Finite Group Databasebeta

← #2228×D79 #34442880

Subgroups — #2228×D79 #34442880

Order 20224.

606 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#499×D79C211yesmaximal, characteristic, complemented
2C4×D8×D79C211yesmaximal, characteristic
3#23765560C211yesmaximal, characteristic, complemented
4#23765559C211yesmaximal, characteristic, complemented
5#23765558C211yesmaximal, characteristic, complemented
6#23765557C211yesmaximal, characteristic, complemented
7#23765556C211yesmaximal, characteristic, complemented
8#23765555C211yesmaximal, characteristic, complemented
9#23765554C211yesmaximal, characteristic, complemented
10#367×D79C211yesmaximal, characteristic, complemented
11#366×D79C211yesmaximal, characteristic, complemented
12C4⋊C16×D79C211yesmaximal, characteristic, complemented
13#357×D79C211yesmaximal, characteristic
14#357×D79C211yesmaximal, characteristic
15C79×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D79C2211yescharacteristic
17#125×D79—21no—
18C4×D4×D79—21no—
19C2×C16×D79C2211yescharacteristic
20C2×C16×D79C2211yescharacteristic
21#19098965C2211yescharacteristic, complemented
22#19098964C2211yescharacteristic, complemented
23#19098964C2211yescharacteristic, complemented
24#19098963—21no—
25#19098962—21no—
26C4×D632C2211yescharacteristic
27D8×Dic79C2211yescharacteristic
28#19098645C2211yescharacteristic
29C4×#11929609—21no—
30#19098643—21no—
31#107×D79C2211yescharacteristic
32#107×D79C2211yescharacteristic
33#107×D79C2211yescharacteristic
34#106×D79—21no—
35#102×D79—21no—
36C4×C8×D79C2211yescharacteristic
37#19098391C2211yescharacteristic, complemented
38#19098390C2211yescharacteristic, complemented
39#19098390C2211yescharacteristic, complemented
40#19098389C2211yescharacteristic, complemented
41#19098388C2211yescharacteristic, complemented
42#19098388C2211yescharacteristic, complemented
43C4⋊(C79⋊C16)C2211yescharacteristic, complemented
44Dic79⋊C16C2211yescharacteristic, complemented
45Dic79⋊C16C2211yescharacteristic, complemented
46#19098365C2211yescharacteristic
47#19098365C2211yescharacteristic
48#19098364C2211yescharacteristic
49#19098364C2211yescharacteristic
50#19098363C2211yescharacteristic
51#19098363C2211yescharacteristic
52#499×C79C2211yescharacteristic, complemented
53C4×D8×C79C2211yescharacteristic
54#367×C79C2211yescharacteristic, complemented
55#366×C79C2211yescharacteristic, complemented
56C4⋊C16×C79C2211yescharacteristic, complemented
57#357×C79C2211yescharacteristic
58#357×C79C2211yescharacteristic
59C2×D4×D79—21no—
60C22×C4×D79—41no—
61C2×D632C2311yescharacteristic
62C2×#11929609—21no—
63D8×D79—22no—
64D8×D79Q814yes—
65C2×C8×D79D411yescharacteristic
66C2×C8×D79C2311yescharacteristic
67#14579153—21no—
68#14579152—21no—
69#14579152—21no—
70#14579151—41no—
71#14579151—41no—
72C4×D316—21no—
73D4×Dic79—21no—
74#14579123—21no—
75C4×C22⋊D79—41no—
76(C22⋊D79)⋊C4—41no—
77C4⋊C4×D79—21no—
78C4⋊C4×D79—21no—
79C4⋊C4×D79—21no—
80C4⋊C4×D79—41no—
81C4⋊C4×D79—41no—
82C22⋊C4×D79—41no—
83C42×D79D411yescharacteristic
84C2×C79⋊C16C2311yescharacteristic
85C2×C79⋊C16C2311yescharacteristic
86C16×D79—22no—
87C16×D79—22no—
