Finite Group Databasebeta

← #33057768

Subgroups — #33057768

Order 18688.

600 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620497C211yesmaximal, characteristic
2#22618937C211yesmaximal, characteristic, complemented
3#22618932C211yesmaximal, characteristic, complemented
4#22608826C211yesmaximal, characteristic, complemented
5#22608813C211yesmaximal, characteristic, complemented
6#22608775C211yesmaximal, characteristic, complemented
7#22608773C211yesmaximal, characteristic, complemented
8#22608769C211yesmaximal, characteristic, complemented
9#22608735C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608676C211yesmaximal, characteristic, complemented
12#22608338C211yesmaximal, characteristic, complemented
13#22608336C211yesmaximal, characteristic, complemented
14#22608210C211yesmaximal, characteristic, complemented
15C73×#1582C211yesmaximal, characteristic, complemented
16#17989124C2211yescharacteristic
17#17989119C2211yescharacteristic
18#17988987C411yescharacteristic
19#17988968C411yescharacteristic
20#17988943C411yescharacteristic
21#17988940C411yescharacteristic
22#17988827C411yescharacteristic
23#17988822C411yescharacteristic
24#17988817C411yescharacteristic
25#17988813C411yescharacteristic
26#17988717C2211yescharacteristic
27Q8×#10596831C2211yescharacteristic
28#17988711C2211yescharacteristic
29C4×#11924018C2211yescharacteristic
30C4×#11924017C2211yescharacteristic
31C4×#11924013C2211yescharacteristic
32#17988665C2211yescharacteristic
33#17988664—21no—
34#17988664C2211yescharacteristic
35#17988662—21no—
36#17988660—21no—
37#17988658—21no—
38C8×D292C2211yescharacteristic
39#17988647—21no—
40#17988645—21no—
41#17988639C2211yescharacteristic
42#17988639C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988544—21no—
45#17988542—21no—
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53#17988317C2211yescharacteristic
54#17988316C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924017C2×C411yescharacteristic
69C2×#11924013C2×C411yescharacteristic
70C2×#11924012—21no—
71C2×#11924011—21no—
72C2×#11924011D411yescharacteristic
73C2×#11924011D411yescharacteristic
74C2×C8×D73—21no—
75C2×C8×D73C2×C411yescharacteristic
76C2×C8×D73C2×C411yescharacteristic
77#14556586—21no—
78#14556584—21no—
79#14556582C2×C411yescharacteristic
80#14556582C2×C411yescharacteristic
81#14556580C2×C411yescharacteristic
82#14556578C2×C411yescharacteristic
83#14556576—21no—
84#14556573—21no—
85#14556571C2×C411yescharacteristic
86#14556567C2×C411yescharacteristic
87#14556566C2×C411yescharacteristic
88#14556562C2×C411yescharacteristic
89C4×Dic146C2311yescharacteristic
90C4×D292—21no—
91C4×D292C2311yescharacteristic
92C4×C22⋊D73—21no—
93#14556550—21no—
94#14556548—21no—
95C42×D73C2311yescharacteristic
96#14556524C2×C411yescharacteristic
97#14556524C2×C411yescharacteristic
98#14556523C2×C411yescharacteristic
99C4⋊#10596831—21no—
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556516C2×C411yescharacteristic
106#14556515C2×C411yescharacteristic
107#14556514C2×C411yescharacteristic
108#14556513C2×C411yescharacteristic
109#14556512C2×C411yescharacteristic
110#14556511C2×C411yescharacteristic
111C22⋊#10596831—21no—
112#14556503—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556501—21no—
118#14556501D411yescharacteristic
119#14556501D411yescharacteristic
120C4×#10596831—21no—
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C8×Dic73C2×C411yescharacteristic
128C8×Dic73C2×C411yescharacteristic
129C2×SD16×C73C2×C411yescharacteristic
130C22×C8×C73—21no—
131C4×Q8×C73C2311yescharacteristic
132C4×D4×C73C2311yescharacteristic
133#106×C73C2×C411yescharacteristic
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140#97×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146C22×C411yescharacteristic
145C2×D292—21no—
146C2×D292C22×C411yescharacteristic
147C2×C22⋊D73—21no—
148C2×C4×D73—21no—
149C2×C4×D73C22×C411yescharacteristic
150C2×C4×D73C2×D411yescharacteristic
151C2×C4×D73#4111yescharacteristic
152#11924018—22no—
153#11924017—41no—
154#11924013—22no—
155#11924012—42no—
156#11924011—22no—
157#11924011—22no—
158#11924011—42no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C8×D73—22no—
