Finite Group Databasebeta

← C2×#23763858 #34290056

Subgroups — C2×#23763858 #34290056

Order 20224.

2066 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579144C211yesmaximal, characteristic
2C22×#14579075C212yesmaximal
3C2×#19098426C211yesmaximal, characteristic, complemented
4#23763858C218yesmaximal, direct product factor
5C2×#19098329C212yesmaximal, complemented
6C22×#117×C79C211yesmaximal, characteristic, complemented
7C23×C22⋊D79C2211yescharacteristic
8C2×#14579144—21no—
9C2×#14579144—21no—
10C2×#14579144—22no—
11C2×#14579144—22no—
12C2×#14579144—22no—
13C2×#14579144C414yescomplemented
14C2×#14579144C2214yes—
15C22×Dic79⋊C4C412yescomplemented
16C22×C22⋊Dic79C2212yes—
17C22×C22⋊Dic79C2211yescharacteristic
18C22×(C2×D79)⋊C4C412yescomplemented
19C2×#14579075—28no—
20C2×#14579075C2218yes—
21#19098426—22no—
22#19098426C2214yescomplemented
23C2×C79⋊#95—22no—
24#19098329C2218yescomplemented
25C24×C4×C79C2211yescharacteristic
26C2×#117×C79—22no—
27C2×#117×C79—28no—
28C2×#117×C79C2214yescomplemented
29C22×C4⋊C4×C79—21no—
30C22×C22⋊C4×C79C2212yes—
31C22×C42×C79—21no—
32C24×D79C2×C411yescharacteristic
33C22×C22⋊D79—24no—
34C22×C22⋊D79—21no—
35C22×C22⋊D79—21no—
36C22×C22⋊D79—21no—
37C22×C22⋊D79—21no—
38C22×C22⋊D79—24no—
39C22×C22⋊D79C2×C412yes—
40C22×C22⋊D79C2312yes—
41C23×Dic79—22no—
42C23×Dic79C2×C411yescharacteristic
43C23×Dic79C2×C412yes—
44#14579144—24no—
45#14579144—24no—
46#14579144—28no—
47#14579144—24no—
48#14579144—24no—
49#14579144—28no—
50C2×Dic79⋊C4—24no—
51C2×Dic79⋊C4—22no—
52C2×Dic79⋊C4—22no—
53C2×Dic79⋊C4C2×C418yescomplemented
54C2×C22⋊Dic79—21no—
55C2×C22⋊Dic79—21no—
56C2×C22⋊Dic79—21no—
57C2×C22⋊Dic79—21no—
58C2×C22⋊Dic79—24no—
59C2×C22⋊Dic79—24no—
60C2×C22⋊Dic79—22no—
61C2×C22⋊Dic79C2×C412yes—
62C2×C22⋊Dic79C2314yes—
63C2×C22⋊Dic79C2312yes—
64C2×(C2×D79)⋊C4—24no—
65C2×(C2×D79)⋊C4—22no—
66C2×(C2×D79)⋊C4—22no—
67C2×(C2×D79)⋊C4C2×C418yescomplemented
68#14579075—216no—
69C79⋊#95—28no—
70C25×C79C2311yescharacteristic
71C23×C4×C79—24no—
72C23×C4×C79—24no—
73C23×C4×C79—22no—
74C23×C4×C79C2×C412yes—
75C23×C4×C79C2×C412yes—
76C23×C4×C79D411yescharacteristic
77C23×C4×C79D411yescharacteristic
78C23×C4×C79D412yes—
79C23×C4×C79D412yes—
80C23×C4×C79D412yes—
81C23×C4×C79C2312yes—
82#117×C79—216no—
83#117×C79—216no—
84C2×C4⋊C4×C79—28no—
85C2×C4⋊C4×C79—24no—
86C2×C22⋊C4×C79—22no—
87C2×C22⋊C4×C79—24no—
88C2×C22⋊C4×C79D418yes—
89C2×C22⋊C4×C79C2314yes—
90C2×C42×C79—28no—
91C2×C42×C79—24no—
92C23×D79—21no—
93C23×D79—21no—
94C23×D79—24no—
95C23×D79—44no—
96C23×D79C22×C412yes—
97C2×C22⋊D79—22no—
98C2×C22⋊D79—22no—
