Finite Group Databasebeta

← #34259346

Subgroups — #34259346

Order 20224.

594 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#23773465C211yesmaximal, characteristic
2#23772415C211yesmaximal, characteristic
3#23762307C211yesmaximal, characteristic, complemented
4#23762295C211yesmaximal, characteristic, complemented
5#23762271C211yesmaximal, characteristic, complemented
6#23762255C211yesmaximal, characteristic, complemented
7#23762250C211yesmaximal, characteristic, complemented
8#23762234C211yesmaximal, characteristic, complemented
9#23762210C211yesmaximal, characteristic, complemented
10C8×#11929611C211yesmaximal, characteristic, complemented
11#23762183C211yesmaximal, characteristic, complemented
12#23761873C211yesmaximal, characteristic, complemented
13#23761785C211yesmaximal, characteristic
14#23761697C211yesmaximal, characteristic, complemented
15C79×#2962C211yesmaximal, characteristic, complemented
16C4×#11929624C2211yescharacteristic
17#19098901C411yescharacteristic
18#19098901C411yescharacteristic
19#19098845C411yescharacteristic
20#19098840C411yescharacteristic
21#19098770C411yescharacteristic
22#19098765C411yescharacteristic
23#19098723C411yescharacteristic
24#19098723C411yescharacteristic
25#19098693C2211yescharacteristic
26#19098693C2211yescharacteristic
27C4×#11929614C2211yescharacteristic
28C4×#11929614C2211yescharacteristic
29C4×#11929611C2211yescharacteristic
30C4×#11929611C2211yescharacteristic
31#19098632—21no—
32#19098632—21no—
33C8×D316C2211yescharacteristic
34C8×D316C2211yescharacteristic
35#19098620C2211yescharacteristic
36#19098618—21no—
37#19098616C2211yescharacteristic
38#19098616C2211yescharacteristic
39#97×D79—21no—
40#19098315C2211yescharacteristic
41#19098315C2211yescharacteristic
42#19098313C2211yescharacteristic
43#19098313C2211yescharacteristic
44Q8⋊(C79⋊C8)C2211yescharacteristic
45Q8⋊(C79⋊C8)C2211yescharacteristic
46Q8⋊(C79⋊C8)C2211yescharacteristic
47Q8⋊(C79⋊C8)C2211yescharacteristic
48#19098293C2211yescharacteristic
49#19098293C2211yescharacteristic
50#19098290C2211yescharacteristic
51#19098290C2211yescharacteristic
52#19098285C2211yescharacteristic
53#19098285C2211yescharacteristic
54#19098284C2211yescharacteristic
55C8×C79⋊C8C2211yescharacteristic
56#533×C79C2211yescharacteristic
57#446×C79—21no—
58#446×C79—21no—
59#446×C79C2211yescharacteristic
60#446×C79C2211yescharacteristic
61C8×Q8×C79C2211yescharacteristic
62C8×Q8×C79C2211yescharacteristic
63#424×C79—21no—
64C2×C4⋊C8×C79C2211yescharacteristic
65#405×C79—21no—
66C4×M16×C79C2211yescharacteristic
67C2×#11929624C2×C411yescharacteristic
68C2×#11929614C2×C411yescharacteristic
69C2×#11929614C2×C411yescharacteristic
70C2×#11929611C2×C411yescharacteristic
71C2×#11929611C2×C411yescharacteristic
72C2×C8×D79—21no—
73C2×C8×D79—21no—
74C4×Dic158C2×C411yescharacteristic
75C4×Dic158C2311yescharacteristic
76C4×D316C2×C411yescharacteristic
77C4×D316C2311yescharacteristic
78C4×C22⋊D79—21no—
79C4×C22⋊D79—21no—
80#14579120C2×C411yescharacteristic
81#14579118—21no—
82C42×D79—21no—
83#14579094C2×C411yescharacteristic
84#14579094C2×C411yescharacteristic
85#14579092C2×C411yescharacteristic
86#14579092C2×C411yescharacteristic
87C4⋊(C79⋊C8)—21no—
88C4⋊(C79⋊C8)C2×C411yescharacteristic
89C4⋊(C79⋊C8)C2×C411yescharacteristic
90C4⋊(C79⋊C8)C2311yescharacteristic
91C4⋊(C79⋊C8)C2311yescharacteristic
92Dic79⋊C8—21no—
93Dic79⋊C8—21no—
