Finite Group Databasebeta

← #34305972

Subgroups — #34305972

Order 20224.

810 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D79C211yesmaximal, characteristic
2#23766276C211yesmaximal, characteristic
3#23766273C211yesmaximal, characteristic
4#23764137C211yesmaximal, characteristic, complemented
5#23764135C211yesmaximal, characteristic, complemented
6#23763973C211yesmaximal, characteristic, complemented
7#23763972C211yesmaximal, characteristic, complemented
8#23763970C211yesmaximal, characteristic, complemented
9#23763489C211yesmaximal, characteristic
10#23763489C211yesmaximal, characteristic
11#23763424C211yesmaximal, characteristic
12#23763298C211yesmaximal, characteristic, complemented
13#23763296C211yesmaximal, characteristic, complemented
14#23763175C211yesmaximal, characteristic
15C79×#1918C211yesmaximal, characteristic, complemented
16C22×C8×D79C2211yescharacteristic
17C2×C4⋊C4×D79C2211yescharacteristic
18C2×C4⋊C4×D79C2211yescharacteristic
19C2×#14579095C2211yescharacteristic
20C2×#14579094C2211yescharacteristic
21C2×#14579094C2211yescharacteristic
22#107×D79C418yescomplemented
23C2×#14579092C2211yescharacteristic
24C2×#14579092C2211yescharacteristic
25C2×(C2×D79)⋊C8C2211yescharacteristic
26C2×#14579072C2211yescharacteristic
27C2×#14579071C2211yescharacteristic
28#19098462C2211yescharacteristic
29#19098461C2211yescharacteristic
30#19098459C2211yescharacteristic
31#19098450—21no—
32#19098447—21no—
33#19098445—21no—
34#19098444—21no—
35#19098422—21no—
36#19098420—21no—
37#19098420C2211yescharacteristic
38#19098420C2211yescharacteristic
39C4⋊C4×Dic79C2211yescharacteristic
40C4⋊C4×Dic79C2211yescharacteristic
41C4×C4⋊Dic79C2211yescharacteristic
42C4×(C2×D79)⋊C4—21no—
43C4×(C2×D79)⋊C4C2211yescharacteristic
44#19098410—21no—
45#19098326C2211yescharacteristic
46#19098326C2211yescharacteristic
47#19098326C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51#19098325C2211yescharacteristic
52#19098317C2211yescharacteristic
53C2×#107×C79C2211yescharacteristic
54#389×C79C2211yescharacteristic
55C4×C4⋊C4×C79C2211yescharacteristic
56#340×C79C2211yescharacteristic
57#340×C79C2211yescharacteristic
58#340×C79C2211yescharacteristic
59#336×C79C2211yescharacteristic
60C22×C4×D79—21no—
61C22×C4×D79—21no—
62C22×C4×D79C2311yescharacteristic
63C22×C79⋊C8C2311yescharacteristic
64C22×C79⋊C8C2311yescharacteristic
65C2×C8×D79—22no—
66C2×C8×D79—22no—
67C2×C8×D79C2×C414yes—
68C2×C4⋊Dic79—21no—
69C2×C4⋊Dic79C2311yescharacteristic
70C2×C4⋊Dic79C2311yescharacteristic
71C2×C4⋊Dic79C2311yescharacteristic
72C2×C4⋊Dic79C2311yescharacteristic
73C2×Dic79⋊C4—21no—
74C2×Dic79⋊C4—21no—
75C2×Dic79⋊C4—21no—
76C2×Dic79⋊C4—21no—
