Finite Group Databasebeta

← C2×#23774634 #35160405

Subgroups — C2×#23774634 #35160405

Order 20224.

2018 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
2C2×#19099100C211yesmaximal, characteristic
3#23774634C2116yesmaximal, direct product factor
4C2×#19098970C212yesmaximal, complemented
5C2×#19098924C212yesmaximal, complemented
6C2×#19098897C212yesmaximal, complemented
7C2×#19098883C212yesmaximal
8C2×#19098848C211yesmaximal, characteristic, complemented
9C2×#19098844C211yesmaximal, characteristic, complemented
10C2×#19098840C211yesmaximal, characteristic, complemented
11C2×#19098619C211yesmaximal, characteristic, complemented
12C2×#475×C79C211yesmaximal, characteristic, complemented
13C22×Q8×D79—21no—
14C2×#14579161C2211yescharacteristic
15C2×#14579160—21no—
16C2×#14579160C2212yes—
17C2×#14579159—21no—
18C4⋊Q8×D79—24no—
19C4⋊Q8×D79C2218yescomplemented
20#19099100—24no—
21#19099100C2218yes—
22C2×#14579156—21no—
23C2×#14579152C2211yescharacteristic
24C2×#14579150C2211yescharacteristic
25C2×#14579146—21no—
26C2×#14579137C2211yescharacteristic
27C2×#14579136C2211yescharacteristic
28C2×C4×D316—21no—
29C2×C4×D316C2211yescharacteristic
30C2×#14579118—21no—
31C2×C4⋊C4×D79—21no—
32C2×C4⋊C4×D79C2212yes—
33C2×C42×D79C2211yescharacteristic
34#19098970C22116yescomplemented
35#19098924C22116yescomplemented
36#19098897C22116yescomplemented
37#19098883C22116yes—
38#19098848C2218yescomplemented
39#19098844C2218yescomplemented
40#19098840C2218yescomplemented
41#19098619C2218yescomplemented
42C2×#14579095C2212yes—
43C2×#14579094C2212yes—
44C2×#14579092C2212yes—
45C2×C4⋊(C79⋊C8)C2211yescharacteristic
46C2×#14579085C2212yes—
47C2×#14579083C2212yes—
48C2×#14579081C2212yes—
49C2×(C2×D79)⋊C8C2212yes—
50C2×#14579071C2212yes—
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—22no—
59C2×Q8×D79—28no—
60C2×Q8×D79—48no—
61C22×D316—21no—
62C22×D316C2311yescharacteristic
63C22×C4×D79—21no—
64C22×C4×D79—22no—
65C22×C4×D79D411yescharacteristic
66C22×C4×D79D411yescharacteristic
67C22×C4×D79C2311yescharacteristic
68C22×C79⋊C8C2312yes—
69#14579161—22no—
70#14579161C2314yes—
71#14579160—24no—
72#14579160—28no—
73#14579160C2318yes—
74#14579159—28no—
75#14579156—28no—
76#14579152—22no—
77#14579152C2314yes—
78#14579150—22no—
79#14579150C2314yes—
80#14579146—28no—
81#14579137—22no—
82#14579137C2314yes—
83#14579136—22no—
84#14579136C2314yes—
85C4×D316—22no—
86C4×D316—28no—
87C4×D316C2314yes—
88#14579118—28no—
89C2×C4⋊Dic79—21no—
90C2×C4⋊Dic79—21no—
91C2×C4⋊Dic79C2312yes—
92C2×C4⋊Dic79C2311yescharacteristic
93C2×Dic79⋊C4—22no—
94C2×Dic79⋊C4—22no—
95C2×Dic79⋊C4—21no—
96C2×Dic79⋊C4—21no—
97C4⋊C4×D79—28no—
98C4⋊C4×D79—24no—
99C4⋊C4×D79C2318yes—
