Finite Group Databasebeta

← #1548×D79 #34256607

Subgroups — #1548×D79 #34256607

Order 20224.

1246 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D79C211yesmaximal, characteristic
2#431×D79C211yesmaximal, characteristic
3#423×D79C211yesmaximal, characteristic
4#23762082C211yesmaximal, characteristic, complemented
5#23762081C211yesmaximal, characteristic, complemented
6#23762080C211yesmaximal, characteristic, complemented
7#23762079C214yesmaximal, complemented
8#333×D79C214yesmaximal, complemented
9C79×#1548C211yesmaximal, characteristic, complemented
10C22×Q8×D79C412yes—
11C2×M16×D79—21no—
12C2×#14579161C2211yescharacteristic
13C2×#14579160—21no—
14C2×#14579160—21no—
15C2×#14579159C412yes—
16C4⋊Q8×D79—21no—
17C4⋊Q8×D79—21no—
18C4⋊Q8×D79—21no—
19C4⋊Q8×D79—21no—
20C4⋊Q8×D79C412yes—
21C4⋊Q8×D79C412yes—
22C4⋊Q8×D79C2212yes—
23C4⋊Q8×D79C2212yes—
24C2×C4⋊C4×D79—21no—
25C2×C4⋊C4×D79—21no—
26C2×C42×D79C2211yescharacteristic
27#19098616C2211yescharacteristic
28#19098615C2212yes—
29#19098614—21no—
30#19098613—21no—
31#19098587C2211yescharacteristic
32#19098586—21no—
33#19098585—21no—
34#19098585C2212yes—
35C4⋊C8×D79—21no—
36C4⋊C8×D79C2212yes—
37C4⋊C8×D79C2212yes—
38C22⋊C8×D79—21no—
39C4×C8×D79—21no—
40#19098312C2214yescomplemented
41#19098311C2214yescomplemented
42#19098311C2214yescomplemented
43C2×C4⋊Q8×C79C2211yescharacteristic
44#431×C79C2211yescharacteristic
45#423×C79C2211yescharacteristic
46#333×C79C2214yescomplemented
47C22×Dic158—22no—
48C22×Dic158C2×C412yes—
49C2×Q8×D79—22no—
50C2×Q8×D79—22no—
51C2×Q8×D79—48no—
52C2×Q8×D79C2×C414yes—
53C2×Q8×D79C2×C414yes—
54C22×C4×D79—22no—
55C22×C4×D79C2×C411yescharacteristic
56C22×C4×D79D411yescharacteristic
57C22×C4×D79D411yescharacteristic
58C2×#11929608—21no—
59C2×#11929607—22no—
60M16×D79—44no—
61C2×C8×D79—22no—
62C2×C8×D79—22no—
63#14579161—21no—
64#14579161—21no—
65#14579161C2×C412yes—
66#14579161C2312yes—
67#14579160—22no—
68#14579160—22no—
69#14579160—22no—
70#14579160—22no—
71#14579160—22no—
72#14579160—22no—
73#14579160—22no—
74#14579160—22no—
75#14579159—22no—
76#14579159—22no—
77#14579159C2×C414yes—
78#14579159C2×C414yes—
79C2×C4⋊Dic79—21no—
80C2×C4⋊Dic79—21no—
81C2×Dic79⋊C4—22no—
82C2×Dic79⋊C4—22no—
83C4⋊C4×D79—22no—
84C4⋊C4×D79—22no—
85C4⋊C4×D79—22no—
86C4⋊C4×D79—22no—
87C4⋊C4×D79—22no—
88C4⋊C4×D79—22no—
89C4⋊C4×D79—22no—
90C4⋊C4×D79—22no—
91C2×C4×Dic79C2×C411yescharacteristic
92C2×C4×Dic79D411yescharacteristic
93C2×C4×Dic79D411yescharacteristic
94C42×D79C2×C411yescharacteristic
95C42×D79C2×C411yescharacteristic
96C42×D79D411yescharacteristic
97C42×D79D411yescharacteristic
98C42×D79D411yescharacteristic
99C42×D79D411yescharacteristic
100C42×D79C2311yescharacteristic
101C42×D79C2311yescharacteristic
