Finite Group Databasebeta

← C2×#23776158 #35168023

Subgroups — C2×#23776158 #35168023

Order 20224.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099296C211yesmaximal, characteristic, complemented
2C2×#19099270C211yesmaximal, characteristic, complemented
3#23776158C2116yesmaximal, direct product factor
4C2×#19098926C211yesmaximal, characteristic, complemented
5C2×#19098923C211yesmaximal, characteristic, complemented
6C2×#19098916C211yesmaximal, characteristic, complemented
7C2×#19098873C211yesmaximal, characteristic, complemented
8C2×#19098862C211yesmaximal, characteristic, complemented
9C2×#19098843C211yesmaximal, characteristic, complemented
10C2×#19098778C211yesmaximal, characteristic, complemented
11C2×#19098776C211yesmaximal, characteristic, complemented
12C2×#19098756C211yesmaximal, characteristic
13C2×#19098691C211yesmaximal, characteristic, complemented
14C2×#19098660C211yesmaximal, characteristic, complemented
15C2×#19098643C211yesmaximal, characteristic, complemented
16C2×#442×C79C211yesmaximal, characteristic, complemented
17C22×#11929612C2211yescharacteristic
18C22×#11929609C2211yescharacteristic
19#19099296—24no—
20#19099296C2218yescomplemented
21#19099270—24no—
22#19099270C2218yescomplemented
23C2×#14579161C2211yescharacteristic
24C2×#14579157C2211yescharacteristic
25C2×#14579152C2211yescharacteristic
26C2×#14579152C2211yescharacteristic
27C2×#14579149C2211yescharacteristic
28C2×#14579148C2211yescharacteristic
29C2×#14579147—21no—
30C2×#14579144—21no—
31C2×#14579143—21no—
32C2×#14579140—21no—
33C2×#14579138—21no—
34C2×#14579138—21no—
35C2×C4×Dic158C2211yescharacteristic
36C2×#14579126C2211yescharacteristic
37C2×D4×Dic79C2211yescharacteristic
38C2×D4×Dic79C2211yescharacteristic
39C2×#14579123C2211yescharacteristic
40C2×C4×C22⋊D79—21no—
41C22×C4⋊Dic79—21no—
42#19098926C2218yescomplemented
43#19098923C2218yescomplemented
44#19098916C2218yescomplemented
45#19098873C2218yescomplemented
46#19098862C2218yescomplemented
47#19098843C2218yescomplemented
48#19098778C2218yescomplemented
49#19098776C2218yescomplemented
50#19098756C2218yes—
51#19098691C2218yescomplemented
52#19098660C2218yescomplemented
53#19098643C2218yescomplemented
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×C4⋊(C79⋊C8)C2211yescharacteristic
57C2×Dic79⋊C8C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579084C2211yescharacteristic
62C2×#14579083C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×D8×C79C2211yescharacteristic
70C2×C4×D4×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#442×C79C2218yescomplemented
73C2×#106×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158D411yescharacteristic
79C22×Dic158C2311yescharacteristic
80C22×D316C2311yescharacteristic
81C22×C22⋊D79—21no—
82C22×C22⋊D79—21no—
83C23×Dic79—21no—
84C23×Dic79—21no—
85C22×C4×D79—21no—
86C2×#11929612—24no—
87C2×#11929612C2314yes—
88C2×#11929609—24no—
89C2×#11929609C2314yes—
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92#14579161—22no—
93#14579161C2314yes—
94#14579157—22no—
95#14579157C2314yes—
96#14579152—22no—
97#14579152—22no—
98#14579152C2314yes—
99#14579152C2314yes—
100#14579149—22no—
101#14579149C2314yes—
102#14579148—22no—
