Finite Group Databasebeta

← C2×#23775812 #35166752

Subgroups — C2×#23775812 #35166752

Order 20224.

1918 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099287C211yesmaximal, characteristic, complemented
2C2×#19099279C211yesmaximal, characteristic
3#23775812C2116yesmaximal, direct product factor
4C2×#19098907C212yesmaximal, complemented
5C2×#19098889C212yesmaximal, complemented
6C2×#19098855C211yesmaximal, characteristic, complemented
7C2×#19098840C211yesmaximal, characteristic, complemented
8C2×#19098793C212yesmaximal, complemented
9C2×C4×#11929613C211yesmaximal, characteristic, complemented
10C2×C8×D316C211yesmaximal, characteristic, complemented
11C2×#19098598C212yesmaximal, complemented
12C2×#498×C79C211yesmaximal, characteristic, complemented
13C22×#11929613C2211yescharacteristic
14C22×C8×D79C2212yes—
15#19099287—24no—
16#19099287C2218yescomplemented
17#19099279—24no—
18#19099279C2218yes—
19C2×#14579156—22no—
20C2×#14579150—21no—
21C2×#14579150—22no—
22C2×#14579141C2212yes—
23C2×#14579136—21no—
24C2×#14579136C2212yes—
25C2×Q8×Dic79—21no—
26C2×C4×Dic158C2211yescharacteristic
27C2×C4×D316C2211yescharacteristic
28C2×C4×D316C2211yescharacteristic
29C2×#14579119—21no—
30C2×#14579119C2212yes—
31C2×#14579119C2212yes—
32#19098907C22116yescomplemented
33#19098889C22116yescomplemented
34#19098855C2218yescomplemented
35#19098840C2218yescomplemented
36#19098793C22116yescomplemented
37C4×#11929613C2218yescomplemented
38C8×D316C2218yescomplemented
39#19098598C22116yescomplemented
40C2×#14579094C2212yes—
41C2×#14579094C2212yes—
42C2×#14579093C2211yescharacteristic
43C2×C4⋊(C79⋊C8)C2211yescharacteristic
44C2×#14579086C2211yescharacteristic
45C2×#14579084C2212yes—
46C2×#14579083C2211yescharacteristic
47C2×#14579081C2212yes—
48C2×(C2×D79)⋊C8C2212yes—
49C2×C4⋊Q8×C79C2211yescharacteristic
50C2×C4⋊Q8×C79C2211yescharacteristic
51#498×C79C2218yescomplemented
52C2×#106×C79C2212yes—
53C2×#106×C79C2212yes—
54C2×C4×C8×C79C2211yescharacteristic
55C22×Dic158C2311yescharacteristic
56C22×D316—22no—
57C22×D316D411yescharacteristic
58C22×D316C2311yescharacteristic
59C22×C4×D79—21no—
60C22×C4×D79C2312yes—
61C2×#11929613—24no—
62C2×#11929613C2314yes—
63C22×C79⋊C8C2312yes—
64C2×C8×D79—28no—
65C2×C8×D79C2318yes—
66#14579156—216no—
67#14579150—28no—
68#14579150—216no—
69#14579141—24no—
70#14579141C2318yes—
71#14579136—28no—
72#14579136—24no—
73#14579136C2318yes—
74Q8×Dic79—28no—
75C4×Dic158—22no—
76C4×Dic158C2314yes—
77C4×D316—22no—
78C4×D316D414yes—
79C4×D316C2314yes—
80C4×D316C2314yes—
81#14579119—24no—
82#14579119—24no—
83#14579119—28no—
84#14579119C2318yes—
85#14579119C2318yes—
86C2×C4⋊Dic79—22no—
87C2×C4⋊Dic79D411yescharacteristic
88C2×C4⋊Dic79C2311yescharacteristic
89C2×C4⋊Dic79C2311yescharacteristic
90C2×Dic79⋊C4—21no—
91C2×(C2×D79)⋊C4—21no—
92C2×(C2×D79)⋊C4—22no—
93C2×(C2×D79)⋊C4—22no—
94C2×(C2×D79)⋊C4—22no—
95C2×(C2×D79)⋊C4—22no—
96C2×(C2×D79)⋊C4D412yes—
97C2×C4×Dic79—21no—
98C2×C4×Dic79—22no—
99C2×C4×Dic79—22no—
100#14579094C2318yes—
101#14579094C2318yes—
102#14579093C2314yes—
103C4⋊(C79⋊C8)C2314yes—
104#14579086C2314yes—
105#14579084C2318yes—
106#14579083C2314yes—
107#14579081C2318yes—