100C2×(C2×D79)⋊C4—21no—
101C2×(C2×D79)⋊C4—21no—
102C2×(C2×D79)⋊C4—21no—
103C2×(C2×D79)⋊C4—21no—
104C2×(C2×D79)⋊C4—21no—
105C2×C4×Dic79D411yescharacteristic
106C2×C4×Dic79D411yescharacteristic
107C2×C4×Dic79C2311yescharacteristic
108C42×D79D414yes—
109C42×D79C2314yes—
110#14579095C2318yes—
111#14579094C2318yes—
112#14579092C2318yes—
113C4⋊(C79⋊C8)C2314yes—
114#14579085C2318yes—
115#14579083C2318yes—
116#14579081C2318yes—
117(C2×D79)⋊C8C2318yes—
118#14579071C2318yes—
119C22×Q8×C79—21no—
120C22×Q8×C79C2311yescharacteristic
121C22×C8×C79C2312yes—
122C4⋊Q8×C79—22no—
123C4⋊Q8×C79C2314yes—
124C4×Q8×C79—22no—
125C4×Q8×C79C2314yes—
126C2×C4⋊C4×C79—21no—
127C2×C4⋊C4×C79—21no—
128C2×C4⋊C4×C79C2311yescharacteristic
129C2×C4⋊C4×C79C2312yes—
130C2×C42×C79—21no—
131C2×C42×C79C2311yescharacteristic
132#106×C79C2318yes—
133C4⋊C8×C79C2314yes—
134#103×C79C2318yes—
135C23×D79—21no—
136C23×D79C2×D411yescharacteristic
137C2×Dic158—28no—
138C2×Dic158—24no—
139C2×Dic158—48no—
140C2×Dic158—44no—
141Q8×D79—432no—
142C2×D316—24no—
143C2×D316—21no—
144C2×D316—22no—
145C2×D316—22no—
146C2×D316—44no—
147C2×D316C2412yes—
148C22×Dic79—22no—
149C22×Dic79—21no—
150C22×Dic79C2×D411yescharacteristic
151C22×Dic79C2×D411yescharacteristic
152C22×Dic79C2×D411yescharacteristic
153C2×C4×D79—24no—
154C2×C4×D79—28no—
155C2×C4×D79—24no—
156C2×C4×D79—24no—
157C2×C4×D79—22no—
158C2×C4×D79—22no—
159C2×C4×D79—48no—
160C2×C4×D79—44no—
161C2×C4×D79C2×D414yes—
162C2×C4×D79C2×D412yes—
163C2×C4×D79C2×D414yes—
164C2×C4×D79C2412yes—
165C2×C79⋊C8—24no—
166C2×C79⋊C8C2414yes—
167C4⋊Dic79—24no—
168C4⋊Dic79—24no—
169C4⋊Dic79—22no—
170C4⋊Dic79—21no—
171C4⋊Dic79C2414yes—
172C4⋊Dic79C2412yes—
173Dic79⋊C4—28no—
174Dic79⋊C4—28no—
175Dic79⋊C4—24no—
176Dic79⋊C4—24no—
177(C2×D79)⋊C4—24no—
178(C2×D79)⋊C4—24no—
179(C2×D79)⋊C4—24no—
180(C2×D79)⋊C4—24no—
181(C2×D79)⋊C4—24no—
182C4×Dic79C2×D412yes—
183C4×Dic79C2×D414yes—
184C4×Dic79C2×D414yes—
185C4×Dic79C2412yes—
186C2×Q8×C79—24no—
187C2×Q8×C79—21no—
188C2×Q8×C79—22no—
189C2×Q8×C79—22no—
190C2×Q8×C79—44no—
191C2×Q8×C79C2412yes—
192C22×C4×C79—22no—
193C22×C4×C79—21no—
194C22×C4×C79—21no—
195C22×C4×C79C2×D411yescharacteristic
196C22×C4×C79C2×D411yescharacteristic
197C22×C4×C79C2411yescharacteristic
198C2×C8×C79—24no—
199C2×C8×C79C2414yes—
200C4⋊C4×C79—24no—
201C4⋊C4×C79—24no—
202C4⋊C4×C79—21no—
203C4⋊C4×C79—22no—
204C4⋊C4×C79C2414yes—
205C4⋊C4×C79C2412yes—
206C42×C79—24no—
207C42×C79C2×D412yes—
208C42×C79C2412yes—
209C23×C79C22×D411yescharacteristic
210C22×D79—22no—
211C22×D79—22no—
212C22×D79—22no—
213C22×D79—42no—
214C22×D79—42no—
215C22×D79—42no—
216C22×D79#13714yes—
217C22×D79C22×D412yes—
218Q8×C79—22no—
219Q8×C79—22no—
220Q8×C79—42no—