94#14579085C2×C411yescharacteristic
95#14579085C2×C411yescharacteristic
96#14579085C2×C411yescharacteristic
97#14579085C2×C411yescharacteristic
98#14579084C2×C411yescharacteristic
99#14579084C2×C411yescharacteristic
100#14579081C2×C411yescharacteristic
101#14579081C2×C411yescharacteristic
102C22⋊(C79⋊C8)—21no—
103C22⋊(C79⋊C8)—21no—
104C22⋊(C79⋊C8)C2×C411yescharacteristic
105C22⋊(C79⋊C8)C2×C411yescharacteristic
106(C2×D79)⋊C8—21no—
107(C2×D79)⋊C8—21no—
108#14579072—21no—
109#14579071—21no—
110#14579071—21no—
111C4×C79⋊C8C2311yescharacteristic
112C4×C79⋊C8C2311yescharacteristic
113C4×C79⋊C8C2311yescharacteristic
114C4×C79⋊C8C2311yescharacteristic
115C2×M16×C79D411yescharacteristic
116C2×M16×C79D411yescharacteristic
117C22×C8×C79—21no—
118C4⋊Q8×C79C2×C411yescharacteristic
119C4⋊Q8×C79C2×C411yescharacteristic
120#125×C79—21no—
121C22⋊Q8×C79—21no—
122C22⋊Q8×C79C2×C411yescharacteristic
123C22⋊Q8×C79C2×C411yescharacteristic
124C4×Q8×C79—21no—
125C4×Q8×C79C2311yescharacteristic
126C4×Q8×C79C2311yescharacteristic
127#117×C79—21no—
128C2×C42×C79C2311yescharacteristic
129C4⋊C8×C79—21no—
130C4⋊C8×C79—21no—
131C4⋊C8×C79—21no—
132C4⋊C8×C79—21no—
133C4⋊C8×C79—21no—
134C4⋊C8×C79C2311yescharacteristic
135C4⋊C8×C79C2311yescharacteristic
136#97×C79—21no—
137#97×C79—21no—
138#97×C79D411yescharacteristic
139#97×C79D411yescharacteristic
140C4×C8×C79—21no—
141C4×C8×C79—21no—
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144#11929624—22no—
145#11929624—41no—
146C2×Dic158C22×C411yescharacteristic
147C2×D316C22×C411yescharacteristic
148C2×C22⋊D79—21no—
149C2×C4×D79—21no—
150C2×C4×D79—21no—
151C2×C4×D79—21no—
152#11929614—41no—
153#11929614—41no—
154#11929611—22no—
155#11929611—22no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8C22×C411yescharacteristic
161C2×C79⋊C8C22×C411yescharacteristic
162C2×C79⋊C8C22×C411yescharacteristic
163C2×C79⋊C8C22×C411yescharacteristic
164C8×D79—42no—
165C8×D79—42no—
166C4⋊Dic79C22×C411yescharacteristic
167C4⋊Dic79C22×C411yescharacteristic
168Dic79⋊C4—21no—
169Dic79⋊C4—21no—
170C22⋊Dic79—21no—
171(C2×D79)⋊C4—21no—
172(C2×D79)⋊C4—21no—
173C4×Dic79—21no—
174C4×Dic79—21no—
175C4×Dic79—21no—
176C2×Q8×C79—21no—
177C2×Q8×C79C22×C411yescharacteristic
178C2×Q8×C79C22×C411yescharacteristic
179C22×C4×C79C22×C411yescharacteristic
180C22×C4×C79C2×D411yescharacteristic
181C22×C4×C79#4111yescharacteristic
182M16×C79—22no—
183M16×C79—41no—
184C2×C8×C79—21no—
185C2×C8×C79—21no—
186C2×C8×C79—42no—
187C2×C8×C79C2×D411yescharacteristic
188C2×C8×C79C2×D411yescharacteristic
189C2×C8×C79C2×D411yescharacteristic
190C2×C8×C79C2×D411yescharacteristic
191C4⋊C4×C79—21no—
192C4⋊C4×C79—21no—
193C4⋊C4×C79—21no—
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—
202C42×C79—21no—
203C42×C79—21no—
204C42×C79C22×C411yescharacteristic
205C42×C79C2×D411yescharacteristic
206C42×C79#4111yescharacteristic
207C42×C79C2411yescharacteristic
208C23×C79C4×D411yescharacteristic
209C22×D79—21no—
210Q8×C79—21no—
211Q8×C79—21no—
212Q8×C79—21no—
213Q8×C79—21no—
214Q8×C79—81no—
215C2×C4×C79—21no—
216C2×C4×C79—21no—
217C2×C4×C79—21no—
218C2×C4×C79—21no—
219C2×C4×C79—21no—
220C2×C4×C79—21no—
221C2×C4×C79—21no—
222C2×C4×C79—21no—
223C2×C4×C79—41no—
224C2×C4×C79C4×D411yescharacteristic
225C2×C4×C79C4×D411yescharacteristic
226C2×C4×C79C4×D411yescharacteristic
227C2×C4×C79C23×C411yescharacteristic
228C2×C4×C79C22×D411yescharacteristic
229C2×C4×C79C2×#4111yescharacteristic
