Finite Group Databasebeta

← C2×#23776359 #35168811

Subgroups — C2×#23776359 #35168811

Order 20224.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099272C211yesmaximal, characteristic, complemented
2C2×#19099270C211yesmaximal, characteristic, complemented
3#23776359C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098970C211yesmaximal, characteristic, complemented
6C2×#19098963C211yesmaximal, characteristic, complemented
7C2×#19098865C211yesmaximal, characteristic, complemented
8C2×#19098865C211yesmaximal, characteristic, complemented
9C2×#19098863C211yesmaximal, characteristic, complemented
10C2×#19098861C211yesmaximal, characteristic, complemented
11C2×#19098843C211yesmaximal, characteristic, complemented
12C2×#19098841C211yesmaximal, characteristic, complemented
13C2×#19098691C211yesmaximal, characteristic, complemented
14C2×#19098675C211yesmaximal, characteristic
15C2×D8×Dic79C211yesmaximal, characteristic
16C2×#442×C79C211yesmaximal, characteristic
17#19099272—24no—
18#19099272C2218yescomplemented
19#19099270—24no—
20#19099270C2218yescomplemented
21C2×#14579161C2211yescharacteristic
22C2×#14579160C2211yescharacteristic
23C2×#14579153C2211yescharacteristic
24C2×#14579152C2211yescharacteristic
25C2×#14579152C2211yescharacteristic
26C2×#14579152C2211yescharacteristic
27C2×#14579140—21no—
28C2×#14579140—21no—
29C2×#14579138—21no—
30C2×#14579138—21no—
31C2×#14579138—21no—
32C2×#14579138—21no—
33C2×C4×Dic158C2211yescharacteristic
34C2×D4×Dic79C2211yescharacteristic
35C2×D4×Dic79C2211yescharacteristic
36C2×D4×Dic79C2211yescharacteristic
37C2×D4×Dic79C2211yescharacteristic
38C22×C4⋊Dic79—21no—
39C22×Dic79⋊C4—21no—
40#19098972C2218yescomplemented
41#19098970C2218yescomplemented
42#19098963C2218yescomplemented
43#19098865C2218yescomplemented
44#19098865C2218yescomplemented
45#19098863C2218yescomplemented
46#19098861C2218yescomplemented
47#19098843C2218yescomplemented
48#19098841C2218yescomplemented
49#19098691C2218yescomplemented
50#19098675C2218yes—
51D8×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×#14579082C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579082C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×D8×C79C2211yescharacteristic
70C2×C4×D4×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#442×C79C2218yes—
73C2×#106×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158D411yescharacteristic
80C23×Dic79—21no—
81C23×Dic79—21no—
82C23×Dic79—21no—
83C23×Dic79—21no—
84C22×C79⋊C8C2311yescharacteristic
85C22×C79⋊C8C2311yescharacteristic
86#14579161—22no—
87#14579161C2314yes—
88#14579160—22no—
89#14579160C2314yes—
90#14579153—22no—
91#14579153C2314yes—
92#14579152—22no—
93#14579152—22no—
94#14579152—22no—
95#14579152C2314yes—
96#14579152C2314yes—
97#14579152C2314yes—
98#14579140—28no—
99#14579140—28no—
100#14579138—28no—
101#14579138—28no—
102#14579138—28no—
103#14579138—28no—
104C4×Dic158D414yes—
105C4×Dic158C2314yes—
106D4×Dic79—22no—
107D4×Dic79—22no—
108D4×Dic79—22no—
109D4×Dic79—22no—
110D4×Dic79C2314yes—
111D4×Dic79C2314yes—
112D4×Dic79C2314yes—
113D4×Dic79C2314yes—
114C2×C4⋊Dic79—21no—
