Finite Group Databasebeta

← C2×#23777547 #35195170

Subgroups — C2×#23777547 #35195170

Order 20224.

6554 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
1#23777547C2132yesmaximal, direct product factor
2C2×C79⋊#564C211yesmaximal, characteristic, complemented
3C2×#19099317C212yesmaximal, complemented
4C2×#19099314C214yesmaximal, complemented
5C2×#19099312C214yesmaximal, complemented
6C2×#19099311C211yesmaximal, characteristic, complemented
7C2×#19099309C214yesmaximal, complemented
8C2×#19099117C214yesmaximal, complemented
9C2×#19099100C214yesmaximal, complemented
10C2×#19099097C212yesmaximal, complemented
11C2×#19099091C214yesmaximal, complemented
12C2×#533×C79C211yesmaximal, characteristic, complemented
13C79⋊#564C22116yescomplemented
14#19099317C22132yescomplemented
15#19099314C22164yescomplemented
16#19099312C22164yescomplemented
17#19099311C22116yescomplemented
18#19099309C22164yescomplemented
19#19099117C22164yescomplemented
20C2×#14579160C2214yes—
21C2×#14579159C2214yes—
22#19099100C22164yescomplemented
23#19099097C22132yescomplemented
24#19099091C22164yescomplemented
25C2×#14579156C2214yes—
26C2×#14579156C2214yes—
27C2×#14579156C2214yes—
28C2×#14579155C2214yes—
29C2×#14579154C2214yes—
30C2×#14579153C2212yes—
31C2×#14579152C2214yes—
32C2×#14579151C2214yes—
33C2×#14579151C2214yes—
34C2×#14579151C2214yes—
35C2×#14579150C2214yes—
36C2×#14579149C2212yes—
37C2×#14579147C2214yes—
38C2×#14579146C2214yes—
39C2×#14579146C2214yes—
40C2×#14579146C2214yes—
41C2×#14579144C2214yes—
42C2×#14579143C2214yes—
43C2×#14579141C2214yes—
44C2×#14579140C2212yes—
45C2×#14579139C2214yes—
46C2×#14579139C2214yes—
47C2×#14579139C2214yes—
48C2×#14579137C2214yes—
49C2×#14579137C2214yes—
50C2×#14579136C2214yes—
51C2×#14579135C2212yes—
52C2×#14579134C2214yes—
53C2×C4×Dic158C2214yes—
54C2×C4×Dic158C2212yes—
55C2×C4×D316C2214yes—
56C2×C4×D316C2212yes—
57C2×C4×C22⋊D79C2214yes—
58C2×#14579118C2214yes—
59C2×#14579118C2214yes—
60C2×C42×D79C2214yes—
61#533×C79C22116yescomplemented
62C2×C4⋊Q8×C79C2212yes—
63C2×#125×C79C2211yescharacteristic
64C2×#125×C79C2211yescharacteristic
65C2×C22⋊Q8×C79C2214yes—
66C2×C4×Q8×C79C2214yes—
67C2×#117×C79C2212yes—
68C22×C42×C79C2211yescharacteristic
69C22×Dic158C2312yes—
70C22×Dic158C2314yes—
71C22×D316C2314yes—
72C22×D316C2312yes—
73C22×C22⋊D79C2314yes—
74C22×C4×D79C2314yes—
75C22×C4×D79C2314yes—
76C22×C4×D79C2314yes—
77#14579160C23132yes—
78#14579159C23132yes—
79#14579156C23132yes—
80#14579156C23132yes—
81#14579156C23132yes—
82#14579155C23132yes—
83#14579154C23132yes—
84#14579153C23116yes—
85#14579152C23132yes—
86#14579151C23132yes—
87#14579151C23132yes—
88#14579151C23132yes—
89#14579150C23132yes—
90#14579149C23116yes—
91#14579147C23132yes—
92#14579146C23132yes—
93#14579146C23132yes—
94#14579146C23132yes—
