Finite Group Databasebeta

← C2×#23773441 #35156309

Subgroups — C2×#23773441 #35156309

Order 20224.

2138 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099118C211yesmaximal, characteristic
2C2×C4×Q8×D79C211yesmaximal, characteristic
3#23773441C2116yesmaximal, direct product factor
4C2×#19098900C212yesmaximal
5C2×#19098855C211yesmaximal, characteristic, complemented
6C2×#19098774C211yesmaximal, characteristic, complemented
7C2×#19098773C211yesmaximal, characteristic, complemented
8C2×#19098720C212yesmaximal
9C2×#19098657C212yesmaximal, complemented
10C2×#19098655C212yesmaximal, complemented
11C2×#19098615C211yesmaximal, characteristic
12C2×#477×C79C211yesmaximal, characteristic, complemented
13C22×Q8×D79C2211yescharacteristic
14C22×Dic316C2212yes—
15C22×#11929614C2212yes—
16#19099118—24no—
17#19099118C2218yes—
18C2×#14579161C2211yescharacteristic
19C2×#14579152—21no—
20C2×#14579141C2212yes—
21C2×#14579137—21no—
22C2×Q8×Dic79—21no—
23C2×Q8×Dic79C2211yescharacteristic
24C2×C4×Dic158—21no—
25C2×C4×Dic158C2211yescharacteristic
26C2×#14579126—21no—
27C2×#14579126C2212yes—
28C2×#14579126C2211yescharacteristic
29C4×Q8×D79—24no—
30C4×Q8×D79C2218yes—
31C2×#14579119—21no—
32C2×C4⋊C4×D79—21no—
33C2×C4⋊C4×D79C2211yescharacteristic
34C2×C42×D79—21no—
35C2×C42×D79C2211yescharacteristic
36#19098900C22116yes—
37#19098855C2218yescomplemented
38#19098774C2218yescomplemented
39#19098773C2218yescomplemented
40#19098720C22116yes—
41#19098657C22116yescomplemented
42#19098655C22116yescomplemented
43#19098615C2218yes—
44C2×#14579094C2212yes—
45C2×C4⋊(C79⋊C8)C2211yescharacteristic
46C2×#14579086C2212yes—
47C2×#14579084C2212yes—
48C2×#14579084C2212yes—
49C2×(C2×D79)⋊C8C2212yes—
50C2×C8×Dic79C2212yes—
51C2×C4⋊Q8×C79C2211yescharacteristic
52C2×C4×Q8×C79C2211yescharacteristic
53#477×C79C2218yescomplemented
54C2×#107×C79C2212yes—
55C2×C4⋊C8×C79C2211yescharacteristic
56C2×#103×C79C2212yes—
57C22×Dic158—21no—
58C22×Dic158C2312yes—
59C22×Dic158C2311yescharacteristic
60C2×Q8×D79—24no—
61C2×Q8×D79—24no—
62C2×Q8×D79—22no—
63C2×Q8×D79C2314yes—
64C22×C4×D79—21no—
65C22×C4×D79—21no—
66C22×C4×D79D411yescharacteristic
67C22×C4×D79D411yescharacteristic
68C22×C4×D79C2311yescharacteristic
69C2×Dic316—28no—
70C2×Dic316C2318yes—
71C2×#11929614—28no—
72C2×#11929614C2318yes—
73C22×C79⋊C8C2312yes—
74#14579161—22no—
75#14579161C2314yes—
76#14579152—28no—
77#14579141—24no—
78#14579141C2318yes—
79#14579137—28no—
80Q8×Dic79—22no—
81Q8×Dic79—28no—
82Q8×Dic79C2314yes—
83C4×Dic158—22no—
84C4×Dic158—28no—
85C4×Dic158C2314yes—
86#14579126—22no—
87#14579126—28no—
88#14579126—24no—
89#14579126C2318yes—
90#14579126C2314yes—
91#14579119—28no—
