Finite Group Databasebeta

← #34259363

Subgroups — #34259363

Order 20224.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773482C211yesmaximal, characteristic
2#23772398C211yesmaximal, characteristic
3#23772351C211yesmaximal, characteristic, complemented
4#23762301C211yesmaximal, characteristic, complemented
5#23762296C211yesmaximal, characteristic, complemented
6#23762277C211yesmaximal, characteristic, complemented
7#23762270C211yesmaximal, characteristic, complemented
8#23762249C211yesmaximal, characteristic, complemented
9#23762235C211yesmaximal, characteristic, complemented
10#23762218C211yesmaximal, characteristic, complemented
11#23762199C211yesmaximal, characteristic, complemented
12#23761863C211yesmaximal, characteristic
13#23761794C211yesmaximal, characteristic, complemented
14#23761695C211yesmaximal, characteristic, complemented
15C79×#1574C211yesmaximal, characteristic, complemented
16#19099097C2211yescharacteristic
17C2×C4×Dic158C2211yescharacteristic
18#19098894C411yescharacteristic
19#19098877C411yescharacteristic
20#19098871C411yescharacteristic
21#19098871C411yescharacteristic
22#19098786C411yescharacteristic
23#19098786C411yescharacteristic
24#19098721C411yescharacteristic
25#19098704C411yescharacteristic
26#19098692—21no—
27#19098692—21no—
28#19098690C2211yescharacteristic
29#19098690C2211yescharacteristic
30#19098690C2211yescharacteristic
31#19098687C2211yescharacteristic
32#19098687C2211yescharacteristic
33#19098687C2211yescharacteristic
34C4×Dic316C2211yescharacteristic
35C4×Dic316C2211yescharacteristic
36C4×#11929613C2211yescharacteristic
37C4×#11929613C2211yescharacteristic
38#19098640C2211yescharacteristic
39#19098638—21no—
40#19098637—21no—
41#19098628C2211yescharacteristic
42#19098622—21no—
43#19098616C2211yescharacteristic
44#19098586—21no—
45#19098517—21no—
46C4×#11929608C2211yescharacteristic
47M16×Dic79—21no—
48#19098293C2211yescharacteristic
49#19098293C2211yescharacteristic
50#19098293C2211yescharacteristic
51#19098293C2211yescharacteristic
52#19098293C2211yescharacteristic
53#19098293C2211yescharacteristic
54#19098290C2211yescharacteristic
55#19098290C2211yescharacteristic
56#19098285C2211yescharacteristic
57#19098285C2211yescharacteristic
58#19098284C2211yescharacteristic
59C8×C79⋊C8C2211yescharacteristic
60#431×C79C2211yescharacteristic
61#431×C79C2211yescharacteristic
62#423×C79C2211yescharacteristic
63#335×C79C2211yescharacteristic
64#335×C79C2211yescharacteristic
65#334×C79C2211yescharacteristic
66#334×C79C2211yescharacteristic
67C22×Dic158C2×C411yescharacteristic
68C2×Dic316C2×C411yescharacteristic
69C2×Dic316C2×C411yescharacteristic
70C2×#11929613C2×C411yescharacteristic
71C2×#11929613C2×C411yescharacteristic
72C2×#11929608D411yescharacteristic