221Q8×C79—48no—
222C2×C4×C79—22no—
223C2×C4×C79—22no—
224C2×C4×C79—22no—
225C2×C4×C79—24no—
226C2×C4×C79—42no—
227C2×C4×C79—44no—
228C2×C4×C79—42no—
229C2×C4×C79AGL(1,ℤ/8)14yes—
230C2×C4×C79C22×D412yes—
231C2×C4×C79C22×D411yescharacteristic
232C2×C4×C79C22×D412yes—
233C2×C4×C792−1+412yes—
234C2×C4×C792−1+412yes—
235C2×C4×C79C2511yescharacteristic
236C2×Dic79—22no—
237C2×Dic79—22no—
238C2×Dic79—22no—
239C2×Dic79—22no—
240C2×Dic79—24no—
241C2×Dic79—42no—
242C2×Dic79—44no—
243C2×Dic79C22×D412yes—
244C2×Dic79C22×D412yes—
245C2×Dic79C22×D412yes—
246D316—22no—
247D316—22no—
248D316—48no—
249D316—42no—
250C4×D79—28no—
251C4×D79—24no—
252C4×D79—28no—
253C4×D79—22no—
254C4×D79—22no—
255C4×D79—416no—
256C4×D79—48no—
257Dic158—416no—
258Dic158—48no—
259C8×C79—24no—
260C79⋊C8—24no—
261C22×C79#53612yes—
262C22×C79C2×AGL(1,ℤ/8)12yes—
263C22×C79C2×#13712yes—
264C22×C79C23×D411yescharacteristic
265C2×D79—22no—
266C2×D79—28no—
267C2×D79—22no—
268C2×D79—42no—
269C2×D79—42no—
270C2×D79—42no—
271C2×D79—84no—
272C2×D79C2×#13714yes—
273C4×C79—22no—
274C4×C79—42no—
275C4×C79—44no—
276C4×C79—42no—
277C4×C79#53612yes—
278C4×C79C2×AGL(1,ℤ/8)14yes—
279C4×C79C2×2−1+411yescharacteristic
280C4×C79C2×2−1+411yescharacteristic
281Dic79—22no—
282Dic79—22no—
283Dic79—22no—
284Dic79—44no—
285Dic79—42no—
286C2×#3239—791nomaximal, Sylow
287C2×C79#323914yescomplemented
288C2×C79C2×#53611yescharacteristic
289C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
290C2×C79C22×#13711yescharacteristic
291D79—24no—
292D79—82no—
293C22×C4⋊Q8—791no—
294C2×#529—791no—
295#3239—7916no—
296C2×#501—792no—
297C2×#489—792no—
298C2×#484—792no—
299C2×#481—792no—
300C2×#475—791no—
301C2×#475D7911yescharacteristic, complemented
302C2×#474—791no—
303C2×#474—791no—
304C2×#432—791no—
305C79C2×#323911yescharacteristic, complemented, Sylow
306C23×Q8—1581no—
307C2×C4⋊Q8—798no—
308C2×C4⋊Q8—792no—
309C2×C4⋊Q8—791no—
310C2×C4⋊Q8—1581no—
311C2×C4⋊Q8—1584no—
312C2×C4⋊Q8—1581no—
313C2×C4⋊Q8C2×D7911yescharacteristic
314#529—798no—
315#529—1584no—
316C2×#126—1581no—
317C2×#125—791no—
318C2×#124—791no—
319C2×#123—1581no—
320C2×C22⋊Q8—791no—
321C2×#121—791no—
322C2×C4×Q8C2×D7911yescharacteristic
323C2×C4×D4—791no—
324C2×C4×D4—1581no—
325C2×#117—1581no—
326C22×C4⋊C4—792no—
327C22×C4⋊C4—1581no—
328C22×C42—791no—
329#501—7916no—
330#489—7916no—
331#484—7916no—
332#481—7916no—
333#475—798no—
334#475C2×D7918yescomplemented
335#474—798no—
336#474—798no—
337#432—798no—
338C2×#107—792no—
339C2×#107—792no—
340C2×#106—792no—
341C2×#106C2×D7912yes—
342C2×C4⋊C8—791no—
343C2×C4⋊C8C2×D7911yescharacteristic
344C2×#103—792no—
345C2×#103C2×D7912yes—
346C2×#102—792no—
347C2×#102—792no—