77C4⋊C4×D79—22no—
78C4⋊C4×D79—22no—
79C4⋊C4×D79C2×C414yes—
80C4⋊C4×D79C2×C414yes—
81C2×(C2×D79)⋊C4—21no—
82C2×(C2×D79)⋊C4—21no—
83C2×(C2×D79)⋊C4D411yescharacteristic
84C2×(C2×D79)⋊C4D411yescharacteristic
85C2×C4×Dic79—21no—
86C2×C4×Dic79—21no—
87C2×C4×Dic79—21no—
88C2×C4×Dic79C2311yescharacteristic
89#14579095C2×C414yes—
90#14579094C2×C414yes—
91#14579094C2×C414yes—
92#14579092—22no—
93#14579092—22no—
94(C2×D79)⋊C8—22no—
95#14579072—22no—
96#14579071—22no—
97C79⋊#95—21no—
98C79⋊#95—21no—
99C79⋊#95—21no—
100C79⋊#95—21no—
101C79⋊#95—21no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C79⋊#95—21no—
105C79⋊#95D411yescharacteristic
106C79⋊#95D411yescharacteristic
107C22×C8×C79C2311yescharacteristic
108C22×C8×C79C2311yescharacteristic
109C2×C4⋊C4×C79—21no—
110C2×C4⋊C4×C79C2311yescharacteristic
111C2×C4⋊C4×C79C2311yescharacteristic
112C2×C4⋊C4×C79C2311yescharacteristic
113C2×C4⋊C4×C79C2311yescharacteristic
114C2×C42×C79—21no—
115C2×C42×C79C2311yescharacteristic
116#107×C79C2×C414yes—
117#95×C79—21no—
118#95×C79—21no—
119C23×D79C2×D411yescharacteristic
120C22×Dic79—21no—
121C22×Dic79—21no—
122C22×Dic79—21no—
123C22×Dic79—21no—
124C22×Dic79C2×D411yescharacteristic
125C22×Dic79C2×D411yescharacteristic
126C22×Dic79C2×D411yescharacteristic
127C2×C4×D79—24no—
128C2×C4×D79—24no—
129C2×C4×D79—21no—
130C2×C4×D79—21no—
131C2×C4×D79—21no—
132C2×C4×D79—21no—
133C2×C4×D79—81no—
134C2×C4×D79—81no—
135C2×C4×D79—81no—
136C2×C4×D79—81no—
137C2×C4×D79C22×C412yes—
138C2×C4×D79#4112yes—
139C2×C79⋊C8—21no—
140C2×C79⋊C8—21no—
141C2×C79⋊C8—21no—
142C2×C79⋊C8C22×C412yes—
143C2×C79⋊C8#4112yes—
144C2×C79⋊C8#4112yes—
145C8×D79—28no—
146C4⋊Dic79—21no—
147C4⋊Dic79—21no—
148C4⋊Dic79—21no—
149C4⋊Dic79—21no—
150C4⋊Dic79—21no—
151C4⋊Dic79—21no—
152C4⋊Dic79—81no—
153C4⋊Dic79C22×C412yes—
154C4⋊Dic79C22×C412yes—
155Dic79⋊C4—24no—
156Dic79⋊C4—24no—
157Dic79⋊C4—81no—
158Dic79⋊C4—81no—
159(C2×D79)⋊C4—22no—
160(C2×D79)⋊C4—22no—
161(C2×D79)⋊C4—42no—
162(C2×D79)⋊C4—42no—
163C4×Dic79—21no—
164C4×Dic79—21no—
165C4×Dic79—81no—
166C4×Dic79—81no—
167C4×Dic79—81no—
168C22×C4×C79—21no—
169C22×C4×C79—21no—
170C22×C4×C79—21no—
171C22×C4×C79—21no—
172C22×C4×C79C2×D411yescharacteristic
173C22×C4×C79C2×D411yescharacteristic
174C22×C4×C79C2411yescharacteristic
175C2×C8×C79—21no—
176C2×C8×C79—21no—
177C2×C8×C79—21no—
178C2×C8×C79—21no—
179C2×C8×C79—21no—
180C2×C8×C79C22×C412yes—
181C4⋊C4×C79—21no—
182C4⋊C4×C79—21no—
183C4⋊C4×C79—21no—
184C4⋊C4×C79—21no—
185C4⋊C4×C79—21no—
186C4⋊C4×C79—21no—
187C4⋊C4×C79—81no—
188C4⋊C4×C79C22×C412yes—
189C4⋊C4×C79C22×C412yes—
190C42×C79—21no—
191C42×C79—21no—
192C42×C79—81no—
193C23×C79C22×D411yescharacteristic
194C22×D79—21no—
195C22×D79—21no—
