Finite Group Databasebeta

← #34260296

Subgroups — #34260296

Order 20224.

564 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773983C211yesmaximal, characteristic
2#23772500C211yesmaximal, characteristic
3#23772498C211yesmaximal, characteristic
4#23762307C211yesmaximal, characteristic, complemented
5#23762306C211yesmaximal, characteristic, complemented
6#23762252C211yesmaximal, characteristic, complemented
7#23762251C211yesmaximal, characteristic, complemented
8#23762249C211yesmaximal, characteristic, complemented
9#23762217C211yesmaximal, characteristic, complemented
10#23762216C211yesmaximal, characteristic, complemented
11#23762147C211yesmaximal, characteristic
12#23761819C211yesmaximal, characteristic
13#23761819C211yesmaximal, characteristic
14#23761688C211yesmaximal, characteristic
15C79×#1584C211yesmaximal, characteristic, complemented
16#19099117C2211yescharacteristic
17#19099117C2211yescharacteristic
18#19098967C411yescharacteristic
19#19098941C411yescharacteristic
20#19098912C411yescharacteristic
21#19098912C411yescharacteristic
22#19098805C411yescharacteristic
23#19098803C411yescharacteristic
24#19098803C411yescharacteristic
25#19098801C411yescharacteristic
26#19098694C2211yescharacteristic
27#19098693C2211yescharacteristic
28#19098692—21no—
29#19098691—21no—
30#19098690C2211yescharacteristic
31Q8×C79⋊C8C2211yescharacteristic
32C8×Dic158—21no—
33C8×Dic158C2211yescharacteristic
34#19098687—21no—
35#19098687C2211yescharacteristic
36C4×Dic316C2211yescharacteristic
37C4×#11929614C2211yescharacteristic
38C4×#11929614C2211yescharacteristic
39#19098625—21no—
40#19098623—21no—
41#19098623—21no—
42#19098622—21no—
43#19098615C2211yescharacteristic
44#19098615C2211yescharacteristic
45#19098614C2211yescharacteristic
46C4×#11929607C2211yescharacteristic
47C4×C8×D79C2211yescharacteristic
48#19098316C2211yescharacteristic
49#19098313C2211yescharacteristic
50#19098313C2211yescharacteristic
51#19098295C2211yescharacteristic
52#19098295C2211yescharacteristic
53Q8⋊(C79⋊C8)C2211yescharacteristic
54Q8⋊(C79⋊C8)C2211yescharacteristic
55#19098293C2211yescharacteristic
56#19098293C2211yescharacteristic
57#19098285C2211yescharacteristic
58#19098285C2211yescharacteristic
59#19098285C2211yescharacteristic
60#446×C79C2211yescharacteristic
61C8×Q8×C79C2211yescharacteristic
62C4×Q16×C79C2211yescharacteristic
63#335×C79C2211yescharacteristic
64Q8⋊C8×C79C2211yescharacteristic
65Q8⋊C8×C79C2211yescharacteristic
66#322×C79C2211yescharacteristic
67C2×Dic316C2×C411yescharacteristic
68C2×#11929614C2×C411yescharacteristic
69C2×#11929614C2×C411yescharacteristic
70C2×#11929607—21no—
71C2×C8×D79C2×C411yescharacteristic
72C2×C8×D79C2×C411yescharacteristic
73#14579160C2×C411yescharacteristic
74#14579160C2×C411yescharacteristic
75#14579159C2×C411yescharacteristic
76#14579159C2×C411yescharacteristic
77#14579151—21no—
78#14579151—21no—
79#14579141C2×C411yescharacteristic
80#14579141C2×C411yescharacteristic
81#14579139—21no—
82#14579139—21no—
83#14579137C2×C411yescharacteristic
84#14579137C2×C411yescharacteristic
85C4×Dic158—21no—
86C4×Dic158—21no—
87C4×Dic158C2311yescharacteristic
88C4×Dic158C2311yescharacteristic
89#14579118—21no—
90#14579118—21no—
91C42×D79C2311yescharacteristic
92#14579095C2×C411yescharacteristic
93#14579094C2×C411yescharacteristic
94#14579094C2×C411yescharacteristic
