Finite Group Databasebeta

← #2099×D79 #34318161

Subgroups — #2099×D79 #34318161

Order 20224.

998 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D79C211yesmaximal, characteristic
2#384×D79C211yesmaximal, characteristic
3#23764961C212yesmaximal, complemented
4#23764960C212yesmaximal, complemented
5#23764959C211yesmaximal, characteristic, complemented
6#23764958C211yesmaximal, characteristic, complemented
7#23764957C211yesmaximal, characteristic, complemented
8#340×D79C212yesmaximal
9#340×D79C212yesmaximal
10#336×D79C211yesmaximal, characteristic
11C79×#2099C211yesmaximal, characteristic, complemented
12C22×C8×D79C2212yes—
13C2×C4⋊C4×D79—21no—
14C2×C4⋊C4×D79—21no—
15C2×C4⋊C4×D79—21no—
16C2×C4⋊C4×D79C2212yes—
17C2×C4⋊C4×D79C2211yescharacteristic
18C2×C4⋊C4×D79C2211yescharacteristic
19C2×C42×D79C2211yescharacteristic
20#19098462C2211yescharacteristic
21#19098461C2211yescharacteristic
22#19098460—21no—
23#19098459C2211yescharacteristic
24#19098458—21no—
25#19098433C2211yescharacteristic
26#19098432—21no—
27#19098432—21no—
28#19098432C2212yes—
29#95×D79—21no—
30#19098326C2212yes—
31#19098326C2212yes—
32#19098325C2212yes—
33#19098325C2212yes—
34#19098325C2212yes—
35#19098325C2212yes—
36#19098318C2211yescharacteristic
37#19098317C2212yes—
38#389×C79C2211yescharacteristic
39#384×C79C2211yescharacteristic
40#340×C79C2212yes—
41#340×C79C2212yes—
42#336×C79C2211yescharacteristic
43C22×C4×D79—21no—
44C22×C4×D79—21no—
45C22×C4×D79—22no—
46C22×C4×D79D411yescharacteristic
47C22×C4×D79D411yescharacteristic
48C22×C4×D79C2311yescharacteristic
49C22×C79⋊C8C2312yes—
50C2×C8×D79—24no—
51C2×C8×D79—24no—
52C2×C8×D79—24no—
53C2×C4⋊Dic79—21no—
54C2×C4⋊Dic79—21no—
55C2×C4⋊Dic79—21no—
56C2×C4⋊Dic79C2312yes—
57C2×C4⋊Dic79C2311yescharacteristic
58C2×C4⋊Dic79C2311yescharacteristic
59C2×Dic79⋊C4—21no—
60C2×Dic79⋊C4—21no—
61C2×Dic79⋊C4—22no—
62C2×Dic79⋊C4—22no—
63C2×Dic79⋊C4—22no—
64C2×Dic79⋊C4—21no—
65C2×Dic79⋊C4—21no—
66C4⋊C4×D79—22no—
67C4⋊C4×D79—24no—
68C4⋊C4×D79—28no—
69C4⋊C4×D79—44no—
70C4⋊C4×D79—44no—
71C4⋊C4×D79—44no—
72C4⋊C4×D79Q814yes—
73C2×C4×Dic79D411yescharacteristic
74C2×C4×Dic79D411yescharacteristic
75C2×C4×Dic79C2311yescharacteristic
76C42×D79—24no—
77C79⋊#95—21no—
78C79⋊#95—21no—
79C79⋊#95—21no—
80C22×C8×C79C2312yes—
81C2×C4⋊C4×C79—21no—
82C2×C4⋊C4×C79—21no—
83C2×C4⋊C4×C79—21no—
84C2×C4⋊C4×C79C2312yes—
85C2×C4⋊C4×C79C2311yescharacteristic
86C2×C4⋊C4×C79C2311yescharacteristic
87C2×C42×C79C2311yescharacteristic
88#95×C79—21no—
89C23×D79C2×D411yescharacteristic
90C22×Dic79—21no—
91C22×Dic79—21no—
92C22×Dic79—22no—
93C22×Dic79C2×D411yescharacteristic
94C22×Dic79C2×D411yescharacteristic
95C22×Dic79C2×D411yescharacteristic
96C2×C4×D79—24no—
97C2×C4×D79—22no—
98C2×C4×D79—22no—
99C2×C4×D79—22no—
