Finite Group Databasebeta

← #34260322

Subgroups — #34260322

Order 20224.

598 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773964C211yesmaximal, characteristic
2#23772562C211yesmaximal, characteristic, complemented
3#23762312C211yesmaximal, characteristic, complemented
4#23762307C211yesmaximal, characteristic, complemented
5#23762243C211yesmaximal, characteristic, complemented
6#23762241C211yesmaximal, characteristic, complemented
7#23762236C211yesmaximal, characteristic, complemented
8#23762234C211yesmaximal, characteristic, complemented
9#23762222C211yesmaximal, characteristic, complemented
10#23762217C211yesmaximal, characteristic, complemented
11C2×#19098313C211yesmaximal, characteristic, complemented
12#23761813C211yesmaximal, characteristic, complemented
13#23761811C211yesmaximal, characteristic, complemented
14#23761690C211yesmaximal, characteristic, complemented
15C79×#2994C211yesmaximal, characteristic, complemented
16#19099097C2211yescharacteristic
17#19098962C411yescharacteristic
18#19098945C411yescharacteristic
19#19098920C411yescharacteristic
20#19098917C411yescharacteristic
21#19098802C411yescharacteristic
22#19098797C411yescharacteristic
23#19098794C411yescharacteristic
24#19098790C411yescharacteristic
25#19098693C2211yescharacteristic
26C8×Dic158C2211yescharacteristic
27C4×#11929614C2211yescharacteristic
28C4×#11929611C2211yescharacteristic
29C4×#11929612C2211yescharacteristic
30C4×#11929609C2211yescharacteristic
31#19098642C2211yescharacteristic
32#19098631—21no—
33C8×D316C2211yescharacteristic
34(C22⋊D79)⋊C8—21no—
35#19098623—21no—
36#19098588—21no—
37C2×C4⋊(C79⋊C8)C2211yescharacteristic
38C4×#11929608C2211yescharacteristic
39C2×C4×C79⋊C8C2211yescharacteristic
40#19098313C2211yescharacteristic
41#19098313C2211yescharacteristic
42#19098313C2211yescharacteristic
43#19098313C2211yescharacteristic
44Q8⋊(C79⋊C8)C2211yescharacteristic
45Q8⋊(C79⋊C8)C2211yescharacteristic
46#19098293C2211yescharacteristic
47#19098293C2211yescharacteristic
48D4⋊(C79⋊C8)C2211yescharacteristic
49D4⋊(C79⋊C8)C2211yescharacteristic
50#19098290C2211yescharacteristic
51#19098290C2211yescharacteristic
52#19098285C2211yescharacteristic
53#19098285C2211yescharacteristic
54#19098284C2211yescharacteristic
55#19098284C2211yescharacteristic
56#529×C79C2211yescharacteristic
57#446×C79C2211yescharacteristic
58C8×Q8×C79C2211yescharacteristic
59#436×C79C2211yescharacteristic
60#435×C79—21no—
61C8×D4×C79—21no—
62C8×D4×C79C2211yescharacteristic
63#433×C79—21no—
64#431×C79C2211yescharacteristic
65#424×C79—21no—
66C2×C4⋊C8×C79C2211yescharacteristic
67C2×#11929614C2×C411yescharacteristic
68C2×#11929612C2×C411yescharacteristic
69C2×#11929611C2×C411yescharacteristic
70C2×#11929609C2×C411yescharacteristic
71C2×#11929608—21no—
72C2×#11929607—21no—
73C22×C79⋊C8—21no—
74C22×C79⋊C8C2×C411yescharacteristic