88#14579095C2311yescharacteristic
89#14579095C2311yescharacteristic
90#14579095C2311yescharacteristic
91#14579094—21no—
92#14579094—21no—
93#14579094—21no—
94#14579093—21no—
95#14579092—21no—
96#14579092—21no—
97#14579083—21no—
98#14579082—21no—
99#14579081—21no—
100C4×C79⋊C8D411yescharacteristic
101C8×Dic79D411yescharacteristic
102C8×Dic79C2311yescharacteristic
103C2×D8×C79C2311yescharacteristic
104#125×C79—21no—
105C4×D4×C79—21no—
106C2×C16×C79C2311yescharacteristic
107C2×C16×C79C2311yescharacteristic
108#107×C79C2311yescharacteristic
109#107×C79C2311yescharacteristic
110#107×C79C2311yescharacteristic
111#106×C79—21no—
112#102×C79—21no—
113C4×C8×C79C2311yescharacteristic
114C23×D79—41no—
115C2×D316—21no—
116C2×C22⋊D79—41no—
117D4×D79—24no—
118D4×D79—42no—
119C22×Dic79—41no—
120C2×C4×D79—41no—
121C2×C4×D79—41no—
122C2×C4×D79—41no—
123C2×C4×D79—41no—
124C2×C4×D79—41no—
125C2×C4×D79—84no—
126C2×C4×D79D811yescharacteristic
127C2×C4×D79D811yescharacteristic
128C2×C4×D79C2×D411yescharacteristic
129D632—21no—
130D632C2×Q812yes—
131#11929609—24no—
132C2×C79⋊C8C2×D411yescharacteristic
133C2×C79⋊C8C2×D411yescharacteristic
134C8×D79—22no—
135C8×D79C2×Q812yes—
136C8×D79#4112yes—
137C4⋊Dic79—21no—
138C4⋊Dic79—21no—
139C4⋊Dic79—21no—
140C4⋊Dic79—41no—
141C4⋊Dic79—41no—
142Dic79⋊C4—41no—
143Dic79⋊C4—41no—
144Dic79⋊C4—41no—
145Dic79⋊C4—41no—
146Dic79⋊C4—41no—
147Dic79⋊C4—41no—
148Dic79⋊C4—41no—
149C22⋊Dic79—41no—
150(C2×D79)⋊C4—41no—
151(C2×D79)⋊C4—41no—
152C4×Dic79D811yescharacteristic
153C4×Dic79D811yescharacteristic
154C4×Dic79C2×D411yescharacteristic
155C79⋊C16—21no—
156C79⋊C16—21no—
157C2×D4×C79—21no—
158C22×C4×C79—41no—
159D8×C79—21no—
160D8×C79C2×Q812yes—
161C2×C8×C79C2×D411yescharacteristic
162C2×C8×C79C2411yescharacteristic
163C4⋊C4×C79—21no—
164C4⋊C4×C79—21no—
165C4⋊C4×C79—21no—
166C4⋊C4×C79—41no—
167C4⋊C4×C79—41no—
168C22⋊C4×C79—41no—
169C42×C79C2×D411yescharacteristic
170C16×C79—21no—
171C16×C79—21no—
172C23×C79—41no—
173C22×D79—41no—
174C22×D79—44no—
175C22×D79—82no—
176C22×D79—82no—
177C22×D79C2×D811yescharacteristic
178D4×C79—22no—
179D4×C79—41no—
180C2×C4×C79—41no—
181C2×C4×C79—41no—
182C2×C4×C79—41no—
183C2×C4×C79—82no—
184C2×C4×C79C2×D811yescharacteristic
185C2×C4×C79C2×D811yescharacteristic
186C2×C4×C79C22×D411yescharacteristic
187C22⋊D79—44no—
188C2×Dic79—41no—
189C2×Dic79—41no—
190C2×Dic79—41no—
191C2×Dic79—82no—
192C2×Dic79C2×D811yescharacteristic
193C2×Dic79C2×D811yescharacteristic
194C2×Dic79C2×D811yescharacteristic
195D316—22no—
196D316—41no—
197C4×D79—22no—
198C4×D79—22no—
199C4×D79—82no—
200C4×D79—82no—
201C4×D79—82no—
202C4×D79—82no—
203C4×D79—82no—
204C4×D79C22⋊Q812yes—
205C4×D79#13712yes—
206C8×C79—21no—
207C8×C79C22×Q811yescharacteristic
208C8×C79C2×#4111yescharacteristic
209C79⋊C8—21no—
210C79⋊C8C22⋊Q812yes—
211C22×C79—42no—
212C22×C79—81no—
213C22×C79—81no—
214C22×C79C22×D811yescharacteristic
215C2×D79—42no—
216C2×D79—81no—
217C2×D79—81no—
218C2×D79—88no—
219C2×D79#47412yes—
220C2×D79#50812yes—
221C2×D79#50912yes—
222C4×C79—21no—
223C4×C79—21no—
224C4×C79—81no—
225C4×C79—81no—
226C4×C79—81no—
227C4×C79C2×C22⋊Q811yescharacteristic
