Finite Group Databasebeta

← C4×#125×D79 #34446754

Subgroups — C4×#125×D79 #34446754

Order 20224.

2622 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D79C211yesmaximal, characteristic
2#125×Dic79C211yesmaximal, characteristic, complemented
3C4×#14579153C211yesmaximal, characteristic, complemented
4#23765959C212yesmaximal, complemented
5C4×#14579152C212yesmaximal, complemented
6#23765957C214yesmaximal, complemented
7C4×#14579151C214yesmaximal, complemented
8#23765955C211yesmaximal, characteristic, complemented
9#389×D79C212yesmaximal
10#387×D79C214yesmaximal
11#382×D79C211yesmaximal, characteristic
12C4×C4⋊C4×D79C214yesmaximal
13C4×C4⋊C4×D79C212yesmaximal
14C43×D79C211yesmaximal, characteristic
15C4×#125×C79C211yesmaximal, characteristic, complemented
16C2×#14579153C2211yescharacteristic
17C2×#14579152C2212yes—
18C2×#14579151C2214yes—
19#125×D79C4116yesdirect product factor
20C2×C4⋊C4×D79C2212yes—
21C2×C4⋊C4×D79C2214yes—
22C2×C4⋊C4×D79C2214yes—
23C2×C4⋊C4×D79C2212yes—
24C2×C42×D79C2212yes—
25C2×C42×D79C2211yescharacteristic
26C2×C42×D79C2212yes—
27C2×C42×D79C2214yes—
28C2×C42×D79C2211yescharacteristic
29C2×C42×D79C2211yescharacteristic
30#19098462C2212yes—
31#19098461C2212yes—
32#19098460C2214yes—
33#19098459C2212yes—
34#19098458C2214yes—
35#19098450C2214yes—
36#19098449C2214yes—
37#19098448C2214yes—
38#19098447C2214yes—
39#19098446C2214yes—
40#19098445C2214yes—
41#19098444C2214yes—
42#19098429C2211yescharacteristic
43#19098428C2212yes—
44#19098427C2214yes—
45C4⋊C4×Dic79C2212yes—
46C4⋊C4×Dic79C2214yes—
47C4⋊C4×Dic79C2214yes—
48C4⋊C4×Dic79C2212yes—
49C4×Dic79⋊C4C2214yes—
50C4×Dic79⋊C4C2214yes—
51C4×Dic79⋊C4C2214yes—
52C4×C4⋊Dic79C2214yes—
53C4×C4⋊Dic79C2212yes—
54#19098414C2214yes—
55#19098414C2214yes—
56#19098414C2214yes—
57#95×D79C2214yes—
58#95×D79C2214yes—
59#95×D79C2214yes—
60C42×Dic79C2211yescharacteristic
61C42×Dic79C2212yes—
62C42×Dic79C2212yes—
63C42×Dic79C2211yescharacteristic
64C42×Dic79C2211yescharacteristic
65C2×#125×C79C2211yescharacteristic
66#389×C79C2212yes—
67#387×C79C2214yes—
68#382×C79C2211yescharacteristic
69C4×C4⋊C4×C79C2214yes—
70C4×C4⋊C4×C79C2212yes—
71C43×C79C2211yescharacteristic
72C22×C4×D79C2314yes—
73C22×C4×D79C2312yes—
74C22×C4×D79C2314yes—
75C22×C4×D79C2311yescharacteristic
76C22×C4×D79C2312yes—
77C22×C4×D79C2311yescharacteristic
78C22×C4×D79C2311yescharacteristic
79#14579153C2×C418yescomplemented
80#14579152C2×C4116yescomplemented
81#14579151C2×C4132yescomplemented
82C2×C4⋊Dic79C2312yes—
83C2×C4⋊Dic79C2314yes—
84C2×C4⋊Dic79C2314yes—
85C2×C4⋊Dic79C2312yes—
86C2×Dic79⋊C4C2314yes—
87C2×Dic79⋊C4C2314yes—
88C2×Dic79⋊C4C2314yes—
89C2×Dic79⋊C4C2314yes—
90C2×Dic79⋊C4C2314yes—
91C2×Dic79⋊C4C2314yes—
92C4⋊C4×D79—28no—
93C4⋊C4×D79—216no—
