Finite Group Databasebeta

← C2×#23776322 #35168771

Subgroups — C2×#23776322 #35168771

Order 20224.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099289C211yesmaximal, characteristic, complemented
2C2×D4×Dic158C211yesmaximal, characteristic
3#23776322C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098971C211yesmaximal, characteristic, complemented
6C2×#19098967C211yesmaximal, characteristic, complemented
7C2×#19098858C211yesmaximal, characteristic, complemented
8C2×#19098856C211yesmaximal, characteristic, complemented
9C2×#19098846C211yesmaximal, characteristic, complemented
10C2×#19098865C211yesmaximal, characteristic
11C2×#19098863C211yesmaximal, characteristic
12C2×#19098841C211yesmaximal, characteristic
13C2×#19098691C211yesmaximal, characteristic, complemented
14C2×#19098664C211yesmaximal, characteristic
15C2×SD16×Dic79C211yesmaximal, characteristic
16C2×#440×C79C211yesmaximal, characteristic
17C23×Dic158—21no—
18#19099289—24no—
19#19099289C2218yescomplemented
20D4×Dic158—24no—
21D4×Dic158C2218yes—
22C2×#14579161C2211yescharacteristic
23C2×#14579160—21no—
24C2×#14579160C2211yescharacteristic
25C2×#14579160C2211yescharacteristic
26C2×#14579160C2211yescharacteristic
27C2×#14579153—21no—
28C2×#14579153C2211yescharacteristic
29C2×#14579152—21no—
30C2×#14579152C2211yescharacteristic
31C2×#14579140—21no—
32C2×#14579138—21no—
33C2×#14579138—21no—
34C2×Q8×Dic79C2211yescharacteristic
35C2×Q8×Dic79C2211yescharacteristic
36C2×C4×Dic158—21no—
37C2×C4×Dic158C2211yescharacteristic
38C2×D4×Dic79C2211yescharacteristic
39C2×D4×Dic79C2211yescharacteristic
40#19098972C2218yescomplemented
41#19098971C2218yescomplemented
42#19098967C2218yescomplemented
43#19098865C2218yes—
44#19098863C2218yes—
45#19098858C2218yescomplemented
46#19098856C2218yescomplemented
47#19098846C2218yescomplemented
48#19098841C2218yes—
49#19098691C2218yescomplemented
50#19098664C2218yes—
51SD16×Dic79C2218yes—
52C2×#14579095C2211yescharacteristic
53C2×#14579095C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579093C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×C4⋊(C79⋊C8)C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×Dic79⋊C8C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579082C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#440×C79C2218yes—
73C2×#107×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—28no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×Dic158—21no—
82C22×Dic158—48no—
83C22×Dic158D411yescharacteristic
84C23×Dic79—21no—
85C23×Dic79—21no—
86C22×C79⋊C8C2311yescharacteristic
87C22×C79⋊C8C2311yescharacteristic
88#14579161—22no—
89#14579161C2314yes—
90#14579160—28no—
91#14579160—22no—
92#14579160—22no—
93#14579160—22no—
94#14579160C2314yes—
95#14579160C2314yes—
96#14579160C2314yes—
97#14579153—22no—
98#14579153—28no—
99#14579153C2314yes—
100#14579152—28no—
101#14579152—22no—
102#14579152C2314yes—
103#14579140—28no—
104#14579138—28no—
105#14579138—28no—
106Q8×Dic79—22no—
107Q8×Dic79—22no—
108Q8×Dic79C2314yes—
109Q8×Dic79C2314yes—
110C4×Dic158—28no—
111C4×Dic158D414yes—
112C4×Dic158C2314yes—
113D4×Dic79—22no—