103#14579148C2314yes—
104#14579147—28no—
105#14579144—28no—
106#14579143—28no—
107#14579140—28no—
108#14579138—28no—
109#14579138—28no—
110C4×Dic158D414yes—
111C4×Dic158C2314yes—
112#14579126—22no—
113#14579126C2314yes—
114D4×Dic79—22no—
115D4×Dic79—22no—
116D4×Dic79C2314yes—
117D4×Dic79C2314yes—
118#14579123—22no—
119#14579123C2314yes—
120C4×C22⋊D79—28no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79—28no—
125C2×C4⋊Dic79D411yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142C2×C4×Dic79C2311yescharacteristic
143#14579094C2314yes—
144#14579094C2314yes—
145C4⋊(C79⋊C8)C2314yes—
146Dic79⋊C8C2314yes—
147Dic79⋊C8C2314yes—
148#14579086C2314yes—
149#14579086C2314yes—
150#14579084C2314yes—
151#14579083C2314yes—
152#14579083C2314yes—
153#14579082C2314yes—
154#14579082C2314yes—
155#14579081C2314yes—
156#14579071C2314yes—
157C8×Dic79C2314yes—
158C22×D4×C79C2311yescharacteristic
159C22×D4×C79C2311yescharacteristic
160C23×C4×C79—21no—
161C23×C4×C79—21no—
162C2×D8×C79—24no—
163C2×D8×C79C2314yes—
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C4×D4×C79—22no—
167C4×D4×C79—22no—
168C4×D4×C79C2314yes—
169C4×D4×C79C2314yes—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#106×C79C2314yes—
176#102×C79C2314yes—
177#102×C79C2314yes—
178#97×C79C2314yes—
179C23×D79—21no—
180C2×Dic158—21no—
181C2×Dic158—24no—
182C2×Dic158—22no—
183C2×Dic158—22no—
184C2×Dic158—42no—
185C2×Dic158—82no—
186C2×Dic158C2×D414yes—
187C2×Dic158C2412yes—
188C2×D316—21no—
189C2×D316—22no—
190C2×D316—22no—
191C2×D316C2412yes—
192C2×C22⋊D79—24no—
193C2×C22⋊D79—24no—
194C2×C22⋊D79—44no—
195C2×C22⋊D79—82no—
196C22×Dic79—24no—
197C22×Dic79—24no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—82no—
202C22×Dic79—82no—
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C22×Dic79C2×D411yescharacteristic
206C22×Dic79C2×D411yescharacteristic
207C2×C4×D79—24no—
208C2×C4×D79—82no—
209#11929612—28no—
210#11929609—28no—
211C2×C79⋊C8—22no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8C2412yes—
214C2×C79⋊C8C2412yes—
215C4⋊Dic79—24no—
216C4⋊Dic79—24no—
217C4⋊Dic79—24no—
218C4⋊Dic79—21no—
219C4⋊Dic79—21no—
220C4⋊Dic79C2×D414yes—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4C2×D414yes—
227Dic79⋊C4C2×D414yes—
228C22⋊Dic79—24no—
229C22⋊Dic79—24no—
230C22⋊Dic79—24no—
231C22⋊Dic79—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235C4×Dic79—24no—
236C4×Dic79C2×D412yes—
237C4×Dic79C2×D412yes—
238C4×Dic79C2412yes—
239C4×Dic79C2412yes—
240C24×C79—21no—
241C24×C79—21no—
242C2×D4×C79—21no—
243C2×D4×C79—21no—
244C2×D4×C79—22no—
245C2×D4×C79—22no—
246C2×D4×C79—22no—
247C2×D4×C79#4114yes—
248C2×D4×C79C2412yes—
249C2×D4×C79C2412yes—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79—24no—
253C22×C4×C79—24no—
254C22×C4×C79—44no—
255C22×C4×C79—82no—
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2411yescharacteristic
259D8×C79—28no—
260C2×C8×C79—22no—
261C2×C8×C79—22no—
262C2×C8×C79C2412yes—
263C2×C8×C79C2412yes—
264C4⋊C4×C79—21no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79C2412yes—
267C4⋊C4×C79C2412yes—
268C22⋊C4×C79—24no—
269C22⋊C4×C79—24no—
270C42×C79C2×D412yes—
271C42×C79C2412yes—
272C23×C79—24no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—42no—