196C22×D79—21no—
197C22×D79—21no—
198C22×D79C4×D412yes—
199C22×D79#13712yes—
200C22×D79#13712yes—
201C2×C4×C79—22no—
202C2×C4×C79—22no—
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—41no—
210C2×C4×C79—41no—
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×C79C23×C411yescharacteristic
220C2×C4×C79C2×#4111yescharacteristic
221C2×C4×C79C2×#4111yescharacteristic
222C2×C4×C79C2×#4111yescharacteristic
223C2×C4×C792−1+411yescharacteristic
224C2×C4×C792−1+411yescharacteristic
225C2×Dic79—21no—
226C2×Dic79—21no—
227C2×Dic79—22no—
228C2×Dic79—22no—
229C2×Dic79—21no—
230C2×Dic79—21no—
231C2×Dic79—21no—
232C2×Dic79—21no—
233C2×Dic79—21no—
234C2×Dic79—21no—
235C2×Dic79—41no—
236C2×Dic79—41no—
237C2×Dic79—41no—
238C2×Dic79—41no—
239C2×Dic79—41no—
240C2×Dic79—41no—
241C2×Dic79—41no—
242C2×Dic79—41no—
243C2×Dic79—41no—
244C2×Dic79—41no—
245C2×Dic79C4×D412yes—
246C4×D79—22no—
247C4×D79—22no—
248C4×D79—22no—
249C4×D79—22no—
250C4×D79—84no—
251C4×D79—84no—
252C8×C79—22no—
253C8×C79—41no—
254C79⋊C8—41no—
255C79⋊C8#11714yes—
256C22×C79C2×C4×D411yescharacteristic
257C22×C79#54711yescharacteristic
258C22×C79#54711yescharacteristic
259C22×C79C2×#13711yescharacteristic
260C22×C79C2×#13711yescharacteristic
261C22×C79#57611yescharacteristic
262C22×C79#57611yescharacteristic
263C2×D79—22no—
264C2×D79—22no—
265C2×D79—22no—
266C2×D79—22no—
267C2×D79—22no—
268C2×D79—22no—
269C2×D79#44114yes—
270C4×C79—41no—
271C4×C79—41no—
272C4×C79—42no—
273C4×C79—42no—
274C4×C79—81no—
275C4×C79—81no—
276C4×C79C2×#11711yescharacteristic
277C4×C79#51911yescharacteristic
278C4×C79#55211yescharacteristic
279C4×C79#55211yescharacteristic
280Dic79—22no—
281Dic79—41no—
282Dic79—41no—
283Dic79—42no—
284Dic79—42no—
285Dic79—81no—
286Dic79—81no—
287#22618—791nomaximal, Sylow
288C2×C79#234411yescharacteristic
289C2×C79C2×#44111yescharacteristic
290C2×C79#294811yescharacteristic
291C2×C79#334611yescharacteristic
292C2×C79#334611yescharacteristic
293C2×C79#334611yescharacteristic
294C2×C79#334611yescharacteristic
295D79—24no—
296C22×#107—791no—
297#2345—791no—
298#2345—791no—
299#1943—791no—
300#1943—791no—
301#1918—791no—
302#1918—791no—
303#1918—791no—
304#1918D7911yescharacteristic, complemented
305#1824—791no—
306#1824—791no—
307#1807—791no—
308#1776—791no—
309#1776—791no—
310#1752—791no—
311C79#2261811yescharacteristic, complemented, Sylow
312C23×C8—791no—
313C22×C4⋊C4—791no—
314C22×C4⋊C4—791no—
315C2×#107—791no—
316C2×#107—791no—
317C2×#107—791no—
318C2×#107—798no—
319C2×#107C2×D7911yescharacteristic
320C2×#106—791no—
321C2×#106—791no—
322C2×C22⋊C8—791no—
323C2×#97—791no—
324C2×#97—791no—
325#389—791no—
326#389—791no—
327#389—791no—