92C2×C4⋊Dic79—21no—
93C2×C4⋊Dic79—21no—
94C2×C4⋊Dic79—21no—
95C2×C4⋊Dic79—22no—
96C2×C4⋊Dic79C2311yescharacteristic
97C2×Dic79⋊C4—21no—
98C2×Dic79⋊C4—21no—
99C2×Dic79⋊C4—21no—
100C2×Dic79⋊C4—22no—
101C4⋊C4×D79—28no—
102C4⋊C4×D79—22no—
103C4⋊C4×D79C2314yes—
104C2×(C2×D79)⋊C4—22no—
105C2×C4×Dic79—21no—
106C2×C4×Dic79—21no—
107C2×C4×Dic79—21no—
108C2×C4×Dic79—22no—
109C2×C4×Dic79D411yescharacteristic
110C2×C4×Dic79D411yescharacteristic
111C2×C4×Dic79C2311yescharacteristic
112C42×D79—28no—
113C42×D79D414yes—
114C42×D79C2314yes—
115#14579094C2318yes—
116C4⋊(C79⋊C8)C2314yes—
117#14579086C2318yes—
118#14579084C2318yes—
119#14579084C2318yes—
120(C2×D79)⋊C8C2318yes—
121C8×Dic79C2318yes—
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#107×C79C2318yes—
136C4⋊C8×C79C2314yes—
137#103×C79C2318yes—
138C23×D79C2×D411yescharacteristic
139C2×Dic158—28no—
140C2×Dic158—24no—
141C2×Dic158—21no—
142C2×Dic158—22no—
143C2×Dic158—22no—
144C2×Dic158—24no—
145C2×Dic158—24no—
146C2×Dic158#4114yes—
147C2×Dic158C2414yes—
148C2×Dic158C2412yes—
149Q8×D79—216no—
150Q8×D79—28no—
151Q8×D79—28no—
152C22×Dic79—21no—
153C22×Dic79—22no—
154C22×Dic79—21no—
155C22×Dic79C2×D411yescharacteristic
156C22×Dic79C2×D411yescharacteristic
157C22×Dic79C2×D411yescharacteristic
158C2×C4×D79—28no—
159C2×C4×D79—24no—
160C2×C4×D79—24no—
161C2×C4×D79—22no—
162C2×C4×D79—22no—
163C2×C4×D79—42no—
164C2×C4×D79—44no—
165C2×C4×D79Q1618yescomplemented
166C2×C4×D79C2×D412yes—
167C2×C4×D79C2×D414yes—
168C2×C4×D79C2×D414yes—
169C2×C4×D79C2412yes—
170Dic316—216no—
171#11929614—216no—
172C2×C79⋊C8—24no—
173C2×C79⋊C8C2414yes—
174C4⋊Dic79—24no—
175C4⋊Dic79—28no—
176C4⋊Dic79—21no—
177C4⋊Dic79—24no—
178C4⋊Dic79—24no—
179C4⋊Dic79C2412yes—
180Dic79⋊C4—24no—
181Dic79⋊C4—24no—
182Dic79⋊C4—28no—
183Dic79⋊C4—24no—
184(C2×D79)⋊C4—28no—
185C4×Dic79—24no—
186C4×Dic79—24no—
187C4×Dic79—28no—
188C4×Dic79—24no—
189C4×Dic79C2×D412yes—
190C4×Dic79C2×D414yes—
191C4×Dic79C2×D414yes—
192C4×Dic79C2412yes—
193C2×Q8×C79—21no—
194C2×Q8×C79—24no—
195C2×Q8×C79—22no—
196C2×Q8×C79—44no—
197C2×Q8×C79#4114yes—
198C2×Q8×C79C2412yes—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—22no—
202C22×C4×C79C2×D411yescharacteristic
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2411yescharacteristic
205C2×C8×C79—24no—
206C2×C8×C79C2414yes—
207C4⋊C4×C79—24no—
208C4⋊C4×C79—24no—
209C4⋊C4×C79—21no—
210C4⋊C4×C79—22no—
211C4⋊C4×C79C2414yes—
212C4⋊C4×C79C2412yes—
213C42×C79—24no—
214C42×C79C2×D412yes—
215C42×C79C2412yes—
216C23×C79C22×D411yescharacteristic
217C22×D79—22no—
218C22×D79—22no—
219C22×D79C2×Q1614yes—
220C22×D79C22×D412yes—
221Q8×C79—24no—
222Q8×C79—22no—
223Q8×C79—48no—