73C2×#11929608D411yescharacteristic
74C2×#11929607—21no—
75C2×C8×D79—21no—
76#14579155—21no—
77#14579153C2×C411yescharacteristic
78#14579149C2×C411yescharacteristic
79#14579144—21no—
80#14579140C2×C411yescharacteristic
81#14579135C2×C411yescharacteristic
82C4×Dic158—21no—
83C4×Dic158—21no—
84C4×Dic158C2×C411yescharacteristic
85C4×Dic158C2×C411yescharacteristic
86C4×Dic158C2311yescharacteristic
87C4×Dic158C2311yescharacteristic
88C4×Dic158C2311yescharacteristic
89C4×D316C2311yescharacteristic
90C4×C22⋊D79—21no—
91#14579118—21no—
92C2×C4⋊Dic79C2×C411yescharacteristic
93C2×Dic79⋊C4—21no—
94C2×C4×Dic79—21no—
95#14579095C2×C411yescharacteristic
96#14579095C2×C411yescharacteristic
97#14579093C2×C411yescharacteristic
98#14579093C2×C411yescharacteristic
99C4⋊(C79⋊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#14579083C2×C411yescharacteristic
113#14579083C2×C411yescharacteristic
114C22⋊(C79⋊C8)—21no—
115(C2×D79)⋊C8—21no—
116(C2×D79)⋊C8—21no—
117#14579072D411yescharacteristic
118#14579072D411yescharacteristic
119#14579071—21no—
120#14579071—21no—
121#14579071—21no—
122C4×C79⋊C8C2311yescharacteristic
123C4×C79⋊C8C2311yescharacteristic
124C4×C79⋊C8C2311yescharacteristic
125C4×C79⋊C8C2311yescharacteristic
126C8×Dic79—21no—
127C8×Dic79—21no—
128C8×Dic79—21no—
129C2×M16×C79—21no—
130C2×C42×C79C2311yescharacteristic
131C4⋊C8×C79—21no—
132C4⋊C8×C79C2×C411yescharacteristic
133C4⋊C8×C79C2×C411yescharacteristic
134C4⋊C8×C79C2311yescharacteristic
135C4⋊C8×C79C2311yescharacteristic
136C4⋊C8×C79C2311yescharacteristic
137C4⋊C8×C79C2311yescharacteristic
138C22⋊C8×C79—21no—
139C22⋊C8×C79C2×C411yescharacteristic
140C22⋊C8×C79C2×C411yescharacteristic
141C4×C8×C79—21no—
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144C2×Dic158—22no—
145C2×Dic158—21no—
146C2×Dic158—41no—
147C2×Dic158C22×C411yescharacteristic
148C2×Dic158C22×C411yescharacteristic
149C2×Dic158C22×C411yescharacteristic
150C2×D316C22×C411yescharacteristic
151C2×C22⋊D79—21no—
152C22×Dic79—21no—
153C22×Dic79—21no—
154C2×C4×D79—21no—
155Dic316—22no—
156Dic316—41no—
157#11929613—22no—
158#11929613—41no—
159#11929608—22no—
160#11929608—41no—
161#11929607—42no—
162C2×C79⋊C8—21no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8C2×D411yescharacteristic
165C2×C79⋊C8C2×D411yescharacteristic
166C2×C79⋊C8C2×D411yescharacteristic
167C2×C79⋊C8C2×D411yescharacteristic
168C8×D79—42no—
169C4⋊Dic79—21no—
170C4⋊Dic79C22×C411yescharacteristic
171C4⋊Dic79C22×C411yescharacteristic
172C4⋊Dic79C22×C411yescharacteristic
173C4⋊Dic79C22×C411yescharacteristic
174Dic79⋊C4—21no—
175Dic79⋊C4—21no—
176Dic79⋊C4—21no—
177Dic79⋊C4—21no—
178Dic79⋊C4—21no—
179Dic79⋊C4—21no—
180Dic79⋊C4—21no—
181Dic79⋊C4—21no—
182C22⋊Dic79—21no—
183(C2×D79)⋊C4—21no—
184(C2×D79)⋊C4—21no—
