Finite Group Databasebeta

← C2×#475×D79 #35155742

Subgroups — C2×#475×D79 #35155742

Order 20224.

2358 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D79C211yesmaximal, characteristic
2C2×C4×Q8×D79C211yesmaximal, characteristic
3C2×#19098849C211yesmaximal, characteristic, complemented
4C2×#19098848C211yesmaximal, characteristic, complemented
5C2×#19098847C212yesmaximal, complemented
6C2×#19098846C212yesmaximal, complemented
7C2×#19098845C211yesmaximal, characteristic, complemented
8#475×D79C2116yesmaximal, direct product factor
9C2×#106×D79C212yesmaximal
10C2×C4⋊C8×D79C211yesmaximal, characteristic
11C2×#103×D79C212yesmaximal
12C2×#475×C79C211yesmaximal, characteristic, complemented
13C22×Q8×D79—21no—
14C22×Q8×D79C2211yescharacteristic
15C22×C8×D79C2212yes—
16C2×#14579161C2211yescharacteristic
17C2×#14579160—21no—
18C2×#14579160C2212yes—
19C2×#14579159—21no—
20C4⋊Q8×D79—24no—
21C4⋊Q8×D79C2218yes—
22C2×Q8×Dic79C2211yescharacteristic
23C2×C4×Dic158—21no—
24C2×C4×Dic158C2211yescharacteristic
25C2×#14579126—21no—
26C2×#14579126C2211yescharacteristic
27C4×Q8×D79—24no—
28C4×Q8×D79C2218yes—
29C2×C4⋊C4×D79—21no—
30C2×C4⋊C4×D79—21no—
31C2×C4⋊C4×D79C2211yescharacteristic
32C2×C4⋊C4×D79C2212yes—
33C2×C42×D79—21no—
34C2×C42×D79C2211yescharacteristic
35#19098849C2218yescomplemented
36#19098848C2218yescomplemented
37#19098847C22116yescomplemented
38#19098846C22116yescomplemented
39#19098845C2218yescomplemented
40C2×#14579093C2212yes—
41C2×#14579092C2212yes—
42C2×#14579092C2212yes—
43#106×D79C22116yes—
44C2×C4⋊(C79⋊C8)C2211yescharacteristic
45C2×Dic79⋊C8C2212yes—
46C4⋊C8×D79C2218yes—
47C2×#14579086C2212yes—
48C2×#14579085C2212yes—
49C2×#14579084C2212yes—
50#103×D79C22116yes—
51C2×C4⋊Q8×C79C2211yescharacteristic
52C2×C4×Q8×C79C2211yescharacteristic
53#475×C79C2218yescomplemented
54C2×#106×C79C2212yes—
55C2×C4⋊C8×C79C2211yescharacteristic
56C2×#103×C79C2212yes—
57C22×Dic158—21no—
58C22×Dic158—21no—
59C22×Dic158—22no—
60C22×Dic158C2311yescharacteristic
61C2×Q8×D79—22no—
62C2×Q8×D79—28no—
63C2×Q8×D79—24no—
64C2×Q8×D79—48no—
65C2×Q8×D79Q818yescomplemented
66C2×Q8×D79C2314yes—
67C22×C4×D79—21no—
68C22×C4×D79—21no—
69C22×C4×D79—22no—
70C22×C4×D79D411yescharacteristic
71C22×C4×D79D411yescharacteristic
72C22×C4×D79C2311yescharacteristic
73C22×C79⋊C8C2312yes—
74C2×C8×D79—28no—
75C2×C8×D79C2318yes—
76#14579161—22no—
77#14579161C2314yes—
78#14579160—24no—
79#14579160—28no—
80#14579160C2318yes—
81#14579159—28no—
82Q8×Dic79—22no—
83Q8×Dic79C2314yes—
84C4×Dic158—22no—
85C4×Dic158—28no—
86C4×Dic158C2314yes—
87#14579126—22no—
88#14579126—28no—
89#14579126C2314yes—
90C2×C4⋊Dic79—21no—
91C2×C4⋊Dic79—21no—
92C2×C4⋊Dic79C2311yescharacteristic
93C2×C4⋊Dic79C2312yes—
94C2×Dic79⋊C4—21no—
95C2×Dic79⋊C4—21no—
96C2×Dic79⋊C4—22no—
97C2×Dic79⋊C4—21no—
98C2×Dic79⋊C4—22no—