224Q8×C79C2×#4114yes—
225C2×C4×C79—24no—
226C2×C4×C79—22no—
227C2×C4×C79—22no—
228C2×C4×C79—24no—
229C2×C4×C79—22no—
230C2×C4×C79—42no—
231C2×C4×C79—44no—
232C2×C4×C79C2×Q1614yes—
233C2×C4×C79C22×D412yes—
234C2×C4×C79C22×D411yescharacteristic
235C2×C4×C79C22×D412yes—
236C2×C4×C79C2×#4112yes—
237C2×C4×C79C2×#4112yes—
238C2×C4×C79C2511yescharacteristic
239C2×Dic79—24no—
240C2×Dic79—22no—
241C2×Dic79—22no—
242C2×Dic79—22no—
243C2×Dic79—22no—
244C2×Dic79—24no—
245C2×Dic79—44no—
246C2×Dic79—42no—
247C2×Dic79C2×Q1614yes—
248C2×Dic79C22×D412yes—
249C2×Dic79C22×D412yes—
250C2×Dic79C22×D412yes—
251C4×D79—216no—
252C4×D79—24no—
253C4×D79—22no—
254C4×D79—22no—
255C4×D79—44no—
256C4×D79—48no—
257C4×D79C2×Q16116yescomplemented
258Dic158—216no—
259Dic158—24no—
260Dic158—22no—
261Dic158—24no—
262Dic158—24no—
263Dic158—44no—
264Dic158C2×#4114yes—
265C8×C79—24no—
266C79⋊C8—24no—
267C22×C79#52512yes—
268C22×C79C22×Q1612yes—
269C22×C79#57512yes—
270C22×C79C23×D411yescharacteristic
271C2×D79—28no—
272C2×D79—22no—
273C2×D79—22no—
274C2×D79C22×Q1614yes—
275C4×C79—24no—
276C4×C79—22no—
277C4×C79—44no—
278C4×C79—42no—
279C4×C79#52512yes—
280C4×C79C22×Q1614yes—
281C4×C79C22×#4111yescharacteristic
282C4×C79C22×#4111yescharacteristic
283Dic79—22no—
284Dic79—24no—
285Dic79—22no—
286Dic79—44no—
287Dic79—42no—
288Dic79C22×Q1614yes—
289C2×#3104—791nomaximal, Sylow
290C2×C79#310414yescomplemented
291C2×C79C2×#52511yescharacteristic
292C2×C79C23×Q1611yescharacteristic
293C2×C79C2×#57511yescharacteristic
294D79—24no—
295C2×#533—791no—
296C22×C4×Q8—791no—
297#3104—7916no—
298C2×#484—792no—
299C2×#477—791no—
300C2×#477D7911yescharacteristic, complemented
301C2×#462—791no—
302C2×#462—791no—
303C2×#451—792no—
304C2×C4×Q16—792no—
305C2×C4×Q16—792no—
306C2×#431—791no—
307C79C2×#310411yescharacteristic, complemented, Sylow
308C23×Q8—791no—
309C22×Q16—792no—
310C22×Q16—792no—
311#533—798no—
312#533—1584no—
313C2×C4⋊Q8—791no—
314C2×C4⋊Q8C2×D7911yescharacteristic
315C2×#125—1581no—
316C2×C22⋊Q8—792no—
317C2×C22⋊Q8—1581no—
318C2×C4×Q8—791no—
319C2×C4×Q8—798no—
320C2×C4×Q8—791no—
321C2×C4×Q8—792no—
322C2×C4×Q8—791no—
323C2×C4×Q8—1581no—
324C2×C4×Q8—1581no—
325C2×C4×Q8—1584no—
326C2×C4×Q8—1581no—
327C2×C4×Q8C2×D7911yescharacteristic
328C2×#117—1581no—
329C22×C4⋊C4—791no—
330C22×C4⋊C4—1581no—
331C22×C42—791no—
332C22×C42—1581no—
333#484—7916no—
334#477—798no—
335#477C2×D7918yescomplemented
336#462—798no—
337#462—798no—
338#451—7916no—
339C4×Q16—7916no—
340C4×Q16—7916no—
341#431—798no—
342C2×#107—792no—
343C2×#107C2×D7912yes—
344C2×C4⋊C8—791no—
345C2×C4⋊C8C2×D7911yescharacteristic
346C2×#103—792no—
347C2×#103—792no—
348C2×#103—792no—
