Finite Group Databasebeta

← #34259661

Subgroups — #34259661

Order 20224.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773440C211yesmaximal, characteristic
2#23772501C211yesmaximal, characteristic
3#23772490C211yesmaximal, characteristic
4#23762308C211yesmaximal, characteristic, complemented
5#23762296C211yesmaximal, characteristic, complemented
6#23762270C211yesmaximal, characteristic, complemented
7#23762270C211yesmaximal, characteristic, complemented
8#23762249C211yesmaximal, characteristic, complemented
9#23762249C211yesmaximal, characteristic, complemented
10#23762218C211yesmaximal, characteristic, complemented
11#23762206C211yesmaximal, characteristic, complemented
12#23761872C211yesmaximal, characteristic
13#23761794C211yesmaximal, characteristic
14#23761700C211yesmaximal, characteristic
15C79×#1572C211yesmaximal, characteristic
16#19099120C2211yescharacteristic
17C2×C4×Dic158C2211yescharacteristic
18#19098899C411yescharacteristic
19#19098899C411yescharacteristic
20#19098859C411yescharacteristic
21#19098859C411yescharacteristic
22#19098774C411yescharacteristic
23#19098774C411yescharacteristic
24#19098721C411yescharacteristic
25#19098721C411yescharacteristic
26#19098693—21no—
27#19098691—21no—
28#19098691—21no—
29#19098690C2211yescharacteristic
30#19098690C2211yescharacteristic
31#19098690C2211yescharacteristic
32#19098690C2211yescharacteristic
33C8×Dic158—21no—
34#19098687C2211yescharacteristic
35#19098687C2211yescharacteristic
36#19098687C2211yescharacteristic
37#19098687C2211yescharacteristic
38C4×Dic316C2211yescharacteristic
39C4×Dic316C2211yescharacteristic
40C4×Dic316C2211yescharacteristic
41C4×Dic316C2211yescharacteristic
42#19098621—21no—
43#19098621—21no—
44#19098617—21no—
45#19098616C2211yescharacteristic
46#19098616C2211yescharacteristic
47#19098613—21no—
48#19098293C2211yescharacteristic
49#19098293C2211yescharacteristic
50#19098293C2211yescharacteristic
51#19098293C2211yescharacteristic
52#19098293C2211yescharacteristic
53#19098293C2211yescharacteristic
54#19098293C2211yescharacteristic
55#19098293C2211yescharacteristic
56#19098285C2211yescharacteristic
57#19098285C2211yescharacteristic
58#19098284C2211yescharacteristic
59C8×C79⋊C8C2211yescharacteristic
60#432×C79C2211yescharacteristic
61#431×C79C2211yescharacteristic
62#431×C79C2211yescharacteristic
63#335×C79C2211yescharacteristic
64#335×C79C2211yescharacteristic
65#334×C79C2211yescharacteristic
66#334×C79C2211yescharacteristic
67C22×Dic158C2×C411yescharacteristic
68C2×Dic316C2×C411yescharacteristic
69C2×Dic316C2×C411yescharacteristic
70C2×Dic316C2×C411yescharacteristic
71C2×Dic316C2×C411yescharacteristic
72#14579161C2×C411yescharacteristic
73#14579161C2×C411yescharacteristic
74#14579153—21no—
75#14579140—21no—
76#14579140C2×C411yescharacteristic
77#14579140C2×C411yescharacteristic
78C4×Dic158—21no—
79C4×Dic158—21no—
80C4×Dic158—21no—
81C4×Dic158C2×C411yescharacteristic
82C4×Dic158C2×C411yescharacteristic
83C4×Dic158C2311yescharacteristic
84C4×Dic158C2311yescharacteristic
85C4×Dic158C2311yescharacteristic
86C4×Dic158C2311yescharacteristic
87#14579120—21no—
88C2×C4⋊Dic79C2×C411yescharacteristic
89C2×Dic79⋊C4—21no—
90C2×C4×Dic79—21no—
91#14579095C2×C411yescharacteristic
92#14579095C2×C411yescharacteristic
93#14579095C2×C411yescharacteristic
94#14579095C2×C411yescharacteristic
95C4⋊(C79⋊C8)—21no—