102C4⋊(C79⋊C8)—21no—
103C4⋊(C79⋊C8)C2312yes—
104C4⋊(C79⋊C8)C2312yes—
105Dic79⋊C8—22no—
106Dic79⋊C8—22no—
107Dic79⋊C8—22no—
108C22⋊(C79⋊C8)—21no—
109(C2×D79)⋊C8—22no—
110C4×C79⋊C8—21no—
111C8×Dic79—22no—
112C22×Q8×C79C2×C412yes—
113C2×M16×C79—21no—
114C4⋊Q8×C79—21no—
115C4⋊Q8×C79—21no—
116C4⋊Q8×C79C2×C412yes—
117C4⋊Q8×C79C2312yes—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79—21no—
120C2×C42×C79C2311yescharacteristic
121C4⋊C8×C79—21no—
122C4⋊C8×C79C2312yes—
123C4⋊C8×C79C2312yes—
124C22⋊C8×C79—21no—
125C4×C8×C79—21no—
126C23×D79C22⋊C411yescharacteristic
127C2×Dic158—24no—
128C2×Dic158—24no—
129C2×Dic158—22no—
130C2×Dic158—44no—
131C2×Dic158—48no—
132C2×Dic158C22×C414yes—
133Q8×D79—48no—
134Q8×D79—48no—
135Q8×D79—48no—
136Q8×D79—48no—
137C22×Dic79—22no—
138C22×Dic79C22⋊C411yescharacteristic
139C22×Dic79C22⋊C411yescharacteristic
140C22×Dic79C22⋊C411yescharacteristic
141C2×C4×D79—24no—
142C2×C4×D79—24no—
143C2×C4×D79—24no—
144C2×C4×D79—24no—
145C2×C4×D79—48no—
146C2×C4×D79C22⋊C411yescharacteristic
147C2×C4×D79C22⋊C411yescharacteristic
148C2×C4×D79C22⋊C411yescharacteristic
149C2×C4×D79C22⋊C411yescharacteristic
150C2×C4×D79C22⋊C411yescharacteristic
151C2×C4×D79C22⋊C411yescharacteristic
152C2×C4×D79SD1614yes—
153C2×C4×D79Q1614yes—
154C2×C4×D79C22×C411yescharacteristic
155C2×C4×D79C22×C411yescharacteristic
156C2×C4×D79C2×D411yescharacteristic
157C2×C4×D79C2×D411yescharacteristic
158C2×C4×D79C2×D411yescharacteristic
159C2×C4×D79C2×D411yescharacteristic
160#11929608—42no—
161#11929607—44no—
162C2×C79⋊C8—22no—
163C2×C79⋊C8—22no—
164C8×D79—44no—
165C8×D79—44no—
166C4⋊Dic79—22no—
167C4⋊Dic79—22no—
168C4⋊Dic79—22no—
169C4⋊Dic79—22no—
170Dic79⋊C4—24no—
171Dic79⋊C4—24no—
172Dic79⋊C4—24no—
173Dic79⋊C4—24no—
174C4×Dic79C22⋊C411yescharacteristic
175C4×Dic79C22⋊C411yescharacteristic
176C4×Dic79C22⋊C411yescharacteristic
177C4×Dic79C22⋊C411yescharacteristic
178C4×Dic79C22⋊C411yescharacteristic
179C4×Dic79C22⋊C411yescharacteristic
180C4×Dic79C22×C411yescharacteristic
181C4×Dic79C22×C411yescharacteristic
182C4×Dic79C2×D411yescharacteristic
183C4×Dic79C2×D411yescharacteristic
184C4×Dic79C2×D411yescharacteristic
185C4×Dic79C2×D411yescharacteristic
186C2×Q8×C79—22no—
187C2×Q8×C79—44no—
188C2×Q8×C79C22×C414yes—
189C22×C4×C79—22no—
190C22×C4×C79C22×C411yescharacteristic
191C22×C4×C79C2×D411yescharacteristic
192C22×C4×C79C2×D411yescharacteristic
193M16×C79—42no—
194C2×C8×C79—22no—
195C2×C8×C79—22no—
196C4⋊C4×C79—22no—
197C4⋊C4×C79—22no—
198C4⋊C4×C79—22no—
199C4⋊C4×C79—22no—
200C42×C79C22×C411yescharacteristic
201C42×C79C2×D411yescharacteristic
202C42×C79C2×D411yescharacteristic
203C42×C79C2411yescharacteristic
204C23×C79C2×C22⋊C411yescharacteristic
205C22×D79—22no—
206C22×D79—22no—
