Finite Group Databasebeta

← C2×#23773183 #35155765

Subgroups — C2×#23773183 #35155765

Order 20224.

2162 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099118C211yesmaximal, characteristic, complemented
2C2×C4×#11929625C211yesmaximal, characteristic
3#23773183C2116yesmaximal, direct product factor
4C2×#19098868C212yesmaximal, complemented
5C2×#19098858C211yesmaximal, characteristic, complemented
6C2×#19098862C212yesmaximal, complemented
7C2×#19098854C211yesmaximal, characteristic, complemented
8C2×#19098840C211yesmaximal, characteristic, complemented
9C2×#19098598C212yesmaximal, complemented
10C2×C4⋊C8×D79C211yesmaximal, characteristic, complemented
11C2×#19098558C212yesmaximal
12C2×#475×C79C211yesmaximal, characteristic, complemented
13C22×#11929625C2211yescharacteristic
14C22×C8×D79C2212yes—
15#19099118—24no—
16#19099118C2218yescomplemented
17C2×#14579161C2211yescharacteristic
18C2×#14579152C2212yes—
19C2×#14579141—21no—
20C2×#14579137—21no—
21C4×#11929625—24no—
22C4×#11929625C2218yes—
23C2×Q8×Dic79—21no—
24C2×Q8×Dic79C2211yescharacteristic
25C2×#14579126—21no—
26C2×C4×D316—21no—
27C2×C4×D316C2211yescharacteristic
28C2×#14579123—21no—
29C2×#14579123C2211yescharacteristic
30C2×#14579119—21no—
31C2×#14579119C2211yescharacteristic
32C2×#14579119C2212yes—
33C2×C42×D79—21no—
34C2×C42×D79C2211yescharacteristic
35#19098868C22116yescomplemented
36#19098862C22116yescomplemented
37#19098858C2218yescomplemented
38#19098854C2218yescomplemented
39#19098840C2218yescomplemented
40#19098598C22116yescomplemented
41C2×#14579094C2212yes—
42C2×#14579094C2212yes—
43C2×#14579093C2212yes—
44C2×C4⋊(C79⋊C8)C2211yescharacteristic
45C2×Dic79⋊C8C2212yes—
46C4⋊C8×D79C2218yescomplemented
47#19098558C22116yes—
48C2×#14579085C2212yes—
49C2×#14579083C2212yes—
50C2×#14579081C2212yes—
51C2×C4⋊Q8×C79C2211yescharacteristic
52C2×C4×Q8×C79C2211yescharacteristic
53#475×C79C2218yescomplemented
54C2×#106×C79C2212yes—
55C2×C4⋊C8×C79C2211yescharacteristic
56C2×#103×C79C2212yes—
57C2×#11929625—22no—
58C2×#11929625—24no—
59C2×#11929625Q818yescomplemented
60C2×#11929625C2314yes—
61C22×Dic158—21no—
62C22×D316—21no—
63C22×D316C2311yescharacteristic
64C22×C4×D79—21no—
65C22×C4×D79—21no—
66C22×C4×D79—21no—
67C22×C4×D79D411yescharacteristic
68C22×C4×D79D411yescharacteristic
69C22×C4×D79C2311yescharacteristic
70C22×C79⋊C8C2312yes—
71C2×C8×D79—28no—
72C2×C8×D79C2318yes—
73#14579161—22no—
74#14579161C2314yes—
75#14579152—24no—
76#14579152C2318yes—
77#14579141—28no—
78#14579137—28no—
79Q8×Dic79—28no—
80Q8×Dic79—22no—
81Q8×Dic79C2314yes—
82#14579126—28no—
83C4×D316—22no—
84C4×D316—28no—
85C4×D316C2314yes—
86#14579123—28no—
87#14579123—22no—
88#14579123C2314yes—
89#14579119—22no—
90#14579119—24no—
91#14579119—28no—