99C2×C22⋊D79—28no—
100C2×C22⋊D79—24no—
101C2×C22⋊D79—22no—
102C2×C22⋊D79—22no—
103C2×C22⋊D79—24no—
104C2×C22⋊D79—42no—
105C2×C22⋊D79—42no—
106C2×C22⋊D79—44no—
107C2×C22⋊D79—44no—
108C2×C22⋊D79—42no—
109C2×C22⋊D79—42no—
110C22×Dic79—22no—
111C22×Dic79—22no—
112C22×Dic79—21no—
113C22×Dic79—21no—
114C22×Dic79—24no—
115C22×Dic79—24no—
116C22×Dic79—44no—
117C22×Dic79—48no—
118C22×Dic79—44no—
119C22×Dic79C22×C412yes—
120C22×Dic79C22×C414yes—
121Dic79⋊C4—28no—
122Dic79⋊C4—28no—
123C22⋊Dic79—22no—
124C22⋊Dic79—22no—
125C22⋊Dic79—22no—
126C22⋊Dic79—22no—
127C22⋊Dic79—24no—
128C22⋊Dic79—24no—
129C22⋊Dic79—44no—
130(C2×D79)⋊C4—28no—
131(C2×D79)⋊C4—28no—
132C24×C79—44no—
133C24×C79C22×C411yescharacteristic
134C24×C79C22×C411yescharacteristic
135C24×C79C2×D411yescharacteristic
136C24×C79C2×D411yescharacteristic
137C24×C79C2×D411yescharacteristic
138C24×C79C2×D411yescharacteristic
139C24×C79C2×D414yes—
140C24×C79#4114yes—
141C24×C79C2411yescharacteristic
142C22×C4×C79—28no—
143C22×C4×C79—28no—
144C22×C4×C79—22no—
145C22×C4×C79—22no—
146C22×C4×C79—24no—
147C22×C4×C79—28no—
148C22×C4×C79—28no—
149C22×C4×C79—22no—
150C22×C4×C79—22no—
151C22×C4×C79—24no—
152C22×C4×C79—24no—
153C22×C4×C79—24no—
154C22×C4×C79—28no—
155C22×C4×C79—24no—
156C22×C4×C79—48no—
157C22×C4×C79C22⋊C414yes—
158C22×C4×C79C22⋊C412yes—
159C22×C4×C79C22⋊C412yes—
160C22×C4×C79C22⋊C412yes—
161C22×C4×C79C22⋊C412yes—
162C22×C4×C79C22⋊C414yes—
163C22×C4×C79C22×C414yes—
164C22×C4×C79C2×D412yes—
165C22×C4×C79C2×D412yes—
166C22×C4×C79C2×D414yes—
167C4⋊C4×C79—216no—
168C22⋊C4×C79—28no—
169C22⋊C4×C79—24no—
170C22⋊C4×C79C2×D418yes—
171C42×C79—216no—
172C23×C79—24no—
173C23×C79—24no—
174C23×C79—24no—
175C23×C79—42no—
176C23×C79—42no—
177C23×C79—48no—
178C23×C79—42no—
179C23×C79—48no—
180C23×C79—42no—
181C23×C79C2×C22⋊C411yescharacteristic
182C23×C79C2×C22⋊C411yescharacteristic
183C23×C79C2×C22⋊C411yescharacteristic
184C23×C79C2×C22⋊C411yescharacteristic
185C23×C79C4×D414yes—
186C23×C79C4×D414yes—
187C23×C79#12012yes—
188C23×C79#12012yes—
189C23×C79#12114yes—
190C23×C79#12114yes—
191C23×C79#12312yes—
192C23×C79#12312yes—
193C23×C79C23×C411yescharacteristic
194C23×C79C22×D411yescharacteristic
195C23×C79C22×D412yes—
196C23×C79C22×D411yescharacteristic
197C23×C79C2×#4112yes—
198C22×D79—22no—
199C22×D79—24no—
200C22×D79—44no—
201C22×D79—42no—
202C22×D79—42no—
203C22×D79—44no—
204C22×D79—44no—
205C22×D79—88no—
206C2×C4×C79—28no—
207C2×C4×C79—22no—
208C2×C4×C79—22no—
209C2×C4×C79—28no—
210C2×C4×C79—22no—
211C2×C4×C79—22no—
212C2×C4×C79—24no—
213C2×C4×C79—24no—