228C4×C79C2×#13711yescharacteristic
229Dic79—21no—
230Dic79—21no—
231Dic79—81no—
232Dic79—81no—
233Dic79—81no—
234Dic79#47412yes—
235C2×#2228—791nomaximal, Sylow
236C2×C79—82no—
237C2×C79C2×#47411yescharacteristic
238C2×C79C2×#50811yescharacteristic
239C2×C79C2×#50911yescharacteristic
240D79—82no—
241D79#222814yesdirect product factor
242C2×#499—791no—
243C2×C4×D8—791no—
244#2228—791no—
245#2228—791no—
246#2228—791no—
247#2228—791no—
248#2228—791no—
249#2228—791no—
250#2228—791no—
251#2228D7911yescharacteristic, direct product factor
252C2×#367—791no—
253C2×#366—791no—
254C2×C4⋊C16—791no—
255C2×#357—791no—
256C2×#357—791no—
257C79C2×#222811yescharacteristic, complemented, Sylow
258C22×D8—791no—
259C2×#125—1581no—
260C2×C4×D4—1581no—
261C22×C16—791no—
262C22×C16—791no—
263#499—791no—
264#499—791no—
265#499—791no—
266#499—1581no—
267#499—1581no—
268#499C2×D7911yescharacteristic, complemented
269C4×D8—791no—
270C4×D8—791no—
271C4×D8—791no—
272C4×D8—1581no—
273C4×D8—1581no—
274C4×D8C2×D7911yescharacteristic
275C2×#107—791no—
276C2×#107—791no—
277C2×#107—791no—
278C2×#106—1581no—
279C2×#102—1581no—
280C2×C4×C8—791no—
281#367—791no—
282#367—791no—
283#367—791no—
284#367C2×D7911yescharacteristic, complemented
285#366—791no—
286#366—791no—
287#366—791no—
288#366C2×D7911yescharacteristic, complemented
289C4⋊C16—791no—
290C4⋊C16—791no—
291C4⋊C16—791no—
292C4⋊C16C2×D7911yescharacteristic, complemented
293#357—791no—
294#357—791no—
295#357—791no—
296#357—791no—
297#357—791no—
298#357—791no—
299#357C2×D7911yescharacteristic
300#357C2×D7911yescharacteristic
301C22×D4—1581no—
302C23×C4—3161no—
303C2×D8—794no—
304C2×D8—791no—
305C2×D8—1582no—
306C2×D8—1581no—
307C2×D8C22×D7911yescharacteristic
308C22×C8—791no—
309C22×C8—791no—
310#125—21no—
311#125—3161no—
312#125—3161no—
313#125—1581no—
314#125—1581no—
315#125—1581no—
316C4×D4—21no—
317C4×D4—3161no—
318C4×D4—3161no—
319C4×D4—1581no—
320C4×D4—1581no—
321C4×D4—1581no—
322C2×C4⋊C4—3161no—
323C2×C4⋊C4—3161no—
324C2×C4⋊C4—1581no—
325C2×C4⋊C4—1581no—
326C2×C4⋊C4—1581no—
327C2×C22⋊C4—3161no—
328C2×C42—791no—
329C2×C16—791no—
330C2×C16—791no—
331C2×C16—1582no—
332C2×C16—1582no—
333C2×C16C22×D7911yescharacteristic
334C2×C16C22×D7911yescharacteristic
335#107—791no—
336#107—791no—
337#107—791no—
338#107—1581no—
339#107—1581no—
340#107—1581no—
341#107C22×D7911yescharacteristic
342#107C22×D7911yescharacteristic
343#107C22×D7911yescharacteristic
344#106—21no—
345#106—1581no—
346#106—1581no—
347#106—1581no—
348#102—21no—
349#102—1581no—
350#102—1581no—
351#102—1581no—
352C4×C8—791no—
353C4×C8—791no—
354C4×C8—791no—
355C4×C8C22×D7911yescharacteristic
356C24—3161no—
357C2×D4—21no—
358C2×D4—3162no—
359C2×D4—3161no—
360C2×D4—1584no—
361C2×D4—1581no—
362C22×C4—41no—
363C22×C4—3161no—
364C22×C4—3161no—
365C22×C4—3161no—
366C22×C4—3161no—
367C22×C4—3161no—
368C22×C4—3161no—
369C22×C4—791no—
370C22×C4—791no—
371C22×C4—791no—
372C22×C4—6324no—
373D8—21no—
374D8—792no—
375D8—1584no—
376D8—1581no—
377D8Q8×D7912yes—
378C2×C8—791no—
379C2×C8—792no—
380C2×C8—792no—
381C2×C8—791no—
382C2×C8—1582no—
383C2×C8D4×D7911yescharacteristic