94C4⋊C4×D79C2×C4116yes—
95C4⋊C4×D79C2×C4132yes—
96C2×C4×Dic79C2312yes—
97C2×C4×Dic79C2312yes—
98C2×C4×Dic79C2312yes—
99C2×C4×Dic79C2312yes—
100C2×C4×Dic79C2312yes—
101C2×C4×Dic79C2312yes—
102C2×C4×Dic79C2312yes—
103C2×C4×Dic79C2311yescharacteristic
104C2×C4×Dic79C2314yes—
105C2×C4×Dic79C2314yes—
106C2×C4×Dic79C2314yes—
107C2×C4×Dic79C2312yes—
108C2×C4×Dic79C2311yescharacteristic
109C2×C4×Dic79C2311yescharacteristic
110C2×C4×Dic79C2311yescharacteristic
111C2×C4×Dic79C2311yescharacteristic
112C42×D79—28no—
113C42×D79—24no—
114C42×D79—28no—
115C42×D79—216no—
116C42×D79C2×C418yes—
117C42×D79Q818yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123C79⋊#95C2314yes—
124C79⋊#95C2314yes—
125C79⋊#95C2314yes—
126C79⋊#95C2314yes—
127#125×C79C2×C418yescomplemented
128C2×C4⋊C4×C79C2312yes—
129C2×C4⋊C4×C79C2314yes—
130C2×C4⋊C4×C79C2314yes—
131C2×C4⋊C4×C79C2312yes—
132C2×C42×C79C2312yes—
133C2×C42×C79C2312yes—
134C2×C42×C79C2311yescharacteristic
135C2×C42×C79C2314yes—
136C2×C42×C79C2311yescharacteristic
137C2×C42×C79C2311yescharacteristic
138#95×C79C2314yes—
139#95×C79C2314yes—
140#95×C79C2314yes—
141C23×D79C2411yescharacteristic
142C22×Dic79C2414yes—
143C22×Dic79C2412yes—
144C22×Dic79C2414yes—
145C22×Dic79C2411yescharacteristic
146C22×Dic79C2412yes—
147C22×Dic79C2411yescharacteristic
148C22×Dic79C2411yescharacteristic
149C2×C4×D79—24no—
150C2×C4×D79—24no—
151C2×C4×D79—28no—
152C2×C4×D79—24no—
153C2×C4×D79—24no—
154C2×C4×D79—24no—
155C2×C4×D79—28no—
156C2×C4×D79—28no—
157C2×C4×D79—28no—
158C2×C4×D79—28no—
159C2×C4×D79C22×C418yes—
160C2×C4×D79C22×C4116yes—
161C2×C4×D79C22×C414yes—
162C2×C4×D79C2×Q814yes—
163C2×C4×D79C2×Q814yes—
164C2×C4×D79C2×Q814yes—
165C2×C4×D79#4118yes—
166C2×C4×D79#4114yes—
167C2×C4×D79#4118yes—
168C4⋊Dic79—28no—
169C4⋊Dic79—24no—
170C4⋊Dic79C22×C4116yes—
171C4⋊Dic79C22×C418yes—
172Dic79⋊C4—28no—
173Dic79⋊C4—28no—
174Dic79⋊C4—28no—
175Dic79⋊C4C22×C4116yes—
176Dic79⋊C4C22×C4116yes—
177Dic79⋊C4C22×C4116yes—
178C4×Dic79—24no—
179C4×Dic79—24no—
180C4×Dic79—24no—
181C4×Dic79—24no—
182C4×Dic79—24no—
183C4×Dic79—28no—
184C4×Dic79—28no—
185C4×Dic79—24no—
186C4×Dic79—22no—
187C4×Dic79—24no—
188C4×Dic79—28no—
189C4×Dic79C22×C418yes—
190C4×Dic79C22×C414yes—
191C4×Dic79C2×Q814yes—
192C4×Dic79C2×Q814yes—
193C4×Dic79C2×Q814yes—
194C22×C4×C79C2414yes—
195C22×C4×C79C2412yes—
196C22×C4×C79C2414yes—
197C22×C4×C79C2411yescharacteristic
198C22×C4×C79C2412yes—
199C22×C4×C79C2411yescharacteristic
200C22×C4×C79C2411yescharacteristic
201C4⋊C4×C79—28no—
202C4⋊C4×C79—24no—
203C4⋊C4×C79C22×C4116yes—
204C4⋊C4×C79C22×C418yes—
205C42×C79—24no—
206C42×C79—22no—
207C42×C79—24no—
208C42×C79—28no—
209C42×C79C22×C414yes—
210C42×C79C2×Q814yes—
211C23×C79C2511yescharacteristic
212C22×D79C23×C412yes—
213C22×D79C22×Q812yes—