214C2×C4×C79—28no—
215C2×C4×C79—28no—
216C2×C4×C79—24no—
217C2×C4×C79—24no—
218C2×C4×C79—28no—
219C2×C4×C79—48no—
220C2×C4×C79—416no—
221C2×C4×C79C2×C22⋊C414yes—
222C2×C4×C79C2×C22⋊C414yes—
223C22⋊D79—42no—
224C22⋊D79—44no—
225C22⋊D79—42no—
226C22⋊D79—44no—
227C22⋊D79—44no—
228C2×Dic79—24no—
229C2×Dic79—22no—
230C2×Dic79—24no—
231C2×Dic79—44no—
232C2×Dic79—42no—
233C2×Dic79—42no—
234C2×Dic79—44no—
235C2×Dic79—44no—
236C2×Dic79—48no—
237C2×Dic79—44no—
238C2×Dic79—88no—
239C22×C79—22no—
240C22×C79—22no—
241C22×C79—22no—
242C22×C79—22no—
243C22×C79—22no—
244C22×C79—22no—
245C22×C79—24no—
246C22×C79—28no—
247C22×C79—28no—
248C22×C79—24no—
249C22×C79—44no—
250C22×C79—42no—
251C22×C79—44no—
252C22×C79—42no—
253C22×C79—42no—
254C22×C79—42no—
255C22×C79#38612yes—
256C22×C79#38612yes—
257C22×C79#38612yes—
258C22×C79#38612yes—
259C22×C79#41014yes—
260C22×C79C22×C22⋊C411yescharacteristic
261C22×C79C2×C4×D412yes—
262C22×C79C2×#12011yescharacteristic
263C22×C79C2×#12112yes—
264C22×C79C2×#12311yescharacteristic
265C2×D79—44no—
266C2×D79—42no—
267C2×D79—84no—
268C2×D79—84no—
269C2×D79—84no—
270C4×C79—24no—
271C4×C79—24no—
272C4×C79—48no—
273Dic79—44no—
274Dic79—42no—
275Dic79—84no—
276C2×#1899—791nomaximal, Sylow
277C2×C79—22no—
278C2×C79—21no—
279C2×C79—22no—
280C2×C79—22no—
281C2×C79—21no—
282C2×C79—22no—
283C2×C79—22no—
284C2×C79#189914yescomplemented
285C2×C79C2×#38611yescharacteristic
286C2×C79C2×#41012yes—
287D79—82no—
288C22×#123—791no—
289C22×#117D7911yescharacteristic, complemented
290C22×#99—792no—
291C2×#381—791no—
292#1899—798no—
293C2×#342—792no—
294C79C2×#189911yescharacteristic, complemented, Sylow
295C23×D4—791no—
296C24×C4C2×D7911yescharacteristic
297C2×#123—794no—
298C2×#123—794no—
299C2×#123—1581no—
300C2×#123—1582no—
301C2×#123—1581no—
302C2×#123—1582no—
303C2×#123—1582no—
304C2×#117—22no—
305C2×#117—28no—
306C2×#117C2×D7914yescomplemented
307C22×C4⋊C4—21no—
308C22×C4⋊C4—792no—
309C22×C22⋊C4—791no—
310C22×C22⋊C4—792no—
311C22×C22⋊C4—792no—
312C22×C22⋊C4C2×D7912yes—
313C22×C42—21no—
314C2×#99—798no—
315C2×#99—1588no—
316#381—794no—
317#381—1582no—
318C2×#95—1582no—
319#342—798no—
320C25—791no—
321C25C22×D7911yescharacteristic
322C22×D4—792no—
323C22×D4—792no—
324C22×D4—1581no—
325C22×D4—1581no—
326C22×D4—1584no—
327C22×D4—1581no—
328C22×D4—1581no—
329C22×D4—1584no—
330C23×C4—24no—
331C23×C4—24no—
332C23×C4—22no—
333C23×C4—792no—
334C23×C4—791no—
335C23×C4—1582no—
336C23×C4C4×D7912yes—
337C23×C4C4×D7912yes—
338C23×C4D31612yes—
339C23×C4D31612yes—
340C23×C4C22⋊D7911yescharacteristic
341C23×C4C22⋊D7912yes—