95C4⋊(C79⋊C8)—21no—
96C4⋊(C79⋊C8)—21no—
97C4⋊(C79⋊C8)C2311yescharacteristic
98C4⋊(C79⋊C8)C2311yescharacteristic
99Dic79⋊C8—21no—
100Dic79⋊C8—21no—
101Dic79⋊C8—21no—
102Dic79⋊C8—21no—
103Dic79⋊C8D411yescharacteristic
104Dic79⋊C8D411yescharacteristic
105#14579086C2×C411yescharacteristic
106#14579086C2×C411yescharacteristic
107#14579085C2×C411yescharacteristic
108#14579085C2×C411yescharacteristic
109#14579084C2×C411yescharacteristic
110#14579084C2×C411yescharacteristic
111(C2×D79)⋊C8—21no—
112(C2×D79)⋊C8—21no—
113(C2×D79)⋊C8D411yescharacteristic
114(C2×D79)⋊C8D411yescharacteristic
115#14579072—21no—
116#14579071—21no—
117#14579071—21no—
118#14579071—21no—
119C4×C79⋊C8—21no—
120C4×C79⋊C8C2311yescharacteristic
121C4×C79⋊C8C2311yescharacteristic
122C4×C79⋊C8C2311yescharacteristic
123C8×Dic79—21no—
124C8×Dic79—21no—
125C8×Dic79—21no—
126C8×Dic79—21no—
127C8×Dic79C2×C411yescharacteristic
128C8×Dic79C2×C411yescharacteristic
129C2×Q16×C79C2×C411yescharacteristic
130C4×Q8×C79C2311yescharacteristic
131C4×Q8×C79C2311yescharacteristic
132#107×C79C2×C411yescharacteristic
133C4⋊C8×C79—21no—
134C4⋊C8×C79—21no—
135C4⋊C8×C79C2311yescharacteristic
136C4⋊C8×C79C2311yescharacteristic
137#103×C79C2×C411yescharacteristic
138#103×C79C2×C411yescharacteristic
139#97×C79—21no—
140C4×C8×C79—21no—
141C4×C8×C79C2311yescharacteristic
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144C2×Dic158—21no—
145C2×Dic158—21no—
146C2×Dic158C22×C411yescharacteristic
147C2×Dic158C22×C411yescharacteristic
148C2×C4×D79C22×C411yescharacteristic
149C2×C4×D79C2×D411yescharacteristic
150C2×C4×D79#4111yescharacteristic
151Dic316—41no—
152#11929614—22no—
153#11929614—22no—
154#11929607—42no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8C22×C411yescharacteristic
159C2×C79⋊C8C22×C411yescharacteristic
160C2×C79⋊C8C2×D411yescharacteristic
161C2×C79⋊C8C2×D411yescharacteristic
162C8×D79—22no—
163C8×D79—41no—
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79C22×C411yescharacteristic
167C4⋊Dic79C22×C411yescharacteristic
168Dic79⋊C4—21no—
169Dic79⋊C4—21no—
170Dic79⋊C4—21no—
171Dic79⋊C4—21no—
172Dic79⋊C4—21no—
173Dic79⋊C4—21no—
174Dic79⋊C4—21no—
175Dic79⋊C4—21no—
176Dic79⋊C4—21no—
177Dic79⋊C4—21no—
178(C2×D79)⋊C4—21no—
179(C2×D79)⋊C4—21no—
180(C2×D79)⋊C4—21no—
181(C2×D79)⋊C4—21no—
182C4×Dic79—21no—
183C4×Dic79—21no—
184C4×Dic79C22×C411yescharacteristic
185C4×Dic79C2×D411yescharacteristic
186C4×Dic79#4111yescharacteristic
187C2×Q8×C79C22×C411yescharacteristic
188C2×Q8×C79C22×C411yescharacteristic
189Q16×C79—41no—
190C2×C8×C79—21no—
191C2×C8×C79—21no—
192C2×C8×C79—21no—
193C2×C8×C79C22×C411yescharacteristic
194C2×C8×C79C22×C411yescharacteristic
195C2×C8×C79C2×D411yescharacteristic
196C2×C8×C79C2×D411yescharacteristic
197C4⋊C4×C79—21no—
198C4⋊C4×C79—21no—
199C4⋊C4×C79C22×C411yescharacteristic
200C4⋊C4×C79C22×C411yescharacteristic
201C42×C79—21no—
202C42×C79—21no—
203C42×C79C2411yescharacteristic
204C22×D79C4×D411yescharacteristic
205Q8×C79—21no—
206Q8×C79—21no—
207Q8×C79—21no—
208Q8×C79—21no—
209C2×C4×C79—21no—
210C2×C4×C79—21no—
211C2×C4×C79—21no—
212C2×C4×C79—21no—
213C2×C4×C79C23×C411yescharacteristic
214C2×C4×C79C22×D411yescharacteristic
215C2×C4×C79C2×#4111yescharacteristic
216C2×Dic79—21no—
217C2×Dic79—21no—
218C2×Dic79—21no—
219C2×Dic79—21no—
220C2×Dic79C4×D411yescharacteristic