115C2×C4⋊Dic79—21no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—28no—
119C2×C4⋊Dic79D411yescharacteristic
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—28no—
131C2×Dic79⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×C4×Dic79C2311yescharacteristic
138C2×C4×Dic79C2311yescharacteristic
139#14579095C2314yes—
140#14579095C2314yes—
141#14579094C2314yes—
142#14579094C2314yes—
143#14579094C2314yes—
144#14579093C2314yes—
145#14579093C2314yes—
146#14579092C2314yes—
147C4⋊(C79⋊C8)C2314yes—
148Dic79⋊C8C2314yes—
149Dic79⋊C8C2314yes—
150#14579082C2314yes—
151#14579082C2314yes—
152#14579082C2314yes—
153#14579082C2314yes—
154#14579071C2314yes—
155C8×Dic79C2314yes—
156C22×D4×C79C2311yescharacteristic
157C22×D4×C79C2311yescharacteristic
158C23×C4×C79—21no—
159C23×C4×C79—21no—
160C2×D8×C79Q818yescomplemented
161C2×D8×C79C2314yes—
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164C4×D4×C79—22no—
165C4×D4×C79—22no—
166C4×D4×C79C2314yes—
167C4×D4×C79C2314yes—
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C22⋊C4×C79—21no—
171C2×C22⋊C4×C79—21no—
172C2×C42×C79C2311yescharacteristic
173#106×C79C2314yes—
174#102×C79C2314yes—
175#102×C79C2314yes—
176#97×C79C2314yes—
177C2×Dic158—24no—
178C2×Dic158—24no—
179C2×Dic158—42no—
180C2×Dic158—82no—
181C2×Dic158—82no—
182C2×Dic158C2×D414yes—
183C22×Dic79—24no—
184C22×Dic79—24no—
185C22×Dic79—24no—
186C22×Dic79—24no—
187C22×Dic79—21no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79—21no—
191C22×Dic79—44no—
192C22×Dic79—82no—
193C22×Dic79—82no—
194C22×Dic79—82no—
195C22×Dic79C2×D411yescharacteristic
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C2×C79⋊C8—22no—
200C2×C79⋊C8—22no—
201C2×C79⋊C8C2412yes—
202C2×C79⋊C8C2412yes—
203C4⋊Dic79—24no—
204C4⋊Dic79—24no—
205C4⋊Dic79—24no—
206C4⋊Dic79—24no—
207C4⋊Dic79—21no—
208C4⋊Dic79—21no—
209C4⋊Dic79—21no—
210C4⋊Dic79—21no—
211C4⋊Dic79C2×D414yes—
212C4⋊Dic79C2412yes—
213C4⋊Dic79C2412yes—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4C2×D414yes—
223Dic79⋊C4C2×D414yes—
224C22⋊Dic79—24no—
225C22⋊Dic79—24no—
226C22⋊Dic79—24no—
227C22⋊Dic79—24no—
228C4×Dic79C2×D412yes—
229C4×Dic79C2×D412yes—
230C4×Dic79C2412yes—
231C4×Dic79C2412yes—
232C24×C79—21no—
233C24×C79—21no—
234C2×D4×C79—21no—
235C2×D4×C79—21no—
236C2×D4×C79—22no—
237C2×D4×C79—22no—
238C2×D4×C79C2×Q814yes—
239C2×D4×C79C2×Q814yes—
240C2×D4×C79C2412yes—
241C2×D4×C79C2412yes—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—24no—
245C22×C4×C79—24no—
246C22×C4×C79—44no—
247C22×C4×C79—82no—
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2411yescharacteristic
251D8×C79C2×Q8116yescomplemented
252C2×C8×C79—22no—
253C2×C8×C79C2×Q814yes—
254C2×C8×C79C2412yes—
255C2×C8×C79C2412yes—
256C4⋊C4×C79—21no—
257C4⋊C4×C79—21no—
258C4⋊C4×C79C2412yes—
259C4⋊C4×C79C2412yes—
260C22⋊C4×C79—24no—
261C22⋊C4×C79—24no—
262C42×C79C2×D412yes—
263C42×C79C2412yes—
264C23×C79—24no—
265C23×C79—24no—
266C23×C79—22no—
267C23×C79—22no—
268C23×C79—42no—
269C23×C79—42no—
270C23×C79—42no—
271C23×C79—42no—
272C23×C79C22×D411yescharacteristic
273D4×C79—24no—
274D4×C79—24no—