95#14579144C23132yes—
96#14579143C23132yes—
97#14579141C23132yes—
98#14579140C23116yes—
99#14579139C23132yes—
100#14579139C23132yes—
101#14579139C23132yes—
102#14579137C23132yes—
103#14579137C23132yes—
104#14579136C23132yes—
105#14579135C23116yes—
106#14579134C23132yes—
107C4×Dic158C23132yes—
108C4×Dic158C23116yes—
109C4×D316C23132yes—
110C4×D316C23116yes—
111C4×C22⋊D79C23132yes—
112#14579118C23132yes—
113#14579118C23132yes—
114C2×C4⋊Dic79C2314yes—
115C2×C4⋊Dic79C2312yes—
116C2×C4⋊Dic79C2312yes—
117C2×C4⋊Dic79C2314yes—
118C2×Dic79⋊C4C2314yes—
119C2×Dic79⋊C4C2314yes—
120C2×Dic79⋊C4C2314yes—
121C2×Dic79⋊C4C2314yes—
122C2×Dic79⋊C4C2314yes—
123C2×Dic79⋊C4C2314yes—
124C2×Dic79⋊C4C2314yes—
125C2×Dic79⋊C4C2314yes—
126C2×C22⋊Dic79C2314yes—
127C2×(C2×D79)⋊C4C2314yes—
128C2×(C2×D79)⋊C4C2314yes—
129C2×(C2×D79)⋊C4C2314yes—
130C2×(C2×D79)⋊C4C2314yes—
131C2×(C2×D79)⋊C4C2314yes—
132C2×(C2×D79)⋊C4C2314yes—
133C2×(C2×D79)⋊C4C2314yes—
134C2×(C2×D79)⋊C4C2314yes—
135C2×C4×Dic79C2314yes—
136C2×C4×Dic79C2314yes—
137C2×C4×Dic79C2314yes—
138C42×D79C23132yes—
139C22×Q8×C79C2314yes—
140C23×C4×C79C2311yescharacteristic
141C23×C4×C79C2312yes—
142C4⋊Q8×C79C23116yes—
143#125×C79C2318yes—
144#125×C79C2318yes—
145C22⋊Q8×C79C23132yes—
146C4×Q8×C79C23132yes—
147#117×C79C23116yes—
148C2×C4⋊C4×C79C2312yes—
149C2×C4⋊C4×C79C2312yes—
150C2×C4⋊C4×C79C2314yes—
151C2×C4⋊C4×C79C2314yes—
152C2×C4⋊C4×C79C2314yes—
153C2×C22⋊C4×C79C2314yes—
154C2×C42×C79C2312yes—
155C2×C42×C79C2311yescharacteristic
156C2×C42×C79C2311yescharacteristic
157C2×C42×C79C2318yes—
158C2×C42×C79C2314yes—
159C23×D79C2414yes—
160C2×Dic158—48no—
161C2×Dic158—44no—
162C2×Dic158C2418yes—
163C2×Dic158C24116yes—
164C2×D316—48no—
165C2×D316—44no—
166C2×D316C24116yes—
167C2×D316C2418yes—
168C2×C22⋊D79—48no—
169C2×C22⋊D79C24116yes—
170C22×Dic79C2414yes—
171C22×Dic79C2414yes—
172C22×Dic79C2414yes—
173C2×C4×D79—216no—
174C2×C4×D79—48no—
175C2×C4×D79—48no—
176C2×C4×D79C24116yes—
177C2×C4×D79C24116yes—
178C2×C4×D79C24116yes—
179C4⋊Dic79C24116yes—
180C4⋊Dic79C2418yes—
181C4⋊Dic79C2418yes—
182C4⋊Dic79C24116yes—
183Dic79⋊C4C24116yes—
184Dic79⋊C4C24116yes—
185Dic79⋊C4C24116yes—
186Dic79⋊C4C24116yes—
187Dic79⋊C4C24116yes—
188Dic79⋊C4C24116yes—
189Dic79⋊C4C24116yes—
190Dic79⋊C4C24116yes—
191C22⋊Dic79C24116yes—
192(C2×D79)⋊C4C24116yes—
193(C2×D79)⋊C4C24116yes—
194(C2×D79)⋊C4C24116yes—
195(C2×D79)⋊C4C24116yes—
196(C2×D79)⋊C4C24116yes—
197(C2×D79)⋊C4C24116yes—
198(C2×D79)⋊C4C24116yes—
199(C2×D79)⋊C4C24116yes—
200C4×Dic79C24116yes—
201C4×Dic79C24116yes—
202C4×Dic79C24116yes—
203C24×C79C2411yescharacteristic
204C2×Q8×C79—48no—
205C2×Q8×C79C24116yes—
206C22×C4×C79—24no—
207C22×C4×C79—44no—
208C22×C4×C79C2412yes—
209C22×C4×C79C2414yes—
210C22×C4×C79C2411yescharacteristic
211C22×C4×C79C2412yes—