214C22×D79C2×#4112yes—
215C22×D79C2×#4114yes—
216C22×D79C2×#4114yes—
217C2×C4×C79—22no—
218C2×C4×C79—24no—
219C2×C4×C79—22no—
220C2×C4×C79—22no—
221C2×C4×C79—22no—
222C2×C4×C79—22no—
223C2×C4×C79—24no—
224C2×C4×C79—24no—
225C2×C4×C79—24no—
226C2×C4×C79—24no—
227C2×C4×C79C23×C414yes—
228C2×C4×C79C23×C418yes—
229C2×C4×C79C23×C412yes—
230C2×C4×C79C22×Q812yes—
231C2×C4×C79C22×Q812yes—
232C2×C4×C79C22×Q812yes—
233C2×C4×C79C2×#4114yes—
234C2×C4×C79C2×#4112yes—
235C2×C4×C79C2×#4114yes—
236C2×Dic79—22no—
237C2×Dic79—24no—
238C2×Dic79—22no—
239C2×Dic79—22no—
240C2×Dic79—22no—
241C2×Dic79—22no—
242C2×Dic79—24no—
243C2×Dic79—24no—
244C2×Dic79—24no—
245C2×Dic79—24no—
246C2×Dic79C23×C414yes—
247C2×Dic79C23×C418yes—
248C2×Dic79C23×C412yes—
249C2×Dic79C22×Q812yes—
250C2×Dic79C22×Q812yes—
251C2×Dic79C22×Q812yes—
252C2×Dic79C2×#4114yes—
253C2×Dic79C2×#4112yes—
254C2×Dic79C2×#4114yes—
255C4×D79—216no—
256C4×D79—232no—
257C4×D79—216no—
258C4×D79—28no—
259C4×D79—416no—
260C4×D79C4×Q8116yes—
261C4×D79#125116yesdirect product factor
262C22×C79C24×C411yescharacteristic
263C22×C79C23×Q811yescharacteristic
264C22×C79C22×#4111yescharacteristic
265C22×C79C22×#4112yes—
266C22×C79C22×#4112yes—
267C2×D79C2×C4×Q814yes—
268C2×D79C4×#4118yes—
269C2×D79C2×#12514yes—
270C2×D79#52918yes—
271C2×D79#53314yes—
272C4×C79—24no—
273C4×C79—28no—
274C4×C79—24no—
275C4×C79—22no—
276C4×C79—44no—
277C4×C79C2×C4×Q814yes—
278C4×C79C2×#12514yescomplemented
279Dic79—24no—
280Dic79—28no—
281Dic79—24no—
282Dic79—22no—
283Dic79—44no—
284Dic79C2×C4×Q814yes—
285Dic79C2×#12514yescomplemented
286C2×C4×#125—791nomaximal, Sylow
287C2×C79C22×C4×Q811yescharacteristic
288C2×C79C2×C4×#4112yes—
289C2×C79C22×#12511yescharacteristic
290C2×C79C2×#52912yes—
291C2×C79C2×#53311yescharacteristic
292D79C4×#12518yesdirect product factor
293C22×#125—791no—
294C4×#125—792no—
295C4×#125—794no—
296C4×#125—791no—
297C4×#125—794no—
298C4×#125—792no—
299C4×#125—791no—
300C4×#125—791no—
301C4×#125D7911yescharacteristic, direct product factor
302C2×#389—792no—
303C2×#387—794no—
304C2×#382—791no—
305C2×C4×C4⋊C4—794no—
306C2×C4×C4⋊C4—792no—
307C2×C43—791no—
308C79C2×C4×#12511yescharacteristic, complemented, Sylow
309C2×#125—7916no—
310C2×#125—794no—
311C2×#125—792no—
312C2×#125—791no—
313C2×#125C2×D7911yescharacteristic
314C22×C4⋊C4—794no—
315C22×C4⋊C4—792no—
316C22×C4⋊C4—792no—
317C22×C4⋊C4—794no—
318C22×C42—791no—
319C22×C42—791no—
320C22×C42—792no—
321C22×C42—792no—
322C22×C42—791no—
323C22×C42—794no—
324#389—794no—
325#389—792no—
326#389—792no—
327#389—792no—
328#389—794no—
329#389C2×D7912yes—
330#387—794no—
331#387—794no—
332#387—794no—
333#387—794no—
334#387—794no—
335#387—794no—
336#387—794no—
337#387C2×D7914yes—
338#382—792no—
339#382—791no—
