Finite Group Databasebeta

← #2234×D79 #34443035

Subgroups — #2234×D79 #34443035

Order 20224.

638 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#466×D79C211yesmaximal, characteristic
2#427×D79C211yesmaximal, characteristic, complemented
3#23765594C211yesmaximal, characteristic, complemented
4#23765593C211yesmaximal, characteristic, complemented
5#23765592C211yesmaximal, characteristic, complemented
6#23765591C211yesmaximal, characteristic, complemented
7#23765590C211yesmaximal, characteristic, complemented
8#23765589C211yesmaximal, characteristic, complemented
9#23765588C211yesmaximal, characteristic, complemented
10#367×D79C211yesmaximal, characteristic, complemented
11#366×D79C211yesmaximal, characteristic, complemented
12#357×D79C211yesmaximal, characteristic, complemented
13#357×D79C211yesmaximal, characteristic, complemented
14C22⋊C16×D79C211yesmaximal, characteristic, complemented
15C79×#2234C211yesmaximal, characteristic, complemented
16C2×D8×D79C2211yescharacteristic
17C22×C8×D79C2211yescharacteristic
18#121×D79—21no—
19#117×D79—21no—
20C2×C16×D79C2211yescharacteristic
21C2×C16×D79C2211yescharacteristic
22#19098800C2211yescharacteristic
23#19098799C2211yescharacteristic
24#19098798—21no—
25#19098797—21no—
26#19098796C2211yescharacteristic
27#19098601C2211yescharacteristic, complemented
28#19098600C2211yescharacteristic, complemented
29#19098600C2211yescharacteristic, complemented
30#19098599—21no—
31#19098598—21no—
32#107×D79C2211yescharacteristic
33#107×D79C2211yescharacteristic
34#107×D79C2211yescharacteristic
35#106×D79—21no—
36#102×D79—21no—
37#19098391C2211yescharacteristic, complemented
38#19098390C2211yescharacteristic, complemented
39#19098390C2211yescharacteristic, complemented
40#19098389C2211yescharacteristic, complemented
41#19098388C2211yescharacteristic, complemented
42#19098388C2211yescharacteristic, complemented
43#19098365C2211yescharacteristic, complemented
44#19098365C2211yescharacteristic, complemented
45#19098364C2211yescharacteristic, complemented
46#19098364C2211yescharacteristic, complemented
47#19098363C2211yescharacteristic, complemented
48#19098363C2211yescharacteristic, complemented
49C22⋊(C79⋊C16)C2211yescharacteristic, complemented
50(C2×D79)⋊C16C2211yescharacteristic, complemented
51(C2×D79)⋊C16C2211yescharacteristic, complemented
52#466×C79C2211yescharacteristic
53#427×C79C2211yescharacteristic, complemented
54#367×C79C2211yescharacteristic, complemented
55#366×C79C2211yescharacteristic, complemented
56#357×C79C2211yescharacteristic, complemented
57#357×C79C2211yescharacteristic, complemented
58C22⋊C16×C79C2211yescharacteristic, complemented
59C2×D4×D79—21no—
60C2×D4×D79—41no—
61C22×C4×D79D411yescharacteristic
62C2×D632C2311yescharacteristic
