Finite Group Databasebeta

← #34347344

Subgroups — #34347344

Order 20224.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23766371C211yesmaximal, characteristic
2#23764934C211yesmaximal, characteristic
3#23764924C211yesmaximal, characteristic
4#23764785C211yesmaximal, characteristic
5#23764785C211yesmaximal, characteristic
6#23764168C211yesmaximal, characteristic, complemented
7#23764166C211yesmaximal, characteristic, complemented
8#23764156C211yesmaximal, characteristic, complemented
9#23764119C211yesmaximal, characteristic, complemented
10#23763982C211yesmaximal, characteristic, complemented
11#23763975C211yesmaximal, characteristic, complemented
12#23763562C211yesmaximal, characteristic, complemented
13#23763407C211yesmaximal, characteristic
14C4×#14579081C211yesmaximal, characteristic
15C79×#2570C211yesmaximal, characteristic, complemented
16C2×C4×D316C2211yescharacteristic
17C2×#14579094C2211yescharacteristic
18C2×#14579094C2211yescharacteristic
19C2×#14579094C2211yescharacteristic
20C2×#14579092C2211yescharacteristic
21C2×#14579092C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×C4⋊(C79⋊C8)C2211yescharacteristic
24C2×C4⋊(C79⋊C8)C2211yescharacteristic
25C2×C4⋊(C79⋊C8)C2211yescharacteristic
26C2×#14579081C2211yescharacteristic
27C2×#14579081C2211yescharacteristic
28C2×#14579081C2211yescharacteristic
29C2×#14579081C2211yescharacteristic
30C2×C4×C79⋊C8C2211yescharacteristic
31#19098465C2211yescharacteristic
32#19098465C2211yescharacteristic
33#19098453—21no—
34#19098453—21no—
35#19098429C2211yescharacteristic
36#19098425—21no—
37C4×C4⋊Dic79C2211yescharacteristic
38C4×C4⋊Dic79C2211yescharacteristic
39#19098410—21no—
40#19098325C2211yescharacteristic
41#19098325C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098318C2211yescharacteristic
47#19098318C2211yescharacteristic
48#400×C79—21no—
49#398×C79—21no—
50#389×C79C2211yescharacteristic
51#389×C79C2211yescharacteristic
52#387×C79—21no—
53#387×C79—21no—
54#384×C79C2211yescharacteristic
55#382×C79C2211yescharacteristic
56#382×C79C2211yescharacteristic
57C4×C4⋊C4×C79C2211yescharacteristic
58C4×C4⋊C4×C79C2211yescharacteristic
59C22×D316C2311yescharacteristic
60C22×C4×D79—21no—
61C22×C79⋊C8C2311yescharacteristic
62C22×C79⋊C8C2311yescharacteristic
63C22×C79⋊C8C2311yescharacteristic
64C22×C79⋊C8C2311yescharacteristic
65C4×D316—22no—
66C4×D316Q814yes—
67C2×C4⋊Dic79C2311yescharacteristic
68C2×C4⋊Dic79C2311yescharacteristic
69C2×C4⋊Dic79C2311yescharacteristic
70C2×(C2×D79)⋊C4—21no—
71C2×(C2×D79)⋊C4—21no—
72C2×(C2×D79)⋊C4—21no—
73C2×(C2×D79)⋊C4—21no—
74C2×(C2×D79)⋊C4—21no—
75C2×C4×Dic79—21no—
76C2×C4×Dic79—21no—
77#14579094—41no—
78#14579094—41no—
79#14579094—41no—
80#14579092—22no—
81#14579092—22no—
82#14579092—41no—
83C4⋊(C79⋊C8)—22no—
84C4⋊(C79⋊C8)—22no—
85C4⋊(C79⋊C8)—22no—
86#14579081—22no—
87#14579081—22no—
88#14579081—41no—
89#14579081—41no—
90C4×C79⋊C8—22no—
91C79⋊#95—21no—
92C79⋊#95—21no—
93C79⋊#95—21no—
94C79⋊#95—21no—
95C2×C4⋊C4×C79—21no—
96C2×C4⋊C4×C79—21no—
97C2×C4⋊C4×C79—21no—
98C2×C4⋊C4×C79—21no—
99C2×C4⋊C4×C79D411yescharacteristic
100C2×C4⋊C4×C79D411yescharacteristic
101C2×C4⋊C4×C79C2311yescharacteristic
102C2×C4⋊C4×C79C2311yescharacteristic
103C2×C4⋊C4×C79C2311yescharacteristic
104C2×C4⋊C4×C79C2311yescharacteristic