108(C2×D79)⋊C8C2318yes—
109C22×Q8×C79—21no—
110C22×Q8×C79—21no—
111C22×C8×C79C2311yescharacteristic
112C22×C8×C79C2311yescharacteristic
113C4⋊Q8×C79—22no—
114C4⋊Q8×C79—22no—
115C4⋊Q8×C79C2314yes—
116C4⋊Q8×C79C2314yes—
117C2×C4⋊C4×C79—21no—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79C2312yes—
120C2×C4⋊C4×C79C2312yes—
121C2×C42×C79C2311yescharacteristic
122#106×C79C2318yes—
123#106×C79C2318yes—
124C4×C8×C79C2314yes—
125C23×D79—21no—
126C23×D79C2×D412yes—
127C2×Dic158—21no—
128C2×Dic158—22no—
129C2×Dic158—22no—
130C2×Dic158C2412yes—
131C2×D316—28no—
132C2×D316—24no—
133C2×D316—21no—
134C2×D316—22no—
135C2×D316—22no—
136C2×D316—84no—
137C2×D316C2×D414yes—
138C2×D316C2412yes—
139C22×Dic79—21no—
140C22×Dic79—21no—
141C22×Dic79—21no—
142C22×Dic79C2×D412yes—
143C2×C4×D79—24no—
144C2×C4×D79—24no—
145C2×C4×D79—24no—
146C2×C4×D79—44no—
147C2×C4×D79C2×D414yes—
148C2×C4×D79C2414yes—
149#11929613—28no—
150C2×C79⋊C8—24no—
151C2×C79⋊C8C2414yes—
152C8×D79—216no—
153C4⋊Dic79—28no—
154C4⋊Dic79—21no—
155C4⋊Dic79—21no—
156C4⋊Dic79C2×D414yes—
157C4⋊Dic79C2412yes—
158C4⋊Dic79C2412yes—
159Dic79⋊C4—24no—
160(C2×D79)⋊C4—28no—
161(C2×D79)⋊C4—28no—
162(C2×D79)⋊C4—28no—
163(C2×D79)⋊C4—28no—
164(C2×D79)⋊C4—24no—
165(C2×D79)⋊C4C2×D418yes—
166C4×Dic79—28no—
167C4×Dic79—28no—
168C4×Dic79—24no—
169C2×Q8×C79—24no—
170C2×Q8×C79—24no—
171C2×Q8×C79—44no—
172C2×Q8×C79—82no—
173C22×C4×C79—22no—
174C22×C4×C79—22no—
175C22×C4×C79C2×D411yescharacteristic
176C22×C4×C79C2×D411yescharacteristic
177C22×C4×C79C2411yescharacteristic
178C2×C8×C79—22no—
179C2×C8×C79#4114yes—
180C2×C8×C79C2412yes—
181C2×C8×C79C2412yes—
182C4⋊C4×C79—24no—
183C4⋊C4×C79—24no—
184C4⋊C4×C79—22no—
185C4⋊C4×C79—22no—
186C4⋊C4×C79C2414yes—
187C4⋊C4×C79C2414yes—
188C42×C79C2×D412yes—
189C42×C79C2412yes—
190C23×C79C22×D411yescharacteristic
191C22×D79—24no—
192C22×D79—24no—
193C22×D79—24no—
194C22×D79—22no—
195C22×D79—42no—
196C22×D79—42no—
197C22×D79—42no—
198C22×D79C22×D414yes—
199Q8×C79—48no—
200Q8×C79—84no—
201C2×C4×C79—22no—
202C2×C4×C79—24no—
203C2×C4×C79—24no—
204C2×C4×C79—44no—
205C2×C4×C79—44no—
206C2×C4×C79#13514yes—
207C2×C4×C79C22×D412yes—
208C2×C4×C79C22×D411yescharacteristic
209C2×C4×C79C22×D412yes—
210C2×C4×C79C2×#4112yes—
211C2×C4×C792−1+412yes—
212C2×C4×C79C2511yescharacteristic
213C2×Dic79—24no—
214C2×Dic79—22no—
215C2×Dic79—22no—
216C2×Dic79—22no—
217C2×Dic79—42no—
218C2×Dic79—42no—
219C2×Dic79—42no—
220C2×Dic79C22×D414yes—
221D316—28no—
222D316—22no—
223D316—22no—
224D316—42no—
225D316—88no—
226C4×D79—28no—
227C4×D79—24no—
228C4×D79—24no—
229C4×D79—48no—
230Dic158—22no—
231Dic158—22no—
232Dic158—42no—
233C8×C79—22no—
234C8×C79C2×#4114yes—
235C79⋊C8—24no—
236C22×C79#54712yes—
237C22×C79C2×#13512yes—
238C22×C79#57712yes—
239C22×C79C23×D411yescharacteristic
240C2×D79—24no—
241C2×D79—24no—
242C2×D79—24no—
243C2×D79—48no—
244C2×D79—42no—
245C2×D79—42no—
246C2×D79—42no—
247C2×D79—84no—
248C4×C79—22no—
249C4×C79—44no—
250C4×C79—44no—
251C4×C79#54712yes—
252C4×C79C2×#13514yes—
253C4×C79C22×#4111yescharacteristic
254C4×C79C2×2−1+411yescharacteristic
255Dic79—24no—
256Dic79—42no—
257Dic79—42no—
258Dic79—42no—
259C2×#3340—791nomaximal, Sylow
