Finite Group Databasebeta

← C2×#23773569 #35156415

Subgroups — C2×#23773569 #35156415

Order 20224.

2150 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099095C211yesmaximal, characteristic
2C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
3#23773569C2116yesmaximal, direct product factor
4C2×#19098900C211yesmaximal, characteristic, complemented
5C2×#19098880C211yesmaximal, characteristic
6C2×#19098869C211yesmaximal, characteristic, complemented
7C2×#19098868C211yesmaximal, characteristic, complemented
8C2×#19098784C211yesmaximal, characteristic, complemented
9C2×#19098783C211yesmaximal, characteristic, complemented
10C2×#19098720C211yesmaximal, characteristic, complemented
11C2×#19098700C211yesmaximal, characteristic
12C2×#19098671C211yesmaximal, characteristic, complemented
13C2×#19098668C211yesmaximal, characteristic, complemented
14C2×#19098663C211yesmaximal, characteristic, complemented
15C2×#19098618C211yesmaximal, characteristic, complemented
16C2×#440×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18C22×Dic316C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20C22×#11929612C2211yescharacteristic
21#19099095—24no—
22#19099095C2218yes—
23C2×#14579154—21no—
24C2×#14579152C2211yescharacteristic
25C2×#14579148C2211yescharacteristic
26C2×#14579143—21no—
27C2×#14579141C2211yescharacteristic
28C2×#14579132C2211yescharacteristic
29C2×Q8×Dic79C2211yescharacteristic
30C2×C4×Dic158—21no—
31C2×C4×Dic158C2211yescharacteristic
32C2×C4×Dic158C2211yescharacteristic
33C2×#14579126—21no—
34C2×#14579126C2211yescharacteristic
35C4×Q8×D79—24no—
36C4×Q8×D79C2218yescomplemented
37C2×C4×C22⋊D79—21no—
38C2×#14579120—21no—
39C2×C4⋊C4×D79—21no—
40C2×C4⋊C4×D79C2211yescharacteristic
41C2×C42×D79—21no—
42C2×C42×D79C2211yescharacteristic
43#19098900C2218yescomplemented
44#19098880C2218yes—
45#19098869C2218yescomplemented
46#19098868C2218yescomplemented
47#19098784C2218yescomplemented
48#19098783C2218yescomplemented
49#19098720C2218yescomplemented
50#19098700C2218yes—
51#19098671C2218yescomplemented
52#19098668C2218yescomplemented
53#19098663C2218yescomplemented
54#19098618C2218yescomplemented
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×#14579072C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#440×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×Dic158C2311yescharacteristic
80C2×Q8×D79—24no—
81C2×Q8×D79—24no—
82C2×Q8×D79—22no—
83C2×Q8×D79C2314yes—
84C22×C22⋊D79—21no—
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79D411yescharacteristic
88C22×C4×D79D411yescharacteristic
89C22×C4×D79C2311yescharacteristic
90C2×Dic316—24no—
91C2×Dic316C2314yes—
92C2×#11929614—24no—
93C2×#11929614C2314yes—
94C2×#11929612—24no—
95C2×#11929612C2314yes—
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2311yescharacteristic
98#14579154—28no—
99#14579152—22no—
100#14579152C2314yes—
101#14579148—22no—
102#14579148C2314yes—
103#14579143—28no—
104#14579141—22no—
105#14579141C2314yes—
106#14579132—22no—
107#14579132C2314yes—
108Q8×Dic79—22no—
109Q8×Dic79C2314yes—
110C4×Dic158—22no—
111C4×Dic158—22no—
112C4×Dic158—28no—
113C4×Dic158C2314yes—
114C4×Dic158C2314yes—
115#14579126—22no—
116#14579126—28no—
117#14579126C2314yes—
118C4×C22⋊D79—28no—