63C2×#11929609—21no—
64D8×D79—22no—
65D8×D79—22no—
66C22×C79⋊C8D411yescharacteristic
67C2×C8×D79—22no—
68C2×C8×D79—22no—
69C2×C8×D79D411yescharacteristic
70C2×C8×D79D411yescharacteristic
71C2×C8×D79C2311yescharacteristic
72C2×C8×D79C2311yescharacteristic
73#14579136—21no—
74#14579135—21no—
75#14579134—41no—
76#14579133—41no—
77#14579132—21no—
78#14579120—21no—
79#14579119—21no—
80#14579119—21no—
81#14579118—41no—
82#14579117—41no—
83C4⋊C4×D79—21no—
84C4⋊C4×D79—21no—
85C4⋊C4×D79—21no—
86C22⋊C4×D79—41no—
87C22⋊C4×D79—41no—
88C42×D79—41no—
89C2×C79⋊C16C2311yescharacteristic
90C2×C79⋊C16C2311yescharacteristic
91C16×D79—22no—
92C16×D79—22no—
93#14579095C2311yescharacteristic
94#14579095C2311yescharacteristic
95#14579095C2311yescharacteristic
96#14579094—21no—
97#14579094—21no—
98#14579094—21no—
99#14579093—21no—
100#14579092—21no—
101#14579092—21no—
102#14579083—21no—
103#14579082—21no—
104#14579081—21no—
105C2×D8×C79C2311yescharacteristic
106C22×C8×C79C2311yescharacteristic
107#121×C79—21no—
108#117×C79—21no—
109C2×C16×C79C2311yescharacteristic
110C2×C16×C79C2311yescharacteristic
111#107×C79C2311yescharacteristic
112#107×C79C2311yescharacteristic
113#107×C79C2311yescharacteristic
114#106×C79—21no—
115#102×C79—21no—
116C23×D79—41no—
117C23×D79D811yescharacteristic
118C2×D316—21no—
119C2×D316—41no—
120C2×C22⋊D79—41no—
121C2×C22⋊D79—41no—
122C2×C22⋊D79—41no—
123D4×D79—42no—
124D4×D79—42no—
125D4×D79—84no—
126C22×Dic79D811yescharacteristic
127C2×C4×D79—22no—
128C2×C4×D79—22no—
129C2×C4×D79—41no—
130C2×C4×D79—41no—
131C2×C4×D79—41no—
132C2×C4×D79D811yescharacteristic
133C2×C4×D79D811yescharacteristic
134C2×C4×D79C2×D411yescharacteristic
135C2×C4×D79C2×D411yescharacteristic
136D632—21no—
137D632—21no—
138#11929609—42no—
139C2×C79⋊C8—22no—
140C2×C79⋊C8C2×D411yescharacteristic
141C2×C79⋊C8C2×D411yescharacteristic
142C8×D79—22no—
143C8×D79—21no—
144C8×D79—21no—
145C8×D79—22no—
146C8×D79#4112yes—
147C8×D79#4112yes—
148C4⋊Dic79—21no—
149C4⋊Dic79—21no—
150C4⋊Dic79—21no—
151Dic79⋊C4—41no—
152Dic79⋊C4—41no—
153Dic79⋊C4—41no—
154C22⋊Dic79—41no—
155C22⋊Dic79—41no—
156(C2×D79)⋊C4—41no—
157(C2×D79)⋊C4—41no—
158(C2×D79)⋊C4—41no—
159(C2×D79)⋊C4—41no—
160C4×Dic79—41no—
161C4×Dic79—41no—
162C4×Dic79—41no—
163C79⋊C16—21no—
164C79⋊C16—21no—
165C2×D4×C79—21no—
166C2×D4×C79—41no—
167C22×C4×C79C2×D411yescharacteristic
168D8×C79—21no—
169D8×C79—21no—
170C2×C8×C79—21no—
171C2×C8×C79—21no—
172C2×C8×C79C2×D411yescharacteristic
173C2×C8×C79C2411yescharacteristic
174C4⋊C4×C79—21no—
175C4⋊C4×C79—21no—
176C4⋊C4×C79—21no—
177C22⋊C4×C79—41no—
178C22⋊C4×C79—41no—
179C42×C79—41no—
180C16×C79—21no—
181C16×C79—21no—
182C23×C79—41no—
183C23×C79C2×D811yescharacteristic
184C22×D79—22no—
185C22×D79—22no—
186C22×D79—22no—