342C23×C4C22⋊D7911yescharacteristic
343C23×C4C22×D7912yes—
344#123—1584no—
345#123—1588no—
346#123—1584no—
347#123—1584no—
348#123—1584no—
349#123—1588no—
350#117—216no—
351#117—216no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—798no—
355C2×C4⋊C4—1584no—
356C2×C4⋊C4—1582no—
357C2×C4⋊C4—1582no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—792no—
361C2×C22⋊C4—792no—
362C2×C22⋊C4—798no—
363C2×C22⋊C4—794no—
364C2×C22⋊C4—1582no—
365C2×C22⋊C4—1584no—
366C2×C22⋊C4—1584no—
367C2×C22⋊C4—1581no—
368C2×C22⋊C4—1581no—
369C2×C22⋊C4—1581no—
370C2×C22⋊C4—1581no—
371C2×C22⋊C4—1584no—
372C2×C22⋊C4—1582no—
373C2×C22⋊C4—1582no—
374C2×C22⋊C4C22⋊D7918yes—
375C2×C22⋊C4C22×D7914yes—
376C2×C42—28no—
377C2×C42—24no—
378#99—15816no—
379#95—1588no—
380C24—44no—
381C24—3164no—
382C24—792no—
383C24—1581no—
384C24—1581no—
385C24—1584no—
386C24C2×C4×D7911yescharacteristic
387C24C2×C4×D7911yescharacteristic
388C24C2×C22⋊D7911yescharacteristic
389C24C2×C22⋊D7911yescharacteristic
390C24C2×C22⋊D7914yes—
391C24C2×D31611yescharacteristic
392C24C2×D31611yescharacteristic
393C24#1192962414yes—
394C24C23×D7911yescharacteristic
395C2×D4—3162no—
396C2×D4—3162no—
397C2×D4—3164no—
398C2×D4—3164no—
399C2×D4—3162no—
400C2×D4—3162no—
401C2×D4—1584no—
402C2×D4—1582no—
403C2×D4—1582no—
404C2×D4—1588no—
405C2×D4—1584no—
406C2×D4—1582no—
407C2×D4—1582no—
408C22×C4—24no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—28no—
421C22×C4—24no—
422C22×C4—48no—
423C22×C4—3164no—
424C22×C4—3168no—
425C22×C4—3164no—
426C22×C4—794no—
427C22×C4—792no—
428C22×C4—1584no—
429C22×C4—1582no—
430C22×C4—1581no—
431C22×C4—1582no—
432C22×C4—1581no—
433C22×C4—1584no—
434C22×C4(C2×D79)⋊C414yes—
435C22×C4(C2×D79)⋊C412yes—
436C22×C4(C2×D79)⋊C414yes—
437C22×C4(C2×D79)⋊C412yes—
438C22×C4(C2×D79)⋊C412yes—
439C22×C4(C2×D79)⋊C412yes—
440C22×C4C2×C4×D7914yes—
441C22×C4C2×C22⋊D7912yes—
442C22×C4C2×C22⋊D7912yes—
443C22×C4C2×D31614yes—
444C4⋊C4—216no—
445C4⋊C4—1588no—
446C4⋊C4—1588no—
447C22⋊C4—28no—
448C22⋊C4—24no—
449C22⋊C4—3164no—
450C22⋊C4—1584no—
451C22⋊C4—1584no—
452C22⋊C4—1582no—
453C22⋊C4—1582no—
454C22⋊C4—1582no—
455C22⋊C4—1582no—
456C22⋊C4—1588no—
457C22⋊C4—1588no—
458C22⋊C4C2×C22⋊D7918yes—
459C42—216no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—42no—
464C23—48no—
465C23—42no—
466C23—42no—
467C23—48no—
468C23—42no—
469C23—3164no—
470C23—3164no—
471C23—3162no—
472C23—3162no—
473C23—3164no—
474C23—6328no—
475C23—1582no—
476C23—1584no—
477C23C2×(C2×D79)⋊C411yescharacteristic
478C23C2×(C2×D79)⋊C411yescharacteristic
479C23C2×(C2×D79)⋊C411yescharacteristic