92#14579119C2314yes—
93#14579119C2318yes—
94C2×C4⋊Dic79—21no—
95C2×C4⋊Dic79—21no—
96C2×C4⋊Dic79—22no—
97C2×C4⋊Dic79C2311yescharacteristic
98C2×C4⋊Dic79C2312yes—
99C2×Dic79⋊C4—22no—
100C2×(C2×D79)⋊C4—21no—
101C2×(C2×D79)⋊C4—21no—
102C2×(C2×D79)⋊C4—22no—
103C2×(C2×D79)⋊C4—21no—
104C2×C4×Dic79—21no—
105C2×C4×Dic79—21no—
106C2×C4×Dic79—22no—
107C2×C4×Dic79D411yescharacteristic
108C2×C4×Dic79D411yescharacteristic
109C2×C4×Dic79C2311yescharacteristic
110C42×D79—28no—
111C42×D79D414yes—
112C42×D79C2314yes—
113#14579094C2318yes—
114#14579094C2318yes—
115#14579093C2318yes—
116C4⋊(C79⋊C8)C2314yes—
117Dic79⋊C8C2318yes—
118#14579085C2318yes—
119#14579083C2318yes—
120#14579081C2318yes—
121C22×Q8×C79—21no—
122C22×Q8×C79C2311yescharacteristic
123C22×C8×C79C2312yes—
124C4⋊Q8×C79—22no—
125C4⋊Q8×C79C2314yes—
126C4×Q8×C79—22no—
127C4×Q8×C79C2314yes—
128C2×C4⋊C4×C79—21no—
129C2×C4⋊C4×C79—21no—
130C2×C4⋊C4×C79C2311yescharacteristic
131C2×C4⋊C4×C79C2312yes—
132C2×C42×C79—21no—
133C2×C42×C79C2311yescharacteristic
134#106×C79C2318yes—
135C4⋊C8×C79C2314yes—
136#103×C79C2318yes—
137C23×D79—21no—
138C23×D79C2×D411yescharacteristic
139#11929625—216no—
140#11929625—28no—
141#11929625C2×Q8116yescomplemented
142C2×Dic158—24no—
143C2×Dic158—44no—
144C2×D316—28no—
145C2×D316—24no—
146C2×D316—21no—
147C2×D316—22no—
148C2×D316C2×Q814yes—
149C2×D316C2412yes—
150C22×Dic79—22no—
151C22×Dic79—21no—
152C22×Dic79C2×D411yescharacteristic
153C22×Dic79C2×D411yescharacteristic
154C22×Dic79C2×D411yescharacteristic
155C2×C4×D79—28no—
156C2×C4×D79—24no—
157C2×C4×D79—24no—
158C2×C4×D79—24no—
159C2×C4×D79—24no—
160C2×C4×D79—42no—
161C2×C4×D79—44no—
162C2×C4×D79—44no—
163C2×C4×D79C2×D414yes—
164C2×C4×D79C2×D414yes—
165C2×C4×D79C2×D412yes—
166C2×C4×D79C2×Q814yes—
167C2×C4×D79#4114yes—
168C2×C4×D79C2412yes—
169C2×C79⋊C8—24no—
170C2×C79⋊C8C2414yes—
171C8×D79—216no—
172C4⋊Dic79—24no—
173C4⋊Dic79—28no—
174C4⋊Dic79—24no—
175C4⋊Dic79—21no—
176C4⋊Dic79—22no—
177C4⋊Dic79C2414yes—
178C4⋊Dic79C2412yes—
179Dic79⋊C4—28no—
180(C2×D79)⋊C4—24no—
181(C2×D79)⋊C4—24no—
182(C2×D79)⋊C4—28no—
183(C2×D79)⋊C4—24no—
184C4×Dic79—24no—
185C4×Dic79—24no—
186C4×Dic79—28no—
187C4×Dic79C2×D414yes—
188C4×Dic79C2×D412yes—
189C4×Dic79C2×D414yes—
190C4×Dic79C2412yes—
191C2×Q8×C79—21no—
192C2×Q8×C79—24no—
193C2×Q8×C79—22no—
194C2×Q8×C79—44no—
195C2×Q8×C79C2×Q814yes—
196C2×Q8×C79C2412yes—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—22no—
200C22×C4×C79C2×D411yescharacteristic
201C22×C4×C79C2×D411yescharacteristic
202C22×C4×C79C2411yescharacteristic
203C2×C8×C79—24no—
204C2×C8×C79C2414yes—
205C4⋊C4×C79—24no—
206C4⋊C4×C79—24no—
207C4⋊C4×C79—21no—
208C4⋊C4×C79—22no—
209C4⋊C4×C79C2414yes—
210C4⋊C4×C79C2412yes—
211C42×C79—24no—
212C42×C79C2×D412yes—
213C42×C79C2412yes—