212C22×C4×C79C2414yes—
213C22×C4×C79C2414yes—
214C22×C4×C79C2418yes—
215C22×C4×C79C2411yescharacteristic
216C4⋊C4×C79C2418yes—
217C4⋊C4×C79C2418yes—
218C4⋊C4×C79C24116yes—
219C4⋊C4×C79C24116yes—
220C4⋊C4×C79C24116yes—
221C22⋊C4×C79C24116yes—
222C42×C79C2418yes—
223C42×C79C2414yes—
224C42×C79C2414yes—
225C42×C79C24116yes—
226C23×C79—22no—
227C23×C79—24no—
228C23×C79C2512yes—
229C23×C79C2511yescharacteristic
230C22×D79—28no—
231C22×D79—28no—
232C22×D79—28no—
233C22×D79C2518yes—
234Q8×C79—416no—
235C2×C4×C79—22no—
236C2×C4×C79—28no—
237C2×C4×C79—28no—
238C2×C4×C79—24no—
239C2×C4×C79—24no—
240C2×C4×C79—28no—
241C2×C4×C79—48no—
242C2×C4×C792−1+414yes—
243C2×C4×C79C2518yes—
244C2×C4×C79C2518yes—
245C2×C4×C79C2512yes—
246C2×C4×C79C2514yes—
247C2×C4×C79C2514yes—
248C2×C4×C79C2512yes—
249C22⋊D79—416no—
250C2×Dic79—28no—
251C2×Dic79—28no—
252C2×Dic79—28no—
253C2×Dic79C2518yes—
254C2×Dic79C2518yes—
255C2×Dic79C2518yes—
256D316—48no—
257D316—416no—
258C4×D79—232no—
259C4×D79—416no—
260C4×D79—416no—
261Dic158—416no—
262Dic158—48no—
263C22×C79—22no—
264C22×C79—24no—
265C22×C79—44no—
266C22×C79C2×2−1+412yes—
267C22×C79#58514yes—
268C22×C79C2611yescharacteristic
269C2×D79—28no—
270C2×D79—28no—
271C2×D79—28no—
272C2×D79—416no—
273C4×C79—22no—
274C4×C79—24no—
275C4×C79—24no—
276C4×C79—28no—
277C4×C79—28no—
278C4×C79C2×2−1+414yes—
279Dic79—28no—
280Dic79—28no—
281Dic79—28no—
282C2×#3531—791nomaximal, Sylow
283C2×C79—42no—
284C2×C79#353114yescomplemented
285C2×C79C22×2−1+411yescharacteristic
286C2×C79C2×#58512yes—
287D79—48no—
288#3531—7932no—
289C2×#564—791no—
290C2×#563—794no—
291C2×#563—792no—
292C2×#563—794no—
293C2×#562—791no—
294C2×#562—794no—
295C2×#533—794no—
296C2×#533D7911yescharacteristic, complemented
297C2×#529—792no—
298C2×#529—794no—
299C2×#529—794no—
300C79C2×#353111yescharacteristic, complemented, Sylow
301#564—7916no—
302#563—7964no—
303#563—7932no—
304#563—7964no—
305#562—7916no—
306#562—7964no—
307#533—7964no—
308#533C2×D79116yescomplemented
309C2×C4⋊Q8—794no—
310C2×C4⋊Q8—794no—
311C2×C4⋊Q8C2×D7912yes—
312#529—7964no—
313#529—7964no—
314#529—7932no—
315C2×#126—794no—
316C2×#126—794no—
317C2×#126—794no—
318C2×#126—794no—
319C2×#126—794no—
320C2×#125—794no—
321C2×#125—794no—
322C2×#125—794no—
323C2×#125—794no—
324C2×#125—792no—
325C2×#125C2×D7911yescharacteristic
326C2×#125C2×D7911yescharacteristic
327C2×#124—794no—
328C2×#124—794no—
329C2×#124—792no—
330C2×#123—794no—
331C2×#123—794no—
332C2×#123—794no—
333C2×#123—794no—
334C2×#123—794no—
335C2×C22⋊Q8—794no—
336C2×C22⋊Q8—794no—
337C2×C22⋊Q8—792no—
338C2×C22⋊Q8—794no—
339C2×C22⋊Q8—794no—
340C2×C22⋊Q8—794no—
341C2×C22⋊Q8—794no—
342C2×C22⋊Q8C2×D7914yes—
343C2×#121—792no—
344C2×#121—794no—
345C2×#121—794no—
346C2×C4×Q8—792no—
347C2×C4×Q8—794no—