105C2×C42×C79—21no—
106C2×C42×C79C2311yescharacteristic
107C2×C42×C79C2311yescharacteristic
108C2×C42×C79C2311yescharacteristic
109#95×C79—21no—
110#95×C79—21no—
111#95×C79—21no—
112#95×C79—21no—
113#95×C79—21no—
114#95×C79—21no—
115#95×C79—21no—
116#95×C79D411yescharacteristic
117#95×C79D411yescharacteristic
118C23×D79—21no—
119C2×D316—21no—
120C2×D316—21no—
121C2×D316—21no—
122C2×D316—21no—
123C2×D316—21no—
124C2×D316C2×Q812yes—
125C22×Dic79—21no—
126C22×Dic79—21no—
127C22×Dic79—21no—
128C2×C4×D79—24no—
129C2×C4×D79—81no—
130C2×C4×D79—81no—
131C2×C79⋊C8—21no—
132C2×C79⋊C8—21no—
133C2×C79⋊C8—21no—
134C2×C79⋊C8—21no—
135C2×C79⋊C8—21no—
136C2×C79⋊C8—21no—
137C2×C79⋊C8—21no—
138C2×C79⋊C8—21no—
139C2×C79⋊C8—21no—
140C2×C79⋊C8—21no—
141C2×C79⋊C8#4112yes—
142C2×C79⋊C8#4112yes—
143C4⋊Dic79—21no—
144C4⋊Dic79—21no—
145C4⋊Dic79—21no—
146C4⋊Dic79—21no—
147C4⋊Dic79—21no—
148C4⋊Dic79C2×Q812yes—
149(C2×D79)⋊C4—24no—
150(C2×D79)⋊C4—42no—
151(C2×D79)⋊C4—42no—
152(C2×D79)⋊C4—81no—
153(C2×D79)⋊C4—81no—
154C4×Dic79—81no—
155C4×Dic79—81no—
156C22×C4×C79—21no—
157C22×C4×C79—21no—
158C22×C4×C79—21no—
159C22×C4×C79—21no—
160C22×C4×C79C2×D411yescharacteristic
161C22×C4×C79C2×D411yescharacteristic
162C22×C4×C79C2×D411yescharacteristic
163C22×C4×C79C2×D411yescharacteristic
164C22×C4×C79C2×D411yescharacteristic
165C22×C4×C79C2×D411yescharacteristic
166C22×C4×C79C2411yescharacteristic
167C4⋊C4×C79—22no—
168C4⋊C4×C79—21no—
169C4⋊C4×C79—21no—
170C4⋊C4×C79—21no—
171C4⋊C4×C79—21no—
172C4⋊C4×C79—21no—
173C4⋊C4×C79—21no—
174C4⋊C4×C79—21no—
175C4⋊C4×C79—21no—
176C4⋊C4×C79—41no—
177C4⋊C4×C79—42no—
178C4⋊C4×C79—42no—
179C4⋊C4×C79—81no—
180C4⋊C4×C79—81no—
181C42×C79—21no—
182C42×C79—21no—
183C42×C79—21no—
184C42×C79—21no—
185C42×C79—81no—
186C42×C79C2×Q812yes—
187C42×C79#4112yes—
188C23×C79C22×D411yescharacteristic
189C22×D79—22no—
190C22×D79—41no—
191C22×D79—41no—
192C22×D79—41no—
193C22×D79—41no—
194C22×D79—41no—
195C22×D79—41no—
196C2×C4×C79—21no—
197C2×C4×C79—21no—
198C2×C4×C79—21no—
199C2×C4×C79—21no—
200C2×C4×C79—21no—
201C2×C4×C79—21no—
202C2×C4×C79—21no—
203C2×C4×C79—21no—
204C2×C4×C79—21no—
205C2×C4×C79—21no—
206C2×C4×C79—21no—
207C2×C4×C79—21no—
208C2×C4×C79—21no—
209C2×C4×C79—21no—
210C2×C4×C79—21no—
211C2×C4×C79—41no—
212C2×C4×C79—41no—
213C2×C4×C79—41no—
214C2×C4×C79—41no—
215C2×C4×C79—41no—
216C2×C4×C79—41no—
217C2×C4×C79—41no—
218C2×C4×C79—41no—
219C2×C4×C79—41no—
220C2×C4×C79—41no—
221C2×C4×C79—41no—
222C2×C4×C79—41no—
223C2×C4×C79C22⋊Q812yes—
224C2×C4×C79C22⋊Q812yes—
225C2×C4×C79#13512yes—
226C2×C4×C79C22×Q811yescharacteristic
227C2×C4×C79C2×#4111yescharacteristic
228C2×C4×C79C2×#4111yescharacteristic
229C2×C4×C79C2×#4111yescharacteristic
230C2×C4×C79H(5,𝔽2)11yescharacteristic
231C2×C4×C792−1+411yescharacteristic
232C2×Dic79—22no—
233C2×Dic79—41no—
234C2×Dic79—41no—
235C2×Dic79—41no—
236C2×Dic79—41no—
237C2×Dic79—41no—
238C2×Dic79—41no—
239C2×Dic79—41no—
240C2×Dic79—41no—
241D316—22no—
242D316—22no—
243D316—41no—
244D316—41no—
245C4×D79—84no—
246C79⋊C8—22no—
247C79⋊C8—22no—
248C79⋊C8—41no—
249C79⋊C8—41no—
250C22×C79C2×C22⋊Q811yescharacteristic
251C22×C79#54711yescharacteristic
252C22×C79#55011yescharacteristic
253C22×C79C2×#13511yescharacteristic
254C22×C79#57511yescharacteristic
255C22×C79#57611yescharacteristic