214C23×C79C22×D411yescharacteristic
215C22×D79—22no—
216C22×D79—22no—
217C22×D79—24no—
218C22×D79—22no—
219C22×D79—42no—
220C22×D79—42no—
221C22×D79C22⋊Q814yes—
222C22×D79C22×D412yes—
223Q8×C79—24no—
224Q8×C79—22no—
225Q8×C79—48no—
226Q8×C79C22×Q814yes—
227C2×C4×C79—24no—
228C2×C4×C79—22no—
229C2×C4×C79—22no—
230C2×C4×C79—22no—
231C2×C4×C79—24no—
232C2×C4×C79—44no—
233C2×C4×C79—42no—
234C2×C4×C79#13514yes—
235C2×C4×C79C22×D412yes—
236C2×C4×C79C22×D411yescharacteristic
237C2×C4×C79C22×D412yes—
238C2×C4×C79C22×Q812yes—
239C2×C4×C79C2×#4112yes—
240C2×C4×C79C2511yescharacteristic
241C2×Dic79—22no—
242C2×Dic79—22no—
243C2×Dic79—22no—
244C2×Dic79—24no—
245C2×Dic79—42no—
246C2×Dic79—44no—
247C2×Dic79C22⋊Q814yes—
248C2×Dic79C22×D412yes—
249C2×Dic79C22×D412yes—
250C2×Dic79C22×D412yes—
251D316—216no—
252D316—24no—
253D316—22no—
254D316C22×Q814yes—
255C4×D79—28no—
256C4×D79—216no—
257C4×D79—44no—
258C4×D79—48no—
259C4×D79—48no—
260C4×D79C22⋊Q818yes—
261C4×D79C22×Q814yes—
262C4×D79C2×#4114yes—
263Dic158—48no—
264C8×C79—24no—
265C79⋊C8—24no—
266C22×C79C2×C22⋊Q812yes—
267C22×C79C2×#13512yes—
268C22×C79#57512yes—
269C22×C79C23×D411yescharacteristic
270C2×D79—28no—
271C2×D79—22no—
272C2×D79—22no—
273C2×D79—24no—
274C2×D79—48no—
275C2×D79—42no—
276C2×D79—42no—
277C2×D79C2×C22⋊Q814yes—
278C4×C79—24no—
279C4×C79—22no—
280C4×C79—44no—
281C4×C79—42no—
282C4×C79C2×C22⋊Q812yes—
283C4×C79C2×#13514yes—
284C4×C79C23×Q811yescharacteristic
285C4×C79C22×#4111yescharacteristic
286Dic79—22no—
287Dic79—22no—
288Dic79—42no—
289Dic79—44no—
290Dic79C2×C22⋊Q814yes—
291C2×#3076—791nomaximal, Sylow
292C2×C79#307614yescomplemented
293C2×C79C22×C22⋊Q811yescharacteristic
294C2×C79C22×#13511yescharacteristic
295C2×C79C2×#57511yescharacteristic
296D79—24no—
297D79—44no—
298C2×#533—791no—
299C2×C4×#41—791no—
300#3076—7916no—
301C2×#479—792no—
302C2×#477—791no—
303C2×#475D7911yescharacteristic, complemented
304C2×#478—792no—
305C2×#476—791no—
306C2×#474—791no—
307C2×#427—792no—
308C22×C4⋊C8—791no—
309C2×#416—792no—
310C79C2×#307611yescharacteristic, complemented, Sylow
311C22×#41—791no—
312C23×C8—792no—
313#533—798no—
314#533—1584no—
315C2×C4⋊Q8—791no—
316C2×C4⋊Q8C2×D7911yescharacteristic
317C2×#125—792no—
318C2×C22⋊Q8—1581no—
319C2×C22⋊Q8—1581no—
320C4×#41—798no—
321C4×#41—1584no—
322C2×C4×Q8—791no—
323C2×C4×Q8—1581no—
324C2×C4×Q8—1581no—
325C2×C4×Q8C2×D7911yescharacteristic
326C2×C4×D4—791no—
327C2×C4×D4—791no—
328C2×C4×D4—1581no—
329C2×C4×D4—1581no—
330C2×#117—792no—
331C2×#117—791no—
332C2×#117—1581no—
333C22×C42—791no—
334C22×C42—1581no—
335#479—7916no—
336#478—7916no—
337#477—798no—
338#476—798no—
339#475C2×D7918yescomplemented
340#474—798no—
341#427—7916no—
342C2×#107—792no—
343C2×#107—792no—
344C2×#106—792no—