275D4×C79—22no—
276D4×C79—22no—
277D4×C79C22×Q814yes—
278D4×C79C22×Q814yes—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—48no—
284C2×C4×C79—42no—
285C2×C4×C79—42no—
286C2×C4×C79—84no—
287C2×C4×C79C22×D412yes—
288C2×C4×C79C22×D412yes—
289C2×C4×C79C22×D411yescharacteristic
290C2×C4×C79C22×Q812yes—
291C2×C4×C792−1+412yes—
292C2×C4×C79C2511yescharacteristic
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—48no—
302C2×Dic79—42no—
303C2×Dic79—42no—
304C2×Dic79—42no—
305C2×Dic79—42no—
306C2×Dic79—84no—
307C2×Dic79—84no—
308C2×Dic79—84no—
309C2×Dic79C22×D412yes—
310C2×Dic79C22×D412yes—
311C2×Dic79C22×D412yes—
312C2×Dic79C22×D412yes—
313Dic158—44no—
314Dic158—84no—
315Dic158—84no—
316C8×C79—22no—
317C8×C79C22×Q814yes—
318C79⋊C8—22no—
319C79⋊C8—22no—
320C22×C79—24no—
321C22×C79—24no—
322C22×C79—48no—
323C22×C79—48no—
324C22×C79—42no—
325C22×C79—42no—
326C22×C79—42no—
327C22×C79—42no—
328C22×C79D4×Q812yes—
329C22×C79#57512yes—
330C22×C79#57612yes—
331C22×C79C23×D411yescharacteristic
332C4×C79—22no—
333C4×C79—22no—
334C4×C79—42no—
335C4×C79—42no—
336C4×C79D4×Q812yes—
337C4×C79C23×Q811yescharacteristic
338C4×C79C2×2−1+411yescharacteristic
339Dic79—22no—
340Dic79—22no—
341Dic79—22no—
342Dic79—22no—
343Dic79—42no—
344Dic79—42no—
345Dic79—42no—
346Dic79—42no—
347C2×#3389—791nomaximal, Sylow
348C2×C79—44no—
349C2×C79—44no—
350C2×C79#338914yescomplemented
351C2×C79C2×D4×Q811yescharacteristic
352C2×C79C2×#57511yescharacteristic
353C2×C79C2×#57611yescharacteristic
354C2×#554—791no—
355C2×#554—791no—
356#3389—7916no—
357C2×#501—791no—
358C2×#501—791no—
359C2×#499—791no—
360C2×#478—791no—
361C2×#478—791no—
362C2×#478—791no—
363C2×#478—791no—
364C2×#474—791no—
365C2×#474—791no—
366C2×#446—791no—
367C2×#442—791no—
368C2×#442D7911yescharacteristic
369C2×C4×D8—791no—
370C79C2×#338911yescharacteristic, complemented, Sylow
371C22×D8C2×D7911yescharacteristic
372#554—798no—
373#554—798no—
374#554—1584no—
375#554—1584no—
376C2×C4⋊Q8—791no—
377C2×C4⋊Q8—791no—
378C2×#125—791no—
379C2×#125—791no—
380C2×#125—791no—
381C2×#125—791no—
382C2×C22⋊Q8—1581no—
383C2×C22⋊Q8—1581no—
384C2×C22⋊Q8—1581no—
385C2×C22⋊Q8—1581no—
386C2×C22⋊Q8—1581no—
387C2×C22⋊Q8—1581no—
388C2×C4×Q8—791no—
389C2×C4×D4—791no—
390C2×C4×D4—791no—
391C2×C4×D4—791no—
392C2×C4×D4—791no—
393C2×C4×D4C2×D7911yescharacteristic
394C2×C4×D4C2×D7911yescharacteristic
395C22×C4⋊C4—1581no—
396C22×C4⋊C4—1581no—
397#501—798no—
398#501—798no—
399#499—798no—
400#478—798no—
401#478—798no—
402#478—798no—
403#478—798no—
404#474—798no—
405#474—798no—
406#446—798no—
407#442—798no—
408#442C2×D7918yes—
409C4×D8—798no—
410C2×#107—791no—
411C2×#107—791no—
412C2×#107—791no—
413C2×#107—791no—
414C2×#107—791no—
415C2×#106—791no—
416C2×#106—791no—
417C2×#106—791no—
418C2×#106C2×D7911yescharacteristic
419C2×C4⋊C8—791no—
420C2×C4⋊C8—791no—
421C2×C4⋊C8—791no—
422C2×#102—791no—
423C2×#102—791no—
424C2×#102—791no—
425C2×#102—791no—
426C2×#102C2×D7911yescharacteristic
427C2×#102C2×D7911yescharacteristic
428C2×#97—791no—
429C2×#97C2×D7911yescharacteristic
430C2×C4×C8—791no—
431C22×Q8—791no—
432C22×Q8—1581no—