99C4⋊C4×D79—28no—
100C4⋊C4×D79—28no—
101C4⋊C4×D79—22no—
102C4⋊C4×D79—24no—
103C4⋊C4×D79C2314yes—
104C4⋊C4×D79C2318yes—
105C2×C4×Dic79—21no—
106C2×C4×Dic79—21no—
107C2×C4×Dic79—21no—
108C2×C4×Dic79D411yescharacteristic
109C2×C4×Dic79D411yescharacteristic
110C2×C4×Dic79C2311yescharacteristic
111C42×D79—28no—
112C42×D79D414yes—
113C42×D79C2314yes—
114#14579093C2318yes—
115#14579092C2318yes—
116#14579092C2318yes—
117C4⋊(C79⋊C8)C2314yes—
118Dic79⋊C8C2318yes—
119#14579086C2318yes—
120#14579085C2318yes—
121#14579084C2318yes—
122C22×Q8×C79—21no—
123C22×Q8×C79C2311yescharacteristic
124C22×C8×C79C2312yes—
125C4⋊Q8×C79—22no—
126C4⋊Q8×C79C2314yes—
127C4×Q8×C79—22no—
128C4×Q8×C79C2314yes—
129C2×C4⋊C4×C79—21no—
130C2×C4⋊C4×C79—21no—
131C2×C4⋊C4×C79C2311yescharacteristic
132C2×C4⋊C4×C79C2312yes—
133C2×C42×C79—21no—
134C2×C42×C79C2311yescharacteristic
135#106×C79C2318yes—
136C4⋊C8×C79C2314yes—
137#103×C79C2318yes—
138C23×D79C2×D411yescharacteristic
139C2×Dic158—28no—
140C2×Dic158—24no—
141C2×Dic158—28no—
142C2×Dic158—21no—
143C2×Dic158—24no—
144C2×Dic158—22no—
145C2×Dic158—48no—
146C2×Dic158—44no—
147C2×Dic158C2×Q814yescomplemented
148C2×Dic158C2412yes—
149Q8×D79—216no—
150Q8×D79—28no—
151Q8×D79—432no—
152Q8×D79C2×Q8116yescomplemented
153C22×Dic79—21no—
154C22×Dic79—22no—
155C22×Dic79—21no—
156C22×Dic79C2×D411yescharacteristic
157C22×Dic79C2×D411yescharacteristic
158C22×Dic79C2×D411yescharacteristic
159C2×C4×D79—28no—
160C2×C4×D79—24no—
161C2×C4×D79—24no—
162C2×C4×D79—28no—
163C2×C4×D79—24no—
164C2×C4×D79—48no—
165C2×C4×D79—44no—
166C2×C4×D79SD1618yes—
167C2×C4×D79C2×D414yes—
168C2×C4×D79C2×D412yes—
169C2×C4×D79C2×D414yes—
170C2×C4×D79C2×Q814yes—
171C2×C4×D79#4114yes—
172C2×C4×D79C2412yes—
173C2×C79⋊C8—24no—
174C2×C79⋊C8C2414yes—
175C8×D79—216no—
176C4⋊Dic79—24no—
177C4⋊Dic79—24no—
178C4⋊Dic79—21no—
179C4⋊Dic79—22no—
180C4⋊Dic79C2414yes—
181C4⋊Dic79C2412yes—
182Dic79⋊C4—24no—
183Dic79⋊C4—28no—
184Dic79⋊C4—24no—
185Dic79⋊C4—28no—
186Dic79⋊C4—24no—
187C4×Dic79—24no—
188C4×Dic79—24no—
189C4×Dic79—24no—
190C4×Dic79C2×D412yes—
191C4×Dic79C2×D414yes—
192C4×Dic79C2×D414yes—
193C4×Dic79C2412yes—
194C2×Q8×C79—21no—
195C2×Q8×C79—24no—
196C2×Q8×C79—22no—
197C2×Q8×C79—44no—
198C2×Q8×C79C2×Q814yescomplemented
199C2×Q8×C79C2412yes—
200C22×C4×C79—21no—
201C22×C4×C79—22no—
202C22×C4×C79—21no—
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2411yescharacteristic
206C2×C8×C79—24no—
207C2×C8×C79C2414yes—
208C4⋊C4×C79—24no—
209C4⋊C4×C79—24no—
210C4⋊C4×C79—21no—
211C4⋊C4×C79—22no—
212C4⋊C4×C79C2414yes—
213C4⋊C4×C79C2412yes—
214C42×C79—24no—
215C42×C79C2×D412yes—
216C42×C79C2412yes—
217C23×C79C22×D411yescharacteristic
218C22×D79C22⋊Q814yes—
219C22×D79C2×SD1614yes—
220C22×D79#13714yes—
221C22×D79C22×D412yes—
222Q8×C79—24no—
223Q8×C79—22no—
224Q8×C79—48no—