119#14579120—28no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C4⋊C4×D79—28no—
131C4⋊C4×D79—22no—
132C4⋊C4×D79C2314yes—
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79D411yescharacteristic
142C2×C4×Dic79D411yescharacteristic
143C2×C4×Dic79C2311yescharacteristic
144C42×D79—28no—
145C42×D79D414yes—
146C42×D79C2314yes—
147#14579094C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150Dic79⋊C8C2314yes—
151Dic79⋊C8C2314yes—
152#14579086C2314yes—
153#14579086C2314yes—
154#14579085C2314yes—
155#14579084C2314yes—
156#14579084C2314yes—
157#14579082C2314yes—
158(C2×D79)⋊C8C2314yes—
159(C2×D79)⋊C8C2314yes—
160#14579072C2314yes—
161C22×Q8×C79C2311yescharacteristic
162C22×D4×C79C2311yescharacteristic
163C23×C4×C79—21no—
164C2×SD16×C79—24no—
165C2×SD16×C79C2314yes—
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168C4×Q8×C79—22no—
169C4×Q8×C79C2314yes—
170C4×D4×C79—22no—
171C4×D4×C79C2314yes—
172C2×C4⋊C4×C79—21no—
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C22⋊C4×C79—21no—
176C2×C42×C79—21no—
177C2×C42×C79C2311yescharacteristic
178#107×C79C2314yes—
179#103×C79C2314yes—
180#102×C79C2314yes—
181#97×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183C2×Dic158—28no—
184C2×Dic158—24no—
185C2×Dic158—21no—
186C2×Dic158—21no—
187C2×Dic158—22no—
188C2×Dic158—22no—
189C2×Dic158—22no—
190C2×Dic158#4114yes—
191C2×Dic158C2412yes—
192C2×Dic158C2412yes—
193Q8×D79—216no—
194Q8×D79—28no—
195Q8×D79—28no—
196C2×C22⋊D79—24no—
197C2×C22⋊D79—44no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C2×C4×D79—28no—
206C2×C4×D79—24no—
207C2×C4×D79—24no—
208C2×C4×D79—24no—
209C2×C4×D79—22no—
210C2×C4×D79—22no—
211C2×C4×D79—42no—
212C2×C4×D79—44no—
213C2×C4×D79C2×D412yes—
214C2×C4×D79C2×D414yes—
215C2×C4×D79C2×D414yes—
216C2×C4×D79C2412yes—
217Dic316—28no—
218#11929614—28no—
219#11929612—28no—
220C2×C79⋊C8—22no—
221C2×C79⋊C8—22no—
222C2×C79⋊C8C2412yes—
223C2×C79⋊C8C2412yes—
224C4⋊Dic79—24no—
225C4⋊Dic79—24no—
226C4⋊Dic79—24no—
227C4⋊Dic79—21no—
228C4⋊Dic79—21no—
229C4⋊Dic79C2412yes—
230C4⋊Dic79C2412yes—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4—24no—
234Dic79⋊C4—24no—
235Dic79⋊C4—24no—
236C22⋊Dic79—24no—
237C22⋊Dic79—24no—
238C22⋊Dic79—24no—
239(C2×D79)⋊C4—24no—
240C4×Dic79—24no—
241C4×Dic79—24no—
242C4×Dic79—24no—
243C4×Dic79—24no—
244C4×Dic79C2×D412yes—
245C4×Dic79C2×D414yes—
246C4×Dic79C2×D414yes—
247C4×Dic79C2412yes—
248C24×C79—21no—
249C2×Q8×C79—21no—
250C2×Q8×C79—22no—
251C2×Q8×C79#4114yes—
252C2×Q8×C79C2412yes—
253C2×D4×C79—21no—
254C2×D4×C79—22no—
255C2×D4×C79—22no—
256C2×D4×C79C2412yes—
257C22×C4×C79—21no—
258C22×C4×C79—21no—
259C22×C4×C79—21no—
260C22×C4×C79—24no—
261C22×C4×C79—44no—
262C22×C4×C79C2×D411yescharacteristic
263C22×C4×C79C2×D411yescharacteristic
264C22×C4×C79C2411yescharacteristic
265SD16×C79—28no—
266C2×C8×C79—22no—
267C2×C8×C79—22no—
268C2×C8×C79C2412yes—
269C2×C8×C79C2412yes—
270C4⋊C4×C79—24no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79—21no—
273C4⋊C4×C79C2412yes—
274C4⋊C4×C79C2412yes—
275C22⋊C4×C79—24no—
276C42×C79—24no—
277C42×C79C2×D412yes—
278C42×C79C2412yes—
279C23×C79—22no—
280C23×C79—42no—
281C23×C79—42no—
282C23×C79—42no—
283C23×C79C22×D411yescharacteristic
284C22×D79—22no—