96C4⋊(C79⋊C8)D411yescharacteristic
97C4⋊(C79⋊C8)D411yescharacteristic
98Dic79⋊C8—21no—
99Dic79⋊C8—21no—
100Dic79⋊C8—21no—
101Dic79⋊C8—21no—
102Dic79⋊C8—21no—
103Dic79⋊C8—21no—
104Dic79⋊C8—21no—
105Dic79⋊C8—21no—
106#14579086C2×C411yescharacteristic
107#14579086C2×C411yescharacteristic
108#14579086C2×C411yescharacteristic
109#14579086C2×C411yescharacteristic
110#14579086C2×C411yescharacteristic
111#14579086C2×C411yescharacteristic
112#14579086C2×C411yescharacteristic
113#14579086C2×C411yescharacteristic
114C22⋊(C79⋊C8)—21no—
115C22⋊(C79⋊C8)D411yescharacteristic
116C22⋊(C79⋊C8)D411yescharacteristic
117#14579071—21no—
118#14579071—21no—
119#14579071—21no—
120#14579071—21no—
121C4×C79⋊C8C2311yescharacteristic
122C4×C79⋊C8C2311yescharacteristic
123C4×C79⋊C8C2311yescharacteristic
124C4×C79⋊C8C2311yescharacteristic
125C8×Dic79—21no—
126C8×Dic79—21no—
127C8×Dic79—21no—
128C8×Dic79—21no—
129C2×C42×C79C2311yescharacteristic
130C4⋊C8×C79C2×C411yescharacteristic
131C4⋊C8×C79C2×C411yescharacteristic
132C4⋊C8×C79C2311yescharacteristic
133C4⋊C8×C79C2311yescharacteristic
134C4⋊C8×C79C2311yescharacteristic
135C4⋊C8×C79C2311yescharacteristic
136C22⋊C8×C79—21no—
137C22⋊C8×C79—21no—
138C22⋊C8×C79C2×C411yescharacteristic
139C22⋊C8×C79C2×C411yescharacteristic
140#97×C79—21no—
141C4×C8×C79—21no—
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144C2×Dic158—22no—
145C2×Dic158—21no—
146C2×Dic158—21no—
147C2×Dic158—41no—
148C2×Dic158C22×C411yescharacteristic
149C2×Dic158C22×C411yescharacteristic
150C2×Dic158C22×C411yescharacteristic
151C2×Dic158C22×C411yescharacteristic
152C22×Dic79—21no—
153C22×Dic79—21no—
154Dic316—22no—
155Dic316—22no—
156Dic316—41no—
157Dic316—41no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8C2×D411yescharacteristic
161C2×C79⋊C8C2×D411yescharacteristic
162C2×C79⋊C8C2×D411yescharacteristic
163C2×C79⋊C8C2×D411yescharacteristic
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79—21no—
167C4⋊Dic79—21no—
168C4⋊Dic79C22×C411yescharacteristic
169C4⋊Dic79C22×C411yescharacteristic
170C4⋊Dic79C22×C411yescharacteristic
171C4⋊Dic79C22×C411yescharacteristic
172Dic79⋊C4—21no—
173Dic79⋊C4—21no—
174Dic79⋊C4—21no—
175Dic79⋊C4—21no—
176Dic79⋊C4—21no—
177Dic79⋊C4—21no—
178Dic79⋊C4—21no—
179Dic79⋊C4—21no—
180C22⋊Dic79—21no—
181C22⋊Dic79—21no—
182C4×Dic79—21no—
183C4×Dic79—21no—
184C4×Dic79—21no—
185C4×Dic79—21no—
186C4×Dic79—21no—
187C4×Dic79—21no—
188C22×C4×C79C22×C411yescharacteristic
189C22×C4×C79C2×D411yescharacteristic
190C22×C4×C79#4111yescharacteristic
191C2×C8×C79—21no—
192C2×C8×C79—21no—
193C2×C8×C79—21no—
194C2×C8×C79—21no—
195C2×C8×C79C22×C411yescharacteristic
196C2×C8×C79C22×C411yescharacteristic
197C2×C8×C79C22×C411yescharacteristic
198C2×C8×C79C22×C411yescharacteristic
199C42×C79C22×C411yescharacteristic
200C42×C79C2×D411yescharacteristic
201C42×C79#4111yescharacteristic
202C42×C79C2411yescharacteristic
203C23×C79C4×D411yescharacteristic
204C2×C4×C79—21no—
205C2×C4×C79—21no—
206C2×C4×C79—21no—
207C2×C4×C79—21no—
208C2×C4×C79—41no—
209C2×C4×C79C4×D411yescharacteristic
210C2×C4×C79C4×D411yescharacteristic
211C2×C4×C79C4×D411yescharacteristic
212C2×C4×C79C23×C411yescharacteristic
213C2×C4×C79C22×D411yescharacteristic
214C2×C4×C79C2×#4111yescharacteristic
215C2×Dic79—21no—
216C2×Dic79—21no—
217C2×Dic79—21no—
218C2×Dic79—21no—
219C2×Dic79—21no—
220C2×Dic79—21no—
221C2×Dic79—21no—
222C2×Dic79—21no—