328#389C2×D7911yescharacteristic
329#387—1581no—
330#387—1581no—
331#387—1581no—
332#387—1581no—
333#380—791no—
334#380—791no—
335#380—1581no—
336#380—1581no—
337C4×C4⋊C4—791no—
338C4×C4⋊C4—791no—
339C4×C4⋊C4—791no—
340C4×C4⋊C4C2×D7911yescharacteristic
341C4×C22⋊C4—791no—
342C4×C22⋊C4—1581no—
343C4×C22⋊C4—1581no—
344#340—791no—
345#340—791no—
346#340—791no—
347#340—791no—
348#340—791no—
349#340—791no—
350#340—791no—
351#340C2×D7911yescharacteristic
352#340C2×D7911yescharacteristic
353#340C2×D7911yescharacteristic
354#336—791no—
355#336C2×D7911yescharacteristic
356C23×C4—791no—
357C23×C4—1581no—
358C23×C4—1581no—
359C22×C8—791no—
360C22×C8—794no—
361C22×C8—791no—
362C22×C8—1582no—
363C22×C8—1582no—
364C22×C8C22×D7911yescharacteristic
365C22×C8C22×D7911yescharacteristic
366C2×C4⋊C4—21no—
367C2×C4⋊C4—791no—
368C2×C4⋊C4—791no—
369C2×C4⋊C4—794no—
370C2×C4⋊C4—794no—
371C2×C4⋊C4—791no—
372C2×C4⋊C4—791no—
373C2×C4⋊C4—1582no—
374C2×C4⋊C4—1582no—
375C2×C4⋊C4—1581no—
376C2×C4⋊C4—1581no—
377C2×C4⋊C4—1581no—
378C2×C4⋊C4—1581no—
379C2×C4⋊C4—1581no—
380C2×C4⋊C4C22×D7911yescharacteristic
381C2×C4⋊C4C22×D7911yescharacteristic
382C2×C4⋊C4C22×D7911yescharacteristic
383C2×C4⋊C4C22×D7911yescharacteristic
384C2×C22⋊C4—791no—
385C2×C22⋊C4—791no—
386C2×C22⋊C4—1581no—
387C2×C22⋊C4—1581no—
388C2×C42—21no—
389C2×C42—791no—
390C2×C42—1581no—
391C2×C42—1581no—
392C2×C42—1581no—
393C2×C42C22×D7911yescharacteristic
394#107—794no—
395#107—794no—
396#107—794no—
397#107C4×D7914yes—
398#106—1582no—
399#106—1582no—
400C22⋊C8—1582no—
401#97—1582no—
402#97—1582no—
403#95—21no—
404#95—21no—
405#95—791no—
406#95—791no—
407#95—1581no—
408#95—1581no—
409#95—1581no—
410#95—1581no—
411#95—1581no—
412#95—1581no—
413#95—1581no—
414#95—1581no—
415C24—791no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—791no—
421C22×C4—792no—
422C22×C4—792no—
423C22×C4—791no—
424C22×C4—791no—
425C22×C4—6321no—
426C22×C4—6321no—
427C22×C4—6321no—
428C22×C4—6321no—
429C22×C4—1584no—
430C22×C4—1584no—
431C22×C4—1581no—
432C22×C4—1581no—
433C22×C4—1581no—
434C22×C4—1581no—
435C22×C4—1581no—
436C22×C4—1581no—
437C22×C4—1581no—
438C22×C4—1581no—
439C22×C4D4×D7911yescharacteristic
440C22×C4D4×D7911yescharacteristic
441C22×C4C23×D7911yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—792no—
448C2×C8—792no—
449C2×C8—792no—
450C2×C8—1588no—
451C2×C8—1581no—
452C2×C8—1581no—
453C2×C8—1581no—
454C2×C8C2×C4×D7912yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—792no—
463C4⋊C4—792no—
464C4⋊C4—6321no—
465C4⋊C4—6321no—
466C4⋊C4—6321no—
467C4⋊C4—1584no—
468C4⋊C4—1584no—
469C4⋊C4—1581no—
470C4⋊C4—1581no—
471C4⋊C4—1581no—
472C4⋊C4—1581no—
473C4⋊C4—1581no—
474C4⋊C4—1581no—