187C22×D79—41no—
188C22×D79—82no—
189C22×D79—82no—
190C22×D79—82no—
191C22×D79C2×D811yescharacteristic
192C22×D79C2×D811yescharacteristic
193D4×C79—41no—
194D4×C79—41no—
195D4×C79—82no—
196C2×C4×C79—21no—
197C2×C4×C79—21no—
198C2×C4×C79—41no—
199C2×C4×C79—41no—
200C2×C4×C79—41no—
201C2×C4×C79C2×D811yescharacteristic
202C2×C4×C79C22×D411yescharacteristic
203C22⋊D79—82no—
204C22⋊D79—82no—
205C22⋊D79—82no—
206C2×Dic79—22no—
207C2×Dic79—41no—
208C2×Dic79—41no—
209C2×Dic79—41no—
210C2×Dic79C2×D811yescharacteristic
211C2×Dic79C2×D811yescharacteristic
212D316—41no—
213D316—41no—
214D316—82no—
215C4×D79—22no—
216C4×D79—21no—
217C4×D79—21no—
218C4×D79—22no—
219C4×D79—82no—
220C4×D79—82no—
221C4×D79—82no—
222C4×D79#12312yes—
223C4×D79#13712yes—
224C8×C79—21no—
225C8×C79C2×#4111yescharacteristic
226C8×C79C2×#4111yescharacteristic
227C79⋊C8—21no—
228C79⋊C8#12312yes—
229C22×C79—21no—
230C22×C79—21no—
231C22×C79—21no—
232C22×C79—81no—
233C22×C79—81no—
234C22×C79—81no—
235C22×C79C22×D811yescharacteristic
236C2×D79—21no—
237C2×D79—21no—
238C2×D79—21no—
239C2×D79—44no—
240C2×D79—81no—
241C2×D79—81no—
242C2×D79—81no—
243C2×D79—164no—
244C2×D79#48012yes—
245C2×D79#50812yes—
246C2×D79#50912yes—
247C4×C79—21no—
248C4×C79—81no—
249C4×C79—81no—
250C4×C79—81no—
251C4×C79C2×#12311yescharacteristic
252C4×C79C2×#13711yescharacteristic
253Dic79—21no—
254Dic79—81no—
255Dic79—81no—
256Dic79—81no—
257Dic79#48012yes—
258C2×#2234—791nomaximal, Sylow
259C2×C79—41no—
260C2×C79—161no—
261C2×C79C2×#48011yescharacteristic
262C2×C79C2×#50811yescharacteristic
263C2×C79C2×#50911yescharacteristic
264D79—41no—
265D79—161no—
266D79#223414yesdirect product factor
267C2×#466—791no—
268C2×#427—791no—
269#2234—791no—
270#2234—791no—
271#2234—791no—
272#2234—791no—
273#2234—791no—
274#2234—791no—
275#2234—791no—
276#2234D7911yescharacteristic, direct product factor
277C2×#367—791no—
278C2×#366—791no—
279C2×#357—791no—
280C2×#357—791no—
281C2×C22⋊C16—791no—
282C79C2×#223411yescharacteristic, complemented, Sylow
283C22×D8—791no—
284C23×C8—791no—
285C2×#121—1581no—
286C2×#117—1581no—
287C22×C16—791no—
288C22×C16—791no—
289#466—791no—
290#466—791no—
291#466—791no—
292#466—1581no—
293#466—1581no—
294#466C2×D7911yescharacteristic
295#427—791no—
296#427—791no—
297#427—791no—
298#427—1581no—
299#427—1581no—
300#427C2×D7911yescharacteristic, complemented
301C2×#107—791no—
302C2×#107—791no—
303C2×#107—791no—
304C2×#106—1581no—
305C2×#102—1581no—
306#367—791no—
307#367—791no—
308#367—791no—
309#367C2×D7911yescharacteristic, complemented
310#366—791no—
311#366—791no—
312#366—791no—
313#366C2×D7911yescharacteristic, complemented
314#357—791no—
315#357—791no—
316#357—791no—
317#357—791no—
318#357—791no—
319#357—791no—
320#357C2×D7911yescharacteristic, complemented