348C2×C22⋊C8—792no—
349C2×#97—792no—
350C22×Q8—21no—
351C22×Q8—3168no—
352C22×Q8—1582no—
353C22×Q8—1588no—
354C22×Q8—1581no—
355C22×Q8C22×D7911yescharacteristic
356C22×D4—791no—
357C22×D4—1581no—
358C23×C4—791no—
359C23×C4—791no—
360C23×C4—791no—
361C23×C4—1582no—
362C23×C4—1581no—
363C22×C8—792no—
364C22×C8C22×D7912yes—
365C4⋊Q8—22no—
366C4⋊Q8—798no—
367C4⋊Q8—794no—
368C4⋊Q8—1584no—
369C4⋊Q8—1588no—
370C4⋊Q8—1588no—
371C4⋊Q8—1582no—
372C4⋊Q8C22×D7914yes—
373#126—1588no—
374#125—794no—
375#125—1582no—
376#124—794no—
377#124—1582no—
378#123—1588no—
379C22⋊Q8—794no—
380C22⋊Q8—1582no—
381#121—794no—
382#121—1582no—
383C4×Q8—22no—
384C4×Q8C22×D7914yes—
385C4×D4—794no—
386C4×D4—1588no—
387C4×D4—1582no—
388#117—1588no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—792no—
392C2×C4⋊C4—791no—
393C2×C4⋊C4—798no—
394C2×C4⋊C4—1584no—
395C2×C4⋊C4—1588no—
396C2×C4⋊C4—1582no—
397C2×C4⋊C4—1582no—
398C2×C4⋊C4—1581no—
399C2×C4⋊C4—1581no—
400C2×C4⋊C4—1581no—
401C2×C4⋊C4—1581no—
402C2×C4⋊C4C22×D7912yes—
403C2×C4⋊C4C22×D7911yescharacteristic
404C2×C22⋊C4—1581no—
405C2×C22⋊C4—1581no—
406C2×C22⋊C4—1581no—
407C2×C22⋊C4—1581no—
408C2×C22⋊C4—1581no—
409C2×C42—21no—
410C2×C42—791no—
411C2×C42—791no—
412C2×C42—791no—
413C2×C42—794no—
414C2×C42—794no—
415C2×C42C22×D7911yescharacteristic
416#107—798no—
417#107—798no—
418#106—798no—
419#106C22×D7918yes—
420C4⋊C8—794no—
421C4⋊C8C22×D7914yes—
422#103—798no—
423#103C22×D7918yes—
424#102—798no—
425#102—798no—
426C22⋊C8—798no—
427#97—798no—
428C24—791no—
429C24—1581no—
430C2×Q8—21no—
431C2×Q8—24no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—44no—
435C2×Q8—3168no—
436C2×Q8—31632no—
437C2×Q8—3164no—
438C2×Q8—1588no—
439C2×Q8—1584no—
440C2×Q8C23×D7912yes—
441C2×D4—3164no—
442C2×D4—792no—
443C2×D4—1584no—
444C2×D4—1582no—
445C2×D4—1582no—
446C2×D4—1581no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—3168no—
451C22×C4—3164no—
452C22×C4—791no—
453C22×C4—791no—
454C22×C4—791no—
455C22×C4—792no—
456C22×C4—792no—
457C22×C4—794no—
458C22×C4—794no—
459C22×C4—1588no—
460C22×C4—1584no—
461C22×C4—1581no—
462C22×C4—1582no—
463C22×C4—1584no—
464C22×C4—1582no—
465C22×C4—1582no—
466C22×C4—1584no—
467C22×C4D4×D7911yescharacteristic
468C22×C4D4×D7911yescharacteristic
469C22×C4C23×D7911yescharacteristic
470C2×C8—24no—
471C2×C8—794no—
472C2×C8—1584no—
473C2×C8C23×D7914yes—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—794no—
479C4⋊C4—792no—
480C4⋊C4—1588no—
481C4⋊C4—1588no—
482C4⋊C4—1584no—
483C4⋊C4—1584no—
484C4⋊C4—1584no—
485C4⋊C4—1582no—
486C4⋊C4—1581no—
487C4⋊C4—1584no—
488C4⋊C4C23×D7914yes—
489C4⋊C4C23×D7912yes—
490C22⋊C4—1584no—
491C22⋊C4—1584no—
492C22⋊C4—1584no—
493C22⋊C4—1584no—