285C22×D79—22no—
286C22×D79#13714yes—
287C22×D79C22×D412yes—
288Q8×C79—24no—
289Q8×C79—22no—
290Q8×C79C2×#4114yes—
291D4×C79—22no—
292D4×C79—22no—
293D4×C79—42no—
294C2×C4×C79—24no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—48no—
301C2×C4×C79—42no—
302C2×C4×C79—42no—
303C2×C4×C79C22×D412yes—
304C2×C4×C79C22×D412yes—
305C2×C4×C79C22×D411yescharacteristic
306C2×C4×C79C2×#4112yes—
307C2×C4×C79C2×#4112yes—
308C2×C4×C79C2511yescharacteristic
309C22⋊D79—48no—
310C2×Dic79—24no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—42no—
321C2×Dic79C22×D412yes—
322C2×Dic79C22×D412yes—
323C2×Dic79C22×D412yes—
324C4×D79—216no—
325C4×D79—28no—
326C4×D79—24no—
327C4×D79—22no—
328C4×D79—22no—
329C4×D79—44no—
330C4×D79—48no—
331Dic158—216no—
332Dic158—24no—
333Dic158—22no—
334Dic158—22no—
335Dic158—22no—
336Dic158—42no—
337Dic158C2×#4114yes—
338C8×C79—22no—
339C8×C79—22no—
340C79⋊C8—22no—
341C79⋊C8—22no—
342C22×C79—42no—
343C22×C79—42no—
344C22×C79—42no—
345C22×C79—84no—
346C22×C79#52512yes—
347C22×C79C2×#13712yes—
348C22×C79#57512yes—
349C22×C79C23×D411yescharacteristic
350C2×D79—28no—
351C2×D79—22no—
352C2×D79—22no—
353C2×D79C2×#13714yes—
354C4×C79—24no—
355C4×C79—22no—
356C4×C79—22no—
357C4×C79—42no—
358C4×C79—42no—
359C4×C79#52512yes—
360C4×C79C22×#4111yescharacteristic
361C4×C79C22×#4111yescharacteristic
362Dic79—22no—
363Dic79—24no—
364Dic79—22no—
365Dic79—22no—
366Dic79—42no—
367Dic79—42no—
368Dic79—42no—
369C2×#3117—791nomaximal, Sylow
370C2×C79—82no—
371C2×C79#311714yescomplemented
372C2×C79C2×#52511yescharacteristic
373C2×C79C22×#13711yescharacteristic
374C2×C79C2×#57511yescharacteristic
375D79—24no—
376C2×#529—791no—
377C22×C4×Q8—791no—
378#3117—7916no—
379C2×#484—791no—
380C2×#481—791no—
381C2×#479—791no—
382C2×#479—791no—
383C2×#464—791no—
384C2×#464—791no—
385C2×#451—791no—
386C2×#448—791no—
387C2×#441—791no—
388C2×#441—791no—
389C2×#440—791no—
390C2×#440D7911yescharacteristic, complemented
391C2×#432—791no—
392C79C2×#311711yescharacteristic, complemented, Sylow
393C23×Q8—791no—
394C22×Q16—791no—
395C22×Q16—791no—
396C22×SD16—791no—
397C22×SD16C2×D7911yescharacteristic
398#529—798no—
399#529—1584no—
400C2×#126—1581no—
401C2×#125—791no—
402C2×#124—791no—
403C2×#123—1581no—
404C2×C22⋊Q8—791no—
405C2×#121—791no—
406C2×C4×Q8—791no—
407C2×C4×Q8—798no—
408C2×C4×Q8—791no—
409C2×C4×Q8—791no—
410C2×C4×Q8—791no—
411C2×C4×Q8—1581no—
412C2×C4×Q8—1581no—
413C2×C4×Q8—1584no—
414C2×C4×Q8C2×D7911yescharacteristic
415C2×C4×D4—1581no—
416C2×C4×D4C2×D7911yescharacteristic
417C2×#117—1581no—
418C22×C4⋊C4—791no—
419C22×C4⋊C4—1581no—
420C22×C42—791no—
421C22×C42—1581no—
422#484—798no—
423#481—798no—
424#479—798no—
425#479—798no—
426#464—798no—
427#464—798no—
428#451—798no—
429#448—798no—
430#441—798no—
431#441—798no—
432#440—798no—
433#440C2×D7918yescomplemented
434#432—798no—
435C2×#107—791no—
436C2×#107C2×D7911yescharacteristic
437C2×#106—791no—
438C2×#106—791no—
439C2×C4⋊C8—791no—
440C2×C4⋊C8—791no—
441C2×#103—791no—
442C2×#103—791no—
443C2×#103—791no—
444C2×#103—791no—
445C2×#103—791no—
446C2×#103C2×D7911yescharacteristic
447C2×#102—791no—
448C2×#102C2×D7911yescharacteristic
449C2×C22⋊C8—791no—
450C2×C22⋊C8—791no—
451C2×#97—791no—
452C2×#97C2×D7911yescharacteristic