207C22×D79#10314yes—
208C22×D79C2×C22⋊C411yescharacteristic
209C22×D79C2×C22⋊C411yescharacteristic
210Q8×C79—44no—
211Q8×C79—44no—
212C2×C4×C79—22no—
213C2×C4×C79—22no—
214C2×C4×C79—24no—
215C2×C4×C79—44no—
216C2×C4×C79C2×C22⋊C411yescharacteristic
217C2×C4×C79C2×C22⋊C411yescharacteristic
218C2×C4×C79C2×C22⋊C411yescharacteristic
219C2×C4×C79C2×SD1612yes—
220C2×C4×C79C2×Q1612yes—
221C2×C4×C79C23×C411yescharacteristic
222C2×C4×C79C22×D411yescharacteristic
223C2×C4×C79C22×D411yescharacteristic
224C2×Dic79—22no—
225C2×Dic79—22no—
226C2×Dic79—24no—
227C2×Dic79—44no—
228C2×Dic79#10314yes—
229C2×Dic79C2×C22⋊C411yescharacteristic
230C2×Dic79C2×C22⋊C411yescharacteristic
231C2×Dic79C2×C22⋊C411yescharacteristic
232C2×Dic79C2×C22⋊C411yescharacteristic
233C2×Dic79C2×C22⋊C411yescharacteristic
234C2×Dic79C2×C22⋊C411yescharacteristic
235C4×D79—22no—
236C4×D79—22no—
237C4×D79—22no—
238C4×D79—22no—
239C4×D79—22no—
240C4×D79—22no—
241C4×D79—48no—
242C4×D79—48no—
243C4×D79#10014yes—
244C4×D79#10314yes—
245C4×D79#10314yes—
246C4×D79C2×SD1612yes—
247C4×D79C2×SD1612yes—
248C4×D79C2×Q1612yes—
249C4×D79C2×Q1612yes—
250C4×D79#13714yes—
251Dic158—48no—
252Dic158—44no—
253Dic158—48no—
254Dic158—44no—
255C8×C79—42no—
256C8×C79—42no—
257C79⋊C8—42no—
258C79⋊C8—42no—
259C22×C79—21no—
260C22×C79—21no—
261C22×C79C2×#10312yes—
262C22×C79C22×C22⋊C411yescharacteristic
263C2×D79—21no—
264C2×D79—21no—
265C2×D79—28no—
266C2×D79C2×#10012yes—
267C2×D79C2×#10312yes—
268C2×D79C2×#10312yes—
269C2×D79#41912yes—
270C4×C79—21no—
271C4×C79—21no—
272C4×C79—44no—
273C4×C79C2×#10012yes—
274C4×C79C2×#10312yes—
275C4×C79C22×SD1611yescharacteristic
276C4×C79C22×Q1611yescharacteristic
277C4×C79C2×#13712yes—
278Dic79—21no—
279Dic79—21no—
280Dic79—44no—
281Dic79C2×#10012yes—
282Dic79C2×#10312yes—
283Dic79C2×#10312yes—
284Dic79#41912yes—
285C2×#1548—791nomaximal, Sylow
286C2×C79—22no—
287C2×C79C22×#10011yescharacteristic
288C2×C79C22×#10311yescharacteristic
289C2×C79C2×#41911yescharacteristic
290D79—22no—
291D79#154814yesdirect product factor
292C22×C4⋊Q8—791no—
293C2×#431—791no—
294C2×#423—791no—
295#1548—791no—
296#1548—791no—
297#1548—794no—
298#1548—791no—
299#1548D7911yescharacteristic, direct product factor
300C2×#333—794no—
301C79C2×#154811yescharacteristic, complemented, Sylow
302C23×Q8—792no—
303C22×M16—1581no—
304C2×C4⋊Q8—792no—
305C2×C4⋊Q8—792no—
306C2×C4⋊Q8—792no—
307C2×C4⋊Q8—792no—
308C2×C4⋊Q8—792no—
309C2×C4⋊Q8—791no—
310C2×C4⋊Q8—1581no—
311C2×C4⋊Q8—1581no—
312C2×C4⋊Q8—1581no—
313C2×C4⋊Q8—1581no—
314C2×C4⋊Q8—1581no—
315C2×C4⋊Q8—1581no—
316C2×C4⋊Q8C2×D7911yescharacteristic
317C22×C4⋊C4—1581no—
318C22×C4⋊C4—1581no—
319C22×C42—791no—
320#431—791no—
321#431—792no—
322#431—1581no—
323#431—1581no—
324#431C2×D7911yescharacteristic