100C2×C4×D79—22no—
101C2×C4×D79—42no—
102C2×C4×D79—44no—
103C2×C4×D79—42no—
104C2×C4×D79—42no—
105C2×C4×D79—44no—
106C2×C4×D79—44no—
107C2×C4×D79—42no—
108C2×C4×D79—42no—
109C2×C4×D79D814yes—
110C2×C4×D79SD1614yes—
111C2×C4×D79C2×Q812yes—
112C2×C4×D79#4112yes—
113C2×C4×D79#4114yes—
114C2×C4×D79#4114yes—
115C2×C79⋊C8—22no—
116C2×C79⋊C8—22no—
117C2×C79⋊C8—22no—
118C8×D79—48no—
119C4⋊Dic79—21no—
120C4⋊Dic79—22no—
121C4⋊Dic79—24no—
122C4⋊Dic79—42no—
123C4⋊Dic79—42no—
124C4⋊Dic79—42no—
125C4⋊Dic79C2×Q812yes—
126Dic79⋊C4—24no—
127Dic79⋊C4—42no—
128Dic79⋊C4—44no—
129Dic79⋊C4—42no—
130Dic79⋊C4—44no—
131Dic79⋊C4—44no—
132Dic79⋊C4—42no—
133C4×Dic79—22no—
134C4×Dic79—22no—
135C4×Dic79—22no—
136C22×C4×C79—21no—
137C22×C4×C79—21no—
138C22×C4×C79—22no—
139C22×C4×C79C2×D411yescharacteristic
140C22×C4×C79C2×D411yescharacteristic
141C22×C4×C79C2411yescharacteristic
142C2×C8×C79—22no—
143C2×C8×C79—22no—
144C2×C8×C79—22no—
145C4⋊C4×C79—21no—
146C4⋊C4×C79—22no—
147C4⋊C4×C79—24no—
148C4⋊C4×C79—42no—
149C4⋊C4×C79—42no—
150C4⋊C4×C79—42no—
151C4⋊C4×C79C2×Q812yes—
152C42×C79—22no—
153C23×C79C22×D411yescharacteristic
154C22×D79C22⋊Q812yes—
155C22×D79#12312yes—
156C22×D79#12412yes—
157C22×D79C2×D812yes—
158C22×D79C2×SD1612yes—
159C22×D79#13712yes—
160C22×D79#13712yes—
161C2×C4×C79—21no—
162C2×C4×C79—21no—
163C2×C4×C79—21no—
164C2×C4×C79—21no—
165C2×C4×C79—22no—
166C2×C4×C79—41no—
167C2×C4×C79—41no—
168C2×C4×C79—41no—
169C2×C4×C79—42no—
170C2×C4×C79—41no—
171C2×C4×C79—42no—
172C2×C4×C79—42no—
173C2×C4×C79—41no—
174C2×C4×C79C2×D812yes—
175C2×C4×C79C2×SD1612yes—
176C2×C4×C79C22×Q811yescharacteristic
177C2×C4×C79C2×#4112yes—
178C2×C4×C79C2×#4112yes—
179C2×C4×C79C2×#4111yescharacteristic
180C2×Dic79—21no—
181C2×Dic79—21no—
182C2×Dic79—21no—
183C2×Dic79—21no—
184C2×Dic79—22no—
185C2×Dic79—41no—
186C2×Dic79—41no—
187C2×Dic79—41no—
188C2×Dic79—42no—
189C2×Dic79—41no—
190C2×Dic79—42no—
191C2×Dic79—42no—
192C2×Dic79—41no—
193C2×Dic79C22⋊Q812yes—
194C2×Dic79#12312yes—
195C2×Dic79#12412yes—
196C2×Dic79C2×D812yes—
197C2×Dic79C2×SD1612yes—
198C4×D79—28no—
199C4×D79—28no—
200C4×D79—48no—
201C4×D79—84no—
202C4×D79—88no—
203C4×D79#12518yes—
204C4×D79#12618yes—
205C8×C79—42no—
206C79⋊C8—42no—
207C22×C79C2×C22⋊Q811yescharacteristic
208C22×C79C2×#12311yescharacteristic
209C22×C79C2×#12411yescharacteristic
210C22×C79C22×D811yescharacteristic
211C22×C79C22×SD1611yescharacteristic
212C22×C79C2×#13711yescharacteristic
213C22×C79C2×#13711yescharacteristic
214C2×D79#40014yes—
215C2×D79#47414yes—
216C2×D79#47514yes—
217C2×D79#48014yes—
218C2×D79#48314yes—
219C2×D79#48614yes—
220C2×D79#49114yes—
221C4×C79—22no—
222C4×C79—22no—
223C4×C79—42no—
224C4×C79—81no—
225C4×C79—82no—
226C4×C79C2×#12512yes—
227C4×C79C2×#12612yes—
228Dic79—22no—