75C22×C79⋊C8C2×C411yescharacteristic
76C2×C8×D79—21no—
77#14579155—21no—
78#14579153C2×C411yescharacteristic
79#14579149C2×C411yescharacteristic
80#14579144—21no—
81#14579140C2×C411yescharacteristic
82#14579135C2×C411yescharacteristic
83C4×Dic158C2311yescharacteristic
84C4×D316C2311yescharacteristic
85C4×C22⋊D79—21no—
86#14579118—21no—
87#14579094C2×C411yescharacteristic
88#14579094C2×C411yescharacteristic
89#14579092C2×C411yescharacteristic
90#14579092C2×C411yescharacteristic
91C4⋊(C79⋊C8)—21no—
92C4⋊(C79⋊C8)C2311yescharacteristic
93C4⋊(C79⋊C8)C2311yescharacteristic
94Dic79⋊C8—21no—
95Dic79⋊C8—21no—
96#14579085C2×C411yescharacteristic
97#14579085C2×C411yescharacteristic
98#14579084C2×C411yescharacteristic
99#14579084C2×C411yescharacteristic
100#14579082C2×C411yescharacteristic
101#14579082C2×C411yescharacteristic
102#14579081C2×C411yescharacteristic
103#14579081C2×C411yescharacteristic
104(C2×D79)⋊C8—21no—
105(C2×D79)⋊C8—21no—
106#14579072—21no—
107#14579071—21no—
108C4×C79⋊C8C2×C411yescharacteristic
109C4×C79⋊C8C2×C411yescharacteristic
110C4×C79⋊C8C2311yescharacteristic
111C4×C79⋊C8C2311yescharacteristic
112C4×C79⋊C8C2311yescharacteristic
113C4×C79⋊C8C2311yescharacteristic
114C8×Dic79—21no—
115C2×M16×C79—21no—
116C22×C8×C79—21no—
117C22×C8×C79—21no—
118#126×C79—21no—
119#125×C79C2×C411yescharacteristic
120#124×C79C2×C411yescharacteristic
121#123×C79—21no—
122C22⋊Q8×C79C2×C411yescharacteristic
123#121×C79C2×C411yescharacteristic
124C4×Q8×C79C2311yescharacteristic
125C4×D4×C79—21no—
126C4×D4×C79C2311yescharacteristic
127#117×C79—21no—
128C2×C42×C79C2311yescharacteristic
129C4⋊C8×C79—21no—
130C4⋊C8×C79—21no—
131C4⋊C8×C79—21no—
132C4⋊C8×C79D411yescharacteristic
133C4⋊C8×C79D411yescharacteristic
134C4⋊C8×C79C2311yescharacteristic
135C4⋊C8×C79C2311yescharacteristic
136C22⋊C8×C79—21no—
137C22⋊C8×C79—21no—
138C22⋊C8×C79D411yescharacteristic
139C22⋊C8×C79D411yescharacteristic
140#97×C79—21no—
141C4×C8×C79—21no—
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144C2×Dic158C22×C411yescharacteristic
145C2×D316C22×C411yescharacteristic
146C2×C22⋊D79—21no—
147C2×C4×D79—21no—
148#11929614—22no—
149#11929612—41no—
150#11929611—41no—
151#11929609—22no—
152#11929608—42no—
153#11929607—81no—
154C2×C79⋊C8—22no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—41no—
160C2×C79⋊C8—81no—
161C2×C79⋊C8C22×C411yescharacteristic
162C2×C79⋊C8C22×C411yescharacteristic
163C2×C79⋊C8C22×C411yescharacteristic
164C2×C79⋊C8C22×C411yescharacteristic
165C8×D79—81no—
166C4⋊Dic79C22×C411yescharacteristic
167C4⋊Dic79C22×C411yescharacteristic
168Dic79⋊C4—21no—
169Dic79⋊C4—21no—
170Dic79⋊C4—21no—
171Dic79⋊C4—21no—
172C22⋊Dic79—21no—
173(C2×D79)⋊C4—21no—
174(C2×D79)⋊C4—21no—
175(C2×D79)⋊C4—21no—
176(C2×D79)⋊C4—21no—
177C4×Dic79—21no—
178C2×Q8×C79C22×C411yescharacteristic
179C2×D4×C79—21no—
180C2×D4×C79C22×C411yescharacteristic
181C22×C4×C79—21no—