167C8×D73—41no—
168C8×D73—42no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178C22⋊Dic73—21no—
179C22⋊Dic73—21no—
180C22⋊Dic73—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187C4×Dic73—21no—
188C4×Dic73C22×C411yescharacteristic
189C4×Dic73C2×D411yescharacteristic
190C4×Dic73#4111yescharacteristic
191C2×Q8×C73C22×C411yescharacteristic
192C2×D4×C73C22×C411yescharacteristic
193C22×C4×C73—21no—
194SD16×C73—41no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—42no—
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C4⋊C4×C73—21no—
204C4⋊C4×C73C22×C411yescharacteristic
205C4⋊C4×C73C22×C411yescharacteristic
206C22⋊C4×C73—21no—
207C42×C73—21no—
208C42×C73C2411yescharacteristic
209C23×C73—21no—
210C22×D73—21no—
211C22×D73C4×D411yescharacteristic
212Q8×C73—21no—
213Q8×C73—21no—
214D4×C73—21no—
215D4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73C23×C411yescharacteristic
222C2×C4×C73C22×D411yescharacteristic
223C2×C4×C73C2×#4111yescharacteristic
224C22⋊D73—81no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73C4×D411yescharacteristic
229C2×Dic73C4×D411yescharacteristic
230C2×Dic73C4×D411yescharacteristic
231D292—21no—
232D292—21no—
233D292—81no—
234C4×D73—21no—
235C4×D73—21no—
236C4×D73—21no—
237C4×D73—21no—
238C4×D73—41no—
239C4×D73—41no—
240C4×D73—41no—
241Dic146—21no—
242Dic146—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—41no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73#13512yes—
250#10596831—21no—
251#10596831—21no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255#10596831#13112yes—
256#10596831#13512yes—
257C22×C73—41no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73C2×C4×D411yescharacteristic
261C2×D73—21no—
262C2×D73—21no—
263C2×D73—21no—
264C2×D73—41no—
265C2×D73—41no—
266C2×D73—41no—
267C4×C73—21no—
268C4×C73—41no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73C2×#13111yescharacteristic
272C4×C73#56811yescharacteristic
273C4×C73C2×#13511yescharacteristic
274C4×C73C2×#13511yescharacteristic
275Dic73—21no—
276Dic73—21no—
277Dic73—21no—
278Dic73—41no—
279Dic73—41no—
280Dic73—41no—
281#18069—731nomaximal, Sylow
282C2×C73—81no—
283C2×C73#293511yescharacteristic
284C2×C73C4×#13511yescharacteristic
285C2×C73#295711yescharacteristic
286D73—41no—
287D73—81no—
288#3168—731no—
289#2969—731no—
290#2969—731no—
291#1591—731no—
292#1589—731no—
293#1583—731no—
294#1583—731no—
295#1582—731no—
296#1582D7311yescharacteristic, complemented
297C8×Q16—731no—
298C8×D8—731no—
299#1564—731no—
300#1482—731no—
301#1482—731no—
302C8×M16—731no—
303C73#1806911yescharacteristic, complemented, Sylow
304#529—731no—
305#529—731no—
306#499—731no—
307#495—731no—
308#488—731no—
309#488—731no—
310#467—731no—
311#466—731no—
312#465—731no—
313#465—731no—
314#446—731no—
315#446C2×D7311yescharacteristic
316C8×Q8—731no—
317C8×Q8—731no—
318C4×Q16—731no—
319C4×SD16—731no—
320C4×SD16C2×D7311yescharacteristic
321C4×D8—731no—
322#436—731no—
323#436—731no—
324#436—1461no—
325#436—1461no—
326#435—1461no—
327#435—1461no—
328C8×D4—731no—
329C8×D4C2×D7311yescharacteristic
330#433—1461no—
331#433—1461no—
332#431—731no—
333#431—731no—
334#431—731no—
335#405—1461no—
336#405—1461no—
337C4×M16—731no—
338C2×C4×C8—731no—
339#335—731no—
340#335—731no—
341#334—731no—
342#334C2×D7311yescharacteristic
343Q8⋊C8—731no—
344Q8⋊C8—731no—
345Q8⋊C8—731no—
346Q8⋊C8C2×D7311yescharacteristic
347D4⋊C8—731no—
348D4⋊C8—731no—
349D4⋊C8—731no—
350D4⋊C8C2×D7311yescharacteristic
351#322—731no—
352#322C2×D7311yescharacteristic
353C82—731no—
354C82—731no—
355C2×Q16—731no—
356C2×SD16—731no—
357C2×SD16C4×D7311yescharacteristic
358C2×D8—731no—
359C2×M16—731no—
360C2×M16—731no—
361C2×M16—1461no—
362C2×M16—1461no—
363C22×C8—21no—
364C22×C8—731no—
365C22×C8—731no—
366C22×C8—1461no—
367#126—1461no—
368#126—1461no—
369#125—731no—
370#125—731no—
371#124—731no—
372#124—731no—
373#123—1461no—
374#123—1461no—
375C22⋊Q8—731no—
376C22⋊Q8—731no—
377#121—731no—
378#121—731no—
379C4×Q8—731no—
380C4×Q8C22×D7311yescharacteristic
381C4×D4—731no—
382C4×D4—1461no—
383C4×D4—1461no—
384C4×D4C22×D7311yescharacteristic
385#117—1461no—
386#117—1461no—