348C2×C4×Q8C2×D7914yes—
349C2×C4×D4—794no—
350C2×C4×D4—792no—
351C2×C4×D4—794no—
352C2×#117—794no—
353C2×#117—794no—
354C2×#117C2×D7912yes—
355C22×C42—794no—
356C22×C42C2×D7911yescharacteristic
357C22×Q8—792no—
358C22×Q8—794no—
359C22×Q8C22×D7914yes—
360C22×D4—794no—
361C22×D4—794no—
362C22×D4—792no—
363C23×C4—794no—
364C23×C4—794no—
365C23×C4—794no—
366C23×C4C22×D7911yescharacteristic
367C23×C4C22×D7912yes—
368C4⋊Q8—7932no—
369C4⋊Q8—7932no—
370C4⋊Q8C22×D79116yes—
371#126—7932no—
372#126—7932no—
373#126—7932no—
374#126—7932no—
375#126—7932no—
376#125—7932no—
377#125—7932no—
378#125—7932no—
379#125—7932no—
380#125—7916no—
381#125C22×D7918yes—
382#125C22×D7918yes—
383#124—7932no—
384#124—7932no—
385#124—7916no—
386#123—7932no—
387#123—7932no—
388#123—7932no—
389#123—7932no—
390#123—7932no—
391C22⋊Q8—7932no—
392C22⋊Q8—7932no—
393C22⋊Q8—7916no—
394C22⋊Q8—7932no—
395C22⋊Q8—7932no—
396C22⋊Q8—7932no—
397C22⋊Q8—7932no—
398C22⋊Q8C22×D79132yes—
399#121—7916no—
400#121—7932no—
401#121—7932no—
402C4×Q8—7932no—
403C4×Q8—7916no—
404C4×Q8C22×D79132yes—
405C4×D4—7932no—
406C4×D4—7932no—
407C4×D4—7916no—
408#117—7932no—
409#117—7932no—
410#117C22×D79116yes—
411C2×C4⋊C4—794no—
412C2×C4⋊C4—794no—
413C2×C4⋊C4—794no—
414C2×C4⋊C4—794no—
415C2×C4⋊C4—794no—
416C2×C4⋊C4—794no—
417C2×C4⋊C4—792no—
418C2×C4⋊C4—794no—
419C2×C4⋊C4—792no—
420C2×C4⋊C4—794no—
421C2×C4⋊C4—794no—
422C2×C4⋊C4—794no—
423C2×C4⋊C4C22×D7912yes—
424C2×C4⋊C4C22×D7912yes—
425C2×C4⋊C4C22×D7914yes—
426C2×C4⋊C4C22×D7914yes—
427C2×C4⋊C4C22×D7914yes—
428C2×C22⋊C4—794no—
429C2×C22⋊C4—794no—
430C2×C22⋊C4—794no—
431C2×C22⋊C4—794no—
432C2×C22⋊C4—794no—
433C2×C22⋊C4—794no—
434C2×C22⋊C4—794no—
435C2×C22⋊C4—794no—
436C2×C22⋊C4—794no—
437C2×C22⋊C4C22×D7914yes—
438C2×C42—794no—
439C2×C42—794no—
440C2×C42—794no—
441C2×C42—7932no—
442C2×C42C22×D7911yescharacteristic
443C2×C42C22×D7911yescharacteristic
444C2×C42C22×D7918yes—
445C2×C42C22×D7912yes—
446C2×C42C22×D7914yes—
447C24—794no—
448C24C23×D7911yescharacteristic
449C2×Q8—48no—
450C2×Q8—3164no—
451C2×Q8—3168no—
452C2×Q8—798no—
453C2×Q8—7916no—
454C2×Q8C23×D79116yes—
455C2×D4—3164no—
456C2×D4—3168no—
457C2×D4—3168no—
458C2×D4—7916no—
459C2×D4—7916no—
460C2×D4—798no—
461C22×C4—24no—
462C22×C4—44no—
463C22×C4—3168no—
464C22×C4—3168no—
465C22×C4—7916no—
466C22×C4—7916no—
467C22×C4—794no—
468C22×C4—794no—
469C22×C4—794no—
470C22×C4—7916no—
471C22×C4—15816no—
472C22×C4C23×D7914yes—
473C22×C4C23×D7914yes—
474C22×C4C23×D7911yescharacteristic
475C22×C4C23×D7912yes—
476C22×C4C23×D7912yes—
477C22×C4C23×D7914yes—
478C22×C4C23×D7918yes—
479C22×C4C23×D7911yescharacteristic
480C4⋊C4—7916no—
481C4⋊C4—7916no—
482C4⋊C4—7916no—
483C4⋊C4—7916no—
484C4⋊C4—7916no—
485C4⋊C4—7916no—
486C4⋊C4—7916no—
487C4⋊C4—7916no—
488C4⋊C4—7916no—
489C4⋊C4—798no—
490C4⋊C4—798no—