276C23×C79—42no—
277C23×C79—42no—
278C23×C79—42no—
279C23×C79—42no—
280C23×C79C22×D411yescharacteristic
281C22×D79—22no—
282C22×D79—42no—
283C22×D79—42no—
284C22×D79—42no—
285D4×C79—24no—
286D4×C79—22no—
287D4×C79—22no—
288D4×C79—22no—
289D4×C79—42no—
290D4×C79C2×#4114yes—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—48no—
296C2×C4×C79—42no—
297C2×C4×C79—42no—
298C2×C4×C79—84no—
299C2×C4×C79C22×D412yes—
300C2×C4×C79C22×D412yes—
301C2×C4×C79C22×D411yescharacteristic
302C2×C4×C79C2×#4112yes—
303C2×C4×C792−1+412yes—
304C2×C4×C79C2511yescharacteristic
305C22⋊D79—48no—
306C22⋊D79—84no—
307C2×Dic79—22no—
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—84no—
318C2×Dic79—84no—
319C2×Dic79C22×D412yes—
320C2×Dic79C22×D412yes—
321C2×Dic79C22×D412yes—
322C2×Dic79C22×D412yes—
323D316—22no—
324D316—22no—
325D316—42no—
326C4×D79—84no—
327Dic158—22no—
328Dic158—22no—
329Dic158—44no—
330Dic158—42no—
331Dic158—84no—
332C8×C79—22no—
333C8×C79—22no—
334C79⋊C8—22no—
335C79⋊C8—22no—
336C22×C79—24no—
337C22×C79—48no—
338C22×C79—42no—
339C22×C79—42no—
340C22×C79—42no—
341C22×C79—42no—
342C22×C79—42no—
343C22×C79—84no—
344C22×C79#54812yes—
345C22×C79#57512yes—
346C22×C79#57612yes—
347C22×C79C23×D411yescharacteristic
348C2×D79—42no—
349C2×D79—42no—
350C2×D79—42no—
351C2×D79—84no—
352C4×C79—22no—
353C4×C79—22no—
354C4×C79—42no—
355C4×C79—42no—
356C4×C79#54812yes—
357C4×C79C22×#4111yescharacteristic
358C4×C79C2×2−1+411yescharacteristic
359Dic79—22no—
360Dic79—22no—
361Dic79—22no—
362Dic79—22no—
363Dic79—42no—
364Dic79—42no—
365Dic79—42no—
366C2×#3370—791nomaximal, Sylow
367C2×C79—44no—
368C2×C79—82no—
369C2×C79#337014yescomplemented
370C2×C79C2×#54811yescharacteristic
371C2×C79C2×#57511yescharacteristic
372C2×C79C2×#57611yescharacteristic
373D79—82no—
374C2×#559—791no—
375C2×#554—791no—
376#3370—7916no—
377C2×#490—791no—
378C2×#489—791no—
379C2×#488—791no—
380C2×#479—791no—
381C2×#478—791no—
382C2×#474—791no—
383C2×#463—791no—
384C2×#463—791no—
385C2×#459—791no—
386C2×#446—791no—
387C2×#442D7911yescharacteristic, complemented
388C2×#440—791no—
389C2×C4×D8—791no—
390C79C2×#337011yescharacteristic, complemented, Sylow
391C22×SD16—791no—
392C22×D8—791no—
393C22×D8C2×D7911yescharacteristic
394#559—798no—
395#559—1584no—
396#554—798no—
397#554—1584no—
398C2×C4⋊Q8—791no—
399C2×#127—791no—
400C2×#125—791no—
401C2×#125—791no—
402C2×#124—791no—
403C2×#124—791no—
404C2×#124—1581no—
405C2×#123—1581no—
406C2×#123—1581no—
407C2×C22⋊Q8—1581no—
408C2×C22⋊Q8—1581no—
409C2×C22⋊Q8—1581no—
410C2×C4×Q8—791no—
411C2×C4×Q8—791no—
412C2×C4×D4—791no—
413C2×C4×D4—791no—
414C2×C4×D4—791no—
415C2×C4×D4—1581no—
416C2×C4×D4C2×D7911yescharacteristic
417C2×C4×D4C2×D7911yescharacteristic
418C22×C4⋊C4—1581no—
419#490—798no—
420#489—798no—
421#488—798no—
422#479—798no—
423#478—798no—
424#474—798no—
425#463—798no—
426#463—798no—
427#459—798no—
428#446—798no—
429#442C2×D7918yescomplemented
430#440—798no—
431C4×D8—798no—
432C2×#107—791no—
433C2×#107—791no—
434C2×#106C2×D7911yescharacteristic
435C2×C4⋊C8—791no—
436C2×C4⋊C8—791no—
437C2×C4⋊C8—791no—
438C2×#103—791no—
439C2×#103—791no—
440C2×#103—791no—
441C2×#102—791no—
442C2×#102—791no—