321#357C2×D7911yescharacteristic, complemented
322C22⋊C16—791no—
323C22⋊C16—791no—
324C22⋊C16—791no—
325C22⋊C16C2×D7911yescharacteristic, complemented
326C22×D4—3161no—
327C22×D4—1581no—
328C23×C4—791no—
329C2×D8—791no—
330C2×D8—1582no—
331C2×D8—1582no—
332C2×D8—1581no—
333C2×D8C22×D7911yescharacteristic
334C22×C8—791no—
335C22×C8—791no—
336C22×C8—791no—
337C22×C8—791no—
338C22×C8—791no—
339C22×C8—1582no—
340C22×C8—1582no—
341C22×C8C22×D7911yescharacteristic
342#121—21no—
343#121—3161no—
344#121—3161no—
345#121—1581no—
346#121—1581no—
347#121—1581no—
348#117—21no—
349#117—3161no—
350#117—3161no—
351#117—1581no—
352#117—1581no—
353#117—1581no—
354C2×C4⋊C4—1581no—
355C2×C4⋊C4—1581no—
356C2×C4⋊C4—1581no—
357C2×C22⋊C4—3161no—
358C2×C22⋊C4—3161no—
359C2×C42—3161no—
360C2×C16—791no—
361C2×C16—791no—
362C2×C16—1582no—
363C2×C16—1582no—
364C2×C16C22×D7911yescharacteristic
365C2×C16C22×D7911yescharacteristic
366#107—791no—
367#107—791no—
368#107—791no—
369#107—1581no—
370#107—1581no—
371#107—1581no—
372#107C22×D7911yescharacteristic
373#107C22×D7911yescharacteristic
374#107C22×D7911yescharacteristic
375#106—21no—
376#106—1581no—
377#106—1581no—
378#106—1581no—
379#102—21no—
380#102—1581no—
381#102—1581no—
382#102—1581no—
383C24—3161no—
384C24—791no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—3161no—
388C2×D4—3161no—
389C2×D4—3161no—
390C2×D4—3162no—
391C2×D4—3162no—
392C2×D4—3161no—
393C2×D4—6324no—
394C2×D4—1581no—
395C22×C4—3161no—
396C22×C4—3161no—
397C22×C4—3161no—
398C22×C4—791no—
399C22×C4—791no—
400C22×C4—791no—
401C22×C4—791no—
402C22×C4—791no—
403C22×C4—1582no—
404C22×C4—1582no—
405C22×C4D4×D7911yescharacteristic
406D8—21no—
407D8—21no—
408D8—3162no—
409D8—1581no—
410D8—1581no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—791no—
414C2×C8—792no—
415C2×C8—792no—
416C2×C8—791no—
417C2×C8—1582no—
418C2×C8—1582no—
419C2×C8—1582no—
420C2×C8—1581no—
421C2×C8—1581no—
422C2×C8D4×D7911yescharacteristic
423C2×C8C23×D7911yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—3161no—
428C4⋊C4—3161no—
429C4⋊C4—3161no—
430C4⋊C4—1581no—
431C4⋊C4—1581no—
432C4⋊C4—1581no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—3161no—
436C22⋊C4—3161no—
437C22⋊C4—3161no—
438C22⋊C4—3161no—
439C22⋊C4—3161no—
440C22⋊C4—3161no—
441C42—41no—
442C42—3161no—
443C42—3161no—
444C42—3161no—
445C16—21no—
446C16—21no—
447C16—1581no—
448C16—1581no—
449C23—41no—
450C23—3161no—
451C23—791no—
452C23—791no—
453C23—6322no—
454C23—6322no—
455C23—6322no—
456C23—1582no—
457C23—1582no—
458C23—1582no—
459C23D8×D7911yescharacteristic
460D4—41no—
461D4—41no—
462D4—82no—
463D4—3161no—
464D4—3161no—
465D4—6322no—
466D4—6322no—
467D4—6322no—
468D4—6322no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—3161no—