185(C2×D79)⋊C4—21no—
186(C2×D79)⋊C4—21no—
187C4×Dic79—21no—
188C4×Dic79—21no—
189C4×Dic79—21no—
190C4×Dic79—21no—
191C4×Dic79—21no—
192C22×C4×C79C22×C411yescharacteristic
193C22×C4×C79C2×D411yescharacteristic
194C22×C4×C79#4111yescharacteristic
195M16×C79—42no—
196C2×C8×C79—21no—
197C2×C8×C79—21no—
198C2×C8×C79—21no—
199C2×C8×C79—21no—
200C2×C8×C79C22×C411yescharacteristic
201C2×C8×C79C22×C411yescharacteristic
202C2×C8×C79C22×C411yescharacteristic
203C2×C8×C79C22×C411yescharacteristic
204C42×C79C22×C411yescharacteristic
205C42×C79C2×D411yescharacteristic
206C42×C79#4111yescharacteristic
207C42×C79C2411yescharacteristic
208C23×C79C4×D411yescharacteristic
209C22×D79—21no—
210C2×C4×C79—21no—
211C2×C4×C79—21no—
212C2×C4×C79—21no—
213C2×C4×C79—21no—
214C2×C4×C79—41no—
215C2×C4×C79C4×D411yescharacteristic
216C2×C4×C79C4×D411yescharacteristic
217C2×C4×C79C4×D411yescharacteristic
218C2×C4×C79C23×C411yescharacteristic
219C2×C4×C79C22×D411yescharacteristic
220C2×C4×C79C2×#4111yescharacteristic
221C22⋊D79—81no—
222C2×Dic79—21no—
223C2×Dic79—21no—
224C2×Dic79—21no—
225C2×Dic79—21no—
226C2×Dic79—21no—
227C2×Dic79—21no—
228C2×Dic79—21no—
229C2×Dic79—42no—
230C2×Dic79—81no—
231D316—21no—
232D316—21no—
233C4×D79—41no—
234C4×D79—41no—
235Dic158—21no—
236Dic158—21no—
237Dic158—21no—
238Dic158—21no—
239Dic158—21no—
240Dic158—42no—
241Dic158#13112yes—
242C8×C79—21no—
243C8×C79—21no—
244C8×C79—21no—
245C8×C79—21no—
246C8×C79—41no—
247C8×C79—41no—
248C8×C79—41no—
249C8×C79—41no—
250C79⋊C8—21no—
251C79⋊C8—21no—
252C79⋊C8—21no—
253C79⋊C8—41no—
254C79⋊C8—41no—
255C79⋊C8#13712yes—
256C22×C79—21no—
257C22×C79—21no—
258C22×C79—21no—
259C22×C79C2×C4×D411yescharacteristic
260C2×D79—41no—
261C2×D79—41no—
262C2×D79—41no—
263C4×C79—21no—
264C4×C79—21no—
265C4×C79—21no—
266C4×C79—21no—
267C4×C79C2×#13111yescharacteristic
268C4×C79#56811yescharacteristic
269C4×C79C2×#13711yescharacteristic
270C4×C79#57511yescharacteristic
271Dic79—22no—
272Dic79—41no—
273Dic79—41no—
274Dic79—41no—
275Dic79—41no—
276Dic79—41no—
277Dic79—41no—
278#18010—791nomaximal, Sylow
279C2×C79—41no—
280C2×C79#293311yescharacteristic
281C2×C79C4×#13711yescharacteristic
282C2×C79#295711yescharacteristic
283D79—81no—
284#3108—791no—
285#2969—791no—
286Q8×M16—791no—
287#1592—791no—
288#1591—791no—
289#1588—791no—
290#1587—791no—
291#1584—791no—
292#1582—791no—
293#1579—791no—
294C8×SD16—791no—
295#1574D7911yescharacteristic, complemented
296#1495—791no—
297#1479—791no—
298#1453—791no—
299C79#1801011yescharacteristic, complemented, Sylow
300#529—791no—
301C2×C4×Q8—791no—
302#483—791no—
303#480—791no—
304#479—791no—
305#479—791no—
306#464—791no—
307#464—791no—
308#451—791no—
309#448—791no—
310#446—791no—
311#446—791no—
312#446—791no—
313#446—1581no—
314#446—1581no—