453C22×Q8—794no—
454C22×Q8—791no—
455C22×Q8—791no—
456C22×Q8—1581no—
457C22×Q8—1582no—
458C22×Q8—1584no—
459C22×Q8—1584no—
460C22×Q8C22×D7911yescharacteristic
461C22×D4—1581no—
462C22×D4C22×D7911yescharacteristic
463C23×C4—21no—
464C23×C4—791no—
465C23×C4—791no—
466C23×C4—791no—
467C23×C4—1581no—
468C23×C4—1581no—
469C2×Q16—794no—
470C2×Q16—794no—
471C2×Q16—1584no—
472C2×Q16—1584no—
473C2×SD16—24no—
474C2×SD16—794no—
475C2×SD16—1584no—
476C2×SD16C22×D7914yes—
477C22×C8—791no—
478C22×C8—791no—
479C22×C8C22×D7911yescharacteristic
480C22×C8C22×D7911yescharacteristic
481#126—1588no—
482#125—794no—
483#125—1582no—
484#124—794no—
485#124—1582no—
486#123—1588no—
487C22⋊Q8—794no—
488C22⋊Q8—1582no—
489#121—794no—
490#121—1582no—
491C4×Q8—22no—
492C4×Q8—794no—
493C4×Q8—794no—
494C4×Q8—794no—
495C4×Q8—794no—
496C4×Q8—1588no—
497C4×Q8—1588no—
498C4×Q8—1582no—
499C4×Q8—1582no—
500C4×Q8—1582no—
501C4×Q8—1582no—
502C4×Q8C22×D7914yes—
503C4×D4—22no—
504C4×D4—1588no—
505C4×D4C22×D7914yes—
506#117—1588no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—794no—
511C2×C4⋊C4—1582no—
512C2×C4⋊C4—1588no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4—1581no—
520C2×C4⋊C4—1581no—
521C2×C4⋊C4C22×D7911yescharacteristic
522C2×C4⋊C4C22×D7911yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C42—21no—
529C2×C42—791no—
530C2×C42—791no—
531C2×C42—791no—
532C2×C42—794no—
533C2×C42—794no—
534C2×C42—1588no—
535C2×C42—1581no—
536C2×C42—1581no—
537C2×C42—1581no—
538C2×C42—1581no—
539C2×C42C22×D7911yescharacteristic
540#107—794no—
541#107C22×D7914yes—
542#106—794no—
543#106—794no—
544C4⋊C8—794no—
545C4⋊C8—794no—
546#103—794no—
547#103—794no—
548#103—794no—
549#103—794no—
550#103—794no—
551#103C22×D7914yes—
552#102—794no—
553#102C22×D7914yes—
554C22⋊C8—794no—
555C22⋊C8—794no—
556#97—794no—
557#97C22×D7914yes—
558C24—21no—
559C24—791no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—794no—
563C2×Q8—792no—
564C2×Q8—792no—
565C2×Q8—1584no—
566C2×Q8—1588no—
567C2×Q8—1582no—
568C2×Q8—1582no—
569C2×Q8—1588no—
570C2×Q8—15816no—
571C2×Q8—1588no—
572C2×Q8—1582no—
573C2×Q8—1581no—
574C2×Q8—1581no—
575C2×Q8#1192962414yes—
576C2×Q8C23×D7912yes—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—3164no—
581C2×D4—1584no—
582C2×D4C23×D7912yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—3162no—
589C22×C4—3164no—
590C22×C4—794no—
591C22×C4—791no—
592C22×C4—791no—
593C22×C4—791no—
594C22×C4—792no—
595C22×C4—794no—
596C22×C4—792no—
597C22×C4—1584no—
598C22×C4—1584no—
599C22×C4—1584no—
600C22×C4—1588no—
601C22×C4—1581no—
602C22×C4—1581no—
603C22×C4—1581no—
604C22×C4—1581no—
605C22×C4—1582no—
606C22×C4—1582no—
607C22×C4D4×D7911yescharacteristic
608C22×C4D4×D7911yescharacteristic
609C22×C4C23×D7911yescharacteristic
610Q16—1588no—
611Q16—1588no—
612SD16—28no—
613SD16—1588no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—792no—
617C2×C8—792no—
618C2×C8—1582no—
619C2×C8—1582no—
620C2×C8C23×D7912yes—
621C2×C8C23×D7912yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—792no—
626C4⋊C4—792no—
627C4⋊C4—1584no—
628C4⋊C4—1584no—
629C4⋊C4—1584no—
630C4⋊C4—1584no—
631C4⋊C4—1584no—
632C4⋊C4—1584no—
633C4⋊C4—1584no—
634C4⋊C4—1584no—
635C4⋊C4—1581no—
636C4⋊C4—1581no—