182C22×C4×C79C22×C411yescharacteristic
183C22×C4×C79C2×D411yescharacteristic
184C22×C4×C79#4111yescharacteristic
185M16×C79—81no—
186C2×C8×C79—21no—
187C2×C8×C79—21no—
188C2×C8×C79—81no—
189C2×C8×C79—81no—
190C2×C8×C79C2×D411yescharacteristic
191C2×C8×C79C2×D411yescharacteristic
192C2×C8×C79C2×D411yescharacteristic
193C2×C8×C79C2×D411yescharacteristic
194C4⋊C4×C79—21no—
195C4⋊C4×C79—21no—
196C4⋊C4×C79—21no—
197C4⋊C4×C79—21no—
198C4⋊C4×C79C22×C411yescharacteristic
199C4⋊C4×C79C22×C411yescharacteristic
200C22⋊C4×C79—21no—
201C22⋊C4×C79—21no—
202C22⋊C4×C79—21no—
203C22⋊C4×C79—21no—
204C22⋊C4×C79—21no—
205C42×C79—21no—
206C42×C79C22×C411yescharacteristic
207C42×C79C2×D411yescharacteristic
208C42×C79#4111yescharacteristic
209C42×C79C2411yescharacteristic
210C23×C79—21no—
211C23×C79C4×D411yescharacteristic
212C22×D79—21no—
213Q8×C79—21no—
214Q8×C79—21no—
215D4×C79—21no—
216D4×C79—21no—
217D4×C79—42no—
218C2×C4×C79—22no—
219C2×C4×C79—21no—
220C2×C4×C79—21no—
221C2×C4×C79—21no—
222C2×C4×C79—21no—
223C2×C4×C79—21no—
224C2×C4×C79—21no—
225C2×C4×C79—21no—
226C2×C4×C79—41no—
227C2×C4×C79—41no—
228C2×C4×C79C4×D411yescharacteristic
229C2×C4×C79C4×D411yescharacteristic
230C2×C4×C79C4×D411yescharacteristic
231C2×C4×C79C23×C411yescharacteristic
232C2×C4×C79C22×D411yescharacteristic
233C2×C4×C79C2×#4111yescharacteristic
234C22⋊D79—42no—
235C2×Dic79—21no—
236C2×Dic79—21no—
237C2×Dic79—21no—
238D316—21no—
239D316—21no—
240C4×D79—41no—
241C4×D79—41no—
242Dic158—21no—
243Dic158—21no—
244C8×C79—21no—
245C8×C79—21no—
246C8×C79—21no—
247C8×C79—21no—
248C8×C79—41no—
249C8×C79—41no—
250C79⋊C8—21no—
251C79⋊C8—21no—
252C79⋊C8—21no—
253C79⋊C8—41no—
254C79⋊C8—41no—
255C79⋊C8—41no—
256C79⋊C8—41no—
257C79⋊C8#13112yes—
258C22×C79—21no—
259C22×C79—21no—
260C22×C79—41no—
261C22×C79—41no—
262C22×C79—41no—
263C22×C79#44412yes—
264C22×C79C2×C4×D411yescharacteristic
265C2×D79—41no—
266C2×D79—41no—
267C2×D79—41no—
268C4×C79—21no—
269C4×C79—21no—
270C4×C79—21no—
271C4×C79—21no—
272C4×C79—41no—
273C4×C79—41no—
274C4×C79—41no—
275C4×C79C2×#13111yescharacteristic
276C4×C79#56811yescharacteristic
277C4×C79#57711yescharacteristic
278C4×C79#57711yescharacteristic
279Dic79—41no—
280Dic79—41no—
281Dic79—41no—
282#18093—791nomaximal, Sylow
283C2×C79—22no—
284C2×C79—81no—
285C2×C79#293511yescharacteristic
286C2×C79#295211yescharacteristic
287C2×C79C2×#44411yescharacteristic
288D79—81no—
289#3168—791no—
290#2994—791no—
291#2994D7911yescharacteristic, complemented
292#1594—791no—
293#1593—791no—
294#1583—791no—
295#1583—791no—
296#1582—791no—
297#1582—791no—
298#1580—791no—
299#1579—791no—
300C2×#334—791no—
301#1483—791no—
302#1483—791no—
303#1451—791no—
304C79#1809311yescharacteristic, complemented, Sylow
305#529—791no—
306#529C2×D7911yescharacteristic
307#499—791no—
308#495—791no—
309#488—791no—
310#488—791no—
311#467—791no—
312#466—791no—