260C2×C79#334014yescomplemented
261C2×C79C2×#54711yescharacteristic
262C2×C79C22×#13511yescharacteristic
263C2×C79C2×#57711yescharacteristic
264D79—44no—
265D79—82no—
266C2×#556—791no—
267C2×#555—791no—
268#3340—7916no—
269C2×#498D7911yescharacteristic, complemented
270C2×#485—792no—
271C2×#482—792no—
272C2×#477—791no—
273C2×#474—791no—
274C2×#465—792no—
275C2×C4×SD16—791no—
276C2×C8×D4—791no—
277C2×#427—792no—
278C79C2×#334011yescharacteristic, complemented, Sylow
279C22×SD16—791no—
280C23×C8—792no—
281#556—798no—
282#556—1584no—
283#555—798no—
284#555—1584no—
285C2×C4⋊Q8C2×D7911yescharacteristic
286C2×C4⋊Q8C2×D7911yescharacteristic
287C2×#126—1582no—
288C2×#124—1582no—
289C2×#124—1581no—
290C2×C22⋊Q8—792no—
291C2×#121—792no—
292C2×#121—1581no—
293C2×C4×Q8—791no—
294C2×C4×Q8—1581no—
295C2×C4×D4—791no—
296C2×C4×D4—791no—
297C2×#117—792no—
298C2×#117—792no—
299C2×#117—1581no—
300#498C2×D7918yescomplemented
301#485—7916no—
302#482—7916no—
303#477—798no—
304#474—798no—
305#465—7916no—
306C4×SD16—798no—
307C8×D4—798no—
308#427—7916no—
309C2×#107—792no—
310C2×#107—792no—
311C2×#106—791no—
312C2×#106C2×D7912yes—
313C2×#106C2×D7912yes—
314C2×C4⋊C8—791no—
315C2×#103—791no—
316C2×#103—792no—
317C2×#102—791no—
318C2×#102—792no—
319C2×C22⋊C8—792no—
320C2×C4×C8C2×D7911yescharacteristic
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8—791no—
324C22×D4—791no—
325C22×D4—791no—
326C22×D4—1582no—
327C23×C4—792no—
328C23×C4—1581no—
329C2×SD16—794no—
330C2×SD16—1584no—
331C22×C8—792no—
332C22×C8—798no—
333C22×C8—1588no—
334C22×C8C22×D7911yescharacteristic
335C22×C8C22×D7911yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8C22×D7914yes—
339C4⋊Q8C22×D7914yes—
340#126—15816no—
341#124—15816no—
342#124—1588no—
343C22⋊Q8—798no—
344C22⋊Q8—1584no—
345#121—798no—
346#121—1584no—
347#121—1588no—
348C4×Q8—794no—
349C4×Q8—1588no—
350C4×Q8—1582no—
351C4×D4—794no—
352C4×D4—794no—
353C4×D4—794no—
354C4×D4—1582no—
355#117—798no—
356#117—798no—
357#117—1588no—
358#117—1584no—
359#117—1584no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—791no—
363C2×C4⋊C4—791no—
364C2×C4⋊C4—791no—
365C2×C4⋊C4—1582no—
366C2×C4⋊C4—1581no—
367C2×C4⋊C4C22×D7912yes—
368C2×C4⋊C4C22×D7912yes—
369C2×C22⋊C4—792no—
370C2×C22⋊C4—1582no—
371C2×C22⋊C4—1582no—
372C2×C22⋊C4—1582no—
373C2×C22⋊C4—1582no—
374C2×C22⋊C4—1581no—
375C2×C42—1582no—
376C2×C42—1582no—
377C2×C42—1581no—
378C2×C42C22×D7911yescharacteristic
379#107—798no—
380#107—798no—
381#106—794no—
382#106C22×D7918yes—
383#106C22×D7918yes—
384C4⋊C8—794no—
385#103—794no—
386#103—798no—
387#102—794no—
388#102—798no—
389C22⋊C8—798no—
390C4×C8C22×D7914yes—
391C24—792no—
392C24—1581no—
393C2×Q8—24no—
394C2×Q8—24no—
395C2×Q8—44no—
396C2×Q8—82no—
397C2×Q8—792no—
398C2×Q8—1582no—
399C2×Q8—1582no—
400C2×Q8—1581no—
401C2×D4—792no—
402C2×D4—794no—
403C2×D4—6324no—
404C2×D4—1588no—
405C2×D4—1582no—
406C2×D4—1582no—
407C2×D4—1584no—
408C2×D4—1581no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—3164no—
412C22×C4—792no—
413C22×C4—794no—
414C22×C4—794no—
415C22×C4—1581no—
416C22×C4—1581no—
417C22×C4—1581no—
418C22×C4—1584no—
419C22×C4—1584no—
420C22×C4—1584no—
421C22×C4D4×D7911yescharacteristic
