
108#14579156—28no—
109#14579156—28no—
110#14579149—22no—
111#14579149—28no—
112#14579149C2314yes—
113#14579145—28no—
114#14579141—22no—
115#14579141C2314yes—
116#14579137—22no—
117#14579137—22no—
118#14579137C2314yes—
119#14579137C2314yescomplemented
120#14579136—22no—
121#14579136C2314yes—
122#14579135—28no—
123#14579131—28no—
124C4×Dic158—28no—
125C4×D316D414yes—
126C4×D316C2314yes—
127#14579119—22no—
128#14579119—22no—
129#14579119C2314yes—
130#14579119C2314yescomplemented
131C2×C4⋊Dic79—21no—
132C2×C4⋊Dic79—21no—
133C2×C4⋊Dic79D411yescharacteristic
134C2×C4⋊Dic79C2311yescharacteristic
135C2×C4⋊Dic79C2311yescharacteristic
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×(C2×D79)⋊C4—21no—
144C2×(C2×D79)⋊C4—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×(C2×D79)⋊C4—28no—
147C2×(C2×D79)⋊C4D411yescharacteristic
148C2×(C2×D79)⋊C4D411yescharacteristic
149C2×C4×Dic79—21no—
150C2×C4×Dic79—21no—
151#14579092C2314yescomplemented
152#14579092C2314yescomplemented
153C4⋊(C79⋊C8)C2314yescomplemented
154#14579086C2314yescomplemented
155#14579086C2314yescomplemented
156#14579084C2314yescomplemented
157#14579083C2314yes—
158#14579083C2314yes—
159#14579082C2314yes—
160#14579082C2314yes—
161#14579081C2314yes—
162(C2×D79)⋊C8C2314yes—
163(C2×D79)⋊C8C2314yescomplemented
164C22×Q8×C79C2311yescharacteristic
165C22×D4×C79C2311yescharacteristic
166C23×C4×C79—21no—
167C2×SD16×C79—24no—
168C2×SD16×C79C2314yes—
169C22×C8×C79C2311yescharacteristic
170C22×C8×C79C2311yescharacteristic
171C4×Q8×C79—22no—
172C4×Q8×C79C2314yescomplemented
173C4×D4×C79—22no—
174C4×D4×C79C2314yes—
175C2×C4⋊C4×C79—21no—
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C22⋊C4×C79—21no—
179C2×C42×C79—21no—
180C2×C42×C79C2311yescharacteristic
181#107×C79C2314yescomplemented
182#103×C79C2314yescomplemented
183#102×C79C2314yes—
184#97×C79C2314yescomplemented
185C23×D79—21no—
186C23×D79—24no—
187C23×D79—44no—
188C23×D79—44no—
189C23×D79—82no—
190C23×D79C2×D411yescharacteristic
191C23×D79C2×D411yescharacteristic
192#11929623—28no—
193#11929623—44no—
194#11929623—48no—
195C2×Dic158—24no—
196C2×Dic158—21no—
197C2×Dic158—22no—
198C2×Dic158—22no—
199C2×Dic158—44no—
200C2×Dic158C2412yes—
201C2×D316—24no—
202C2×D316—21no—
203C2×D316—22no—
204C2×D316—22no—
205C2×D316—42no—
206C2×D316—82no—
207C2×D316C2×D414yes—
208C2×D316C2412yes—
209C2×C22⋊D79—24no—
210C2×C22⋊D79—24no—
211C2×C22⋊D79—44no—
212C2×C22⋊D79—44no—
213D4×D79—28no—
214D4×D79—44no—
215D4×D79—48no—
216C22×Dic79—24no—
217C22×Dic79—21no—
218C22×Dic79—21no—
219C22×Dic79—21no—
220C22×Dic79—44no—
221C22×Dic79C2×D411yescharacteristic
222C22×Dic79C2×D411yescharacteristic
223C2×C4×D79—22no—
224C2×C4×D79—22no—
225C2×C4×D79—22no—
226C2×C4×D79—22no—
227C2×C4×D79C2×D412yes—