256C22×C79#57711yescharacteristic
257C2×D79—42no—
258C2×D79—42no—
259C2×D79—42no—
260C2×D79—81no—
261C2×D79—81no—
262C2×D79—81no—
263C2×D79—81no—
264C4×C79—22no—
265C4×C79—22no—
266C4×C79—22no—
267C4×C79—41no—
268C4×C79—41no—
269C4×C79—41no—
270C4×C79—81no—
271C4×C79—81no—
272C4×C79—81no—
273C4×C79—81no—
274C4×C79#53311yescharacteristic
275C4×C79#54411yescharacteristic
276C4×C79#55211yescharacteristic
277C4×C79#55311yescharacteristic
278Dic79—42no—
279Dic79—81no—
280Dic79—81no—
281#26096—791nomaximal, Sylow
282C2×C79#244111yescharacteristic
283C2×C79#307611yescharacteristic
284C2×C79#308111yescharacteristic
285C2×C79#333911yescharacteristic
286C2×C79#335111yescharacteristic
287C2×C79#339411yescharacteristic
288C2×C79#340311yescharacteristic
289D79—82no—
290#2570D7911yescharacteristic, complemented
291#2357—791no—
292#2094—791no—
293#2092—791no—
294#2067—791no—
295#2067—791no—
296#1949—791no—
297#1949—791no—
298#1947—791no—
299#1939—791no—
300#1920—791no—
301#1919—791no—
302#1846—791no—
303#1804—791no—
304C4×#102—791no—
305C79#2609611yescharacteristic, complemented, Sylow
306C2×C4×D4—791no—
307C2×#107—791no—
308C2×#107—791no—
309C2×#107—791no—
310C2×#106—791no—
311C2×#106—791no—
312C2×#106—791no—
313C2×C4⋊C8—791no—
314C2×C4⋊C8—791no—
315C2×C4⋊C8—791no—
316C2×#102—791no—
317C2×#102—791no—
318C2×#102—791no—
319C2×#102—791no—
320C2×C4×C8—791no—
321#400—21no—
322#398—21no—
323#390—791no—
324#390—791no—
325#389C2×D7911yescharacteristic
326#389C2×D7911yescharacteristic
327#388—1581no—
328#388—1581no—
329#387—21no—
330#387—21no—
331#384C2×D7911yescharacteristic
332#382—791no—
333#382C2×D7911yescharacteristic
334#382C2×D7911yescharacteristic
335#381—1581no—
336C4×C4⋊C4—791no—
337C4×C4⋊C4—791no—
338C4×C4⋊C4C2×D7911yescharacteristic
339C4×C4⋊C4C2×D7911yescharacteristic
340C4×C22⋊C4—1581no—
341#340—791no—
342#340—791no—
343#340—791no—
344#340—791no—
345#340—791no—
346#340—791no—
347#336—791no—
348#336—791no—
349C22×D4—791no—
350C23×C4—1581no—
351C22×C8—791no—
352C22×C8—791no—
353C22×C8—791no—
354C22×C8—791no—
355C4×D4—794no—
356C4×D4—1582no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—791no—
362C2×C4⋊C4—791no—
363C2×C4⋊C4—791no—
364C2×C4⋊C4C22⋊D7911yescharacteristic
365C2×C4⋊C4C22⋊D7911yescharacteristic
366C2×C4⋊C4C22×D7911yescharacteristic
367C2×C4⋊C4C22×D7911yescharacteristic
368C2×C4⋊C4C22×D7911yescharacteristic
369C2×C4⋊C4C22×D7911yescharacteristic
370C2×C22⋊C4—1581no—
371C2×C22⋊C4—1581no—
372C2×C22⋊C4—1581no—
373C2×C22⋊C4—1581no—
374C2×C22⋊C4—1581no—
375C2×C42—21no—
376C2×C42—1581no—
377C2×C42—1581no—
378C2×C42C22×D7911yescharacteristic
379C2×C42C22×D7911yescharacteristic
380C2×C42C22×D7911yescharacteristic
381#107—3161no—
382#107—3161no—
383#107—3161no—
384#106—3161no—
385#106—1582no—
386#106—1582no—
387C4⋊C8—1582no—
388C4⋊C8—1582no—
389C4⋊C8—1582no—
390#102—3161no—
391#102—3161no—
392#102—1582no—
393#102—1582no—
394C4×C8—1582no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—1581no—
403#95—1581no—
404#95—1581no—
405#95—1581no—
406#95C22⋊D7911yescharacteristic
407#95C22⋊D7911yescharacteristic
408C24—1581no—
409C2×D4—792no—
410C2×D4—1581no—
411C2×D4—1581no—
412C2×D4—1581no—
413C2×D4—1581no—
414C2×D4—1581no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—6321no—
420C22×C4—6321no—