637C4⋊C4C23×D7912yes—
638C4⋊C4C23×D7912yes—
639C22⋊C4—24no—
640C22⋊C4—1584no—
641C22⋊C4—1584no—
642C22⋊C4—1584no—
643C22⋊C4—1584no—
644C42—24no—
645C42—792no—
646C42—794no—
647C42—792no—
648C42—794no—
649C42—1584no—
650C42—1584no—
651C42—1584no—
652C42—1584no—
653C42D4×D7912yes—
654C42C23×D7912yes—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—794no—
660C23—792no—
661C23—1582no—
662C23—1582no—
663C23C2×D4×D7911yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—3162no—
667Q8—794no—
668Q8—15816no—
669Q8—1582no—
670Q8—1582no—
671Q8—1584no—
672Q8—1582no—
673Q8C2×#1192962414yes—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—3168no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—3164no—
688C2×C4—3168no—
689C2×C4—3162no—
690C2×C4—3162no—
691C2×C4—3162no—
692C2×C4—792no—
693C2×C4—792no—
694C2×C4—792no—
695C2×C4—1588no—
696C2×C4—15816no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4—1582no—
701C2×C4—1584no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1584no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4C2×D4×D7912yes—
709C2×C4C2×D4×D7912yes—
710C2×C4C2×D4×D7911yescharacteristic
711C2×C4#41×D7912yes—
712C2×C4C2×#1192962412yes—
713C2×C4C24×D7911yescharacteristic
714C8—22no—
715C8—22no—
716C8—1582no—
717C8—1582no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—794no—
723C22—1582no—
724C22—1582no—
725C22—1588no—
726C22#1909907212yes—
727C22#137×D7912yes—
728C22#1909935912yes—
729C22C22×D4×D7911yescharacteristic
730C4—22no—
731C4—22no—
732C4—24no—
733C4—42no—
734C4—42no—
735C4—3162no—
736C4—3162no—
737C4—3162no—
738C4—1582no—
739C4—1582no—
740C4—1582no—
741C4—1584no—
742C4#1909907212yes—
743C4C2×#41×D7911yescharacteristic
744C4C22×#1192962411yescharacteristic
745C2—82no—
746C2—1584no—
747C2#2377356914yesdirect product factor
748C2C2×#1909907211yescharacteristic
749C2C2×#137×D7911yescharacteristic
750C2C2×#1909935911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#440×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579132C22
hypercenterC2×#440D79
hypocenterC79C2×#3117
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
2. C2×C4×Q8×D79C2semidirect
3. #23773569C2direct (N × H)
4. C2×#19098900C2semidirect
6. C2×#19098869C2semidirect
7. C2×#19098868C2semidirect
8. C2×#19098784C2semidirect
9. C2×#19098783C2semidirect
10. C2×#19098720C2semidirect
12. C2×#19098671C2semidirect
13. C2×#19098668C2semidirect
14. C2×#19098663C2semidirect
15. C2×#19098618C2semidirect
16. C2×#440×C79C2semidirect
36. C4×Q8×D79C22semidirect
43. #19098900C22semidirect
45. #19098869C22semidirect
46. #19098868C22semidirect
47. #19098784C22semidirect
48. #19098783C22semidirect
49. #19098720C22semidirect
51. #19098671C22semidirect
52. #19098668C22semidirect
53. #19098663C22semidirect
54. #19098618C22semidirect
72. #440×C79C22semidirect
371. C2×C79#3117semidirect
390. C2×#440D79semidirect
392. C79C2×#3117semidirect
433. #440C2×D79semidirect
747. C2#23773569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990952
C2×C4×Q8×D792
#237735692
C2×#190989002
C2×#190988802
C2×#190988692
C2×#190988682
C2×#190987842
C2×#190987832
C2×#190987202
C2×#190987002
C2×#190986712
C2×#190986682
C2×#190986632
C2×#190986182
C2×#440×C792
C2×#311779