345C2×#106C2×D7912yes—
346C2×C4⋊C8—792no—
347C2×C4⋊C8—791no—
348C2×C4⋊C8—798no—
349C2×C4⋊C8C2×D7911yescharacteristic
350#416—7916no—
351C2×#103—792no—
352C2×#103C2×D7912yes—
353C2×#102—792no—
354C2×#102—792no—
355C2×#41—798no—
356C2×#41—794no—
357C2×#41—1582no—
358C2×#41—1584no—
359C22×Q8—21no—
360C22×Q8—1581no—
361C22×Q8C22×D7911yescharacteristic
362C22×D4—791no—
363C22×D4—1581no—
364C23×C4—791no—
365C23×C4—791no—
366C23×C4—791no—
367C23×C4—1581no—
368C23×C4—1581no—
369C23×C4—1581no—
370C22×C8—792no—
371C22×C8—798no—
372C22×C8—1588no—
373C22×C8C22×D7912yes—
374C4⋊Q8—22no—
375C4⋊Q8—794no—
376C4⋊Q8—1582no—
377C4⋊Q8C22×D7914yes—
378#125—798no—
379#125—1584no—
380C22⋊Q8—1588no—
381C22⋊Q8—1588no—
382C4×Q8—22no—
383C4×Q8—794no—
384C4×Q8—1588no—
385C4×Q8—1582no—
386C4×Q8—1588no—
387C4×Q8C22×D7914yes—
388C4×D4—794no—
389C4×D4—794no—
390C4×D4—1588no—
391C4×D4—1582no—
392C4×D4—1588no—
393C4×D4—1582no—
394#117—794no—
395#117—798no—
396#117—1588no—
397#117—1582no—
398#117—1584no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—791no—
402C2×C4⋊C4—792no—
403C2×C4⋊C4—1581no—
404C2×C4⋊C4—1582no—
405C2×C4⋊C4—1582no—
406C2×C4⋊C4—1581no—
407C2×C4⋊C4C22×D7911yescharacteristic
408C2×C4⋊C4C22×D7912yes—
409C2×C22⋊C4—1581no—
410C2×C22⋊C4—1581no—
411C2×C22⋊C4—1582no—
412C2×C22⋊C4—1581no—
413C2×C42—21no—
414C2×C42—791no—
415C2×C42—791no—
416C2×C42—791no—
417C2×C42—794no—
418C2×C42—794no—
419C2×C42—1588no—
420C2×C42—1581no—
421C2×C42—1582no—
422C2×C42—1581no—
423C2×C42C22×D7911yescharacteristic
424#107—798no—
425#107—798no—
426#106—798no—
427#106C22×D7918yes—
428C4⋊C8—798no—
429C4⋊C8—794no—
430C4⋊C8C22×D7914yes—
431#103—798no—
432#103C22×D7918yes—
433#102—798no—
434#102—798no—
435C24—791no—
436C24—1581no—
437#41—7916no—
438#41—15816no—
439#41—1588no—
440C2×Q8—22no—
441C2×Q8—21no—
442C2×Q8—24no—
443C2×Q8—44no—
444C2×Q8—3164no—
445C2×Q8—1584no—
446C2×Q8Q8×D7914yes—
447C2×Q8C23×D7912yes—
448C2×D4—794no—
449C2×D4—792no—
450C2×D4—1584no—
451C2×D4—1588no—
452C2×D4—1582no—
453C2×D4—1581no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—3162no—
458C22×C4—3164no—
459C22×C4—3164no—
460C22×C4—794no—
461C22×C4—791no—
462C22×C4—794no—
463C22×C4—794no—
464C22×C4—792no—
465C22×C4—792no—
466C22×C4—791no—
467C22×C4—791no—
468C22×C4—794no—
469C22×C4—1584no—
470C22×C4—1584no—
471C22×C4—1588no—
472C22×C4—1581no—
473C22×C4—1582no—
474C22×C4—1584no—
475C22×C4—1584no—
476C22×C4D4×D7911yescharacteristic
477C22×C4D4×D7911yescharacteristic
478C22×C4C23×D7911yescharacteristic
479C2×C8—24no—
480C2×C8—794no—
481C2×C8—15816no—
482C2×C8—1584no—
483C2×C8C23×D7914yes—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—794no—
489C4⋊C4—792no—
490C4⋊C4—1588no—
491C4⋊C4—1584no—
492C4⋊C4—1588no—
493C4⋊C4—1581no—
494C4⋊C4—1582no—
495C4⋊C4—1584no—