491C4⋊C4—7916no—
492C4⋊C4C23×D7918yes—
493C4⋊C4C23×D7918yes—
494C4⋊C4C23×D79116yes—
495C4⋊C4C23×D79116yes—
496C4⋊C4C23×D79116yes—
497C22⋊C4—7916no—
498C22⋊C4—7916no—
499C22⋊C4—7916no—
500C22⋊C4—7916no—
501C22⋊C4—7916no—
502C22⋊C4—7916no—
503C22⋊C4—7916no—
504C22⋊C4—7916no—
505C22⋊C4—7916no—
506C22⋊C4C23×D79116yes—
507C42—7916no—
508C42—7916no—
509C42—7916no—
510C42C23×D79116yes—
511C42C23×D7918yes—
512C42C23×D7914yes—
513C42C23×D7914yes—
514C23—22no—
515C23—24no—
516C23—798no—
517C23—1588no—
518C23—1588no—
519C23—1588no—
520C23C24×D7912yes—
521C23C24×D7911yescharacteristic
522Q8—416no—
523Q8—3168no—
524Q8—31616no—
525D4—3168no—
526D4—31616no—
527D4—31616no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—28no—
532C2×C4—28no—
533C2×C4—28no—
534C2×C4—48no—
535C2×C4—31616no—
536C2×C4—31616no—
537C2×C4—798no—
538C2×C4—798no—
539C2×C4—798no—
540C2×C4—1588no—
541C2×C4—1588no—
542C2×C4—1588no—
543C2×C4—15832no—
544C2×C4#1457920914yes—
545C2×C4C24×D7918yes—
546C2×C4C24×D7918yes—
547C2×C4C24×D7912yes—
548C2×C4C24×D7914yes—
549C2×C4C24×D7914yes—
550C2×C4C24×D7912yes—
551C22—22no—
552C22—24no—
553C22—44no—
554C22—31616no—
555C22—1588no—
556C22—1588no—
557C22—1588no—
558C22C2×#1457920912yes—
559C22#1909939914yes—
560C22C25×D7911yescharacteristic
561C4—22no—
562C4—24no—
563C4—24no—
564C4—28no—
565C4—28no—
566C4—1588no—
567C4—1588no—
568C4—1588no—
569C4C2×#1457920914yes—
570C2—42no—
571C2—3168no—
572C2#2377754714yesdirect product factor
573C2C22×#1457920911yescharacteristic
574C2C2×#1909939912yes—
subgroupG/H
centerC22×C4C23×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#533×C79C2
socleC23×C79C25
hypercenterC2×#533D79
hypocenterC79C2×#3531
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #23777547C2direct (N × H)
2. C2×C79⋊#564C2semidirect
3. C2×#19099317C2semidirect
4. C2×#19099314C2semidirect
5. C2×#19099312C2semidirect
6. C2×#19099311C2semidirect
7. C2×#19099309C2semidirect
8. C2×#19099117C2semidirect
9. C2×#19099100C2semidirect
10. C2×#19099097C2semidirect
11. C2×#19099091C2semidirect
12. C2×#533×C79C2semidirect
13. C79⋊#564C22semidirect
14. #19099317C22semidirect
15. #19099314C22semidirect
16. #19099312C22semidirect
17. #19099311C22semidirect
18. #19099309C22semidirect
19. #19099117C22semidirect
22. #19099100C22semidirect
23. #19099097C22semidirect
24. #19099091C22semidirect
61. #533×C79C22semidirect
284. C2×C79#3531semidirect
296. C2×#533D79semidirect
300. C79C2×#3531semidirect
308. #533C2×D79semidirect
572. C2#23777547direct (N × H)

Maximal subgroups

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

subgroupindex
#237775472
C2×C79⋊#5642
C2×#190993172
C2×#190993142
C2×#190993122
C2×#190993112
C2×#190993092
C2×#190991172
C2×#190991002
C2×#190990972
C2×#190990912
C2×#533×C792
C2×#353179