480C23C2×(C2×D79)⋊C411yescharacteristic
481C23C4×C22⋊D7914yes—
482C23C4×C22⋊D7914yes—
483C23#1457913012yes—
484C23#1457913012yes—
485C23#1457913514yes—
486C23#1457913514yes—
487C23#1457914412yes—
488C23#1457914412yes—
489C23C22×C4×D7911yescharacteristic
490C23C22×C22⋊D7911yescharacteristic
491C23C22×C22⋊D7912yes—
492C23C22×D31611yescharacteristic
493C23C2×#1192962412yes—
494D4—3164no—
495D4—3164no—
496D4—3162no—
497D4—3164no—
498D4—3162no—
499C2×C4—28no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—28no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—28no—
512C2×C4—416no—
513C2×C4—48no—
514C2×C4—3164no—
515C2×C4—3162no—
516C2×C4—3162no—
517C2×C4—3164no—
518C2×C4—3164no—
519C2×C4—3168no—
520C2×C4—3164no—
521C2×C4—6328no—
522C2×C4—1584no—
523C2×C4—1582no—
524C2×C4—1584no—
525C2×C4C2×(C2×D79)⋊C414yes—
526C2×C4C2×(C2×D79)⋊C414yes—
527C22—24no—
528C22—28no—
529C22—28no—
530C22—24no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—42no—
538C22—44no—
539C22—42no—
540C22—44no—
541C22—42no—
542C22—42no—
543C22—3162no—
544C22—3164no—
545C22—6324no—
546C22—6324no—
547C22—6324no—
548C22#1909844212yes—
549C22#1909844212yes—
550C22#1909844212yes—
551C22#1909844212yes—
552C22#1909853614yes—
553C22C22×(C2×D79)⋊C411yescharacteristic
554C22C2×C4×C22⋊D7912yes—
555C22C2×#1457913011yescharacteristic
556C22C2×#1457913512yes—
557C22C2×#1457914411yescharacteristic
558C4—24no—
559C4—24no—
560C4—48no—
561C4—3162no—
562C4—3164no—
563C4—6324no—
564C2—21no—
565C2—22no—
566C2—22no—
567C2—22no—
568C2—22no—
569C2—22no—
570C2—21no—
571C2—6322no—
572C2#2376385814yesdirect product factor
573C2C2×#1909844211yescharacteristic
574C2C2×#1909853612yes—
subgroupG/H
centerC23C2×(C2×D79)⋊C4
commutatorC23×C79C23×C4
FrattiniC24C23×D79
FittingC22×#117×C79C2
socleC23×C79C2×C22⋊C4
prime radicalC23×C22⋊D79C22
cosocleC24×C79C24
hypercenterC22×#117D79
hypocenterC79C2×#1899
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
3. C2×#19098426C2semidirect
4. #23763858C2direct (N × H)
5. C2×#19098329C2semidirect
6. C22×#117×C79C2semidirect
13. C2×#14579144C4semidirect
15. C22×Dic79⋊C4C4semidirect
18. C22×(C2×D79)⋊C4C4semidirect
22. #19098426C22semidirect
24. #19098329C22semidirect
28. C2×#117×C79C22semidirect
53. C2×Dic79⋊C4C2×C4semidirect
67. C2×(C2×D79)⋊C4C2×C4semidirect
284. C2×C79#1899semidirect
289. C22×#117D79semidirect
294. C79C2×#1899semidirect
306. C2×#117C2×D79semidirect
572. C2#23763858direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791442
C22×#145790752
C2×#190984262
#237638582
C2×#190983292
C22×#117×C792
C2×#189979