443C2×#102—791no—
444C2×#102—791no—
445C2×#102—791no—
446C2×#102C2×D7911yescharacteristic
447C2×#102C2×D7911yescharacteristic
448C2×#97—791no—
449C2×#97C2×D7911yescharacteristic
450C2×C4×C8—791no—
451C22×Q8—791no—
452C22×Q8—791no—
453C22×Q8—1581no—
454C22×D4—791no—
455C22×D4—1581no—
456C22×D4—1581no—
457C22×D4C22×D7911yescharacteristic
458C22×D4C22×D7911yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—1581no—
462C23×C4—1581no—
463C23×C4—1581no—
464C2×SD16—794no—
465C2×SD16—1584no—
466C2×D8—24no—
467C2×D8—794no—
468C2×D8—1584no—
469C2×D8C22×D7914yes—
470C22×C8—791no—
471C22×C8—791no—
472C22×C8C22×D7911yescharacteristic
473C22×C8C22×D7911yescharacteristic
474C4⋊Q8—794no—
475C4⋊Q8—1582no—
476#127—794no—
477#127—1582no—
478#125—794no—
479#125—794no—
480#125—1582no—
481#125—1582no—
482#124—794no—
483#124—794no—
484#124—1582no—
485#124—1588no—
486#124—1582no—
487#123—1588no—
488#123—1588no—
489C22⋊Q8—1588no—
490C22⋊Q8—1588no—
491C22⋊Q8—1588no—
492C4×Q8—794no—
493C4×Q8—794no—
494C4×Q8—794no—
495C4×Q8—1582no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—794no—
499C4×D4—794no—
500C4×D4—794no—
501C4×D4—1582no—
502C4×D4—1582no—
503C4×D4—1582no—
504C4×D4—1588no—
505C4×D4C22×D7914yes—
506C4×D4C22×D7914yes—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—791no—
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⋊C4C22×D7911yescharacteristic
520C2×C4⋊C4C22×D7911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4—1581no—
529C2×C22⋊C4—1581no—
530C2×C42—791no—
531C2×C42—791no—
532C2×C42—1581no—
533C2×C42C22×D7911yescharacteristic
534#107—794no—
535#107—794no—
536#106C22×D7914yes—
537C4⋊C8—794no—
538C4⋊C8—794no—
539C4⋊C8—794no—
540#103—794no—
541#103—794no—
542#103—794no—
543#102—794no—
544#102—794no—
545#102—794no—
546#102—794no—
547#102—794no—
548#102C22×D7914yes—
549#102C22×D7914yes—
550#97—794no—
551#97C22×D7914yes—
552C4×C8—794no—
553C24—21no—
554C24—21no—
555C24—1581no—
556C2×Q8—3162no—
557C2×Q8—794no—
558C2×Q8—792no—
559C2×Q8—6322no—
560C2×Q8—1582no—
561C2×Q8—1582no—
562C2×Q8—1581no—
563C2×Q8—1584no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—3164no—
570C2×D4—792no—
571C2×D4—6322no—
572C2×D4—1584no—
573C2×D4—1584no—
574C2×D4—1582no—
575C2×D4—1582no—
576C2×D4—1581no—
577C2×D4#1192962414yes—
578C2×D4C23×D7912yes—
579C2×D4C23×D7912yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—44no—
585C22×C4—82no—
586C22×C4—791no—
587C22×C4—791no—
588C22×C4—791no—
589C22×C4—791no—
590C22×C4—6322no—
591C22×C4—6322no—
592C22×C4—6322no—
593C22×C4—1584no—
594C22×C4—1581no—
595C22×C4—1581no—
596C22×C4—1581no—
597C22×C4—1584no—
598C22×C4—1584no—
599C22×C4D4×D7911yescharacteristic
600C22×C4D4×D7911yescharacteristic
601C22×C4C23×D7911yescharacteristic
602SD16—1588no—
603D8—28no—
604D8—1588no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—792no—
608C2×C8—792no—
609C2×C8—1582no—
610C2×C8—1582no—
611C2×C8C23×D7912yes—
612C2×C8C23×D7912yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—794no—
616C4⋊C4—794no—
617C4⋊C4—794no—
618C4⋊C4—792no—
619C4⋊C4—792no—
620C4⋊C4—1584no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1581no—
626C4⋊C4—1581no—
627C4⋊C4—1584no—
628C4⋊C4C23×D7912yes—