433C22×Q8—1581no—
434C22×D4C22×D7911yescharacteristic
435C22×D4C22×D7911yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—1581no—
439C23×C4—1581no—
440C23×C4—1581no—
441C23×C4—1581no—
442C2×D8Dic15818yescomplemented
443C2×D8C22×D7914yes—
444C22×C8—791no—
445C22×C8—791no—
446C22×C8C22×D7911yescharacteristic
447C22×C8C22×D7911yescharacteristic
448C4⋊Q8—794no—
449C4⋊Q8—794no—
450C4⋊Q8—1582no—
451C4⋊Q8—1582no—
452#125—794no—
453#125—794no—
454#125—794no—
455#125—794no—
456#125—1582no—
457#125—1582no—
458#125—1582no—
459#125—1582no—
460C22⋊Q8—1588no—
461C22⋊Q8—1588no—
462C22⋊Q8—1588no—
463C22⋊Q8—1588no—
464C22⋊Q8—1588no—
465C22⋊Q8—1588no—
466C4×Q8—794no—
467C4×Q8—794no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—794no—
471C4×D4—794no—
472C4×D4—794no—
473C4×D4—794no—
474C4×D4—1582no—
475C4×D4—1582no—
476C4×D4—1582no—
477C4×D4—1582no—
478C4×D4C22×D7914yes—
479C4×D4C22×D7914yes—
480C2×C4⋊C4—791no—
481C2×C4⋊C4—791no—
482C2×C4⋊C4—791no—
483C2×C4⋊C4—791no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—791no—
486C2×C4⋊C4—791no—
487C2×C4⋊C4—1588no—
488C2×C4⋊C4—1588no—
489C2×C4⋊C4—1581no—
490C2×C4⋊C4—1581no—
491C2×C4⋊C4—1581no—
492C2×C4⋊C4—1581no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4—1581no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—1581no—
504C2×C22⋊C4—1581no—
505C2×C22⋊C4—1581no—
506C2×C22⋊C4—1581no—
507C2×C42—791no—
508C2×C42—791no—
509C2×C42C22×D7911yescharacteristic
510#107—794no—
511#107—794no—
512#107—794no—
513#107—794no—
514#107—794no—
515#106—794no—
516#106—794no—
517#106—794no—
518#106C22×D7914yes—
519C4⋊C8—794no—
520C4⋊C8—794no—
521C4⋊C8—794no—
522#102—794no—
523#102—794no—
524#102—794no—
525#102—794no—
526#102C22×D7914yes—
527#102C22×D7914yes—
528#97—794no—
529#97C22×D7914yes—
530C4×C8—794no—
531C24—21no—
532C24—21no—
533C2×Q8—3162no—
534C2×Q8—794no—
535C2×Q8—6322no—
536C2×Q8—6322no—
537C2×Q8—1584no—
538C2×Q8—1584no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4C2×Dic15814yes—
544C2×D4C2×Dic15814yes—
545C2×D4C23×D7912yes—
546C2×D4C23×D7912yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—44no—
552C22×C4—82no—
553C22×C4—3164no—
554C22×C4—791no—
555C22×C4—791no—
556C22×C4—791no—
557C22×C4—791no—
558C22×C4—6322no—
559C22×C4—6322no—
560C22×C4—6322no—
561C22×C4—1584no—
562C22×C4—1581no—
563C22×C4—1581no—
564C22×C4—1581no—
565C22×C4—1581no—
566C22×C4—1584no—
567C22×C4—1584no—
568C22×C4—1584no—
569C22×C4D4×D7911yescharacteristic
570C22×C4D4×D7911yescharacteristic
571C22×C4C23×D7911yescharacteristic
572D8C2×Dic158116yescomplemented
573C2×C8—22no—
574C2×C8—792no—
575C2×C8—792no—
576C2×C8—1582no—
577C2×C8—1582no—
578C2×C8C2×Dic15814yes—
579C2×C8C23×D7912yes—
580C2×C8C23×D7912yes—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—794no—
584C4⋊C4—794no—
585C4⋊C4—794no—
586C4⋊C4—792no—
587C4⋊C4—792no—
588C4⋊C4—792no—
589C4⋊C4—792no—
590C4⋊C4—1584no—
591C4⋊C4—1584no—
592C4⋊C4—1584no—
593C4⋊C4—1584no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1584no—
597C4⋊C4—1584no—
598C4⋊C4—1584no—
599C4⋊C4—1581no—
600C4⋊C4—1581no—
601C4⋊C4—1581no—
602C4⋊C4—1581no—
603C4⋊C4—1584no—