315C8×Q8—791no—
316C8×Q8—791no—
317C8×Q8—791no—
318C4×Q16—791no—
319C4×Q16—791no—
320C4×SD16—791no—
321C4×SD16—791no—
322#436—791no—
323#436—1581no—
324#435—1581no—
325C8×D4—791no—
326#433—1581no—
327#431—791no—
328#431C2×D7911yescharacteristic
329#431C2×D7911yescharacteristic
330#423—1581no—
331#423C2×D7911yescharacteristic
332#405—1581no—
333C4×M16—791no—
334C4×M16—1581no—
335#335C2×D7911yescharacteristic
336#335C2×D7911yescharacteristic
337#334C2×D7911yescharacteristic
338#334C2×D7911yescharacteristic
339Q8⋊C8—791no—
340Q8⋊C8—791no—
341Q8⋊C8—791no—
342Q8⋊C8—791no—
343Q8⋊C8—791no—
344Q8⋊C8—791no—
345D4⋊C8—791no—
346D4⋊C8—791no—
347#322—791no—
348#322—791no—
349#322—791no—
350C82—791no—
351C22×Q8—791no—
352C2×Q16—791no—
353C2×Q16—791no—
354C2×SD16—791no—
355C2×SD16—791no—
356C2×M16—21no—
357C2×M16—791no—
358C2×M16—791no—
359C2×M16—1581no—
360C22×C8—1581no—
361#126—1581no—
362#125—791no—
363#124—791no—
364#123—1581no—
365C22⋊Q8—791no—
366#121—791no—
367C4×Q8—791no—
368C4×Q8—791no—
369C4×Q8—791no—
370C4×Q8—791no—
371C4×Q8—791no—
372C4×Q8—1581no—
373C4×Q8—1581no—
374C4×D4—791no—
375C4×D4—1581no—
376#117—1581no—
377C2×C4⋊C4—791no—
378C2×C4⋊C4—1581no—
379C2×C42—1581no—
380C2×C42C22×D7911yescharacteristic
381#107—791no—
382#107—791no—
383#106—791no—
384#106—791no—
385C4⋊C8—21no—
386C4⋊C8—1581no—
387C4⋊C8—1581no—
388C4⋊C8—1581no—
389C4⋊C8—1581no—
390C4⋊C8—1581no—
391C4⋊C8—1581no—
392C4⋊C8—1581no—
393C4⋊C8C4×D7911yescharacteristic
394C4⋊C8C4×D7911yescharacteristic
395C4⋊C8C22×D7911yescharacteristic
396C4⋊C8C22×D7911yescharacteristic
397C4⋊C8C22×D7911yescharacteristic
398C4⋊C8C22×D7911yescharacteristic
399#103—791no—
400#103—791no—
401#103—791no—
402#103—791no—
403#103—791no—
404#103—791no—
405#102—791no—
406#102—791no—
407C22⋊C8—21no—
408C22⋊C8—1581no—
409C22⋊C8—1581no—
410C22⋊C8—1581no—
411C22⋊C8C4×D7911yescharacteristic
412C22⋊C8C4×D7911yescharacteristic
413#97—791no—
414#97—791no—
415#97—1581no—
416#97—1581no—
417#97—1581no—
418C4×C8—21no—
419C4×C8—791no—
420C4×C8—791no—
421C4×C8—791no—
422C4×C8—791no—
423C4×C8—1581no—
424C4×C8—1581no—
425C4×C8—1581no—
426C4×C8C22×D7911yescharacteristic
427C4×C8C22×D7911yescharacteristic
428C2×Q8—3161no—
429C2×Q8—791no—
430C2×Q8—791no—
431C2×Q8—791no—
432C2×Q8—1582no—
433C2×Q8—1581no—
434C2×D4—791no—
435C2×D4—1581no—
436C22×C4—1581no—
437C22×C4—1581no—
438C22×C4—1581no—
439C22×C4C2×C4×D7911yescharacteristic
440C22×C4D4×D7911yescharacteristic
441C22×C4#1192962511yescharacteristic
442Q16—3161no—
443Q16—1582no—
444SD16—3161no—
445SD16—1582no—
446M16—42no—
447M16—3162no—
448M16—3161no—
449M16—1582no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—3162no—
455C2×C8—791no—
456C2×C8—791no—
457C2×C8—791no—
458C2×C8—791no—
459C2×C8—1581no—
460C2×C8—1581no—
461C2×C8C2×C4×D7911yescharacteristic