340#382—794no—
341#382C2×D7911yescharacteristic
342C4×C4⋊C4—794no—
343C4×C4⋊C4—794no—
344C4×C4⋊C4—792no—
345C4×C4⋊C4—792no—
346C4×C4⋊C4—794no—
347C4×C4⋊C4—792no—
348C4×C4⋊C4—794no—
349C4×C4⋊C4—794no—
350C4×C4⋊C4—794no—
351C4×C4⋊C4—794no—
352C4×C4⋊C4—794no—
353C4×C4⋊C4—794no—
354C4×C4⋊C4C2×D7914yes—
355C4×C4⋊C4C2×D7912yes—
356C2×#95—794no—
357C2×#95—794no—
358C2×#95—794no—
359C43—791no—
360C43—792no—
361C43—792no—
362C43—791no—
363C43—791no—
364C43C2×D7911yescharacteristic
365C23×C4—791no—
366C23×C4—791no—
367C23×C4—794no—
368C23×C4—792no—
369C23×C4—792no—
370C23×C4—791no—
371C23×C4—794no—
372#125—7932no—
373#125—7916no—
374#125—798no—
375#125C4×D7918yesdirect product factor
376C2×C4⋊C4—794no—
377C2×C4⋊C4—794no—
378C2×C4⋊C4—794no—
379C2×C4⋊C4—794no—
380C2×C4⋊C4—792no—
381C2×C4⋊C4—7916no—
382C2×C4⋊C4—7932no—
383C2×C4⋊C4—794no—
384C2×C4⋊C4—792no—
385C2×C4⋊C4—794no—
386C2×C4⋊C4—794no—
387C2×C4⋊C4—794no—
388C2×C4⋊C4—1588no—
389C2×C4⋊C4—15816no—
390C2×C4⋊C4C22×D7912yes—
391C2×C4⋊C4C22×D7914yes—
392C2×C4⋊C4C22×D7914yes—
393C2×C4⋊C4C22×D7912yes—
394C2×C42—792no—
395C2×C42—791no—
396C2×C42—791no—
397C2×C42—791no—
398C2×C42—791no—
399C2×C42—798no—
400C2×C42—798no—
401C2×C42—792no—
402C2×C42—792no—
403C2×C42—792no—
404C2×C42—792no—
405C2×C42—792no—
406C2×C42—792no—
407C2×C42—791no—
408C2×C42—794no—
409C2×C42—794no—
410C2×C42—792no—
411C2×C42—794no—
412C2×C42—15816no—
413C2×C42—1588no—
414C2×C42—1584no—
415C2×C42—1588no—
416C2×C42C22×D7912yes—
417C2×C42C22×D7911yescharacteristic
418C2×C42C22×D7912yes—
419C2×C42C22×D7914yes—
420C2×C42C22×D7911yescharacteristic
421C2×C42C22×D7911yescharacteristic
422#95—794no—
423#95—794no—
424#95—794no—
425#95—794no—
426#95—794no—
427#95—794no—
428#95—794no—
429#95—794no—
430#95—794no—
431#95C22×D7914yes—
432#95C22×D7914yes—
433#95C22×D7914yes—
434C24—791no—
435C22×C4—791no—
436C22×C4—791no—
437C22×C4—794no—
438C22×C4—794no—
439C22×C4—798no—
440C22×C4—794no—
441C22×C4—794no—
442C22×C4—791no—
443C22×C4—792no—
444C22×C4—792no—
445C22×C4—794no—
446C22×C4—794no—
447C22×C4—798no—
448C22×C4—798no—
449C22×C4—7916no—
450C22×C4—794no—
451C22×C4—1588no—
452C22×C4—1588no—
453C22×C4—1588no—
454C22×C4—1588no—
455C22×C4—1584no—
456C22×C4—1584no—
457C22×C4—1584no—
458C22×C4—1584no—
459C22×C4—1584no—
460C22×C4—1588no—
461C22×C4C23×D7914yes—
462C22×C4C23×D7911yescharacteristic
463C22×C4C23×D7912yes—
464C22×C4C23×D7912yes—
465C22×C4C23×D7914yes—
466C22×C4C23×D7911yescharacteristic
467C22×C4C23×D7911yescharacteristic
468C4⋊C4—28no—
469C4⋊C4—24no—
470C4⋊C4—7916no—
471C4⋊C4—7916no—
472C4⋊C4—7916no—
473C4⋊C4—7916no—
474C4⋊C4—798no—
475C4⋊C4—1588no—
476C4⋊C4—1588no—
477C4⋊C4—1588no—
478C4⋊C4—1588no—
479C4⋊C4—1584no—
480C4⋊C4C2×C4×D79116yes—
481C4⋊C4C2×C4×D7918yes—
482C42—24no—