114D4×Dic79—22no—
115D4×Dic79C2314yes—
116D4×Dic79C2314yes—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79D411yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4D411yescharacteristic
133C2×Dic79⋊C4D411yescharacteristic
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79C2311yescharacteristic
139C2×C4×Dic79C2311yescharacteristic
140#14579095C2314yes—
141#14579095C2314yes—
142#14579094C2314yes—
143#14579094C2314yes—
144#14579094C2314yes—
145#14579093C2314yes—
146#14579093C2314yes—
147#14579092C2314yes—
148C4⋊(C79⋊C8)C2314yes—
149Dic79⋊C8C2314yes—
150Dic79⋊C8C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579082C2314yes—
154#14579082C2314yes—
155#14579071C2314yes—
156C8×Dic79C2314yes—
157C22×Q8×C79C2311yescharacteristic
158C22×D4×C79C2311yescharacteristic
159C23×C4×C79—21no—
160C2×SD16×C79Q818yescomplemented
161C2×SD16×C79C2314yes—
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164C4×Q8×C79—22no—
165C4×Q8×C79C2314yes—
166C4×D4×C79—22no—
167C4×D4×C79C2314yes—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C22⋊C4×C79—21no—
172C2×C42×C79—21no—
173C2×C42×C79C2311yescharacteristic
174#107×C79C2314yes—
175#103×C79C2314yes—
176#102×C79C2314yes—
177#97×C79C2314yes—
178C2×Dic158—24no—
179C2×Dic158—24no—
180C2×Dic158—24no—
181C2×Dic158—24no—
182C2×Dic158—24no—
183C2×Dic158—44no—
184C2×Dic158—432no—
185C2×Dic158—44no—
186C2×Dic158—44no—
187C2×Dic158—44no—
188C2×Dic158C2×D414yes—
189C22×Dic79—24no—
190C22×Dic79—24no—
191C22×Dic79—21no—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—44no—
196C22×Dic79—44no—
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C2×C79⋊C8—22no—
202C2×C79⋊C8—22no—
203C2×C79⋊C8C2412yes—
204C2×C79⋊C8C2412yes—
205C4⋊Dic79—24no—
206C4⋊Dic79—24no—
207C4⋊Dic79—24no—
208C4⋊Dic79—24no—
209C4⋊Dic79—21no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79C2×D414yes—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216C4⋊Dic79C2412yes—
217C4⋊Dic79C2412yes—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4C2×D414yes—
225Dic79⋊C4C2×D414yes—
226C22⋊Dic79—24no—
227C22⋊Dic79—24no—
228C4×Dic79—24no—
229C4×Dic79—24no—
230C4×Dic79C2×D412yes—
231C4×Dic79C2×D412yes—
232C4×Dic79C2412yes—
233C4×Dic79C2412yes—
234C24×C79—21no—
235C2×Q8×C79—21no—
236C2×Q8×C79—22no—
237C2×Q8×C79C2×Q814yescomplemented
238C2×Q8×C79C2412yes—
239C2×D4×C79—21no—
240C2×D4×C79—22no—
241C2×D4×C79C2×Q814yes—
242C2×D4×C79C2412yes—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79—24no—
247C22×C4×C79—44no—
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2411yescharacteristic
251SD16×C79C2×Q8116yescomplemented
252C2×C8×C79—22no—
253C2×C8×C79C2×Q814yescomplemented
254C2×C8×C79C2412yes—
255C2×C8×C79C2412yes—
256C4⋊C4×C79—24no—
257C4⋊C4×C79—21no—
258C4⋊C4×C79—21no—
259C4⋊C4×C79C2412yes—
260C4⋊C4×C79C2412yes—
261C22⋊C4×C79—24no—
262C42×C79—24no—
263C42×C79C2×D412yes—
264C42×C79C2412yes—
265C23×C79—24no—
266C23×C79—22no—
267C23×C79—42no—
268C23×C79—42no—
269C23×C79C22×D411yescharacteristic
270Q8×C79—24no—
271Q8×C79—22no—
272Q8×C79C22×Q814yescomplemented
273D4×C79—24no—
274D4×C79—22no—
275D4×C79C22×Q814yes—