462C2×C8C2×C4×D7911yescharacteristic
463C2×C8C2×C4×D7911yescharacteristic
464C2×C8C2×C4×D7911yescharacteristic
465C4⋊C4—791no—
466C4⋊C4—791no—
467C4⋊C4—791no—
468C4⋊C4—791no—
469C4⋊C4—1581no—
470C4⋊C4—1581no—
471C4⋊C4—1581no—
472C4⋊C4—1581no—
473C4⋊C4—1581no—
474C4⋊C4—1581no—
475C4⋊C4—1581no—
476C4⋊C4—1581no—
477C4⋊C4—1581no—
478C22⋊C4—1581no—
479C22⋊C4—1581no—
480C22⋊C4—1581no—
481C22⋊C4—1581no—
482C22⋊C4—1581no—
483C42—1581no—
484C42—1581no—
485C42—1581no—
486C42—1581no—
487C42—1581no—
488C42C2×C4×D7911yescharacteristic
489C42D4×D7911yescharacteristic
490C42#1192962511yescharacteristic
491C42C23×D7911yescharacteristic
492C23—1581no—
493C23#1457912311yescharacteristic
494Q8—3162no—
495Q8—792no—
496Q8—1581no—
497Q8—1581no—
498Q8—1581no—
499Q8—1581no—
500Q8—1581no—
501D4—6321no—
502D4—1581no—
503D4—1581no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—3162no—
510C2×C4—3161no—
511C2×C4—3161no—
512C2×C4—6321no—
513C2×C4—1581no—
514C2×C4—1581no—
515C2×C4—1581no—
516C2×C4—1581no—
517C2×C4—1581no—
518C2×C4—1581no—
519C2×C4—1581no—
520C2×C4#1457912311yescharacteristic
521C2×C4#1457912311yescharacteristic
522C2×C4#1457912311yescharacteristic
523C2×C4C22×C4×D7911yescharacteristic
524C2×C4C2×D4×D7911yescharacteristic
525C2×C4C2×#1192962511yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—3161no—
535C8—3161no—
536C8—792no—
537C8—1581no—
538C8—1581no—
539C8—1581no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—3161no—
544C22—3161no—
545C22—3161no—
546C22C2×#1457912311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—3161no—
552C4—3161no—
553C4—3161no—
554C4—3161no—
555C4—3161no—
556C4—3161no—
557C4—1582no—
558C4#131×D7911yescharacteristic
559C4#1909932811yescharacteristic
560C4#137×D7911yescharacteristic
561C4#1909935911yescharacteristic
562C2—41no—
563C2—6321no—
564C2#2377212411yescharacteristic
565C2#2377221811yescharacteristic
566C2#2377231611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#1574C2
socleC22×C79C2×C4×D4
prime radical#14579135C2×C4
cosocleC42×C79C24
hypercenter#1574D79
hypocenterC79#18010
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
3. #23772351C2semidirect
4. #23762301C2semidirect
5. #23762296C2semidirect
6. #23762277C2semidirect
7. #23762270C2semidirect
8. #23762249C2semidirect
9. #23762235C2semidirect
10. #23762218C2semidirect
11. #23762199C2semidirect
13. #23761794C2semidirect
14. #23761695C2semidirect
15. C79×#1574C2semidirect
295. #1574D79semidirect
299. C79#18010semidirect

Maximal subgroups

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

subgroupindex
#237734822
#237723982
#237723512
#237623012
#237622962
#237622772
#237622702
#237622492
#237622352
#237622182
#237621992
#237618632
#237617942
#237616952
C79×#15742
#1801079