422C22×C4D4×D7911yescharacteristic
423C22×C4C23×D7911yescharacteristic
424SD16—1588no—
425C2×C8—22no—
426C2×C8—794no—
427C2×C8—1584no—
428C2×C8—15816no—
429C2×C8#1192962514yes—
430C2×C8C23×D7912yes—
431C2×C8C23×D7912yes—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—794no—
437C4⋊C4—792no—
438C4⋊C4—792no—
439C4⋊C4—1588no—
440C4⋊C4—1584no—
441C4⋊C4—1581no—
442C4⋊C4—1581no—
443C4⋊C4C23×D7914yes—
444C4⋊C4C23×D7914yes—
445C22⋊C4—798no—
446C22⋊C4—1588no—
447C22⋊C4—1588no—
448C22⋊C4—1588no—
449C22⋊C4—1588no—
450C22⋊C4—1584no—
451C42—1588no—
452C42—1588no—
453C42—1584no—
454C42D4×D7912yes—
455C42C23×D7912yes—
456C23—3162no—
457C23—3162no—
458C23—3162no—
459C23—794no—
460C23—1582no—
461C23—1584no—
462C23—1584no—
463C23—1584no—
464C23C2×D4×D7911yescharacteristic
465Q8—48no—
466Q8—84no—
467Q8—3162no—
468Q8—1582no—
469Q8—1582no—
470D4—3162no—
471D4—6328no—
472D4—1582no—
473D4—1588no—
474D4—1582no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—3162no—
481C2×C4—3162no—
482C2×C4—3162no—
483C2×C4—3168no—
484C2×C4—794no—
485C2×C4—1582no—
486C2×C4—1582no—
487C2×C4—1582no—
488C2×C4—1584no—
489C2×C4—1584no—
490C2×C4—1588no—
491C2×C4—1584no—
492C2×C4#1457918214yes—
493C2×C4C2×D4×D7912yes—
494C2×C4C2×D4×D7911yescharacteristic
495C2×C4C2×D4×D7912yes—
496C2×C4C2×#1192962512yes—
497C2×C4#1457920912yes—
498C2×C4C24×D7911yescharacteristic
499C8—22no—
500C8—1584no—
501C8C2×#1192962514yes—
502C22—3168no—
503C22—3162no—
504C22—3162no—
505C22—3162no—
506C22—6324no—
507C22—1584no—
508C22—1584no—
509C22—1584no—
510C22#1909921612yes—
511C22C2×#1457918212yes—
512C22#1909936912yes—
513C22C22×D4×D7911yescharacteristic
514C4—22no—
515C4—44no—
516C4—44no—
517C4—3162no—
518C4—3162no—
519C4—3162no—
520C4—1584no—
521C4#1909921612yes—
522C4C2×#1457918214yes—
523C4C22×#1192962511yescharacteristic
524C4C2×#1457920911yescharacteristic
525C2—3164no—
526C2—6322no—
527C2#2377581214yesdirect product factor
528C2C2×#1909921611yescharacteristic
529C2C22×#1457918211yescharacteristic
530C2C2×#1909936911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#498×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099279C2
hypercenterC2×#498D79
hypocenterC79C2×#3340
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
1. C2×#19099287C2semidirect
3. #23775812C2direct (N × H)
4. C2×#19098907C2semidirect
5. C2×#19098889C2semidirect
6. C2×#19098855C2semidirect
7. C2×#19098840C2semidirect
8. C2×#19098793C2semidirect
9. C2×C4×#11929613C2semidirect
10. C2×C8×D316C2semidirect
11. C2×#19098598C2semidirect
12. C2×#498×C79C2semidirect
16. #19099287C22semidirect
32. #19098907C22semidirect
33. #19098889C22semidirect
34. #19098855C22semidirect
35. #19098840C22semidirect
36. #19098793C22semidirect
37. C4×#11929613C22semidirect
38. C8×D316C22semidirect
39. #19098598C22semidirect
51. #498×C79C22semidirect
260. C2×C79#3340semidirect
269. C2×#498D79semidirect
278. C79C2×#3340semidirect
300. #498C2×D79semidirect
527. C2#23775812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992872
C2×#190992792
#237758122
C2×#190989072
C2×#190988892
C2×#190988552
C2×#190988402
C2×#190987932
C2×C4×#119296132
C2×C8×D3162
C2×#190985982
C2×#498×C792
C2×#334079