Finite Group Databasebeta

← C4×#19098956 #34296820

Subgroups — C4×#19098956 #34296820

Order 20224.

1094 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098956C211yesmaximal, characteristic
2C2×C4×#11929614C211yesmaximal, characteristic, complemented
3C2×C4×#11929613C211yesmaximal, characteristic
4C2×C4×#11929611C211yesmaximal, characteristic
5C4×#14579159C211yesmaximal, characteristic, complemented
6C4×#14579150C211yesmaximal, characteristic
7#23764279C211yesmaximal, characteristic
8#23764278C211yesmaximal, characteristic
9#23764272C211yesmaximal, characteristic, complemented
10#23764268C211yesmaximal, characteristic, complemented
11#23764218C211yesmaximal, characteristic, complemented
12#23764213C211yesmaximal, characteristic
13#23763567C211yesmaximal, characteristic, complemented
14C4×#14579071C211yesmaximal, characteristic, complemented
15C2×C4×Q16×C79C211yesmaximal, characteristic, complemented
16C22×#11929614C2211yescharacteristic
17C22×#11929613C2211yescharacteristic
18C22×#11929611C2211yescharacteristic
19C2×#14579159C2211yescharacteristic
20C2×#14579150C2211yescharacteristic
21C2×C4×Dic158C2211yescharacteristic
22C2×C4×D316C2211yescharacteristic
23#19098956C418yesdirect product factor
24C4×#11929614—24no—
25C4×#11929613—24no—
26C4×#11929611—24no—
27C2×#14579094C2211yescharacteristic
28C2×#14579093C2211yescharacteristic
29C2×#14579092C2211yescharacteristic
30C2×#14579086C2211yescharacteristic
31C2×#14579085C2211yescharacteristic
32C2×#14579085C2211yescharacteristic
33C2×#14579084C2211yescharacteristic
34C2×#14579083C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×#14579071C2211yescharacteristic
37C2×#14579071C2211yescharacteristic
38C2×#14579071C2211yescharacteristic
39C2×#14579071C2211yescharacteristic
40C2×C4×C79⋊C8C2211yescharacteristic
41#19098470C2211yescharacteristic
42#19098470C2211yescharacteristic
43#19098468C2211yescharacteristic
44#19098464C2211yescharacteristic
45#19098458—22no—
46#19098453—22no—
47#19098432C2211yescharacteristic
48#19098428C2211yescharacteristic
49C4×Dic79⋊C4—22no—
50C4×(C2×D79)⋊C4—22no—
51C42×Dic79C2211yescharacteristic
52C22×Q16×C79C2211yescharacteristic
53C2×C4×Q8×C79C2211yescharacteristic
54C2×C4×Q8×C79C2211yescharacteristic
55C4×Q16×C79—24no—
56C2×#107×C79C2211yescharacteristic
57C2×#103×C79C2211yescharacteristic
58C2×#103×C79C2211yescharacteristic
59C2×C4×C8×C79C2211yescharacteristic
60C22×Dic158C2311yescharacteristic
61C22×D316C2311yescharacteristic
62C22×C4×D79—21no—
63C2×#11929614—22no—
64C2×#11929614—22no—
65C2×#11929614C2×C414yescomplemented
66C2×#11929613—22no—
67C2×#11929613—22no—
68C2×#11929613C2×C414yes—
69C2×#11929611—22no—
70C2×#11929611—22no—
71C2×#11929611C2×C414yes—
72C22×C79⋊C8C2311yescharacteristic
73C22×C79⋊C8C2311yescharacteristic
74#14579159—22no—
75#14579159C2×C414yescomplemented
76#14579150—22no—
77#14579150C2×C414yes—
78C4×Dic158—22no—