225Q8×C79C22×Q814yescomplemented
226C2×C4×C79—24no—
227C2×C4×C79—22no—
228C2×C4×C79—22no—
229C2×C4×C79—22no—
230C2×C4×C79—24no—
231C2×C4×C79—44no—
232C2×C4×C79—42no—
233C2×C4×C79C2×SD1614yes—
234C2×C4×C79C22×D412yes—
235C2×C4×C79C22×D411yescharacteristic
236C2×C4×C79C22×D412yes—
237C2×C4×C79C22×Q812yes—
238C2×C4×C79C2×#4112yes—
239C2×C4×C79C2511yescharacteristic
240C2×Dic79—24no—
241C2×Dic79—22no—
242C2×Dic79—22no—
243C2×Dic79—22no—
244C2×Dic79—24no—
245C2×Dic79—44no—
246C2×Dic79—42no—
247C2×Dic79C22⋊Q814yes—
248C2×Dic79C2×SD1614yes—
249C2×Dic79C22×D412yes—
250C2×Dic79C22×D412yes—
251C2×Dic79C22×D412yes—
252C4×D79—216no—
253C4×D79—28no—
254C4×D79—416no—
255C4×D79—48no—
256C4×D79C22⋊Q818yes—
257C4×D79C2×SD16116yes—
258C4×D79C22×Q814yes—
259C4×D79C2×#4114yes—
260Dic158—24no—
261Dic158—22no—
262Dic158—216no—
263Dic158—48no—
264Dic158—416no—
265Dic158C22×Q814yescomplemented
266C8×C79—24no—
267C79⋊C8—24no—
268C22×C79C2×C22⋊Q812yes—
269C22×C79C22×SD1612yes—
270C22×C79C2×#13712yes—
271C22×C79C23×D411yescharacteristic
272C2×D79#475116yesdirect product factor
273C2×D79C2×C22⋊Q814yes—
274C2×D79C22×SD1614yes—
275C2×D79C2×#13714yes—
276C4×C79—24no—
277C4×C79—22no—
278C4×C79—44no—
279C4×C79—42no—
280C4×C79C2×C22⋊Q812yes—
281C4×C79C22×SD1614yes—
282C4×C79C23×Q811yescharacteristic
283C4×C79C22×#4111yescharacteristic
284Dic79—24no—
285Dic79—22no—
286Dic79—44no—
287Dic79—42no—
288Dic79C2×C22⋊Q814yes—
289Dic79C22×SD1614yes—
290C22×#475—791nomaximal, Sylow
291C2×C79C2×#47514yescomplemented
292C2×C79C22×C22⋊Q811yescharacteristic
293C2×C79C23×SD1611yescharacteristic
294C2×C79C22×#13711yescharacteristic
295D79C2×#47518yesdirect product factor
296C22×C4⋊Q8—791no—
297C22×C4×Q8—791no—
298C2×#475—7916no—
299C2×#475—792no—
300C2×#475—791no—
301C2×#475—792no—
302C2×#475—791no—
303C2×#475—791no—
304C2×#475D7911yescharacteristic, direct product factor
305C22×#106—792no—
306C22×C4⋊C8—791no—
307C22×#103—792no—
308C79C22×#47511yescharacteristic, complemented, Sylow
309C23×Q8—791no—
310C23×Q8—1581no—
311C23×C8—792no—
312C2×C4⋊Q8—798no—
313C2×C4⋊Q8—792no—
314C2×C4⋊Q8—791no—
315C2×C4⋊Q8—1581no—
316C2×C4⋊Q8—1584no—
317C2×C4⋊Q8—1581no—
318C2×C4⋊Q8C2×D7911yescharacteristic
319C2×C4×Q8—791no—
320C2×C4×Q8—798no—
321C2×C4×Q8—791no—
322C2×C4×Q8—791no—
323C2×C4×Q8—1581no—
324C2×C4×Q8—1581no—
325C2×C4×Q8—1584no—
326C2×C4×Q8C2×D7911yescharacteristic
327C22×C4⋊C4—792no—
328C22×C4⋊C4—791no—
329C22×C4⋊C4—1581no—
330C22×C4⋊C4—1581no—
331C22×C42—791no—
332C22×C42—1581no—
333#475—798no—
334#475—798no—
335#475—7916no—
336#475—798no—
337#475—7916no—
338#475C2×D7918yesdirect product factor
339C2×#106—792no—
340C2×#106—792no—
341C2×#106—792no—
342C2×#106—7916no—
343C2×#106C2×D7912yes—
344C2×C4⋊C8—792no—
345C2×C4⋊C8—791no—
346C2×C4⋊C8—798no—
347C2×C4⋊C8C2×D7911yescharacteristic