223C2×Dic79—42no—
224C2×Dic79—42no—
225Dic158—21no—
226Dic158—21no—
227Dic158—21no—
228Dic158—21no—
229Dic158—21no—
230Dic158—21no—
231Dic158—21no—
232Dic158—42no—
233Dic158—42no—
234Dic158#13112yes—
235C8×C79—21no—
236C8×C79—21no—
237C8×C79—21no—
238C8×C79—21no—
239C8×C79—41no—
240C8×C79—41no—
241C8×C79—41no—
242C8×C79—41no—
243C79⋊C8—21no—
244C79⋊C8—21no—
245C79⋊C8—21no—
246C79⋊C8—21no—
247C79⋊C8—41no—
248C79⋊C8—41no—
249C22×C79—21no—
250C22×C79—21no—
251C22×C79—21no—
252C22×C79C2×C4×D411yescharacteristic
253C4×C79—21no—
254C4×C79—21no—
255C4×C79—21no—
256C4×C79—21no—
257C4×C79C2×#13111yescharacteristic
258C4×C79#56811yescharacteristic
259C4×C79#57811yescharacteristic
260C4×C79#57811yescharacteristic
261Dic79—22no—
262Dic79—41no—
263Dic79—41no—
264Dic79—41no—
265Dic79—41no—
266Dic79—41no—
267Dic79—41no—
268Dic79—41no—
269#18032—791nomaximal, Sylow
270C2×C79—41no—
271C2×C79#293311yescharacteristic
272C2×C79#295011yescharacteristic
273C2×C79#295511yescharacteristic
274#3104—791no—
275#2986—791no—
276#2984—791no—
277#1593—791no—
278#1591—791no—
279#1587—791no—
280#1587—791no—
281#1584—791no—
282#1584—791no—
283#1579—791no—
284C8×Q16—791no—
285#1572D7911yescharacteristic
286#1497—791no—
287#1479—791no—
288#1454—791no—
289C79#1803211yescharacteristic, complemented, Sylow
290#533—791no—
291C2×C4×Q8—791no—
292#484—791no—
293#484—791no—
294#477—791no—
295#477—791no—
296#462—791no—
297#462—791no—
298#451—791no—
299#451—791no—
300#446—791no—
301#446—791no—
302#446—791no—
303#446—791no—
304#446—1581no—
305#446—1581no—
306#446—1581no—
307C8×Q8—791no—
308C8×Q8—791no—
309C8×Q8—791no—
310C8×Q8—791no—
311C8×Q8—1581no—
312C4×Q16—791no—
313C4×Q16—791no—
314C4×Q16—791no—
315C4×Q16—791no—
316#433—1581no—
317#433—1581no—
318#432—1581no—
319#432C2×D7911yescharacteristic
320#431—791no—
321#431—791no—
322#431—1581no—
323#431C2×D7911yescharacteristic
324#431C2×D7911yescharacteristic
325#335C2×D7911yescharacteristic
326#335C2×D7911yescharacteristic
327#334C2×D7911yescharacteristic
328#334C2×D7911yescharacteristic
329Q8⋊C8—791no—
330Q8⋊C8—791no—
331Q8⋊C8—791no—
332Q8⋊C8—791no—
333Q8⋊C8—791no—
334Q8⋊C8—791no—
335Q8⋊C8—791no—
336Q8⋊C8—791no—
337#322—791no—
338#322—791no—
339#322—791no—
340C82—791no—
341C22×Q8—791no—
342C2×Q16—791no—
343C2×Q16—791no—
344C2×Q16—791no—
345C2×Q16—791no—
346C4⋊Q8—791no—
347C4⋊Q8—791no—
348#125—1581no—
349C22⋊Q8—791no—
350C22⋊Q8—791no—
351C22⋊Q8—1581no—
352C4×Q8—791no—
353C4×Q8—791no—
354C4×Q8—791no—
355C4×Q8—791no—
356C4×Q8—791no—
357C4×Q8—791no—
358C4×Q8—1581no—
359C4×Q8—1581no—
360C4×Q8—1581no—
361#117—1581no—
362C2×C4⋊C4—791no—
363C2×C4⋊C4—1581no—
364C2×C42—1581no—
365C2×C42C22×D7911yescharacteristic
366#107—791no—
367#107—791no—
368#107—791no—
369#107—791no—
370C4⋊C8—791no—
371C4⋊C8—791no—
372C4⋊C8—1581no—
373C4⋊C8—1581no—
374C4⋊C8—1581no—
375C4⋊C8—1581no—
376C4⋊C8—1581no—
377C4⋊C8—1581no—
378C4⋊C8—1581no—
379C4⋊C8—1581no—
380C4⋊C8—1581no—
381C4⋊C8C4×D7911yescharacteristic
382C4⋊C8C4×D7911yescharacteristic
383C4⋊C8C22×D7911yescharacteristic
384C4⋊C8C22×D7911yescharacteristic
385C4⋊C8C22×D7911yescharacteristic
386C4⋊C8C22×D7911yescharacteristic
387#103—791no—
388#103—791no—
389#103—791no—
390#103—791no—
391#103—791no—
392#103—791no—
393#103—791no—
394#103—791no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—791no—
398C22⋊C8—791no—
399C22⋊C8—1581no—
400C22⋊C8C4×D7911yescharacteristic