313#465—791no—
314#465—791no—
315#446—791no—
316#446C2×D7911yescharacteristic
317C8×Q8—791no—
318C8×Q8C2×D7911yescharacteristic
319C4×Q16—791no—
320C4×SD16—791no—
321C4×SD16—791no—
322C4×D8—791no—
323#436—791no—
324#436C2×D7911yescharacteristic
325#435—21no—
326#435—1581no—
327C8×D4—21no—
328C8×D4—791no—
329C8×D4—1581no—
330C8×D4C2×D7911yescharacteristic
331#433—21no—
332#433—1581no—
333#431C2×D7911yescharacteristic
334#424—21no—
335#424—1581no—
336C2×C4⋊C8—791no—
337C2×C4⋊C8C2×D7911yescharacteristic
338C4×M16—791no—
339C2×C4×C8—791no—
340#334—791no—
341#334—791no—
342#334—791no—
343#334—791no—
344Q8⋊C8—791no—
345Q8⋊C8—791no—
346Q8⋊C8—791no—
347Q8⋊C8—791no—
348D4⋊C8—791no—
349D4⋊C8—791no—
350D4⋊C8—791no—
351D4⋊C8—791no—
352#322—791no—
353#322—791no—
354#322—791no—
355#322—791no—
356C2×Q16—791no—
357C2×SD16—791no—
358C2×SD16—791no—
359C2×D8—791no—
360C2×M16—21no—
361C2×M16—1581no—
362C2×M16—1581no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—791no—
366C22×C8—791no—
367C22×C8—1581no—
368C22×C8—1581no—
369#126—21no—
370#126—1581no—
371#125—791no—
372#125C4×D7911yescharacteristic
373#124—791no—
374#124C4×D7911yescharacteristic
375#123—21no—
376#123—1581no—
377C22⋊Q8—791no—
378C22⋊Q8C4×D7911yescharacteristic
379#121—791no—
380#121C4×D7911yescharacteristic
381C4×Q8—791no—
382C4×Q8C22×D7911yescharacteristic
383C4×D4—21no—
384C4×D4—791no—
385C4×D4—1581no—
386C4×D4C22×D7911yescharacteristic
387#117—21no—
388#117—1581no—
389C2×C42C22×D7911yescharacteristic
390#107—791no—
391#107—791no—
392#106—791no—
393#106—791no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—791no—
398C4⋊C8—791no—
399C4⋊C8—1581no—
400C4⋊C8—1581no—
401C4⋊C8—1581no—
402C4⋊C8C22⋊D7911yescharacteristic
403C4⋊C8C22⋊D7911yescharacteristic
404C4⋊C8C22×D7911yescharacteristic
405C4⋊C8C22×D7911yescharacteristic
406#103—791no—
407#103—791no—
408#103—791no—
409#103—791no—
410#102—791no—
411#102—791no—
412#102—791no—
413#102—791no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—1581no—
417C22⋊C8—1581no—
418C22⋊C8C22⋊D7911yescharacteristic
419C22⋊C8C22⋊D7911yescharacteristic
420#97—21no—
421#97—1581no—
422#97—1581no—
423C4×C8—21no—
424C4×C8—791no—
425C4×C8—791no—
426C4×C8—791no—
427C4×C8—791no—
428C4×C8—791no—
429C4×C8—791no—
430C4×C8—1581no—
431C4×C8C22×D7911yescharacteristic
432C4×C8C22×D7911yescharacteristic
433C2×Q8—791no—
434C2×Q8C2×C4×D7911yescharacteristic
435C2×D4—21no—
436C2×D4—791no—
437C2×D4—1581no—
438C2×D4C2×C4×D7911yescharacteristic
439C22×C4—21no—
440C22×C4—1581no—
441C22×C4C2×C4×D7911yescharacteristic
442C22×C4C2×C22⋊D7911yescharacteristic
443C22×C4#1192962411yescharacteristic
444Q16—1582no—
445SD16—3161no—
446SD16—3161no—
447D8—1582no—
448M16—81no—
449M16—3162no—
450M16—6321no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8—81no—
455C2×C8—3161no—
456C2×C8—791no—
457C2×C8—791no—
458C2×C8—791no—
459C2×C8—791no—