604C4⋊C4C23×D7912yes—
605C4⋊C4C23×D7912yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—1584no—
609C22⋊C4—1584no—
610C22⋊C4—1584no—
611C22⋊C4—1584no—
612C42—792no—
613C42—792no—
614C42—792no—
615C42—792no—
616C42D4×D7912yes—
617C42C23×D7912yes—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23C2×D4×D7911yescharacteristic
627Q8—3164no—
628Q8—6324no—
629Q8—6324no—
630D4—22no—
631D4—22no—
632D4—24no—
633D4—24no—
634D4C22×Dic15814yes—
635D4C22×Dic15814yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—48no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—84no—
644C2×C4—3162no—
645C2×C4—3162no—
646C2×C4—3162no—
647C2×C4—3162no—
648C2×C4—3168no—
649C2×C4—792no—
650C2×C4—792no—
651C2×C4—792no—
652C2×C4—792no—
653C2×C4—6324no—
654C2×C4—6324no—
655C2×C4—6324no—
656C2×C4—1582no—
657C2×C4—1582no—
658C2×C4—1582no—
659C2×C4—1582no—
660C2×C4—1582no—
661C2×C4—1582no—
662C2×C4—1582no—
663C2×C4—1582no—
664C2×C4C2×D4×D7912yes—
665C2×C4C2×D4×D7912yes—
666C2×C4C2×D4×D7911yescharacteristic
667C2×C4C22×Dic15812yes—
668C2×C4#1457920812yes—
669C2×C4C24×D7911yescharacteristic
670C8—22no—
671C8—1582no—
672C8—1582no—
673C8C22×Dic15814yes—
674C22—24no—
675C22—24no—
676C22—42no—
677C22—42no—
678C22—48no—
679C22—48no—
680C22—42no—
681C22—42no—
682C22D4×Dic15812yes—
683C22#1909935912yes—
684C22#1909936712yes—
685C22C22×D4×D7911yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—3162no—
691C4—3162no—
692C4—3162no—
693C4—3162no—
694C4—1582no—
695C4—1582no—
696C4—1582no—
697C4—1582no—
698C4D4×Dic15812yes—
699C4C23×Dic15811yescharacteristic
700C4C2×#1457920811yescharacteristic
701C2—44no—
702C2—44no—
703C2#2377635914yesdirect product factor
704C2C2×D4×Dic15811yescharacteristic
705C2C2×#1909935911yescharacteristic
706C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#442×C79C2
socleC23×C79C22×D4
prime radicalC22×D8×C79C22
hypercenterC2×#442D79
hypocenterC79C2×#3389
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×#19099272C2semidirect
2. C2×#19099270C2semidirect
3. #23776359C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098970C2semidirect
6. C2×#19098963C2semidirect
7. C2×#19098865C2semidirect
8. C2×#19098865C2semidirect
9. C2×#19098863C2semidirect
10. C2×#19098861C2semidirect
11. C2×#19098843C2semidirect
12. C2×#19098841C2semidirect
13. C2×#19098691C2semidirect
18. #19099272C22semidirect
20. #19099270C22semidirect
40. #19098972C22semidirect
41. #19098970C22semidirect
42. #19098963C22semidirect
43. #19098865C22semidirect
44. #19098865C22semidirect
45. #19098863C22semidirect
46. #19098861C22semidirect
47. #19098843C22semidirect
48. #19098841C22semidirect
49. #19098691C22semidirect
160. C2×D8×C79Q8semidirect
251. D8×C79C2×Q8semidirect
350. C2×C79#3389semidirect
370. C79C2×#3389semidirect
442. C2×D8Dic158semidirect
572. D8C2×Dic158semidirect
703. C2#23776359direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992722
C2×#190992702
#237763592
C2×#190989722
C2×#190989702
C2×#190989632
C2×#190988652
C2×#190988632
C2×#190988612
C2×#190988432
C2×#190988412
C2×#190986912
C2×#190986752
C2×D8×Dic792
C2×#442×C792
C2×#338979