349C2×#103C2×D7912yes—
350C2×C22⋊C8—792no—
351C2×C4×C8—792no—
352C22×Q8—21no—
353C22×Q8—794no—
354C22×Q8—791no—
355C22×Q8—792no—
356C22×Q8—1581no—
357C22×Q8—1582no—
358C22×Q8—1584no—
359C22×Q8—1584no—
360C22×Q8C22×D7911yescharacteristic
361C23×C4—791no—
362C23×C4—791no—
363C23×C4—791no—
364C23×C4—1581no—
365C23×C4—1581no—
366C2×Q16—798no—
367C2×Q16—798no—
368C2×Q16—1588no—
369C2×Q16—1588no—
370C22×C8—792no—
371C22×C8C22×D7912yes—
372C4⋊Q8—22no—
373C4⋊Q8—794no—
374C4⋊Q8—1582no—
375C4⋊Q8C22×D7914yes—
376#125—1588no—
377C22⋊Q8—798no—
378C22⋊Q8—1584no—
379C22⋊Q8—1588no—
380C4×Q8—22no—
381C4×Q8—794no—
382C4×Q8—794no—
383C4×Q8—798no—
384C4×Q8—794no—
385C4×Q8—1588no—
386C4×Q8—1588no—
387C4×Q8—1582no—
388C4×Q8—1584no—
389C4×Q8—1582no—
390C4×Q8—1588no—
391C4×Q8—1582no—
392C4×Q8C22×D7914yes—
393#117—1588no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—791no—
397C2×C4⋊C4—794no—
398C2×C4⋊C4—1582no—
399C2×C4⋊C4—1588no—
400C2×C4⋊C4—1581no—
401C2×C4⋊C4—1581no—
402C2×C4⋊C4—1581no—
403C2×C4⋊C4—1582no—
404C2×C4⋊C4—1582no—
405C2×C4⋊C4—1581no—
406C2×C4⋊C4—1581no—
407C2×C4⋊C4—1581no—
408C2×C4⋊C4C22×D7911yescharacteristic
409C2×C4⋊C4C22×D7912yes—
410C2×C22⋊C4—1582no—
411C2×C42—21no—
412C2×C42—791no—
413C2×C42—791no—
414C2×C42—791no—
415C2×C42—794no—
416C2×C42—794no—
417C2×C42—1588no—
418C2×C42—1582no—
419C2×C42—1581no—
420C2×C42—1581no—
421C2×C42—1581no—
422C2×C42C22×D7911yescharacteristic
423#107—798no—
424#107C22×D7918yes—
425C4⋊C8—794no—
426C4⋊C8C22×D7914yes—
427#103—798no—
428#103—798no—
429#103—798no—
430#103C22×D7918yes—
431C22⋊C8—798no—
432C4×C8—798no—
433C24—791no—
434C2×Q8—22no—
435C2×Q8—21no—
436C2×Q8—24no—
437C2×Q8—44no—
438C2×Q8—794no—
439C2×Q8—792no—
440C2×Q8—794no—
441C2×Q8—1584no—
442C2×Q8—1588no—
443C2×Q8—1584no—
444C2×Q8—1584no—
445C2×Q8—1588no—
446C2×Q8—15816no—
447C2×Q8—1588no—
448C2×Q8—1582no—
449C2×Q8—1582no—
450C2×Q8—1581no—
451C2×Q8#1192962514yes—
452C2×Q8C23×D7912yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—3162no—
457C22×C4—3164no—
458C22×C4—794no—
459C22×C4—791no—
460C22×C4—798no—
461C22×C4—794no—
462C22×C4—791no—
463C22×C4—791no—
464C22×C4—792no—
465C22×C4—792no—
466C22×C4—1584no—
467C22×C4—1584no—
468C22×C4—1588no—
469C22×C4—1581no—
470C22×C4—1582no—
471C22×C4—1581no—
472C22×C4—1582no—
473C22×C4—1582no—
474C22×C4D4×D7911yescharacteristic
475C22×C4D4×D7911yescharacteristic
476C22×C4C23×D7911yescharacteristic
477Q16—15816no—
478Q16—15816no—
479C2×C8—24no—
480C2×C8—794no—
481C2×C8—1584no—
482C2×C8C23×D7914yes—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—792no—
488C4⋊C4—1584no—
489C4⋊C4—1584no—
490C4⋊C4—1588no—
491C4⋊C4—1584no—
492C4⋊C4—1588no—
493C4⋊C4—1584no—