401C22⋊C8C4×D7911yescharacteristic
402#97—21no—
403#97—1581no—
404#97—1581no—
405#97—1581no—
406#97—1581no—
407C4×C8—21no—
408C4×C8—791no—
409C4×C8—791no—
410C4×C8—791no—
411C4×C8—791no—
412C4×C8—1581no—
413C4×C8—1581no—
414C4×C8—1581no—
415C4×C8—1581no—
416C4×C8C22×D7911yescharacteristic
417C4×C8C22×D7911yescharacteristic
418C2×Q8—3161no—
419C2×Q8—791no—
420C2×Q8—791no—
421C2×Q8—791no—
422C2×Q8—791no—
423C2×Q8—1582no—
424C2×Q8—1581no—
425C2×Q8—1581no—
426C22×C4—1581no—
427C22×C4—1581no—
428C22×C4C2×C4×D7911yescharacteristic
429C22×C4D4×D7911yescharacteristic
430C22×C4#1192962511yescharacteristic
431Q16—3161no—
432Q16—3161no—
433Q16—1582no—
434Q16—1582no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—791no—
440C2×C8—791no—
441C2×C8—791no—
442C2×C8—791no—
443C2×C8—1581no—
444C2×C8—1581no—
445C2×C8C2×C4×D7911yescharacteristic
446C2×C8C2×C4×D7911yescharacteristic
447C2×C8C2×C4×D7911yescharacteristic
448C2×C8C2×C4×D7911yescharacteristic
449C4⋊C4—791no—
450C4⋊C4—791no—
451C4⋊C4—791no—
452C4⋊C4—791no—
453C4⋊C4—1581no—
454C4⋊C4—1581no—
455C4⋊C4—1581no—
456C4⋊C4—1581no—
457C4⋊C4—1581no—
458C4⋊C4—1581no—
459C4⋊C4—1581no—
460C4⋊C4—1581no—
461C4⋊C4—1581no—
462C4⋊C4—1581no—
463C4⋊C4—1581no—
464C4⋊C4—1581no—
465C22⋊C4—1581no—
466C22⋊C4—1581no—
467C42—1581no—
468C42—1581no—
469C42—1581no—
470C42—1581no—
471C42—1581no—
472C42—1581no—
473C42C2×C4×D7911yescharacteristic
474C42D4×D7911yescharacteristic
475C42#1192962511yescharacteristic
476C42C23×D7911yescharacteristic
477C23#1457912311yescharacteristic
478Q8—3162no—
479Q8—3162no—
480Q8—792no—
481Q8—1581no—
482Q8—1581no—
483Q8—1581no—
484Q8—1581no—
485Q8—1581no—
486Q8—1581no—
487Q8—1581no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—3162no—
494C2×C4—3162no—
495C2×C4—1581no—
496C2×C4—1581no—
497C2×C4—1581no—
498C2×C4—1581no—
499C2×C4—1581no—
500C2×C4—1581no—
501C2×C4—1581no—
502C2×C4—1581no—
503C2×C4#1457912311yescharacteristic
504C2×C4#1457912311yescharacteristic
505C2×C4#1457912311yescharacteristic
506C2×C4C22×C4×D7911yescharacteristic
507C2×C4C2×D4×D7911yescharacteristic
508C2×C4C2×#1192962511yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—3161no—
518C8—3161no—
519C8—1581no—
520C8—1581no—
521C8—1581no—
522C8—1581no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×#1457912311yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—3161no—
532C4—3161no—
533C4—3161no—
534C4—3161no—
535C4—3161no—
536C4—3161no—
537C4—3161no—
538C4—1582no—
539C4#131×D7911yescharacteristic
540C4#1909932811yescharacteristic
541C4#1909937711yescharacteristic
542C4#1909937711yescharacteristic
543C2—41no—
544C2#2377212411yescharacteristic
545C2#2377226711yescharacteristic
546C2#2377230211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#1572C2
socleC22×C79C2×C4×D4
prime radicalC23×C79C4×D4
cosocleC42×C79C24
hypercenter#1572D79
hypocenterC79#18032
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
4. #23762308C2semidirect
5. #23762296C2semidirect
6. #23762270C2semidirect
7. #23762270C2semidirect
8. #23762249C2semidirect
9. #23762249C2semidirect
10. #23762218C2semidirect
11. #23762206C2semidirect
289. C79#18032semidirect

Maximal subgroups

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

subgroupindex
#237734402
#237725012
#237724902
#237623082
#237622962
#237622702
#237622492
#237622182
#237622062
#237618722
#237617942
#237617002
C79×#15722
#1803279