629C4⋊C4C23×D7912yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—1584no—
633C22⋊C4—1584no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C22⋊C4—1584no—
639C42—792no—
640C42—792no—
641C42—792no—
642C42—792no—
643C42—1584no—
644C42D4×D7912yes—
645C42C23×D7912yes—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—3162no—
655C23—3162no—
656C23—3162no—
657C23—1582no—
658C23C2×D4×D7911yescharacteristic
659Q8—3164no—
660Q8—3162no—
661Q8—6324no—
662Q8—1582no—
663Q8—1582no—
664D4—22no—
665D4—22no—
666D4—24no—
667D4—22no—
668D4—42no—
669D4—3168no—
670D4—3162no—
671D4—6324no—
672D4—1582no—
673D4—1582no—
674D4C2×#1192962414yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—48no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—84no—
683C2×C4—3162no—
684C2×C4—3162no—
685C2×C4—3162no—
686C2×C4—792no—
687C2×C4—792no—
688C2×C4—792no—
689C2×C4—792no—
690C2×C4—6324no—
691C2×C4—6324no—
692C2×C4—6324no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4C2×D4×D7912yes—
701C2×C4C2×D4×D7912yes—
702C2×C4C2×D4×D7911yescharacteristic
703C2×C4C2×#1192962412yes—
704C2×C4#1457920812yes—
705C2×C4C24×D7911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1582no—
709C8—1582no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—3162no—
719C22—3162no—
720C22—3162no—
721C22—6324no—
722C22#1909922212yes—
723C22#1909935912yes—
724C22#1909936712yes—
725C22C22×D4×D7911yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—3162no—
731C4—3162no—
732C4—3162no—
733C4—1582no—
734C4—1582no—
735C4—1582no—
736C4—1582no—
737C4#1909922212yes—
738C4C22×#1192962411yescharacteristic
739C4C2×#1457920811yescharacteristic
740C2—44no—
741C2—82no—
742C2—6322no—
743C2#2377615814yesdirect product factor
744C2C2×#1909922211yescharacteristic
745C2C2×#1909935911yescharacteristic
746C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#442×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098756C2
hypercenterC2×#442D79
hypocenterC79C2×#3370
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#19099296C2semidirect
2. C2×#19099270C2semidirect
3. #23776158C2direct (N × H)
4. C2×#19098926C2semidirect
5. C2×#19098923C2semidirect
6. C2×#19098916C2semidirect
7. C2×#19098873C2semidirect
8. C2×#19098862C2semidirect
9. C2×#19098843C2semidirect
10. C2×#19098778C2semidirect
11. C2×#19098776C2semidirect
13. C2×#19098691C2semidirect
14. C2×#19098660C2semidirect
15. C2×#19098643C2semidirect
16. C2×#442×C79C2semidirect
20. #19099296C22semidirect
22. #19099270C22semidirect
42. #19098926C22semidirect
43. #19098923C22semidirect
44. #19098916C22semidirect
45. #19098873C22semidirect
46. #19098862C22semidirect
47. #19098843C22semidirect
48. #19098778C22semidirect
49. #19098776C22semidirect
51. #19098691C22semidirect
52. #19098660C22semidirect
53. #19098643C22semidirect
72. #442×C79C22semidirect
369. C2×C79#3370semidirect
387. C2×#442D79semidirect
390. C79C2×#3370semidirect
429. #442C2×D79semidirect
743. C2#23776158direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992962
C2×#190992702
#237761582
C2×#190989262
C2×#190989232
C2×#190989162
C2×#190988732
C2×#190988622
C2×#190988432
C2×#190987782
C2×#190987762
C2×#190987562
C2×#190986912
C2×#190986602
C2×#190986432
C2×#442×C792
C2×#337079