494C4⋊C4—1581no—
495C4⋊C4—1584no—
496C4⋊C4—1584no—
497C4⋊C4C23×D7912yes—
498C4⋊C4C23×D7914yes—
499C22⋊C4—1588no—
500C42—24no—
501C42—792no—
502C42—792no—
503C42—794no—
504C42—794no—
505C42—1584no—
506C42—1584no—
507C42—1588no—
508C42—1584no—
509C42D4×D7912yes—
510C42C23×D7912yes—
511C23—794no—
512C23—792no—
513C23—1582no—
514C23—1582no—
515C23C2×D4×D7911yescharacteristic
516Q8—24no—
517Q8—22no—
518Q8—48no—
519Q8—3164no—
520Q8—794no—
521Q8—15816no—
522Q8—1584no—
523Q8—1584no—
524Q8—1584no—
525Q8—1582no—
526Q8C2×#1192962514yes—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—3164no—
535C2×C4—3168no—
536C2×C4—3164no—
537C2×C4—3162no—
538C2×C4—794no—
539C2×C4—792no—
540C2×C4—7916no—
541C2×C4—792no—
542C2×C4—792no—
543C2×C4—15816no—
544C2×C4—1582no—
545C2×C4—1584no—
546C2×C4—1582no—
547C2×C4—1584no—
548C2×C4—1582no—
549C2×C4—1582no—
550C2×C4—1584no—
551C2×C4—1582no—
552C2×C4—1582no—
553C2×C4Q16×D7914yes—
554C2×C4C2×D4×D7912yes—
555C2×C4C2×D4×D7911yescharacteristic
556C2×C4C2×D4×D7912yes—
557C2×C4#41×D7912yes—
558C2×C4C2×#1192962512yes—
559C2×C4C24×D7911yescharacteristic
560C8—24no—
561C8—1584no—
562C22—794no—
563C22—1588no—
564C22—1582no—
565C22—1582no—
566C22#1909907612yes—
567C22C2×Q16×D7912yes—
568C22#1909935912yes—
569C22C22×D4×D7911yescharacteristic
570C4—22no—
571C4—24no—
572C4—42no—
573C4—44no—
574C4—3162no—
575C4—3164no—
576C4—794no—
577C4—1582no—
578C4—1582no—
579C4—1584no—
580C4#1909907612yes—
581C4C2×Q16×D7914yes—
582C4C2×#41×D7911yescharacteristic
583C4C22×#1192962511yescharacteristic
584C2—1584no—
585C2#2377344114yesdirect product factor
586C2C2×#1909907611yescharacteristic
587C2C22×Q16×D7911yescharacteristic
588C2C2×#1909935911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#477×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenterC2×#477D79
hypocenterC79C2×#3104
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #23773441C2direct (N × H)
5. C2×#19098855C2semidirect
6. C2×#19098774C2semidirect
7. C2×#19098773C2semidirect
9. C2×#19098657C2semidirect
10. C2×#19098655C2semidirect
12. C2×#477×C79C2semidirect
37. #19098855C22semidirect
38. #19098774C22semidirect
39. #19098773C22semidirect
41. #19098657C22semidirect
42. #19098655C22semidirect
53. #477×C79C22semidirect
165. C2×C4×D79Q16semidirect
257. C4×D79C2×Q16semidirect
290. C2×C79#3104semidirect
300. C2×#477D79semidirect
307. C79C2×#3104semidirect
335. #477C2×D79semidirect
585. C2#23773441direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991182
C2×C4×Q8×D792
#237734412
C2×#190989002
C2×#190988552
C2×#190987742
C2×#190987732
C2×#190987202
C2×#190986572
C2×#190986552
C2×#190986152
C2×#477×C792
C2×#310479