421C22×C4—1581no—
422C22×C4—1581no—
423C22×C4—1581no—
424C22×C4—1584no—
425C22×C4C2×C22⋊D7911yescharacteristic
426C22×C4C2×C22⋊D7911yescharacteristic
427C22×C4C2×C22⋊D7911yescharacteristic
428C22×C4C2×C22⋊D7911yescharacteristic
429C22×C4C2×C22⋊D7911yescharacteristic
430C22×C4C2×C22⋊D7911yescharacteristic
431C22×C4C23×D7911yescharacteristic
432C2×C8—792no—
433C2×C8—792no—
434C2×C8—1581no—
435C2×C8—1581no—
436C2×C8—1581no—
437C2×C8—1581no—
438C2×C8—1581no—
439C2×C8—1581no—
440C2×C8—1581no—
441C2×C8—1581no—
442C2×C8—1581no—
443C2×C8—1581no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—792no—
459C4⋊C4—1581no—
460C4⋊C4—1581no—
461C4⋊C4—1581no—
462C4⋊C4—1581no—
463C4⋊C4—1581no—
464C22⋊C4—3162no—
465C22⋊C4—3162no—
466C22⋊C4—6321no—
467C22⋊C4—6321no—
468C22⋊C4—1584no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—81no—
474C42—6321no—
475C42—6321no—
476C42Q8×D7912yes—
477C42#1192962512yes—
478C23—3161no—
479C23—3161no—
480C23—3161no—
481C23—3161no—
482C23—3161no—
483C23—3161no—
484C23—1582no—
485C23C22×C22⋊D7911yescharacteristic
486D4—3161no—
487D4—3161no—
488D4—1582no—
489D4—1582no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—3161no—
518C2×C4—3161no—
519C2×C4—3161no—
520C2×C4—3161no—
521C2×C4—3161no—
522C2×C4—3161no—
523C2×C4—3161no—
524C2×C4—3161no—
525C2×C4—6324no—
526C2×C4—1582no—
527C2×C4#1457913712yes—
528C2×C4#1457913712yes—
529C2×C4#1457918112yes—
530C2×C4C2×Q8×D7911yescharacteristic
531C2×C4#41×D7911yescharacteristic
532C2×C4#41×D7911yescharacteristic
533C2×C4C2×#1192962511yescharacteristic
534C2×C4#1457920711yescharacteristic
535C2×C4#1457920811yescharacteristic
536C8—3161no—
537C8—3161no—
538C8—1582no—
539C8—1582no—
540C22—3162no—
541C22—3162no—
542C22—3162no—
543C22—6321no—
544C22—6321no—
545C22—6321no—
546C22—6321no—
547C22C2×#1457913711yescharacteristic
548C22#1909921211yescharacteristic
549C22#1909923211yescharacteristic
550C22C2×#1457918111yescharacteristic
551C22#1909936111yescharacteristic
552C22#1909936611yescharacteristic
553C22#1909937111yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—3162no—
565C4—6321no—
566C4—6321no—
567C4#1909911911yescharacteristic
568C4#1909919311yescharacteristic
569C4#1909925111yescharacteristic
570C4#1909926611yescharacteristic
571C2—6322no—
572C2#2376710911yescharacteristic
573C2#2377318211yescharacteristic
574C2#2377322511yescharacteristic
575C2#2377579611yescharacteristic
576C2#2377596011yescharacteristic
577C2#2377639611yescharacteristic
578C2#2377648411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2570C2
socleC23×C79C22×D4
prime radicalC22×D316C23
hypercenter#2570D79
hypocenterC79#26096
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2570

Complements

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

NH ≅ G/Ntype
6. #23764168C2semidirect
7. #23764166C2semidirect
8. #23764156C2semidirect
9. #23764119C2semidirect
10. #23763982C2semidirect
11. #23763975C2semidirect
12. #23763562C2semidirect
15. C79×#2570C2semidirect
290. #2570D79semidirect
305. C79#26096semidirect

Maximal subgroups

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

subgroupindex
#237663712
#237649342
#237649242
#237647852
#237641682
#237641662
#237641562
#237641192
#237639822
#237639752
#237635622
#237634072
C4×#145790812
C79×#25702
#2609679