325#423—791no—
326#423—792no—
327#423—1581no—
328#423—1581no—
329#423C2×D7911yescharacteristic
330C2×C4⋊C8—792no—
331C2×C4⋊C8—792no—
332C2×C4⋊C8—1581no—
333C2×C22⋊C8—1581no—
334C2×C4×C8—1581no—
335#333—794no—
336#333—794no—
337#333—794no—
338#333C2×D7914yescomplemented
339C22×Q8—3168no—
340C22×Q8—794no—
341C22×Q8—794no—
342C22×Q8—792no—
343C22×Q8—1582no—
344C22×Q8—1582no—
345C22×Q8—1582no—
346C22×Q8C4×D7912yes—
347C23×C4—791no—
348C23×C4—791no—
349C23×C4—791no—
350C23×C4—1582no—
351C2×M16—21no—
352C2×M16—3164no—
353C2×M16—1582no—
354C2×M16—1581no—
355C22×C8—1582no—
356C22×C8—1582no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—794no—
360C4⋊Q8—794no—
361C4⋊Q8—792no—
362C4⋊Q8—792no—
363C4⋊Q8—1582no—
364C4⋊Q8—1582no—
365C4⋊Q8—1582no—
366C4⋊Q8—1582no—
367C4⋊Q8—1582no—
368C4⋊Q8—1582no—
369C4⋊Q8—1582no—
370C4⋊Q8—1582no—
371C4⋊Q8—1582no—
372C4⋊Q8—1582no—
373C4⋊Q8—1581no—
374C4⋊Q8—1581no—
375C4⋊Q8C4×D7912yes—
376C4⋊Q8C22×D7912yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—1582no—
380C2×C4⋊C4—1582no—
381C2×C4⋊C4—1582no—
382C2×C4⋊C4—1582no—
383C2×C4⋊C4—1582no—
384C2×C4⋊C4—1582no—
385C2×C4⋊C4—1582no—
386C2×C4⋊C4—1582no—
387C2×C4⋊C4—1582no—
388C2×C4⋊C4—1582no—
389C2×C4⋊C4—1581no—
390C2×C4⋊C4—1581no—
391C2×C42—791no—
392C2×C42—791no—
393C2×C42—791no—
394C2×C42—791no—
395C2×C42—791no—
396C2×C42—791no—
397C2×C42—791no—
398C2×C42—791no—
399C2×C42—791no—
400C2×C42—791no—
401C2×C42—791no—
402C2×C42C22×D7911yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—792no—
405C4⋊C8—792no—
406C4⋊C8—1582no—
407C4⋊C8—1582no—
408C4⋊C8—1582no—
409C4⋊C8—1581no—
410C4⋊C8C22×D7912yes—
411C4⋊C8C22×D7912yes—
412C22⋊C8—21no—
413C22⋊C8—1582no—
414C22⋊C8—1581no—
415C4×C8—21no—
416C4×C8—1582no—
417C4×C8—1581no—
418C24—791no—
419C2×Q8—22no—
420C2×Q8—44no—
421C2×Q8—3164no—
422C2×Q8—3168no—
423C2×Q8—3168no—
424C2×Q8—3168no—
425C2×Q8—3168no—
426C2×Q8—3168no—
427C2×Q8—794no—
428C2×Q8—1584no—
429C2×Q8—1584no—
430C2×Q8—1582no—
431C2×Q8C2×C4×D7914yes—
432C22×C4—22no—
433C22×C4—3168no—
434C22×C4—791no—
435C22×C4—791no—
436C22×C4—791no—
437C22×C4—791no—
438C22×C4—794no—
439C22×C4—794no—
440C22×C4—791no—
441C22×C4—791no—
442C22×C4—791no—
443C22×C4—791no—
444C22×C4—791no—
445C22×C4—791no—
446C22×C4—791no—
447C22×C4—791no—
448C22×C4—791no—
449C22×C4—791no—
450C22×C4—791no—
451C22×C4—1584no—
452C22×C4—1584no—
453C22×C4—1584no—
454C22×C4—1584no—
455C22×C4—1582no—
456C22×C4C2×C4×D7911yescharacteristic
457C22×C4D4×D7911yescharacteristic
458C22×C4D4×D7911yescharacteristic
459M16—42no—
460M16—3164no—
461M16—3162no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—3164no—
465C2×C8—3164no—
466C2×C8—1582no—
467C2×C8—1582no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—1584no—
473C4⋊C4—1584no—