229Dic79—22no—
230Dic79—42no—
231Dic79—81no—
232Dic79—82no—
233Dic79#40014yes—
234C2×#2099—791nomaximal, Sylow
235C2×C79C2×#40011yescharacteristic
236C2×C79C2×#47411yescharacteristic
237C2×C79C2×#47511yescharacteristic
238C2×C79C2×#48011yescharacteristic
239C2×C79C2×#48311yescharacteristic
240C2×C79C2×#48611yescharacteristic
241C2×C79C2×#49111yescharacteristic
242D79#209918yesdirect product factor
243C2×#389—791no—
244C2×#384—791no—
245#2099—791no—
246#2099—791no—
247#2099—792no—
248#2099—792no—
249#2099—791no—
250#2099D7911yescharacteristic, direct product factor
251C2×#340—792no—
252C2×#340—792no—
253C2×#336—791no—
254C79C2×#209911yescharacteristic, complemented, Sylow
255C23×C8—792no—
256C22×C4⋊C4—791no—
257C22×C4⋊C4—792no—
258C22×C4⋊C4—791no—
259C22×C4⋊C4—1581no—
260C22×C4⋊C4—1581no—
261C22×C4⋊C4—1581no—
262C22×C42—791no—
263#389—791no—
264#389—791no—
265#389—791no—
266#389—1581no—
267#389—1581no—
268#389C2×D7911yescharacteristic
269#384—792no—
270#384—791no—
271#384—1581no—
272#384—1581no—
273#384C2×D7911yescharacteristic
274C2×#95—1581no—
275#340—792no—
276#340—792no—
277#340—792no—
278#340—792no—
279#340—792no—
280#340—792no—
281#340C2×D7912yes—
282#340C2×D7912yes—
283#336—792no—
284#336—791no—
285#336C2×D7911yescharacteristic
286C23×C4—791no—
287C23×C4—791no—
288C23×C4—791no—
289C23×C4—1582no—
290C23×C4—1581no—
291C23×C4—1581no—
292C22×C8—792no—
293C22×C8—1584no—
294C22×C8—1584no—
295C22×C8—1584no—
296C22×C8C22×D7912yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—3164no—
301C2×C4⋊C4—3164no—
302C2×C4⋊C4—3164no—
303C2×C4⋊C4—791no—
304C2×C4⋊C4—794no—
305C2×C4⋊C4—792no—
306C2×C4⋊C4—791no—
307C2×C4⋊C4—1584no—
308C2×C4⋊C4—1588no—
309C2×C4⋊C4—1582no—
310C2×C4⋊C4—1582no—
311C2×C4⋊C4—1581no—
312C2×C4⋊C4—1582no—
313C2×C4⋊C4—1582no—
314C2×C4⋊C4—1581no—
315C2×C4⋊C4—1581no—
316C2×C4⋊C4—1581no—
317C2×C4⋊C4—1581no—
318C2×C4⋊C4—1581no—
319C2×C4⋊C4—1581no—
320C2×C4⋊C4C22×D7912yes—
321C2×C4⋊C4C22×D7911yescharacteristic
322C2×C4⋊C4C22×D7911yescharacteristic
323C2×C42—791no—
324C2×C42—791no—
325C2×C42—791no—
326C2×C42—1584no—
327C2×C42C22×D7911yescharacteristic
328#95—21no—
329#95—1581no—
330#95—1581no—
331#95—1581no—
332C24—791no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—3162no—
337C22×C4—3162no—
338C22×C4—3164no—
339C22×C4—3162no—
340C22×C4—3164no—
341C22×C4—3162no—
342C22×C4—3164no—
343C22×C4—3162no—
344C22×C4—791no—
345C22×C4—792no—
346C22×C4—794no—
347C22×C4—794no—
348C22×C4—792no—
349C22×C4—791no—
350C22×C4—791no—
351C22×C4—794no—
352C22×C4—794no—
353C22×C4—1584no—
354C22×C4—1582no—
355C22×C4—1582no—
356C22×C4—1582no—
357C22×C4—1582no—
358C22×C4—1581no—
359C22×C4—1582no—
360C22×C4—1581no—
361C22×C4D4×D7911yescharacteristic
362C22×C4D4×D7911yescharacteristic