460C2×C8—6321no—
461C2×C8—6321no—
462C2×C8—1581no—
463C2×C8—1581no—
464C2×C8—1581no—
465C2×C8—1581no—
466C2×C8—1582no—
467C2×C8C2×C22⋊D7911yescharacteristic
468C2×C8C2×C22⋊D7911yescharacteristic
469C2×C8C2×C22⋊D7911yescharacteristic
470C2×C8C2×C22⋊D7911yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—791no—
476C4⋊C4—791no—
477C4⋊C4—1581no—
478C4⋊C4—1581no—
479C4⋊C4—1581no—
480C4⋊C4—1581no—
481C4⋊C4C2×C4×D7911yescharacteristic
482C4⋊C4C2×C4×D7911yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1581no—
489C22⋊C4—1581no—
490C22⋊C4—1581no—
491C22⋊C4—1581no—
492C22⋊C4—1581no—
493C42—21no—
494C42—1581no—
495C42C2×C4×D7911yescharacteristic
496C42C2×C22⋊D7911yescharacteristic
497C42#1192962411yescharacteristic
498C42C23×D7911yescharacteristic
499C23—21no—
500C23—1581no—
501C23C4×C22⋊D7911yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—1581no—
505Q8—1581no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—3162no—
510D4—1581no—
511D4—1581no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—3161no—
523C2×C4—3161no—
524C2×C4—1581no—
525C2×C4—1581no—
526C2×C4—1581no—
527C2×C4C4×C22⋊D7911yescharacteristic
528C2×C4C4×C22⋊D7911yescharacteristic
529C2×C4C4×C22⋊D7911yescharacteristic
530C2×C4C22×C4×D7911yescharacteristic
531C2×C4C22×C22⋊D7911yescharacteristic
532C2×C4C2×#1192962411yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—3161no—
540C8—3161no—
541C8—3161no—
542C8—3161no—
543C8—792no—
544C8—1581no—
545C8—1581no—
546C8—1581no—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—3161no—
553C22—3161no—
554C22—3161no—
555C22#1909868312yes—
556C22C2×C4×C22⋊D7911yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—3161no—
565C4—3161no—
566C4—3161no—
567C4#131×D7911yescharacteristic
568C4#1909932811yescharacteristic
569C4#1909937111yescharacteristic
570C4#1909937411yescharacteristic
571C2—22no—
572C2—81no—
573C2—6321no—
574C2#2377214211yescharacteristic
575C2#2377228111yescharacteristic
576C2C2×#1909868311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#2994C2
socleC22×C79C2×C4×D4
prime radical#19098797C4
cosocleC42×C79C24
hypercenter#2994D79
hypocenterC79#18093
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #23772562C2semidirect
3. #23762312C2semidirect
4. #23762307C2semidirect
5. #23762243C2semidirect
6. #23762241C2semidirect
7. #23762236C2semidirect
8. #23762234C2semidirect
9. #23762222C2semidirect
10. #23762217C2semidirect
11. C2×#19098313C2semidirect
12. #23761813C2semidirect
13. #23761811C2semidirect
14. #23761690C2semidirect
15. C79×#2994C2semidirect
291. #2994D79semidirect
304. C79#18093semidirect

Maximal subgroups

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

subgroupindex
#237739642
#237725622
#237623122
#237623072
#237622432
#237622412
#237622362
#237622342
#237622222
#237622172
C2×#190983132
#237618132
#237618112
#237616902
C79×#29942
#1809379