228C2×C4×D79C2×D412yes—
229C2×C4×D79C2412yes—
230C2×C4×D79C2412yes—
231#11929614—44no—
232#11929611—44no—
233#11929607—44no—
234C2×C79⋊C8—22no—
235C2×C79⋊C8—22no—
236C2×C79⋊C8C2412yes—
237C2×C79⋊C8C2412yes—
238C8×D79—44no—
239C4⋊Dic79—24no—
240C4⋊Dic79—24no—
241C4⋊Dic79—21no—
242C4⋊Dic79—21no—
243C4⋊Dic79C2×D414yes—
244C4⋊Dic79C2412yes—
245C4⋊Dic79C2412yes—
246Dic79⋊C4—24no—
247Dic79⋊C4—24no—
248(C2×D79)⋊C4—24no—
249(C2×D79)⋊C4—24no—
250(C2×D79)⋊C4—24no—
251(C2×D79)⋊C4—24no—
252(C2×D79)⋊C4—24no—
253(C2×D79)⋊C4—24no—
254(C2×D79)⋊C4—24no—
255(C2×D79)⋊C4—24no—
256(C2×D79)⋊C4C2×D414yes—
257(C2×D79)⋊C4C2×D414yes—
258C4×Dic79—24no—
259C4×Dic79—24no—
260C24×C79—21no—
261C2×Q8×C79—21no—
262C2×Q8×C79—22no—
263C2×Q8×C79—22no—
264C2×Q8×C79C2412yes—
265C2×D4×C79—21no—
266C2×D4×C79—22no—
267C2×D4×C79#4114yes—
268C2×D4×C79C2412yes—
269C22×C4×C79—21no—
270C22×C4×C79—21no—
271C22×C4×C79—21no—
272C22×C4×C79—24no—
273C22×C4×C79—82no—
274C22×C4×C79C2×D411yescharacteristic
275C22×C4×C79C2×D411yescharacteristic
276C22×C4×C79C2411yescharacteristic
277SD16×C79—28no—
278C2×C8×C79—22no—
279C2×C8×C79—22no—
280C2×C8×C79C2412yes—
281C2×C8×C79C2412yes—
282C4⋊C4×C79—24no—
283C4⋊C4×C79—21no—
284C4⋊C4×C79—21no—
285C4⋊C4×C79C2412yes—
286C4⋊C4×C79C2412yes—
287C22⋊C4×C79—24no—
288C42×C79—24no—
289C42×C79C2×D412yes—
290C42×C79C2412yes—
291C23×C79—24no—
292C23×C79—22no—
293C23×C79—42no—
294C23×C79—42no—
295C23×C79C22×D411yescharacteristic
296C22×D79—22no—
297C22×D79—22no—
298C22×D79—22no—
299C22×D79—22no—
300C22×D79—22no—
301C22×D79—22no—
302C22×D79—22no—
303C22×D79—48no—
304C22×D79—48no—
305C22×D79—42no—
306C22×D79—42no—
307C22×D79—42no—
308C22×D79—84no—
309C22×D79—816no—
310C22×D79C22×D412yes—
311C22×D79C22×D412yes—
312Q8×C79—22no—
313Q8×C79—22no—
314Q8×C79—42no—
315D4×C79—24no—
316D4×C79—22no—
317D4×C79C2×#4114yes—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—22no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—42no—
324C2×C4×C79—42no—
325C2×C4×C79—42no—
326C2×C4×C79—84no—
327C2×C4×C79C22×D412yes—
328C2×C4×C79C22×D412yes—
329C2×C4×C79C22×D411yescharacteristic
330C2×C4×C79C2×#4112yes—
331C2×C4×C79H(5,𝔽2)12yes—
332C2×C4×C79C2511yescharacteristic
333C22⋊D79—48no—
334C22⋊D79—48no—
335C2×Dic79—22no—
336C2×Dic79—22no—
337C2×Dic79—22no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—48no—
341C2×Dic79—42no—
342C2×Dic79—42no—
343C2×Dic79—42no—
344C2×Dic79C22×D412yes—
345C2×Dic79C22×D412yes—
346D316—22no—
347D316—22no—
348D316—44no—
349D316—42no—
350D316—84no—
351C4×D79—24no—
352C4×D79—24no—
353C4×D79—22no—
354C4×D79—22no—
355C4×D79—22no—
356C4×D79—22no—
357Dic158—22no—
358Dic158—22no—
359Dic158—48no—
360Dic158—42no—
361C8×C79—22no—
362C8×C79—22no—
363C79⋊C8—22no—
364C79⋊C8—22no—