276C2×C4×C79—24no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—48no—
283C2×C4×C79—42no—
284C2×C4×C79—42no—
285C2×C4×C79C22×D412yes—
286C2×C4×C79C22×D412yes—
287C2×C4×C79C22×D411yescharacteristic
288C2×C4×C79C22×Q812yes—
289C2×C4×C792−1+412yes—
290C2×C4×C79C2511yescharacteristic
291C2×Dic79—22no—
292C2×Dic79—22no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—48no—
299C2×Dic79—42no—
300C2×Dic79—42no—
301C2×Dic79—42no—
302C2×Dic79—42no—
303C2×Dic79—48no—
304C2×Dic79AGL(1,ℤ/8)14yes—
305C2×Dic79C22×D412yes—
306C2×Dic79C22×D412yes—
307C2×Dic79C22×D412yes—
308C2×Dic79C22×D412yes—
309Dic158—28no—
310Dic158—48no—
311Dic158—48no—
312Dic158—48no—
313Dic158—48no—
314C8×C79—22no—
315C8×C79C22×Q814yescomplemented
316C79⋊C8—22no—
317C79⋊C8—22no—
318C22×C79—24no—
319C22×C79—48no—
320C22×C79—42no—
321C22×C79—42no—
322C22×C79D4×Q812yes—
323C22×C79C2×AGL(1,ℤ/8)12yes—
324C22×C79#57812yes—
325C22×C79C23×D411yescharacteristic
326C4×C79—24no—
327C4×C79—22no—
328C4×C79—22no—
329C4×C79—42no—
330C4×C79—42no—
331C4×C79D4×Q812yes—
332C4×C79C23×Q811yescharacteristic
333C4×C79C2×2−1+411yescharacteristic
334Dic79—22no—
335Dic79—22no—
336Dic79—22no—
337Dic79—42no—
338Dic79—42no—
339Dic79—42no—
340Dic79—42no—
341Dic79C2×AGL(1,ℤ/8)14yes—
342C2×#3386—791nomaximal, Sylow
343C2×C79—44no—
344C2×C79#338614yescomplemented
345C2×C79C2×D4×Q811yescharacteristic
346C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
347C2×C79C2×#57811yescharacteristic
348C2×#557—791no—
349C2×D4×Q8—791no—
350#3386—7916no—
351C2×#501—791no—
352C2×#501—791no—
353C2×#500—791no—
354C2×#477—791no—
355C2×#477—791no—
356C2×#475—791no—
357C2×#478—791no—
358C2×#478—791no—
359C2×#474—791no—
360C2×#446—791no—
361C2×#440—791no—
362C2×#440D7911yescharacteristic
363C2×C4×SD16—791no—
364C79C2×#338611yescharacteristic, complemented, Sylow
365C23×Q8—1581no—
366C22×SD16C2×D7911yescharacteristic
367#557—798no—
368#557—1584no—
369D4×Q8—798no—
370D4×Q8—1584no—
371C2×C4⋊Q8—791no—
372C2×C4⋊Q8—791no—
373C2×C4⋊Q8—791no—
374C2×C4⋊Q8—791no—
375C2×C4⋊Q8—1581no—
376C2×#125—791no—
377C2×#125—791no—
378C2×#125—1581no—
379C2×#125—1581no—
380C2×C22⋊Q8—1581no—
381C2×C22⋊Q8—1581no—
382C2×C22⋊Q8—1581no—
383C2×C4×Q8—791no—
384C2×C4×Q8—791no—
385C2×C4×Q8—791no—
386C2×C4×Q8—1581no—
387C2×C4×Q8C2×D7911yescharacteristic
388C2×C4×D4—791no—
389C2×C4×D4—791no—
390C2×C4×D4C2×D7911yescharacteristic
391#501—798no—
392#501—798no—
393#500—798no—
394#478—798no—
395#478—798no—
396#477—798no—
397#477—798no—
398#475—798no—
399#474—798no—
400#446—798no—
401#440—798no—
402#440C2×D7918yes—
403C4×SD16—798no—
404C2×#107—791no—
405C2×#107—791no—
406C2×#107—791no—
407C2×#107—791no—
408C2×#107—791no—
409C2×#107C2×D7911yescharacteristic
410C2×#106—791no—
411C2×#106—791no—
412C2×#106—791no—
413C2×C4⋊C8—791no—
414C2×C4⋊C8—791no—
415C2×C4⋊C8—791no—
416C2×#103—791no—
417C2×#103—791no—
418C2×#103C2×D7911yescharacteristic
419C2×#102—791no—
420C2×#102—791no—
421C2×#102C2×D7911yescharacteristic
422C2×#97—791no—
423C2×#97C2×D7911yescharacteristic
424C2×C4×C8—791no—
425C22×Q8—3168no—
426C22×Q8—791no—
427C22×Q8—1581no—
428C22×Q8—1581no—
429C22×Q8—1581no—
430C22×Q8—1588no—