348C2×#103—792no—
349C2×#103—792no—
350C2×#103—792no—
351C2×#103—7916no—
352C2×#103C2×D7912yes—
353C22×Q8—21no—
354C22×Q8—3168no—
355C22×Q8—798no—
356C22×Q8—794no—
357C22×Q8—791no—
358C22×Q8—1582no—
359C22×Q8—1581no—
360C22×Q8—1588no—
361C22×Q8—1582no—
362C22×Q8—1584no—
363C22×Q8—1581no—
364C22×Q8C22×D7911yescharacteristic
365C23×C4—791no—
366C23×C4—791no—
367C23×C4—791no—
368C23×C4—1582no—
369C23×C4—1581no—
370C23×C4—1581no—
371C22×C8—792no—
372C22×C8—798no—
373C22×C8—1588no—
374C22×C8C22×D7912yes—
375C4⋊Q8—22no—
376C4⋊Q8—798no—
377C4⋊Q8—794no—
378C4⋊Q8—1588no—
379C4⋊Q8—1584no—
380C4⋊Q8—1588no—
381C4⋊Q8—1582no—
382C4⋊Q8C22×D7914yes—
383C4×Q8—22no—
384C4×Q8—794no—
385C4×Q8—794no—
386C4×Q8—794no—
387C4×Q8—1588no—
388C4×Q8—1588no—
389C4×Q8—1582no—
390C4×Q8—1582no—
391C4×Q8—1582no—
392C4×Q8C22×D7914yes—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—791no—
396C2×C4⋊C4—792no—
397C2×C4⋊C4—794no—
398C2×C4⋊C4—798no—
399C2×C4⋊C4—1582no—
400C2×C4⋊C4—1584no—
401C2×C4⋊C4—1588no—
402C2×C4⋊C4—1588no—
403C2×C4⋊C4—1581no—
404C2×C4⋊C4—1582no—
405C2×C4⋊C4—1581no—
406C2×C4⋊C4—1581no—
407C2×C4⋊C4—1582no—
408C2×C4⋊C4—1581no—
409C2×C4⋊C4—1581no—
410C2×C4⋊C4C22×D7911yescharacteristic
411C2×C4⋊C4C22×D7912yes—
412C2×C42—21no—
413C2×C42—791no—
414C2×C42—791no—
415C2×C42—791no—
416C2×C42—794no—
417C2×C42—794no—
418C2×C42—1588no—
419C2×C42—1581no—
420C2×C42—1581no—
421C2×C42—1581no—
422C2×C42C22×D7911yescharacteristic
423#106—798no—
424#106—798no—
425#106—798no—
426#106C22×D7918yes—
427C4⋊C8—798no—
428C4⋊C8—794no—
429C4⋊C8C22×D7914yes—
430#103—798no—
431#103—798no—
432#103—798no—
433#103C22×D7918yes—
434C24—791no—
435C2×Q8—22no—
436C2×Q8—21no—
437C2×Q8—24no—
438C2×Q8—44no—
439C2×Q8—3168no—
440C2×Q8—31632no—
441C2×Q8—3164no—
442C2×Q8—7916no—
443C2×Q8—794no—
444C2×Q8—792no—
445C2×Q8—1588no—
446C2×Q8—1584no—
447C2×Q8—1588no—
448C2×Q8—15816no—
449C2×Q8—1588no—
450C2×Q8—1582no—
451C2×Q8—1584no—
452C2×Q8—1581no—
453C2×Q8Q8×D7914yescomplemented
454C2×Q8C23×D7912yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—3164no—
459C22×C4—3168no—
460C22×C4—791no—
461C22×C4—791no—
462C22×C4—794no—
463C22×C4—794no—
464C22×C4—792no—
465C22×C4—798no—
466C22×C4—794no—
467C22×C4—792no—
468C22×C4—791no—
469C22×C4—794no—
470C22×C4—1584no—
471C22×C4—1588no—
472C22×C4—1584no—
473C22×C4—1584no—
474C22×C4—1588no—
475C22×C4—1581no—
476C22×C4—1582no—
477C22×C4—1581no—
478C22×C4D4×D7911yescharacteristic
479C22×C4D4×D7911yescharacteristic
480C22×C4C23×D7911yescharacteristic
481C2×C8—24no—
482C2×C8—794no—
483C2×C8—15816no—
484C2×C8—1584no—
485C2×C8C23×D7914yes—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—794no—
491C4⋊C4—792no—
492C4⋊C4—1584no—
493C4⋊C4—1588no—
494C4⋊C4—1584no—
495C4⋊C4—1588no—
496C4⋊C4—1584no—
497C4⋊C4—1584no—
498C4⋊C4—1581no—
499C4⋊C4—1582no—
500C4⋊C4—1584no—