79C4×Dic158—22no—
80C4×D316—22no—
81C4×D316—22no—
82C2×C4⋊Dic79C2311yescharacteristic
83C2×C4⋊Dic79C2311yescharacteristic
84C2×Dic79⋊C4—22no—
85C2×Dic79⋊C4—21no—
86C2×Dic79⋊C4—22no—
87C2×(C2×D79)⋊C4—22no—
88C2×(C2×D79)⋊C4—21no—
89C2×(C2×D79)⋊C4—22no—
90C2×C4×Dic79—21no—
91C2×C4×Dic79D412yes—
92C2×C4×Dic79D412yes—
93C2×C4×Dic79C2311yescharacteristic
94C2×C4×Dic79C2311yescharacteristic
95#14579094—22no—
96#14579093—22no—
97#14579092—22no—
98#14579086—22no—
99#14579085—22no—
100#14579085—22no—
101#14579084—22no—
102#14579083—22no—
103#14579081—22no—
104#14579071—22no—
105#14579071—22no—
106#14579071—22no—
107#14579071C2×C414yescomplemented
108C4×C79⋊C8D414yes—
109C79⋊#95—22no—
110C79⋊#95—22no—
111C79⋊#95—22no—
112C79⋊#95—22no—
113C22×Q8×C79C2311yescharacteristic
114C22×Q8×C79C2311yescharacteristic
115C2×Q16×C79—22no—
116C2×Q16×C79—22no—
117C2×Q16×C79C2×C414yescomplemented
118C22×C8×C79C2311yescharacteristic
119C22×C8×C79C2311yescharacteristic
120C4×Q8×C79—22no—
121C4×Q8×C79—22no—
122C4×Q8×C79—22no—
123C4×Q8×C79—22no—
124C2×C4⋊C4×C79—21no—
125C2×C4⋊C4×C79—21no—
126C2×C4⋊C4×C79C2311yescharacteristic
127C2×C4⋊C4×C79C2311yescharacteristic
128C2×C42×C79—21no—
129C2×C42×C79—21no—
130C2×C42×C79C2311yescharacteristic
131#107×C79—22no—
132#103×C79—22no—
133#103×C79—22no—
134C4×C8×C79D414yes—
135C23×D79—21no—
136C2×Dic158—21no—
137C2×Dic158—21no—
138C2×Dic158—21no—
139C2×Dic158—21no—
140C2×Dic158—21no—
141C2×Dic158C22×C412yes—
142C2×D316—21no—
143C2×D316—21no—
144C2×D316—21no—
145C2×D316—21no—
146C2×D316—21no—
147C2×D316C22×C412yes—
148C22×Dic79—21no—
149C22×Dic79—21no—
150C22×Dic79—21no—
151C22×Dic79C2×D412yes—
152C22×Dic79C2×D412yes—
153C2×C4×D79—42no—
154C2×C4×D79—44no—
155#11929614—28no—
156#11929613—28no—
157#11929611—28no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8C22×C412yes—
161C2×C79⋊C8C2×D412yes—
162C2×C79⋊C8C2×D412yes—
163C2×C79⋊C8#4112yes—
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79—21no—
167C4⋊Dic79—21no—
168Dic79⋊C4—28no—
169Dic79⋊C4—44no—
170Dic79⋊C4—42no—
171(C2×D79)⋊C4—28no—
172(C2×D79)⋊C4—44no—
173(C2×D79)⋊C4—42no—
174C4×Dic79—24no—
175C4×Dic79—21no—
176C4×Dic79—21no—
177C4×Dic79—42no—
178C4×Dic79—42no—
179C4×Dic79C22×C412yes—
180C4×Dic79#4112yes—
181C2×Q8×C79—21no—
182C2×Q8×C79—21no—
183C2×Q8×C79—21no—
184C2×Q8×C79—21no—
185C2×Q8×C79—21no—
186C2×Q8×C79—21no—
187C2×Q8×C79—21no—
188C2×Q8×C79—21no—
189C2×Q8×C79—21no—
190C2×Q8×C79—21no—
191C2×Q8×C79C22×C412yes—
192C2×Q8×C79C22×C412yes—
193C22×C4×C79—21no—
194C22×C4×C79—21no—
195C22×C4×C79—21no—
196C22×C4×C79—21no—
197C22×C4×C79C2×D411yescharacteristic
198C22×C4×C79C2×D411yescharacteristic
199C22×C4×C79C2411yescharacteristic
200Q16×C79—28no—
201C2×C8×C79—21no—
202C2×C8×C79—21no—
203C2×C8×C79C22×C412yes—
204C2×C8×C79C2×D412yes—
205C2×C8×C79C2×D412yes—
206C2×C8×C79#4112yes—
207C4⋊C4×C79—21no—
208C4⋊C4×C79—21no—
209C4⋊C4×C79—21no—
210C4⋊C4×C79—21no—
211C4⋊C4×C79—42no—