365C22×C79—24no—
366C22×C79—48no—
367C22×C79—42no—
368C22×C79—42no—
369C22×C79#54612yes—
370C22×C79#57512yes—
371C22×C79#57712yes—
372C22×C79C23×D411yescharacteristic
373C2×D79—22no—
374C2×D79—22no—
375C2×D79—22no—
376C2×D79—22no—
377C2×D79—22no—
378C2×D79—22no—
379C2×D79—44no—
380C2×D79—44no—
381C2×D79—42no—
382C2×D79—42no—
383C2×D79—42no—
384C2×D79—816no—
385C2×D79—84no—
386C4×C79—22no—
387C4×C79—22no—
388C4×C79—42no—
389C4×C79—42no—
390C4×C79—42no—
391C4×C79#54612yes—
392C4×C79C22×#4111yescharacteristic
393C4×C79C2×H(5,𝔽2)11yescharacteristic
394Dic79—22no—
395Dic79—22no—
396Dic79—42no—
397Dic79—42no—
398Dic79—42no—
399C2×#3311—791nomaximal, Sylow
400C2×C79—44no—
401C2×C79#331114yescomplemented
402C2×C79C2×#54611yescharacteristic
403C2×C79C2×#57511yescharacteristic
404C2×C79C2×#57711yescharacteristic
405D79—42no—
406D79—42no—
407D79—82no—
408C2×#556—791no—
409C2×#546—791no—
410#3311—7916no—
411C2×#489—791no—
412C2×#485—791no—
413C2×#482—791no—
414C2×#476—791no—
415C2×#470—791no—
416C2×#465—791no—
417C2×#464—791no—
418C2×#452—791no—
419C2×#450—791no—
420C2×#440D7911yescharacteristic, complemented
421C2×#435—791no—
422C2×#418—791no—
423C2×#416—791no—
424C79C2×#331111yescharacteristic, complemented, Sylow
425C22×#41—791no—
426C23×D4—791no—
427C22×Q16—791no—
428C22×SD16—791no—
429C22×SD16C2×D7911yescharacteristic
430C22×M16—791no—
431C23×C8—791no—
432#556—798no—
433#556—1584no—
434#546—798no—
435#546—1584no—
436C2×C4⋊Q8—791no—
437C2×#126—1581no—
438C2×#126—1581no—
439C2×#124—791no—
440C2×#124—1581no—
441C2×#123—1581no—
442C2×C22⋊Q8—791no—
443C2×C22⋊Q8—791no—
444C2×C22⋊Q8—791no—
445C2×#121—791no—
446C2×#121—1581no—
447C2×#120—1581no—
448C2×C4×Q8—1581no—
449C2×C4×Q8C2×D7911yescharacteristic, complemented
450C2×C4×D4—791no—
451C2×C4×D4C2×D7911yescharacteristic
452C2×#117—791no—
453C2×#117—791no—
454C22×C22⋊C4—1581no—
455#489—798no—
456#485—798no—
457#482—798no—
458#476—798no—
459#470—798no—
460#465—798no—
461#464—798no—
462#452—798no—
463#450—798no—
464#440C2×D7918yescomplemented
465#435—798no—
466C2×#107C2×D7911yescharacteristic, complemented
467C2×#106—791no—
468C2×#106—791no—
469C2×C4⋊C8—791no—
470#418—798no—
471#416—798no—
472C2×#103—791no—
473C2×#103—791no—
474C2×#103—791no—
475C2×#103C2×D7911yescharacteristic, complemented
476C2×#102—791no—
477C2×#102—791no—
478C2×#102—791no—
479C2×#102—791no—
480C2×#102—791no—
481C2×#102C2×D7911yescharacteristic
482C2×C22⋊C8—791no—
483C2×C22⋊C8—791no—
484C2×#97C2×D7911yescharacteristic, complemented
485C25—1581no—
486C2×#41—3162no—
487C2×#41—794no—
488C2×#41—1584no—
489C2×#41—1582no—
490C22×Q8—791no—
491C22×Q8—1581no—
492C22×Q8C22×D7911yescharacteristic
493C22×D4—3162no—
494C22×D4—794no—
495C22×D4—791no—
496C22×D4—791no—
497C22×D4—1581no—