363C22×C4C23×D7911yescharacteristic
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—3168no—
368C2×C8—1582no—
369C2×C8—1582no—
370C2×C8—1582no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—24no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—3162no—
378C4⋊C4—3164no—
379C4⋊C4—3164no—
380C4⋊C4—3162no—
381C4⋊C4—3164no—
382C4⋊C4—3162no—
383C4⋊C4—3162no—
384C4⋊C4—3162no—
385C4⋊C4—3162no—
386C4⋊C4—792no—
387C4⋊C4—1584no—
388C4⋊C4—1582no—
389C4⋊C4—1584no—
390C4⋊C4—1581no—
391C4⋊C4Q8×D7912yes—
392C42—22no—
393C42—1582no—
394C42—1582no—
395C42—1582no—
396C23—792no—
397C23—792no—
398C23—792no—
399C23—792no—
400C23—792no—
401C23—792no—
402C23—792no—
403C23C2×D4×D7911yescharacteristic
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—3168no—
418C2×C4—3161no—
419C2×C4—3161no—
420C2×C4—3161no—
421C2×C4—3162no—
422C2×C4—3161no—
423C2×C4—3162no—
424C2×C4—3162no—
425C2×C4—3161no—
426C2×C4—792no—
427C2×C4—792no—
428C2×C4—792no—
429C2×C4—798no—
430C2×C4—798no—
431C2×C4—792no—
432C2×C4—792no—
433C2×C4—6328no—
434C2×C4—6324no—
435C2×C4—1588no—
436C2×C4—1588no—
437C2×C4—1582no—
438C2×C4—1581no—
439C2×C4—1581no—
440C2×C4—1581no—
441C2×C4—1581no—
442C2×C4D8×D7912yes—
443C2×C4SD16×D7912yes—
444C2×C4C2×Q8×D7911yescharacteristic
445C2×C4#41×D7912yes—
446C2×C4#41×D7912yes—
447C2×C4#41×D7911yescharacteristic
448C8—42no—
449C8—3162no—
450C22—794no—
451C22—794no—
452C22—794no—
453C22—794no—
454C22—794no—
455C22—794no—
456C22—794no—
457C22C22⋊Q8×D7911yescharacteristic
458C22#123×D7911yescharacteristic
459C22#124×D7911yescharacteristic
460C22C2×D8×D7911yescharacteristic
461C22C2×SD16×D7911yescharacteristic
462C22#137×D7911yescharacteristic
463C22#137×D7911yescharacteristic
464C4—22no—
465C4—22no—
466C4—42no—
467C4—82no—
468C4—81no—
469C4—3162no—
470C4—794no—
471C4—6322no—
472C4—6321no—
473C4—1582no—
474C4—1582no—
475C4#125×D7912yes—
476C4#126×D7912yes—
477C2—798no—
478C2#400×D7911yescharacteristic
479C2#474×D7911yescharacteristic
480C2#475×D7911yescharacteristic
481C2#480×D7911yescharacteristic
482C2#483×D7911yescharacteristic
483C2#486×D7911yescharacteristic
484C2#491×D7911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2099C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenter#2099D79
hypocenterC79C2×#2099
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. #23764961C2semidirect
4. #23764960C2semidirect
5. #23764959C2semidirect
6. #23764958C2semidirect
7. #23764957C2semidirect
11. C79×#2099C2semidirect
242. D79#2099direct (N × H)
250. #2099D79direct (N × H)
254. C79C2×#2099semidirect

Maximal subgroups

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

subgroupindex
#389×D792
#384×D792
#237649612
#237649602
#237649592
#237649582
#237649572
#340×D792
#336×D792
C79×#20992
C2×#209979