387C2×C42—731no—
388#107—731no—
389#107—731no—
390#106—731no—
391#106C4×D7311yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—731no—
394C4⋊C8—731no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8—1461no—
398C4⋊C8—1461no—
399C4⋊C8C22×D7311yescharacteristic
400C4⋊C8C22×D7311yescharacteristic
401#103—731no—
402#103—731no—
403#103—731no—
404#103C4×D7311yescharacteristic
405#102—731no—
406#102—731no—
407#102—731no—
408#102C4×D7311yescharacteristic
409C22⋊C8—21no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413C22⋊C8—1461no—
414C22⋊C8—1461no—
415C22⋊C8—1461no—
416#97—21no—
417#97—731no—
418#97—731no—
419#97—1461no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—731no—
423C4×C8—731no—
424C4×C8—731no—
425C4×C8—1461no—
426C4×C8—1461no—
427C4×C8—1461no—
428C4×C8—1461no—
429C4×C8C22×D7311yescharacteristic
430C4×C8C22×D7311yescharacteristic
431C4×C8C22×D7311yescharacteristic
432C2×Q8—731no—
433C2×Q8C2×C4×D7311yescharacteristic
434C2×D4—731no—
435C2×D4—1461no—
436C2×D4—1461no—
437C2×D4C2×C4×D7311yescharacteristic
438C22×C4—21no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—1461no—
443Q16—1462no—
444SD16—41no—
445SD16—2921no—
446D8—1462no—
447M16—2922no—
448M16—2922no—
449M16—1462no—
450M16—1462no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—42no—
455C2×C8—2921no—
456C2×C8—2922no—
457C2×C8—731no—
458C2×C8—731no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—1462no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8C2×C4×D7311yescharacteristic
466C2×C8C2×C4×D7311yescharacteristic
467C2×C8D4×D7311yescharacteristic
468C2×C8D4×D7311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—731no—
471C4⋊C4—731no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4C2×C4×D7311yescharacteristic
480C4⋊C4C2×C4×D7311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—1461no—
483C22⋊C4—1461no—
484C22⋊C4—1461no—
485C22⋊C4—1461no—
486C22⋊C4—1461no—
487C22⋊C4—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C42—21no—
492C42—731no—
493C42—731no—
494C42—731no—
495C42—1461no—
496C42C23×D7311yescharacteristic
497C23—21no—
498C23—731no—
499C23—1461no—
500Q8—21no—
501Q8—21no—
502Q8—1461no—
503Q8—1461no—
504D4—21no—
505D4—21no—
506D4—5841no—
507D4—5841no—
508D4—1461no—
509D4—1461no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—2921no—
516C2×C4—2921no—
517C2×C4—2921no—
518C2×C4—731no—
519C2×C4—731no—
520C2×C4—731no—
521C2×C4—1461no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4C22×C4×D7311yescharacteristic
529C2×C4C2×D4×D7311yescharacteristic
530C2×C4#41×D7311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—2921no—
538C8—2921no—
539C8—2921no—
540C8—732no—
541C8—732no—
542C8—1461no—
543C8—1461no—
544C8#1455661212yes—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—2921no—
549C22—2921no—
550C22—2921no—
551C22—1461no—
552C22—1461no—
553C22—1461no—
554C22C4×D4×D7311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—2921no—
560C4—2921no—
561C4—2921no—
562C4—1461no—
563C4—1461no—
564C4—1461no—
565C4#131×D7311yescharacteristic
566C4#1798935311yescharacteristic
567C4#135×D7311yescharacteristic
568C4C2×#1455661211yescharacteristic
569C2—81no—
570C2—2921no—
571C2—5841no—
572C2#2261867211yescharacteristic
573C2C4×#1455661211yescharacteristic
574C2#2261884511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1582C2
socleC22×C73C2×C4×D4
prime radical#17988822C4
cosocleC42×C73C24
hypercenter#1582D73
hypocenterC73#18069
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #22618937C2semidirect
3. #22618932C2semidirect
4. #22608826C2semidirect
5. #22608813C2semidirect
6. #22608775C2semidirect
7. #22608773C2semidirect
8. #22608769C2semidirect
9. #22608735C2semidirect
10. C8×#11924013C2semidirect
11. #22608676C2semidirect
12. #22608338C2semidirect
13. #22608336C2semidirect
14. #22608210C2semidirect
15. C73×#1582C2semidirect
296. #1582D73semidirect
303. C73#18069semidirect

Maximal subgroups

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

subgroupindex
#226204972
#226189372
#226189322
#226088262
#226088132
#226087752
#226087732
#226087692
#226087352
C8×#119240132
#226086762
#226083382
#226083362
#226082102
C73×#15822
#1806973