498C22×D4—1582no—
499C22×D4—1581no—
500C22×D4—1581no—
501C22×D4—1584no—
502C22×D4C22×D7911yescharacteristic
503C23×C4—21no—
504C23×C4—791no—
505C23×C4—791no—
506C23×C4—1581no—
507C2×Q16—3162no—
508C2×Q16—794no—
509C2×SD16—24no—
510C2×SD16—3162no—
511C2×SD16—794no—
512C2×SD16C22×D7914yes—
513C2×M16—3162no—
514C2×M16—794no—
515C22×C8—3162no—
516C22×C8—794no—
517C22×C8—791no—
518C22×C8—791no—
519C22×C8C22×D7911yescharacteristic
520C22×C8C22×D7911yescharacteristic
521C4⋊Q8—794no—
522C4⋊Q8—1582no—
523#126—1588no—
524#126—1588no—
525#124—794no—
526#124—1588no—
527#124—1582no—
528#123—1588no—
529C22⋊Q8—794no—
530C22⋊Q8—794no—
531C22⋊Q8—794no—
532C22⋊Q8—1582no—
533C22⋊Q8—1582no—
534C22⋊Q8—1582no—
535#121—794no—
536#121—1588no—
537#121—1582no—
538#120—1588no—
539C4×Q8—22no—
540C4×Q8—1588no—
541C4×Q8C22×D7914yescomplemented
542C4×D4—22no—
543C4×D4—794no—
544C4×D4—794no—
545C4×D4C22×D7914yes—
546#117—794no—
547#117—794no—
548#117—1582no—
549#117—1582no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—791no—
552C2×C4⋊C4—791no—
553C2×C4⋊C4—791no—
554C2×C4⋊C4—1581no—
555C2×C4⋊C4—1581no—
556C2×C4⋊C4—1581no—
557C2×C4⋊C4—1581no—
558C2×C4⋊C4C22×D7911yescharacteristic
559C2×C4⋊C4C22×D7911yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—791no—
562C2×C22⋊C4—791no—
563C2×C22⋊C4—1588no—
564C2×C22⋊C4—1581no—
565C2×C22⋊C4—1581no—
566C2×C22⋊C4—1581no—
567C2×C22⋊C4—1581no—
568C2×C22⋊C4—1581no—
569C2×C22⋊C4—1581no—
570C2×C22⋊C4—1581no—
571C2×C22⋊C4—1581no—
572C2×C42—21no—
573C2×C42—1581no—
574C2×C42—1581no—
575C2×C42C22×D7911yescharacteristic
576#107C22×D7914yescomplemented
577#106—794no—
578#106—794no—
579C4⋊C8—794no—
580#103—794no—
581#103—794no—
582#103—794no—
583#103C22×D7914yescomplemented
584#102—794no—
585#102—794no—
586#102—794no—
587#102—794no—
588#102—794no—
589#102C22×D7914yes—
590C22⋊C8—794no—
591C22⋊C8—794no—
592#97C22×D7914yescomplemented
593C24—21no—
594C24—3164no—
595C24—3164no—
596C24—791no—
597C24—791no—
598C24—6322no—
599C24—1584no—
600C24—1581no—
601#41—3168no—
602#41—3164no—
603#41—1588no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—3164no—
608C2×Q8—792no—
609C2×Q8—1582no—
610C2×Q8—1582no—
611C2×Q8—1584no—
612C2×Q8—1581no—
613C2×Q8C23×D7912yes—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—3162no—
617C2×D4—3164no—
618C2×D4—3168no—
619C2×D4—3164no—
620C2×D4—3164no—
621C2×D4—792no—
622C2×D4—794no—
623C2×D4—6322no—
624C2×D4—1584no—
625C2×D4—1584no—
626C2×D4—1584no—
627C2×D4—1588no—
628C2×D4—1582no—
629C2×D4—1582no—
630C2×D4—1581no—
631C2×D4#1192962414yes—
632C2×D4C23×D7912yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—82no—
638C22×C4—3164no—
639C22×C4—791no—
640C22×C4—791no—
641C22×C4—792no—
642C22×C4—792no—
643C22×C4—792no—
644C22×C4—792no—