475C4⋊C4C2×C4×D7912yes—
476C4⋊C4C2×C4×D7912yes—
477C22⋊C4—3162no—
478C22⋊C4—3162no—
479C22⋊C4—1582no—
480C22⋊C4—1582no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—6321no—
485C42—6321no—
486C42—6321no—
487C42—1581no—
488C42—1581no—
489C23—792no—
490C23—792no—
491C23—792no—
492C23—1581no—
493C23—1581no—
494C23—1581no—
495C23—1581no—
496C23C2×D4×D7911yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
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—3161no—
516C2×C4—3161no—
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—792no—
526C2×C4—6324no—
527C2×C4—6324no—
528C2×C4—1581no—
529C2×C4—1581no—
530C2×C4—1582no—
531C2×C4—1582no—
532C2×C4—1581no—
533C2×C4—1581no—
534C2×C4—1581no—
535C2×C4—1581no—
536C2×C4—1581no—
537C2×C4—1581no—
538C2×C4—1582no—
539C2×C4—1582no—
540C2×C4—1582no—
541C2×C4—1582no—
542C2×C4C22×C4×D7911yescharacteristic
543C2×C4#41×D7911yescharacteristic
544C2×C4#41×D7911yescharacteristic
545C2×C4#41×D7911yescharacteristic
546C2×C4#1457920811yescharacteristic
547C2×C4#1457920911yescharacteristic
548C8—22no—
549C8—41no—
550C8—3161no—
551C8—794no—
552C22—794no—
553C22—1582no—
554C22—1582no—
555C22—1582no—
556C22—1582no—
557C22—1582no—
558C22—1582no—
559C22C4×D4×D7911yescharacteristic
560C22#1909921111yescharacteristic
561C22#1909921511yescharacteristic
562C22#137×D7911yescharacteristic
563C22#137×D7911yescharacteristic
564C22#1909936411yescharacteristic
565C22#1909936511yescharacteristic
566C4—42no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—3162no—
573C4—3162no—
574C4—3161no—
575C4—3161no—
576C4—6321no—
577C4—6321no—
578C4—1582no—
579C4#117×D7911yescharacteristic
580C4#1909903911yescharacteristic
581C4#1909924511yescharacteristic
582C4#1909924911yescharacteristic
583C2—1584no—
584C2#2376626611yescharacteristic
585C2#441×D7911yescharacteristic
586C2#2377224711yescharacteristic
587C2#2377587811yescharacteristic
588C2#2377588211yescharacteristic
589C2#2377588811yescharacteristic
590C2#2377589211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1918C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
cosocleC22×C4×C79C24
hypercenter#1918D79
hypocenterC79#22618
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #23764137C2semidirect
5. #23764135C2semidirect
6. #23763973C2semidirect
7. #23763972C2semidirect
8. #23763970C2semidirect
12. #23763298C2semidirect
13. #23763296C2semidirect
15. C79×#1918C2semidirect
22. #107×D79C4semidirect
304. #1918D79semidirect
311. C79#22618semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D792
#237662762
#237662732
#237641372
#237641352
#237639732
#237639722
#237639702
#237634892
#237634242
#237632982
#237632962
#237631752
C79×#19182
#2261879