483C42—22no—
484C42—24no—
485C42—28no—
486C42—794no—
487C42—794no—
488C42—794no—
489C42—798no—
490C42—794no—
491C42—1588no—
492C42—1584no—
493C42—1584no—
494C42—1584no—
495C42—1584no—
496C42—1584no—
497C42—1588no—
498C42—1588no—
499C42—1584no—
500C42—1582no—
501C42—1584no—
502C42C2×C4×D7914yes—
503C42Q8×D7914yes—
504C23—792no—
505C23—792no—
506C23—792no—
507C23—794no—
508C23—794no—
509C23C24×D7911yescharacteristic
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—31616no—
521C2×C4—792no—
522C2×C4—792no—
523C2×C4—792no—
524C2×C4—794no—
525C2×C4—792no—
526C2×C4—7916no—
527C2×C4—7916no—
528C2×C4—794no—
529C2×C4—798no—
530C2×C4—792no—
531C2×C4—794no—
532C2×C4—15816no—
533C2×C4—15832no—
534C2×C4—15816no—
535C2×C4—1588no—
536C2×C4—1584no—
537C2×C4—1584no—
538C2×C4—1584no—
539C2×C4—1582no—
540C2×C4—1584no—
541C2×C4—1582no—
542C2×C4—1582no—
543C2×C4—1582no—
544C2×C4—1582no—
545C2×C4—1584no—
546C2×C4C22×C4×D7914yes—
547C2×C4C22×C4×D7918yes—
548C2×C4C22×C4×D7912yes—
549C2×C4C2×Q8×D7912yes—
550C2×C4C2×Q8×D7912yes—
551C2×C4C2×Q8×D7912yes—
552C2×C4#41×D7914yes—
553C2×C4#41×D7912yes—
554C2×C4#41×D7914yes—
555C22—794no—
556C22—798no—
557C22—794no—
558C22—798no—
559C22—794no—
560C22C23×C4×D7911yescharacteristic
561C22C22×Q8×D7911yescharacteristic
562C22C2×#41×D7911yescharacteristic
563C22C2×#41×D7912yes—
564C22C2×#41×D7912yes—
565C4—24no—
566C4—28no—
567C4—24no—
568C4—22no—
569C4—44no—
570C4—3164no—
571C4—794no—
572C4—794no—
573C4—1584no—
574C4—1588no—
575C4—1584no—
576C4—1582no—
577C4C4×Q8×D7914yes—
578C4#125×D7914yesdirect product factor
579C2—798no—
580C2C2×C4×Q8×D7911yescharacteristic
581C2C4×#41×D7912yes—
582C2C2×#125×D7911yescharacteristic
583C2#529×D7912yes—
584C2#533×D7911yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC4×#125×C79C2
socle, cosocleC23×C79C25
prime radicalC23×D79C24
hypercenterC4×#125D79
hypocenterC79C2×C4×#125
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
2. #125×Dic79C2semidirect
3. C4×#14579153C2semidirect
4. #23765959C2semidirect
5. C4×#14579152C2semidirect
6. #23765957C2semidirect
7. C4×#14579151C2semidirect
8. #23765955C2semidirect
15. C4×#125×C79C2semidirect
19. #125×D79C4direct (N × H)
79. #14579153C2×C4semidirect
80. #14579152C2×C4semidirect
81. #14579151C2×C4semidirect
127. #125×C79C2×C4semidirect
261. C4×D79#125direct (N × H)
278. C4×C79C2×#125semidirect
285. Dic79C2×#125semidirect
292. D79C4×#125direct (N × H)
301. C4×#125D79direct (N × H)
308. C79C2×C4×#125semidirect
375. #125C4×D79direct (N × H)
578. C4#125×D79direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D792
#125×Dic792
C4×#145791532
#237659592
C4×#145791522
#237659572
C4×#145791512
#237659552
#389×D792
#387×D792
#382×D792
C4×C4⋊C4×D792
C43×D792
C4×#125×C792
C2×C4×#12579