645C22×C4—1584no—
646C22×C4—1581no—
647C22×C4—1581no—
648C22×C4—1581no—
649C22×C4—1582no—
650C22×C4—1582no—
651C22×C4—1582no—
652C22×C4—1582no—
653C22×C4D4×D7911yescharacteristic
654C22×C4D4×D7911yescharacteristic
655C22×C4C23×D7911yescharacteristic
656Q16—3164no—
657SD16—28no—
658SD16—3164no—
659M16—3164no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—3164no—
663C2×C8—792no—
664C2×C8—792no—
665C2×C8—1582no—
666C2×C8—1582no—
667C2×C8C23×D7912yes—
668C2×C8C23×D7912yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—794no—
673C4⋊C4—792no—
674C4⋊C4—792no—
675C4⋊C4—1584no—
676C4⋊C4—1584no—
677C4⋊C4—1584no—
678C4⋊C4—1581no—
679C4⋊C4—1581no—
680C4⋊C4—1584no—
681C4⋊C4C23×D7912yes—
682C4⋊C4C23×D7912yes—
683C22⋊C4—24no—
684C22⋊C4—794no—
685C22⋊C4—794no—
686C22⋊C4—1584no—
687C22⋊C4—1584no—
688C22⋊C4—1584no—
689C22⋊C4—1584no—
690C22⋊C4—1584no—
691C22⋊C4—1584no—
692C22⋊C4—1584no—
693C22⋊C4—1584no—
694C42—24no—
695C42—1584no—
696C42—1584no—
697C42D4×D7912yes—
698C42C23×D7912yes—
699C23—24no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—3168no—
704C23—3168no—
705C23—3162no—
706C23—3162no—
707C23—3162no—
708C23—792no—
709C23—792no—
710C23—63216no—
711C23—6324no—
712C23—1582no—
713C23—1582no—
714C23—1582no—
715C23—1582no—
716C23—1582no—
717C23—1582no—
718C23—1582no—
719C23C2×D4×D7911yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—3168no—
724Q8—3162no—
725Q8—1582no—
726Q8—1582no—
727D4—22no—
728D4—24no—
729D4—3164no—
730D4—3168no—
731D4—3168no—
732D4—3162no—
733D4—6324no—
734D4—1582no—
735D4—1582no—
736D4C2×#1192962414yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—84no—
746C2×C4—3162no—
747C2×C4—3162no—
748C2×C4—3162no—
749C2×C4—3168no—
750C2×C4—792no—
751C2×C4—792no—
752C2×C4—1582no—
753C2×C4—1582no—
754C2×C4—1582no—
755C2×C4—1582no—
756C2×C4—1582no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4—1584no—
760C2×C4—1584no—
761C2×C4—1582no—
762C2×C4—1582no—
763C2×C4C2×D4×D7912yes—
764C2×C4C2×D4×D7912yes—
765C2×C4C2×D4×D7911yescharacteristic
766C2×C4C2×#1192962412yes—
767C2×C4#1457920712yes—
768C2×C4C24×D7911yescharacteristic
769C8—22no—
770C8—22no—
771C8—1582no—
772C8—1582no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—3164no—
778C22—3164no—
779C22—3162no—
780C22—3162no—
781C22—3162no—
782C22—63216no—
783C22—6324no—
784C22—1582no—
785C22—1582no—
786C22—1582no—
787C22—1582no—
788C22—1582no—
789C22—1582no—
790C22#1909920912yes—
791C22#1909936212yes—
792C22#1909937312yes—
793C22C22×D4×D7911yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—3162no—
800C4—3162no—
801C4—3162no—
802C4—1582no—
803C4—1582no—
804C4#1909920912yes—
805C4C22×#1192962411yescharacteristic
806C4C2×#1457920711yescharacteristic
807C2—44no—
808C2—3162no—
809C2—3162no—