212C4⋊C4×C79—42no—
213C42×C79—42no—
214C42×C79—42no—
215C42×C79C2×D412yes—
216C42×C79C2×D412yes—
217C23×C79C22×D411yescharacteristic
218C22×D79—22no—
219C22×D79—41no—
220C22×D79—41no—
221C22×D79—42no—
222C22×D79—42no—
223Q8×C79—22no—
224Q8×C79—22no—
225Q8×C79—22no—
226Q8×C79—22no—
227Q8×C79—41no—
228Q8×C79—41no—
229Q8×C79—41no—
230Q8×C79—41no—
231C2×C4×C79—22no—
232C2×C4×C79—22no—
233C2×C4×C79—22no—
234C2×C4×C79—41no—
235C2×C4×C79—41no—
236C2×C4×C79—41no—
237C2×C4×C79—41no—
238C2×C4×C79—41no—
239C2×C4×C79—41no—
240C2×C4×C79—42no—
241C2×C4×C79—42no—
242C2×C4×C79#12712yes—
243C2×C4×C79#12712yes—
244C2×C4×C79#13714yes—
245C2×C4×C79C23×C411yescharacteristic
246C2×C4×C79C22×D411yescharacteristic
247C2×C4×C79C22×D411yescharacteristic
248C2×C4×C79C2×#4111yescharacteristic
249C2×C4×C79C2×#4111yescharacteristic
250C2×C4×C79C2×#4111yescharacteristic
251C2×Dic79—22no—
252C2×Dic79—22no—
253C2×Dic79—22no—
254C2×Dic79—22no—
255C2×Dic79—22no—
256C2×Dic79—22no—
257C2×Dic79—41no—
258C2×Dic79—41no—
259C2×Dic79—41no—
260C2×Dic79—41no—
261C2×Dic79—42no—
262C2×Dic79—42no—
263C2×Dic79C4×D414yes—
264D316—22no—
265D316—22no—
266D316—41no—
267D316—41no—
268C4×D79—84no—
269Dic158—22no—
270Dic158—22no—
271Dic158—41no—
272Dic158—41no—
273C8×C79—22no—
274C8×C79C4×D414yes—
275C79⋊C8—22no—
276C79⋊C8C4×D414yes—
277C22×C79C2×C4×D411yescharacteristic
278C22×C79C2×#12711yescharacteristic
279C22×C79#53211yescharacteristic
280C22×C79C2×#13712yes—
281C22×C79#57512yes—
282C2×D79—42no—
283C2×D79—44no—
284C2×D79—81no—
285C2×D79—81no—
286C2×D79—82no—
287C4×C79—22no—
288C4×C79—42no—
289C4×C79—42no—
290C4×C79—81no—
291C4×C79—81no—
292C4×C79#49714yescomplemented
293C4×C79C2×C4×D411yescharacteristic
294C4×C79C2×C4×D411yescharacteristic
295C4×C79#53211yescharacteristic
296C4×C79#53211yescharacteristic
297Dic79—24no—
298Dic79—42no—
299Dic79—42no—
300Dic79—81no—
301Dic79—81no—
302C4×#497—791nomaximal, Sylow
303C2×C79C4×#12711yescharacteristic
304C2×C79C4×#13712yes—
305C2×C79C2×#49711yescharacteristic
306C2×C79#315011yescharacteristic
307C2×C79#317212yes—
308D79—82no—
309C2×#497—791no—
310C2×C4×Q16—791no—
311C2×C4×Q16D7911yescharacteristic, complemented
312C2×C4×SD16—791no—
313C2×C4×SD16—791no—
314C4×C4⋊Q8—791no—
315C4×#124—791no—
316#1973—791no—
317#1973—791no—
318#1971—791no—
319#1971—791no—
320#1960—791no—
321#1959—791no—
322#1847—791no—
323C4×#97—791no—
324C79C4×#49711yescharacteristic, complemented, Sylow
325C22×Q16—791no—
326C22×Q16C2×D7911yescharacteristic
327C22×SD16—791no—
328C22×SD16—791no—
329C2×C4⋊Q8—791no—
330C2×#124—791no—
331C2×C4×Q8—791no—
332C2×C4×Q8C2×D7911yescharacteristic
333C2×C4×Q8C2×D7911yescharacteristic
334C2×C4×D4—791no—
335#497—798no—
336C4×Q16—24no—
337C4×Q16—1584no—
338C4×SD16—1584no—
339C4×SD16—1584no—
340C2×#107—791no—
341C2×#107C2×D7911yescharacteristic
342C2×#106—791no—
343C2×#106—791no—
344C2×#103—791no—
345C2×#103—791no—