221C2×Dic79C4×D411yescharacteristic
222C2×Dic79C4×D411yescharacteristic
223C4×D79—21no—
224C4×D79—21no—
225C4×D79—21no—
226C4×D79—21no—
227C4×D79—22no—
228Dic158—21no—
229Dic158—21no—
230Dic158—21no—
231Dic158—21no—
232Dic158—42no—
233Dic158—42no—
234C8×C79—21no—
235C8×C79—21no—
236C8×C79—21no—
237C8×C79—21no—
238C8×C79—41no—
239C8×C79—41no—
240C8×C79—41no—
241C79⋊C8—21no—
242C79⋊C8—21no—
243C79⋊C8—21no—
244C79⋊C8—41no—
245C79⋊C8—41no—
246C79⋊C8—41no—
247C79⋊C8#13112yes—
248C22×C79C2×C4×D411yescharacteristic
249C2×D79—21no—
250C2×D79—21no—
251C2×D79—21no—
252C4×C79—21no—
253C4×C79—41no—
254C4×C79—41no—
255C4×C79—41no—
256C4×C79—41no—
257C4×C79C2×#13111yescharacteristic
258C4×C79#56811yescharacteristic
259C4×C79#57811yescharacteristic
260C4×C79#57811yescharacteristic
261Dic79—21no—
262Dic79—21no—
263Dic79—41no—
264Dic79—41no—
265Dic79—41no—
266Dic79—41no—
267Dic79#44412yes—
268#18090—791nomaximal, Sylow
269C2×C79#293511yescharacteristic
270C2×C79#295011yescharacteristic
271C2×C79C2×#44411yescharacteristic
272D79—41no—
273#3170—791no—
274#2986—791no—
275#2986—791no—
276#1593—791no—
277#1593—791no—
278#1584—791no—
279#1584—791no—
280#1584—791no—
281#1584D7911yescharacteristic, complemented
282#1579—791no—
283#1579—791no—
284#1564—791no—
285#1485—791no—
286#1485—791no—
287#1451—791no—
288C79#1809011yescharacteristic, complemented, Sylow
289#533—791no—
290#533—791no—
291#500—791no—
292#494—791no—
293#487—791no—
294#487—791no—
295#467—791no—
296#467—791no—
297#467—791no—
298#467—791no—
299#446—791no—
300#446—791no—
301#446—791no—
302#446—1581no—
303#446—1581no—
304#446C2×D7911yescharacteristic
305C8×Q8—791no—
306C8×Q8—791no—
307C8×Q8—791no—
308C8×Q8—1581no—
309C8×Q8—1581no—
310C8×Q8C2×D7911yescharacteristic
311C4×Q16—791no—
312C4×Q16—791no—
313C4×Q16—791no—
314C4×Q16C2×D7911yescharacteristic
315#433—1581no—
316#433—1581no—
317#433—1581no—
318#433—1581no—
319#431—791no—
320#431—791no—
321#431—791no—
322C4×M16—791no—
323C2×C4×C8—791no—
324#335—791no—
325#335C2×D7911yescharacteristic
326#334—791no—
327#334—791no—
328Q8⋊C8—791no—
329Q8⋊C8—791no—
330Q8⋊C8—791no—
331Q8⋊C8—791no—
332Q8⋊C8—791no—
333Q8⋊C8—791no—
334Q8⋊C8C2×D7911yescharacteristic
335Q8⋊C8C2×D7911yescharacteristic
336#322—791no—
337#322—791no—
338#322—791no—
339#322C2×D7911yescharacteristic
340C2×Q16—791no—
341C2×Q16—791no—
342C2×Q16—791no—
343C2×Q16C4×D7911yescharacteristic
344C2×M16—1581no—
345C22×C8—791no—
346C22×C8—791no—
347C4⋊Q8—791no—
348C4⋊Q8—791no—
349C4⋊Q8—791no—
350C4⋊Q8—791no—
351#125—1581no—
352#125—1581no—
353C22⋊Q8—791no—
354C22⋊Q8—791no—
355C22⋊Q8—791no—
356C22⋊Q8—791no—
357C22⋊Q8—1581no—
358C22⋊Q8—1581no—
359C4×Q8—791no—
360C4×Q8—791no—
361C4×Q8—1581no—
362C4×Q8—1581no—
363C4×Q8C22×D7911yescharacteristic
364C4×Q8C22×D7911yescharacteristic
365#117—1581no—
366#117—1581no—
367C2×C42—791no—
368#107—791no—
369#107—791no—
370#107—791no—
371#107C4×D7911yescharacteristic
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—791no—
375C4⋊C8—791no—
376C4⋊C8—791no—
377C4⋊C8—791no—
378C4⋊C8—1581no—
379C4⋊C8—1581no—
380C4⋊C8—1581no—
381C4⋊C8—1581no—
382C4⋊C8—1581no—
383C4⋊C8—1581no—
384C4⋊C8C22×D7911yescharacteristic
385C4⋊C8C22×D7911yescharacteristic
386#103—791no—
387#103—791no—
388#103—791no—
389#103—791no—
390#103—791no—
391#103—791no—
392#103C4×D7911yescharacteristic
393#103C4×D7911yescharacteristic