810C2—6322no—
811C2#2377544114yesdirect product factor
812C2C2×#1909920911yescharacteristic
813C2C2×#1909936211yescharacteristic
814C2C2×#1909937311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#440×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099208C2
hypercenterC2×#440D79
hypocenterC79C2×#3311
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#19099286C2semidirect
3. #23775441C2direct (N × H)
4. C2×#19098923C2semidirect
5. C2×#19098906C2semidirect
6. C2×#19098890C2semidirect
7. C2×#19098853C2semidirect
8. C2×#19098820C2semidirect
9. C2×#19098795C2semidirect
10. C2×#19098785C2semidirect
11. C2×#19098722C2semidirect
12. C2×#19098712C2semidirect
13. C2×#19098636C2semidirect
14. C2×#19098566C2semidirect
15. C2×#19098556C2semidirect
16. C2×#440×C79C2semidirect
19. C22×#11929614C22semidirect
22. C22×C8×D79C22semidirect
24. #19099286C22semidirect
27. C2×#14579161C22semidirect
35. C2×#14579137C22semidirect
42. C2×#14579119C22semidirect
44. #19098923C22semidirect
45. #19098906C22semidirect
46. #19098890C22semidirect
47. #19098853C22semidirect
48. #19098820C22semidirect
49. #19098795C22semidirect
50. #19098785C22semidirect
51. #19098722C22semidirect
52. #19098712C22semidirect
53. #19098636C22semidirect
54. C2×#14579092C22semidirect
55. C2×#14579092C22semidirect
56. C2×C4⋊(C79⋊C8)C22semidirect
57. #19098566C22semidirect
58. #19098556C22semidirect
59. C2×#14579086C22semidirect
60. C2×#14579086C22semidirect
61. C2×#14579084C22semidirect
68. C2×(C2×D79)⋊C8C22semidirect
70. C2×C4×Q8×C79C22semidirect
72. #440×C79C22semidirect
73. C2×#107×C79C22semidirect
74. C2×#103×C79C22semidirect
76. C2×#97×C79C22semidirect
97. C2×#11929614C23semidirect
105. C2×C8×D79C23semidirect
107. #14579161C23semidirect
119. #14579137C23semidirect
130. #14579119C23semidirect
151. #14579092C23semidirect
152. #14579092C23semidirect
153. C4⋊(C79⋊C8)C23semidirect
154. #14579086C23semidirect
155. #14579086C23semidirect
156. #14579084C23semidirect
163. (C2×D79)⋊C8C23semidirect
172. C4×Q8×C79C23semidirect
181. #107×C79C23semidirect
182. #103×C79C23semidirect
184. #97×C79C23semidirect
401. C2×C79#3311semidirect
420. C2×#440D79semidirect
424. C79C2×#3311semidirect
449. C2×C4×Q8C2×D79semidirect
464. #440C2×D79semidirect
466. C2×#107C2×D79semidirect
475. C2×#103C2×D79semidirect
484. C2×#97C2×D79semidirect
541. C4×Q8C22×D79semidirect
576. #107C22×D79semidirect
583. #103C22×D79semidirect
592. #97C22×D79semidirect
811. C2#23775441direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992862
C2×#190992082
#237754412
C2×#190989232
C2×#190989062
C2×#190988902
C2×#190988532
C2×#190988202
C2×#190987952
C2×#190987852
C2×#190987222
C2×#190987122
C2×#190986362
C2×#190985662
C2×#190985562
C2×#440×C792
C2×#331179