501C4⋊C4C23×D7914yes—
502C4⋊C4C23×D7912yes—
503C42—24no—
504C42—792no—
505C42—794no—
506C42—792no—
507C42—794no—
508C42—1584no—
509C42—1584no—
510C42—1584no—
511C42D4×D7912yes—
512C42C23×D7912yes—
513C23—794no—
514C23—794no—
515C23—794no—
516C23—792no—
517C23C2×D4×D7911yescharacteristic
518Q8—24no—
519Q8—22no—
520Q8—48no—
521Q8—31616no—
522Q8—3168no—
523Q8—794no—
524Q8—15816no—
525Q8—1584no—
526Q8—1582no—
527Q8C2×Q8×D7914yescomplemented
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—31616no—
536C2×C4—3168no—
537C2×C4—3164no—
538C2×C4—3162no—
539C2×C4—794no—
540C2×C4—794no—
541C2×C4—792no—
542C2×C4—792no—
543C2×C4—798no—
544C2×C4—7916no—
545C2×C4—794no—
546C2×C4—794no—
547C2×C4—792no—
548C2×C4—1588no—
549C2×C4—15816no—
550C2×C4—1582no—
551C2×C4—1584no—
552C2×C4—1584no—
553C2×C4—1582no—
554C2×C4—1582no—
555C2×C4SD16×D7914yes—
556C2×C4C2×D4×D7912yes—
557C2×C4C2×D4×D7911yescharacteristic
558C2×C4C2×D4×D7912yes—
559C2×C4C2×Q8×D7912yes—
560C2×C4#41×D7912yes—
561C2×C4C24×D7911yescharacteristic
562C8—24no—
563C8—1584no—
564C22—794no—
565C22—794no—
566C22—794no—
567C22—7916no—
568C22C22⋊Q8×D7912yes—
569C22C2×SD16×D7912yes—
570C22#137×D7912yes—
571C22C22×D4×D7911yescharacteristic
572C4—22no—
573C4—24no—
574C4—44no—
575C4—42no—
576C4—3164no—
577C4—3162no—
578C4—794no—
579C4—794no—
580C4—1582no—
581C4—1584no—
582C4C22⋊Q8×D7912yes—
583C4C2×SD16×D7914yes—
584C4C22×Q8×D7911yescharacteristic
585C4C2×#41×D7911yescharacteristic
586C2—798no—
587C2#475×D7914yesdirect product factor
588C2C2×C22⋊Q8×D7911yescharacteristic
589C2C22×SD16×D7911yescharacteristic
590C2C2×#137×D7911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#475×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenterC2×#475D79
hypocenterC79C22×#475
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. C2×#19098849C2semidirect
4. C2×#19098848C2semidirect
5. C2×#19098847C2semidirect
6. C2×#19098846C2semidirect
7. C2×#19098845C2semidirect
8. #475×D79C2direct (N × H)
12. C2×#475×C79C2semidirect
35. #19098849C22semidirect
36. #19098848C22semidirect
37. #19098847C22semidirect
38. #19098846C22semidirect
39. #19098845C22semidirect
53. #475×C79C22semidirect
65. C2×Q8×D79Q8semidirect
147. C2×Dic158C2×Q8semidirect
152. Q8×D79C2×Q8semidirect
198. C2×Q8×C79C2×Q8semidirect
225. Q8×C79C22×Q8semidirect
265. Dic158C22×Q8semidirect
272. C2×D79#475direct (N × H)
291. C2×C79C2×#475semidirect
295. D79C2×#475direct (N × H)
304. C2×#475D79direct (N × H)
308. C79C22×#475semidirect
338. #475C2×D79direct (N × H)
453. C2×Q8Q8×D79semidirect
527. Q8C2×Q8×D79semidirect
587. C2#475×D79direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D792
C2×C4×Q8×D792
C2×#190988492
C2×#190988482
C2×#190988472
C2×#190988462
C2×#190988452
#475×D792
C2×#106×D792
C2×C4⋊C8×D792
C2×#103×D792
C2×#475×C792
C22×#47579