346C2×#103—791no—
347C2×#103—791no—
348C2×#103C2×D7911yescharacteristic
349C2×#103C2×D7911yescharacteristic
350C2×#102—791no—
351C2×#102—791no—
352C2×#97—791no—
353C2×#97—791no—
354C2×#97—791no—
355C2×#97—791no—
356C2×C4×C8—791no—
357C2×C4×C8C2×D7911yescharacteristic
358#391—791no—
359#391—791no—
360#391—791no—
361#390—791no—
362#389—1582no—
363#388—1582no—
364#384—791no—
365#382—791no—
366C4×C4⋊C4—1582no—
367C4×C22⋊C4—1582no—
368C43—791no—
369C22×Q8—791no—
370C22×Q8C22×D7911yescharacteristic
371C22×Q8C22×D7911yescharacteristic
372C22×D4—791no—
373C23×C4—1581no—
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16—794no—
377C2×Q16—1582no—
378C2×Q16—1582no—
379C2×Q16C4×D7914yescomplemented
380C2×SD16—794no—
381C2×SD16—794no—
382C2×SD16—1582no—
383C2×SD16—1582no—
384C2×SD16—1582no—
385C2×SD16—1582no—
386C22×C8—791no—
387C22×C8—791no—
388C22×C8C22×D7911yescharacteristic
389C22×C8C22×D7911yescharacteristic
390C4⋊Q8—794no—
391C4⋊Q8—1582no—
392#124—794no—
393#124—1582no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—1582no—
399C4×Q8—1582no—
400C4×D4—1582no—
401C4×D4—1582no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—791no—
405C2×C4⋊C4—791no—
406C2×C4⋊C4—1582no—
407C2×C4⋊C4—1581no—
408C2×C4⋊C4—1582no—
409C2×C4⋊C4C22×D7911yescharacteristic
410C2×C4⋊C4C22×D7911yescharacteristic
411C2×C22⋊C4—1582no—
412C2×C22⋊C4—1581no—
413C2×C22⋊C4—1582no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—792no—
417C2×C42—791no—
418C2×C42—792no—
419C2×C42—791no—
420C2×C42—1581no—
421C2×C42C22×D7911yescharacteristic
422#107—22no—
423#107—1582no—
424#106—1582no—
425#106—1582no—
426#103—22no—
427#103—22no—
428#103—1582no—
429#103—1582no—
430#103—1582no—
431#103—1582no—
432#102—1582no—
433#102—1582no—
434#97—794no—
435#97—1582no—
436#97—1582no—
437#97—1582no—
438C4×C8—794no—
439C4×C8C22⋊D7914yes—
440#95—1582no—
441#95—1582no—
442#95—1582no—
443#95—1582no—
444C24—1581no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—792no—
456C2×Q8—1581no—
457C2×Q8—1581no—
458C2×Q8—1581no—
459C2×Q8—1581no—
460C2×Q8—1581no—
461C2×Q8C2×C4×D7912yes—
462C2×Q8C2×C4×D7912yes—
463C2×D4—792no—
464C2×D4—1581no—
465C2×D4—1581no—
466C2×D4—1581no—
467C2×D4—1581no—
468C2×D4—1581no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—3162no—
474C22×C4—3164no—
475C22×C4—792no—
476C22×C4—792no—
477C22×C4—1581no—
478C22×C4—1581no—
479C22×C4—1581no—
480C22×C4D4×D7911yescharacteristic
481C22×C4D4×D7911yescharacteristic
482C22×C4C23×D7911yescharacteristic
483Q16—28no—
484Q16—1588no—
485SD16—1588no—
486SD16—1588no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—792no—
490C2×C8—792no—
491C2×C8—792no—
492C2×C8—792no—
493C2×C8—1581no—
494C2×C8—1581no—
495C2×C8C2×C4×D7912yes—
496C2×C8C2×C22⋊D7912yes—
497C2×C8C2×C22⋊D7912yes—
498C2×C8#1192962412yes—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—3164no—
506C4⋊C4—3162no—
507C4⋊C4—1588no—
508C4⋊C4—1581no—
509C4⋊C4—1581no—