474C4⋊C4—1584no—
475C4⋊C4—1584no—
476C4⋊C4—1582no—
477C4⋊C4—1582no—
478C4⋊C4—1582no—
479C4⋊C4—1582no—
480C42—791no—
481C42—791no—
482C42—791no—
483C42—791no—
484C42—791no—
485C42—791no—
486C42—791no—
487C42—791no—
488C42—791no—
489C42—791no—
490C42—791no—
491C42—791no—
492C42C2×C4×D7911yescharacteristic
493C42D4×D7911yescharacteristic
494C42D4×D7911yescharacteristic
495C42C23×D7911yescharacteristic
496C23—791no—
497C23—791no—
498C23—794no—
499C23—1582no—
500C23—1582no—
501C23C22⋊C4×D7911yescharacteristic
502Q8—44no—
503Q8—44no—
504Q8—3164no—
505Q8—3168no—
506Q8—3168no—
507Q8—3164no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—3168no—
513C2×C4—3168no—
514C2×C4—3164no—
515C2×C4—791no—
516C2×C4—791no—
517C2×C4—791no—
518C2×C4—791no—
519C2×C4—794no—
520C2×C4—794no—
521C2×C4—794no—
522C2×C4—794no—
523C2×C4—792no—
524C2×C4—792no—
525C2×C4—792no—
526C2×C4—792no—
527C2×C4—794no—
528C2×C4—791no—
529C2×C4—791no—
530C2×C4—1582no—
531C2×C4—1582no—
532C2×C4—1582no—
533C2×C4—1582no—
534C2×C4—1584no—
535C2×C4—1582no—
536C2×C4—1582no—
537C2×C4—1582no—
538C2×C4—1582no—
539C2×C4C22⋊C4×D7911yescharacteristic
540C2×C4C22⋊C4×D7911yescharacteristic
541C2×C4C22⋊C4×D7911yescharacteristic
542C2×C4SD16×D7912yes—
543C2×C4Q16×D7912yes—
544C2×C4C22×C4×D7911yescharacteristic
545C2×C4C2×D4×D7911yescharacteristic
546C2×C4C2×D4×D7911yescharacteristic
547C8—42no—
548C8—42no—
549C8—3162no—
550C8—3162no—
551C22—21no—
552C22—21no—
553C22—792no—
554C22—792no—
555C22—792no—
556C22—792no—
557C22—1588no—
558C22—1581no—
559C22—1581no—
560C22#103×D7912yes—
561C22C2×C22⋊C4×D7911yescharacteristic
562C4—21no—
563C4—21no—
564C4—44no—
565C4—3164no—
566C4—792no—
567C4—792no—
568C4—792no—
569C4—792no—
570C4—1581no—
571C4—1581no—
572C4#100×D7912yes—
573C4#103×D7912yes—
574C4C2×SD16×D7911yescharacteristic
575C4C2×Q16×D7911yescharacteristic
576C4#137×D7912yes—
577C2—22no—
578C2—794no—
579C2—1582no—
580C2C2×#100×D7911yescharacteristic
581C2C2×#103×D7911yescharacteristic
582C2#419×D7911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#1548C2
socleC22×C79C22×C22⋊C4
prime radicalC23×D79C22⋊C4
cosocleC42×C79C24
hypercenter#1548D79
hypocenterC79C2×#1548
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
4. #23762082C2semidirect
5. #23762081C2semidirect
6. #23762080C2semidirect
7. #23762079C2semidirect
8. #333×D79C2semidirect
9. C79×#1548C2semidirect
40. #19098312C22semidirect
41. #19098311C22semidirect
42. #19098311C22semidirect
46. #333×C79C22semidirect
291. D79#1548direct (N × H)
299. #1548D79direct (N × H)
301. C79C2×#1548semidirect
338. #333C2×D79semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D792
#431×D792
#423×D792
#237620822
#237620812
#237620802
#237620792
#333×D792
C79×#15482
C2×#154879