494C22⋊C4—1584no—
495C42—24no—
496C42—792no—
497C42—794no—
498C42—792no—
499C42—794no—
500C42D4×D7912yes—
501C42C23×D7912yes—
502C23—3162no—
503C23—3162no—
504C23—3162no—
505C23—794no—
506C23—792no—
507C23—1582no—
508C23—1582no—
509C23—1582no—
510C23C2×D4×D7911yescharacteristic
511Q8—22no—
512Q8—22no—
513Q8—42no—
514Q8—48no—
515Q8—31616no—
516Q8—3168no—
517D4—3168no—
518D4—3162no—
519D4—1582no—
520D4—1582no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—31616no—
529C2×C4—3164no—
530C2×C4—3162no—
531C2×C4—3168no—
532C2×C4—792no—
533C2×C4—792no—
534C2×C4—792no—
535C2×C4—1588no—
536C2×C4—1582no—
537C2×C4—1584no—
538C2×C4—1582no—
539C2×C4—1582no—
540C2×C4—1582no—
541C2×C4—1584no—
542C2×C4—1582no—
543C2×C4—1582no—
544C2×C4—1588no—
545C2×C4#1457918814yes—
546C2×C4C2×D4×D7912yes—
547C2×C4C2×D4×D7911yescharacteristic
548C2×C4C2×D4×D7912yes—
549C2×C4#1457920812yes—
550C2×C4#1457920912yes—
551C2×C4C24×D7911yescharacteristic
552C8—24no—
553C8—1584no—
554C22—3162no—
555C22—3162no—
556C22—3162no—
557C22—794no—
558C22—6324no—
559C22—1582no—
560C22—1588no—
561C22—1582no—
562C22#1909913612yes—
563C22C2×#1457918812yes—
564C22#137×D7912yes—
565C22C22×D4×D7911yescharacteristic
566C4—22no—
567C4—44no—
568C4—42no—
569C4—42no—
570C4—3164no—
571C4—3162no—
572C4—1582no—
573C4—1582no—
574C4—1582no—
575C4#1909913612yes—
576C4C2×#1457918814yes—
577C4C2×#1457920811yescharacteristic
578C4C2×#1457920911yescharacteristic
579C2—6322no—
580C2—1584no—
581C2#2377463414yesdirect product factor
582C2C2×#1909913611yescharacteristic
583C2C22×#1457918811yescharacteristic
584C2C2×#137×D7911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#475×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579136C22
hypercenterC2×#475D79
hypocenterC79C2×#3239
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
1. C2×C4⋊Q8×D79C2semidirect
3. #23774634C2direct (N × H)
4. C2×#19098970C2semidirect
5. C2×#19098924C2semidirect
6. C2×#19098897C2semidirect
8. C2×#19098848C2semidirect
9. C2×#19098844C2semidirect
10. C2×#19098840C2semidirect
11. C2×#19098619C2semidirect
12. C2×#475×C79C2semidirect
19. C4⋊Q8×D79C22semidirect
34. #19098970C22semidirect
35. #19098924C22semidirect
36. #19098897C22semidirect
38. #19098848C22semidirect
39. #19098844C22semidirect
40. #19098840C22semidirect
41. #19098619C22semidirect
53. #475×C79C22semidirect
287. C2×C79#3239semidirect
301. C2×#475D79semidirect
305. C79C2×#3239semidirect
334. #475C2×D79semidirect
581. C2#23774634direct (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×#190991002
#237746342
C2×#190989702
C2×#190989242
C2×#190988972
C2×#190988832
C2×#190988482
C2×#190988442
C2×#190988402
C2×#190986192
C2×#475×C792
C2×#323979