394C22⋊C8—791no—
395C22⋊C8—791no—
396C22⋊C8—1581no—
397C22⋊C8—1581no—
398#97—21no—
399#97—1581no—
400#97—1581no—
401#97—1581no—
402#97—1581no—
403C4×C8—21no—
404C4×C8—791no—
405C4×C8—791no—
406C4×C8—791no—
407C4×C8—791no—
408C4×C8—791no—
409C4×C8—1581no—
410C4×C8—1581no—
411C4×C8—1581no—
412C4×C8—1581no—
413C4×C8—1581no—
414C4×C8C22×D7911yescharacteristic
415C4×C8C22×D7911yescharacteristic
416C4×C8C22×D7911yescharacteristic
417C2×Q8—791no—
418C2×Q8—791no—
419C2×Q8—1581no—
420C2×Q8—1581no—
421C2×Q8C2×C4×D7911yescharacteristic
422C2×Q8C2×C4×D7911yescharacteristic
423C22×C4—791no—
424C22×C4—791no—
425C22×C4—791no—
426Q16—41no—
427Q16—3161no—
428Q16—1582no—
429Q16—1582no—
430M16—3162no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—3161no—
435C2×C8—791no—
436C2×C8—791no—
437C2×C8—791no—
438C2×C8—791no—
439C2×C8—1582no—
440C2×C8—1581no—
441C2×C8—1581no—
442C2×C8—1581no—
443C2×C8C2×C4×D7911yescharacteristic
444C2×C8C2×C4×D7911yescharacteristic
445C2×C8D4×D7911yescharacteristic
446C2×C8D4×D7911yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—791no—
450C4⋊C4—791no—
451C4⋊C4—1581no—
452C4⋊C4—1581no—
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⋊C4C2×C4×D7911yescharacteristic
464C4⋊C4C2×C4×D7911yescharacteristic
465C22⋊C4—1581no—
466C22⋊C4—1581no—
467C22⋊C4—1581no—
468C22⋊C4—1581no—
469C42—21no—
470C42—21no—
471C42—791no—
472C42—791no—
473C42—791no—
474C42—1581no—
475C42—1581no—
476C42C23×D7911yescharacteristic
477C23—791no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—3162no—
483Q8—3162no—
484Q8—1581no—
485Q8—1581no—
486Q8—1581no—
487Q8—1581no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—791no—
493C2×C4—791no—
494C2×C4—791no—
495C2×C4—1582no—
496C2×C4—1581no—
497C2×C4—1581no—
498C2×C4—1581no—
499C2×C4—1581no—
500C2×C4—1581no—
501C2×C4—1581no—
502C2×C4—1581no—
503C2×C4—1581no—
504C2×C4C22×C4×D7911yescharacteristic
505C2×C4C2×D4×D7911yescharacteristic
506C2×C4#41×D7911yescharacteristic
507C8—21no—
508C8—21no—
509C8—21no—
510C8—21no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8—3161no—
515C8—3161no—
516C8—3161no—
517C8—792no—
518C8—1581no—
519C8—1581no—
520C8—1581no—
521C22—1581no—
522C22—1581no—
523C22—1581no—
524C22C4×D4×D7911yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—3161no—
531C4—3161no—
532C4—3161no—
533C4—3161no—
534C4—792no—
535C4—1581no—
536C4—1581no—
537C4#131×D7911yescharacteristic
538C4#1909932911yescharacteristic
539C4#1909937611yescharacteristic
540C4#1909937711yescharacteristic
541C2—3161no—
542C2#2377214111yescharacteristic
543C2#2377226311yescharacteristic
544C2#444×D7911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#1584C2
socleC22×C79C2×C4×D4
prime radicalC22×D79C4×D4
cosocleC42×C79C24
hypercenter#1584D79
hypocenterC79#18090
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #23762307C2semidirect
5. #23762306C2semidirect
6. #23762252C2semidirect
7. #23762251C2semidirect
8. #23762249C2semidirect
9. #23762217C2semidirect
10. #23762216C2semidirect
15. C79×#1584C2semidirect
281. #1584D79semidirect
288. C79#18090semidirect

Maximal subgroups

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

subgroupindex
#237739832
#237725002
#237724982
#237623072
#237623062
#237622522
#237622512
#237622492
#237622172
#237622162
#237621472
#237618192
#237616882
C79×#15842
#1809079