230C22⋊D79—42no—
231C2×Dic79—21no—
232C2×Dic79—21no—
233C2×Dic79—21no—
234D316—21no—
235D316#13112yes—
236C4×D79—42no—
237C4×D79—41no—
238C4×D79—41no—
239C4×D79—81no—
240Dic158—21no—
241Dic158—21no—
242C8×C79—21no—
243C8×C79—21no—
244C8×C79—21no—
245C8×C79—41no—
246C8×C79—41no—
247C8×C79#13712yes—
248C79⋊C8—21no—
249C79⋊C8—21no—
250C79⋊C8—21no—
251C79⋊C8—21no—
252C79⋊C8—41no—
253C79⋊C8—41no—
254C79⋊C8—41no—
255C79⋊C8—41no—
256C22×C79—21no—
257C22×C79—21no—
258C22×C79—21no—
259C22×C79C2×C4×D411yescharacteristic
260C2×D79—22no—
261C2×D79—41no—
262C2×D79—41no—
263C4×C79—21no—
264C4×C79—21no—
265C4×C79—21no—
266C4×C79—21no—
267C4×C79—41no—
268C4×C79—41no—
269C4×C79—41no—
270C4×C79—41no—
271C4×C79C2×#13111yescharacteristic
272C4×C79#56811yescharacteristic
273C4×C79C2×#13711yescharacteristic
274C4×C79#57511yescharacteristic
275Dic79—41no—
276Dic79—41no—
277Dic79—41no—
278#18009—791nomaximal, Sylow
279C2×C79—41no—
280C2×C79#293311yescharacteristic
281C2×C79C4×#13711yescharacteristic
282C2×C79#295711yescharacteristic
283D79—42no—
284#3107—791no—
285#2970—791no—
286#2962D7911yescharacteristic, complemented
287#1593—791no—
288#1591—791no—
289#1587—791no—
290#1585—791no—
291#1584—791no—
292#1582—791no—
293SD16⋊C8—791no—
294C8×SD16—791no—
295#1573—791no—
296#1497—791no—
297#1477—791no—
298#1453—791no—
299C79#1800911yescharacteristic, complemented, Sylow
300#533C2×D7911yescharacteristic
301C4×#41—791no—
302#485—791no—
303#485—791no—
304#475—791no—
305#474—791no—
306#462—791no—
307#461—791no—
308#452—791no—
309#452—791no—
310#446—21no—
311#446—21no—
312#446—791no—
313#446—791no—
314#446C2×D7911yescharacteristic
315#446C2×D7911yescharacteristic
316C8×Q8C2×D7911yescharacteristic
317C8×Q8C2×D7911yescharacteristic
318C4×Q16—791no—
319C4×Q16—791no—
320C4×SD16—791no—
321C4×SD16—791no—
322#435—1581no—
323#435—1581no—
324C8×D4—791no—
325C8×D4—791no—
326#432—791no—
327#432—1581no—
328#431—791no—
329#431—791no—
330#424—21no—
331C2×C4⋊C8C2×D7911yescharacteristic
332#405—21no—
333C4×M16C2×D7911yescharacteristic
334C2×#97—1581no—
335#335—791no—
336#335—791no—
337#334—791no—
338#334—791no—
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—
351C2×#41—791no—
352C2×Q16—791no—
353C2×Q16—791no—
354C2×SD16—791no—
355C2×SD16—791no—
356C2×M16C22⋊D7911yescharacteristic
357C2×M16C22⋊D7911yescharacteristic
358C22×C8—21no—
359C22×C8—1581no—
360C22×C8—1581no—
361C4⋊Q8C4×D7911yescharacteristic
362C4⋊Q8C4×D7911yescharacteristic
363#125—21no—
364C22⋊Q8—21no—
365C22⋊Q8C4×D7911yescharacteristic
366C22⋊Q8C4×D7911yescharacteristic
367C4×Q8—21no—
368C4×Q8—791no—
369C4×Q8—791no—
370C4×Q8C22×D7911yescharacteristic
371C4×Q8C22×D7911yescharacteristic
372C4×D4—791no—
373C4×D4—791no—
374C4×D4—1581no—
375C4×D4—1581no—
376#117—21no—
377#117—791no—
378#117—1581no—
379C2×C42—1581no—
380C2×C42C22×D7911yescharacteristic
381#107—791no—
382#107—791no—
383#106—791no—
384#106—791no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—791no—
391C4⋊C8—791no—
392C4⋊C8—791no—
393C4⋊C8—791no—
394C4⋊C8—1581no—
395C4⋊C8—1581no—
396C4⋊C8—1581no—
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—791no—
408C22⋊C8—791no—
409C22⋊C8—1581no—
410C22⋊C8—1581no—
411C22⋊C8—1581no—
412C22⋊C8—1581no—
413#97—21no—
414#97—21no—
415#97—1581no—
416#97—1581no—
417#97—1581no—
418#97C22⋊D7911yescharacteristic
419#97C22⋊D7911yescharacteristic
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—791no—