431C22×Q8—1581no—
432C22×Q8C22×D7911yescharacteristic
433C22×D4C22×D7911yescharacteristic
434C23×C4—21no—
435C23×C4—1581no—
436C23×C4—1581no—
437C2×SD16Dic15818yescomplemented
438C2×SD16C22×D7914yes—
439C22×C8—791no—
440C22×C8—791no—
441C22×C8C22×D7911yescharacteristic
442C22×C8C22×D7911yescharacteristic
443C4⋊Q8—794no—
444C4⋊Q8—794no—
445C4⋊Q8—794no—
446C4⋊Q8—794no—
447C4⋊Q8—1582no—
448C4⋊Q8—1582no—
449C4⋊Q8—1582no—
450C4⋊Q8—1588no—
451C4⋊Q8—1582no—
452#125—794no—
453#125—794no—
454#125—1588no—
455#125—1582no—
456#125—1588no—
457#125—1582no—
458C22⋊Q8—1588no—
459C22⋊Q8—1588no—
460C22⋊Q8—1588no—
461C4×Q8—22no—
462C4×Q8—794no—
463C4×Q8—794no—
464C4×Q8—794no—
465C4×Q8—794no—
466C4×Q8—1588no—
467C4×Q8—1582no—
468C4×Q8—1582no—
469C4×Q8C22×D7914yes—
470C4×D4—22no—
471C4×D4—794no—
472C4×D4—794no—
473C4×D4—1582no—
474C4×D4—1582no—
475C4×D4C22×D7914yes—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—791no—
478C2×C4⋊C4—791no—
479C2×C4⋊C4—791no—
480C2×C4⋊C4—791no—
481C2×C4⋊C4—791no—
482C2×C4⋊C4—791no—
483C2×C4⋊C4—791no—
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⋊C4—1581no—
492C2×C4⋊C4—1581no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4C22×D7911yescharacteristic
495C2×C4⋊C4C22×D7911yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1581no—
498C2×C22⋊C4—1581no—
499C2×C42—21no—
500C2×C42—791no—
501C2×C42—791no—
502C2×C42—1581no—
503C2×C42—1581no—
504C2×C42C22×D7911yescharacteristic
505#107—794no—
506#107—794no—
507#107—794no—
508#107—794no—
509#107—794no—
510#107C22×D7914yes—
511#106—794no—
512#106—794no—
513#106—794no—
514C4⋊C8—794no—
515C4⋊C8—794no—
516C4⋊C8—794no—
517#103—794no—
518#103—794no—
519#103C22×D7914yes—
520#102—794no—
521#102—794no—
522#102C22×D7914yes—
523#97—794no—
524#97C22×D7914yes—
525C4×C8—794no—
526C24—21no—
527C2×Q8—22no—
528C2×Q8—21no—
529C2×Q8—3164no—
530C2×Q8—31632no—
531C2×Q8—3164no—
532C2×Q8—3164no—
533C2×Q8—3164no—
534C2×Q8—794no—
535C2×Q8—1584no—
536C2×Q8—1584no—
537C2×Q8—1584no—
538C2×Q8—1584no—
539C2×Q8—1584no—
540C2×Q8C2×Dic15814yescomplemented
541C2×Q8C23×D7912yes—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4C2×Dic15814yes—
545C2×D4C23×D7912yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—44no—
551C22×C4—3164no—
552C22×C4—3164no—
553C22×C4—791no—
554C22×C4—791no—
555C22×C4—791no—
556C22×C4—791no—
557C22×C4—1584no—
558C22×C4—1584no—
559C22×C4—1581no—
560C22×C4—1581no—
561C22×C4—1581no—
562C22×C4—1581no—
563C22×C4D4×D7911yescharacteristic
564C22×C4D4×D7911yescharacteristic
565C22×C4C23×D7911yescharacteristic
566SD16C2×Dic158116yescomplemented
567C2×C8—22no—
568C2×C8—792no—
569C2×C8—792no—
570C2×C8—1582no—
571C2×C8—1582no—
572C2×C8C2×Dic15814yescomplemented
573C2×C8C23×D7912yes—
574C2×C8C23×D7912yes—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—794no—
579C4⋊C4—794no—
580C4⋊C4—794no—
581C4⋊C4—792no—
582C4⋊C4—792no—
583C4⋊C4—792no—
584C4⋊C4—792no—
585C4⋊C4—1584no—
586C4⋊C4—1584no—
587C4⋊C4—1584no—
588C4⋊C4—1584no—
589C4⋊C4—1584no—
590C4⋊C4—1584no—
591C4⋊C4—1584no—
592C4⋊C4—1584no—
593C4⋊C4—1584no—
594C4⋊C4—1581no—
595C4⋊C4—1581no—
596C4⋊C4—1581no—
597C4⋊C4—1581no—