496C4⋊C4C23×D7914yes—
497C4⋊C4C23×D7912yes—
498C22⋊C4—1584no—
499C22⋊C4—1584no—
500C22⋊C4—1588no—
501C22⋊C4—1584no—
502C42—24no—
503C42—792no—
504C42—794no—
505C42—794no—
506C42—792no—
507C42—1584no—
508C42—1584no—
509C42—1588no—
510C42D4×D7912yes—
511C42C23×D7912yes—
512C23—3162no—
513C23—3162no—
514C23—794no—
515C23—792no—
516C23—1584no—
517C23—1582no—
518C23—1582no—
519C23—1582no—
520C23C2×D4×D7911yescharacteristic
521Q8—24no—
522Q8—22no—
523Q8—48no—
524Q8—3168no—
525Q8C2×Q8×D7914yes—
526D4—794no—
527D4—15816no—
528D4—1584no—
529D4—1582no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—3164no—
538C2×C4—3168no—
539C2×C4—3162no—
540C2×C4—3164no—
541C2×C4—3168no—
542C2×C4—794no—
543C2×C4—792no—
544C2×C4—798no—
545C2×C4—794no—
546C2×C4—794no—
547C2×C4—792no—
548C2×C4—792no—
549C2×C4—15816no—
550C2×C4—1582no—
551C2×C4—1584no—
552C2×C4—1582no—
553C2×C4—1582no—
554C2×C4—1588no—
555C2×C4#1457918214yes—
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—3162no—
565C22—3162no—
566C22—3168no—
567C22—794no—
568C22—1584no—
569C22—1582no—
570C22—1582no—
571C22—1588no—
572C22C22⋊Q8×D7912yes—
573C22C2×#1457918212yes—
574C22#1909936212yes—
575C22C22×D4×D7911yescharacteristic
576C4—22no—
577C4—24no—
578C4—44no—
579C4—42no—
580C4—3162no—
581C4—3164no—
582C4—794no—
583C4—1582no—
584C4—1582no—
585C4C22⋊Q8×D7912yes—
586C4C2×#1457918214yes—
587C4C22×Q8×D7911yescharacteristic
588C4C2×#41×D7911yescharacteristic
589C2—3164no—
590C2—1584no—
591C2#2377318314yesdirect product factor
592C2C2×C22⋊Q8×D7911yescharacteristic
593C2C22×#1457918211yescharacteristic
594C2C2×#1909936211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#475×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929625C22
hypercenterC2×#475D79
hypocenterC79C2×#3076
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×#19099118C2semidirect
3. #23773183C2direct (N × H)
4. C2×#19098868C2semidirect
5. C2×#19098858C2semidirect
6. C2×#19098862C2semidirect
7. C2×#19098854C2semidirect
8. C2×#19098840C2semidirect
9. C2×#19098598C2semidirect
10. C2×C4⋊C8×D79C2semidirect
12. C2×#475×C79C2semidirect
16. #19099118C22semidirect
35. #19098868C22semidirect
36. #19098862C22semidirect
37. #19098858C22semidirect
38. #19098854C22semidirect
39. #19098840C22semidirect
40. #19098598C22semidirect
46. C4⋊C8×D79C22semidirect
53. #475×C79C22semidirect
59. C2×#11929625Q8semidirect
141. #11929625C2×Q8semidirect
292. C2×C79#3076semidirect
303. C2×#475D79semidirect
310. C79C2×#3076semidirect
339. #475C2×D79semidirect
591. C2#23773183direct (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×#119296252
#237731832
C2×#190988682
C2×#190988582
C2×#190988622
C2×#190988542
C2×#190988402
C2×#190985982
C2×C4⋊C8×D792
C2×#190985582
C2×#475×C792
C2×#307679