384C2×C8C23×D7911yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—3161no—
391C4⋊C4—3161no—
392C4⋊C4—3161no—
393C4⋊C4—3161no—
394C4⋊C4—3161no—
395C4⋊C4—3161no—
396C4⋊C4—3161no—
397C4⋊C4—3161no—
398C4⋊C4—3161no—
399C4⋊C4—1581no—
400C4⋊C4—1581no—
401C4⋊C4—1581no—
402C22⋊C4—41no—
403C22⋊C4—3161no—
404C22⋊C4—3161no—
405C22⋊C4—3161no—
406C42—791no—
407C42—791no—
408C42—791no—
409C42D4×D7911yescharacteristic
410C16—21no—
411C16—21no—
412C16—1581no—
413C16—1581no—
414C23—41no—
415C23—3164no—
416C23—3161no—
417C23—791no—
418C23—6322no—
419C23—6322no—
420D4—22no—
421D4—41no—
422D4—3164no—
423D4—3161no—
424D4—1582no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—82no—
429C2×C4—3161no—
430C2×C4—3161no—
431C2×C4—3161no—
432C2×C4—791no—
433C2×C4—792no—
434C2×C4—792no—
435C2×C4—791no—
436C2×C4—791no—
437C2×C4—6322no—
438C2×C4—6322no—
439C2×C4—6322no—
440C2×C4—6322no—
441C2×C4—6322no—
442C2×C4—6322no—
443C2×C4—1582no—
444C2×C4—1582no—
445C2×C4D8×D7911yescharacteristic
446C2×C4D8×D7911yescharacteristic
447C2×C4C2×D4×D7911yescharacteristic
448C8—21no—
449C8—792no—
450C8—1581no—
451C8C2×Q8×D7911yescharacteristic
452C8#41×D7911yescharacteristic
453C22—42no—
454C22—81no—
455C22—81no—
456C22—3162no—
457C22—792no—
458C22—792no—
459C22—792no—
460C22—6328no—
461C22—6321no—
462C22—6321no—
463C22C2×D8×D7911yescharacteristic
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—792no—
470C4—6321no—
471C4—6321no—
472C4—6321no—
473C4—1581no—
474C4—1581no—
475C4C22⋊Q8×D7911yescharacteristic
476C4#137×D7911yescharacteristic
477C2—82no—
478C2—794no—
479C2—6322no—
480C2#474×D7911yescharacteristic
481C2#508×D7911yescharacteristic
482C2#509×D7911yescharacteristic
subgroupG/H
centerC22C2×D8×D79
commutator, cosocleC2×C8×C79C24
FrattiniC2×C8C23×D79
FittingC79×#2228C2
socleC22×C79C22×D8
prime radicalC2×D8×D79C22
hypercenter#2228D79
hypocenterC79C2×#2228
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #499×D79C2semidirect
3. #23765560C2semidirect
4. #23765559C2semidirect
5. #23765558C2semidirect
6. #23765557C2semidirect
7. #23765556C2semidirect
8. #23765555C2semidirect
9. #23765554C2semidirect
10. #367×D79C2semidirect
11. #366×D79C2semidirect
12. C4⋊C16×D79C2semidirect
15. C79×#2228C2semidirect
21. #19098965C22semidirect
22. #19098964C22semidirect
23. #19098964C22semidirect
37. #19098391C22semidirect
38. #19098390C22semidirect
39. #19098390C22semidirect
40. #19098389C22semidirect
41. #19098388C22semidirect
42. #19098388C22semidirect
43. C4⋊(C79⋊C16)C22semidirect
44. Dic79⋊C16C22semidirect
45. Dic79⋊C16C22semidirect
52. #499×C79C22semidirect
54. #367×C79C22semidirect
55. #366×C79C22semidirect
56. C4⋊C16×C79C22semidirect
241. D79#2228direct (N × H)
251. #2228D79direct (N × H)
257. C79C2×#2228semidirect
268. #499C2×D79semidirect
284. #367C2×D79semidirect
288. #366C2×D79semidirect
292. C4⋊C16C2×D79semidirect

Maximal subgroups

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

subgroupindex
#499×D792
C4×D8×D792
#237655602
#237655592
#237655582
#237655572
#237655562
#237655552
#237655542
#367×D792
#366×D792
C4⋊C16×D792
#357×D792
C79×#22282
C2×#222879