423C4×C8—791no—
424C4×C8—791no—
425C4×C8—791no—
426C4×C8C22×D7911yescharacteristic
427C4×C8C22×D7911yescharacteristic
428#41—3161no—
429#41—1582no—
430C2×Q8—21no—
431C2×Q8—791no—
432C2×Q8C2×C4×D7911yescharacteristic
433C2×Q8C2×C4×D7911yescharacteristic
434C2×D4—791no—
435C2×D4—1581no—
436C22×C4—1581no—
437C22×C4—1581no—
438C22×C4—1581no—
439C22×C4C2×C4×D7911yescharacteristic
440C22×C4C2×C22⋊D7911yescharacteristic
441C22×C4#1192962411yescharacteristic
442Q16—3161no—
443Q16—3161no—
444SD16—1582no—
445SD16—1582no—
446M16—22no—
447M16—41no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—3162no—
452C2×C8—3162no—
453C2×C8—791no—
454C2×C8—791no—
455C2×C8—791no—
456C2×C8—791no—
457C2×C8—1581no—
458C2×C8—1581no—
459C2×C8—1581no—
460C2×C8—1581no—
461C2×C8C2×C22⋊D7911yescharacteristic
462C2×C8C2×C22⋊D7911yescharacteristic
463C2×C8C2×C22⋊D7911yescharacteristic
464C2×C8C2×C22⋊D7911yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—791no—
473C4⋊C4—791no—
474C4⋊C4—1581no—
475C4⋊C4—1581no—
476C4⋊C4C2×C4×D7911yescharacteristic
477C4⋊C4C2×C4×D7911yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—1581no—
481C22⋊C4—1581no—
482C22⋊C4—1581no—
483C42—21no—
484C42—21no—
485C42—1581no—
486C42—1581no—
487C42—1581no—
488C42C2×C4×D7911yescharacteristic
489C42C2×C22⋊D7911yescharacteristic
490C42#1192962411yescharacteristic
491C42C23×D7911yescharacteristic
492C23—1581no—
493C23C4×C22⋊D7911yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—1581no—
500Q8—1581no—
501D4—3162no—
502D4—792no—
503D4—1581no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—3162no—
514C2×C4—3161no—
515C2×C4—3161no—
516C2×C4—6321no—
517C2×C4—1581no—
518C2×C4—1581no—
519C2×C4—1581no—
520C2×C4C4×C22⋊D7911yescharacteristic
521C2×C4C4×C22⋊D7911yescharacteristic
522C2×C4C4×C22⋊D7911yescharacteristic
523C2×C4C22×C4×D7911yescharacteristic
524C2×C4C22×C22⋊D7911yescharacteristic
525C2×C4C2×#1192962411yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—3161no—
532C8—3161no—
533C8—3161no—
534C8—3161no—
535C8—1581no—
536C8—1581no—
537C8—1581no—
538C8—1581no—
539C8#1457919212yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—3161no—
544C22—3161no—
545C22—1582no—
546C22C2×C4×C22⋊D7911yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—3161no—
556C4—3161no—
557C4—3161no—
558C4#131×D7911yescharacteristic
559C4#1909932811yescharacteristic
560C4C2×#1457919211yescharacteristic
561C4#1909936111yescharacteristic
562C2—41no—
563C2—3162no—
564C2#2377212211yescharacteristic
565C2C4×#1457919211yescharacteristic
566C2#2377231511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#2962C2
socleC22×C79C2×C4×D4
prime radicalC2×#11929624C2×C4
cosocleC42×C79C24
hypercenter#2962D79
hypocenterC79#18009
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #23762307C2semidirect
4. #23762295C2semidirect
5. #23762271C2semidirect
6. #23762255C2semidirect
7. #23762250C2semidirect
8. #23762234C2semidirect
9. #23762210C2semidirect
10. C8×#11929611C2semidirect
11. #23762183C2semidirect
12. #23761873C2semidirect
14. #23761697C2semidirect
15. C79×#2962C2semidirect
286. #2962D79semidirect
299. C79#18009semidirect

Maximal subgroups

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

subgroupindex
#237734652
#237724152
#237623072
#237622952
#237622712
#237622552
#237622502
#237622342
#237622102
C8×#119296112
#237621832
#237618732
#237617852
#237616972
C79×#29622
#1800979