475C2×C4—3161no—
476C2×C4—3161no—
477C2×C4—791no—
478C2×C4—792no—
479C2×C4—792no—
480C2×C4—791no—
481C2×C4—6322no—
482C2×C4—6322no—
483C2×C4—6322no—
484C2×C4—1582no—
485C2×C4—1582no—
486C2×C4—1582no—
487C2×C4—1581no—
488C2×C4—1581no—
489C2×C4D8×D7911yescharacteristic
490C2×C4C2×D4×D7911yescharacteristic
491C8—21no—
492C8—792no—
493C8—1581no—
494C8#41×D7911yescharacteristic
495C8#41×D7911yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—3164no—
503C22—792no—
504C22—792no—
505C22—792no—
506C22—6321no—
507C22—6321no—
508C22—6321no—
509C22—1581no—
510C22—1581no—
511C22—1581no—
512C22—12644no—
513C22C2×D8×D7911yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—792no—
519C4—6321no—
520C4—6321no—
521C4—6321no—
522C4—1581no—
523C4#123×D7911yescharacteristic
524C4#137×D7911yescharacteristic
525C2—41no—
526C2—161no—
527C2—3161no—
528C2—794no—
529C2—12641no—
530C2#480×D7911yescharacteristic
531C2#508×D7911yescharacteristic
532C2#509×D7911yescharacteristic
subgroupG/H
centerC22C2×D8×D79
commutator, cosocleC2×C8×C79C24
FrattiniC2×C8C23×D79
FittingC79×#2234C2
socleC22×C79C22×D8
prime radical#466×D79C2
hypercenter#2234D79
hypocenterC79C2×#2234
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
2. #427×D79C2semidirect
3. #23765594C2semidirect
4. #23765593C2semidirect
5. #23765592C2semidirect
6. #23765591C2semidirect
7. #23765590C2semidirect
8. #23765589C2semidirect
9. #23765588C2semidirect
10. #367×D79C2semidirect
11. #366×D79C2semidirect
12. #357×D79C2semidirect
13. #357×D79C2semidirect
14. C22⋊C16×D79C2semidirect
15. C79×#2234C2semidirect
27. #19098601C22semidirect
28. #19098600C22semidirect
29. #19098600C22semidirect
37. #19098391C22semidirect
38. #19098390C22semidirect
39. #19098390C22semidirect
40. #19098389C22semidirect
41. #19098388C22semidirect
42. #19098388C22semidirect
43. #19098365C22semidirect
44. #19098365C22semidirect
45. #19098364C22semidirect
46. #19098364C22semidirect
47. #19098363C22semidirect
48. #19098363C22semidirect
49. C22⋊(C79⋊C16)C22semidirect
50. (C2×D79)⋊C16C22semidirect
51. (C2×D79)⋊C16C22semidirect
53. #427×C79C22semidirect
54. #367×C79C22semidirect
55. #366×C79C22semidirect
56. #357×C79C22semidirect
57. #357×C79C22semidirect
58. C22⋊C16×C79C22semidirect
266. D79#2234direct (N × H)
276. #2234D79direct (N × H)
282. C79C2×#2234semidirect
300. #427C2×D79semidirect
309. #367C2×D79semidirect
313. #366C2×D79semidirect
320. #357C2×D79semidirect
321. #357C2×D79semidirect
325. C22⋊C16C2×D79semidirect

Maximal subgroups

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

subgroupindex
#466×D792
#427×D792
#237655942
#237655932
#237655922
#237655912
#237655902
#237655892
#237655882
#367×D792
#366×D792
#357×D792
C22⋊C16×D792
C79×#22342
C2×#223479