510C4⋊C4—1581no—
511C4⋊C4—1581no—
512C22⋊C4—3164no—
513C22⋊C4—3162no—
514C22⋊C4—1588no—
515C42—42no—
516C42—42no—
517C42—3162no—
518C42—3162no—
519C42—792no—
520C42—792no—
521C42—1581no—
522C42—1581no—
523C42—1584no—
524C42D4×D7912yes—
525C42C2×C22⋊D7912yes—
526C23—3162no—
527C23—3161no—
528C23—3162no—
529C23—3161no—
530C23—1582no—
531C23C2×D4×D7911yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540Q8—3161no—
541Q8—3161no—
542Q8—1582no—
543Q8—1582no—
544D4—3161no—
545D4—3161no—
546D4—1582no—
547D4—1582no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—3161no—
560C2×C4—3161no—
561C2×C4—3162no—
562C2×C4—3161no—
563C2×C4—3161no—
564C2×C4—3162no—
565C2×C4—794no—
566C2×C4—6324no—
567C2×C4—1582no—
568C2×C4—1582no—
569C2×C4—1582no—
570C2×C4—1582no—
571C2×C4—1582no—
572C2×C4—1582no—
573C2×C4#1457915712yes—
574C2×C4#1457915712yes—
575C2×C4#1457919314yes—
576C2×C4C22×C4×D7911yescharacteristic
577C2×C4C2×D4×D7911yescharacteristic
578C2×C4C22×C22⋊D7911yescharacteristic
579C2×C4#41×D7911yescharacteristic
580C2×C4#41×D7911yescharacteristic
581C2×C4C2×#1192962411yescharacteristic
582C8—22no—
583C8—794no—
584C8—1582no—
585C8C4×C22⋊D7914yes—
586C22—3164no—
587C22—3162no—
588C22—6322no—
589C22—6321no—
590C22—6321no—
591C22C4×D4×D7911yescharacteristic
592C22C2×#1457915711yescharacteristic
593C22#1909911011yescharacteristic
594C22C2×#1457919312yes—
595C22#1909936012yes—
596C4—22no—
597C4—42no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—3162no—
602C4—3162no—
603C4—6321no—
604C4—6321no—
605C4—1584no—
606C4#1909895614yesdirect product factor
607C4C4×D4×D7911yescharacteristic
608C4C2×C4×C22⋊D7911yescharacteristic
609C4#1909910911yescharacteristic
610C4#1909911011yescharacteristic
611C2—6322no—
612C2C4×#1457915711yescharacteristic
613C2C4×#1457919312yes—
614C2C2×#1909895611yescharacteristic
615C2#2377384311yescharacteristic
616C2#2377400412yes—
subgroupG/H
centerC22×C4D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×C4×Q16×C79C2
socleC23×C79C22×D4
prime radicalC22×D316C23
cosocleC22×C4×C79C24
hypercenterC2×C4×Q16D79
hypocenterC79C4×#497
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11929614C2semidirect
5. C4×#14579159C2semidirect
9. #23764272C2semidirect
10. #23764268C2semidirect
11. #23764218C2semidirect
13. #23763567C2semidirect
14. C4×#14579071C2semidirect
15. C2×C4×Q16×C79C2semidirect
23. #19098956C4direct (N × H)
65. C2×#11929614C2×C4semidirect
75. #14579159C2×C4semidirect
107. #14579071C2×C4semidirect
117. C2×Q16×C79C2×C4semidirect
292. C4×C79#497semidirect
311. C2×C4×Q16D79semidirect
324. C79C4×#497semidirect
379. C2×Q16C4×D79semidirect
606. C4#19098956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190989562
C2×C4×#119296142
C2×C4×#119296132
C2×C4×#119296112
C4×#145791592
C4×#145791502
#237642792
#237642782
#237642722
#237642682
#237642182
#237642132
#237635672
C4×#145790712
C2×C4×Q16×C792
C4×#49779