598C4⋊C4—1584no—
599C4⋊C4C23×D7912yes—
600C4⋊C4C23×D7912yes—
601C22⋊C4—24no—
602C22⋊C4—1584no—
603C22⋊C4—1584no—
604C42—24no—
605C42—792no—
606C42—792no—
607C42—792no—
608C42—792no—
609C42—1584no—
610C42—1584no—
611C42D4×D7912yes—
612C42C23×D7912yes—
613C23—24no—
614C23—22no—
615C23—42no—
616C23—42no—
617C23C2×D4×D7911yescharacteristic
618Q8—22no—
619Q8—24no—
620Q8—3168no—
621Q8—3168no—
622Q8—3168no—
623Q8—3168no—
624Q8—1588no—
625Q8C22×Dic15814yescomplemented
626D4—22no—
627D4—24no—
628D4C22×Dic15814yes—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—48no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—3162no—
639C2×C4—3162no—
640C2×C4—3162no—
641C2×C4—3162no—
642C2×C4—3168no—
643C2×C4—3168no—
644C2×C4—794no—
645C2×C4—792no—
646C2×C4—792no—
647C2×C4—792no—
648C2×C4—792no—
649C2×C4—1582no—
650C2×C4—1582no—
651C2×C4—1582no—
652C2×C4—1582no—
653C2×C4—1582no—
654C2×C4—1582no—
655C2×C4—1582no—
656C2×C4C2×D4×D7912yes—
657C2×C4C2×D4×D7912yes—
658C2×C4C2×D4×D7911yescharacteristic
659C2×C4C22×Dic15812yes—
660C2×C4#1457920812yes—
661C2×C4C24×D7911yescharacteristic
662C8—22no—
663C8—1582no—
664C8—1582no—
665C8C22×Dic15814yescomplemented
666C22—24no—
667C22—48no—
668C22—42no—
669C22—42no—
670C22D4×Dic15812yes—
671C22AGL(1,ℤ/8)×D7912yes—
672C22#1909937912yes—
673C22C22×D4×D7911yescharacteristic
674C4—22no—
675C4—24no—
676C4—22no—
677C4—42no—
678C4—42no—
679C4—3162no—
680C4—3162no—
681C4—3162no—
682C4—3162no—
683C4—794no—
684C4—1582no—
685C4—1582no—
686C4—1582no—
687C4D4×Dic15812yes—
688C4C23×Dic15811yescharacteristic
689C4C2×#1457920811yescharacteristic
690C2—44no—
691C2#2377632214yesdirect product factor
692C2C2×D4×Dic15811yescharacteristic
693C2C2×AGL(1,ℤ/8)×D7911yescharacteristic
694C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#440×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79C23
hypercenterC2×#440D79
hypocenterC79C2×#3386
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×#19099289C2semidirect
3. #23776322C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098971C2semidirect
6. C2×#19098967C2semidirect
7. C2×#19098858C2semidirect
8. C2×#19098856C2semidirect
9. C2×#19098846C2semidirect
13. C2×#19098691C2semidirect
19. #19099289C22semidirect
40. #19098972C22semidirect
41. #19098971C22semidirect
42. #19098967C22semidirect
45. #19098858C22semidirect
46. #19098856C22semidirect
47. #19098846C22semidirect
49. #19098691C22semidirect
160. C2×SD16×C79Q8semidirect
237. C2×Q8×C79C2×Q8semidirect
251. SD16×C79C2×Q8semidirect
253. C2×C8×C79C2×Q8semidirect
272. Q8×C79C22×Q8semidirect
315. C8×C79C22×Q8semidirect
344. C2×C79#3386semidirect
364. C79C2×#3386semidirect
437. C2×SD16Dic158semidirect
540. C2×Q8C2×Dic158semidirect
566. SD16C2×Dic158semidirect
572. C2×C8C2×Dic158semidirect
625. Q8C22×Dic158semidirect
665. C8C22×Dic158semidirect
691. C2#23776322direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992892
C2×D4×Dic1582
#237763222
C2×#190989722
C2×#190989712
C2×#190989672
C2×#190988582
C2×#190988562
C2×#190988462
C2×#190988652
C2×#190988632
C2×#190988412
C2×#190986912
C2×#190986642
C2×SD16×Dic792
C2×#440×C792
C2×#338679