Finite Group Databasebeta

← #33056017

Subgroups — #33056017

Order 18688.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619998C211yesmaximal, characteristic
2C8×#11924027C211yesmaximal, characteristic
3#22618862C211yesmaximal, characteristic, complemented
4#22608783C211yesmaximal, characteristic, complemented
5#22608779C211yesmaximal, characteristic, complemented
6#22608767C211yesmaximal, characteristic, complemented
7#22608749C211yesmaximal, characteristic, complemented
8#22608747C211yesmaximal, characteristic, complemented
9SD16⋊#10596831C211yesmaximal, characteristic, complemented
10#22608740C211yesmaximal, characteristic, complemented
11#22608718C211yesmaximal, characteristic, complemented
12#22608367C211yesmaximal, characteristic
13#22608350C211yesmaximal, characteristic, complemented
14#22608217C211yesmaximal, characteristic, complemented
15C73×#1582C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×#11924027C2211yescharacteristic
18#17988931C411yescharacteristic
19#17988927C411yescharacteristic
20#17988871C411yescharacteristic
21#17988865C411yescharacteristic
22#17988796C411yescharacteristic
23#17988790C411yescharacteristic
24#17988750C411yescharacteristic
25#17988746C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988715—21no—
28Q8×#10596831C2211yescharacteristic
29C8×Dic146C2211yescharacteristic
30#17988711—21no—
31#17988711C2211yescharacteristic
32#17988711C2211yescharacteristic
33C4×Dic292C2211yescharacteristic
34C4×#11924018C2211yescharacteristic
35C4×#11924016C2211yescharacteristic
36D4×#10596831C2211yescharacteristic
37C8×C22⋊D73—21no—
38#17988650—21no—
39#17988639C2211yescharacteristic
40#17988638C2211yescharacteristic
41#17988637—21no—
42#17988612—21no—
43#17988609C2211yescharacteristic
44#17988544—21no—
45C4×#11924011C2211yescharacteristic
46C2×C8×Dic73—21no—
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988319C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988317C2211yescharacteristic
56D4⋊#10596831C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59#17988308C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924027C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924011—21no—
72C2×#11924011—21no—
73C22×#10596831—21no—
74C2×C8×D73D411yescharacteristic
75C2×C8×D73D411yescharacteristic
76#14556590C2×C411yescharacteristic
77#14556589C2×C411yescharacteristic
78#14556581—21no—
79#14556571C2×C411yescharacteristic
80#14556569—21no—
81#14556567C2×C411yescharacteristic
82C4×Dic146—21no—
83C4×Dic146C2311yescharacteristic
84C4×Dic146C2311yescharacteristic
85#14556556C2×C411yescharacteristic
86D4×Dic73C2×C411yescharacteristic
87C4×C22⋊D73—21no—
88#14556551—21no—
89#14556549C2×C411yescharacteristic
90#14556548—21no—
91#14556547—21no—
92C2×C4×Dic73—21no—
93C42×D73C2311yescharacteristic
94#14556525C2×C411yescharacteristic
95#14556524C2×C411yescharacteristic
96#14556522C2×C411yescharacteristic
97C4⋊#10596831—21no—
98C4⋊#10596831C2311yescharacteristic
99C4⋊#10596831C2311yescharacteristic
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520C2×C411yescharacteristic
106#14556520C2×C411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556514C2×C411yescharacteristic
112#14556512C2×C411yescharacteristic
113C22⋊#10596831—21no—
114#14556503—21no—
115#14556503C2×C411yescharacteristic
116#14556503C2×C411yescharacteristic
117#14556501—21no—
118#14556501—21no—
119C4×#10596831—21no—
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C8×Dic73—21no—
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C8×Dic73D411yescharacteristic
128C8×Dic73D411yescharacteristic
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
144#11924027—22no—
145#11924027—22no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148C2×Dic146C22×C411yescharacteristic
149C2×C22⋊D73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C2×C4×D73C22×C411yescharacteristic
153C2×C4×D73C2×D411yescharacteristic
154C2×C4×D73#4111yescharacteristic
155Dic292—22no—
156#11924018—22no—
157#11924016—22no—
158#11924011—42no—
159#11924011—42no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—42no—
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C8×D73—22no—
169C8×D73—41no—
170C4⋊Dic73—21no—
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180C22⋊Dic73—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—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—22no—
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×D73C4×D411yescharacteristic
211Q8×C73—21no—
212Q8×C73—21no—
213D4×C73—21no—
214D4×C73#13112yes—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73C23×C411yescharacteristic
221C2×C4×C73C22×D411yescharacteristic
222C2×C4×C73C2×#4111yescharacteristic
223C22⋊D73—24no—
224C2×Dic73—24no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—42no—
230C2×Dic73C4×D411yescharacteristic
231C2×Dic73C4×D411yescharacteristic
232C2×Dic73C4×D411yescharacteristic
233C4×D73—21no—
234C4×D73—21no—
235C4×D73—21no—
236C4×D73—21no—
237C4×D73—22no—
238Dic146—21no—
239Dic146—21no—
240Dic146—21no—
241Dic146—42no—
242Dic146#13112yes—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—41no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73#13712yes—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—21no—
254#10596831—41no—
255#10596831—41no—
256#10596831—41no—
257C22×C73—22no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73C2×C4×D411yescharacteristic
261C2×D73—21no—
262C2×D73—21no—
263C2×D73—21no—
264C4×C73—21no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73C2×#13111yescharacteristic
269C4×C73C2×#13111yescharacteristic
270C4×C73C2×#13711yescharacteristic
271C4×C73#57511yescharacteristic
272Dic73—22no—
273Dic73—21no—
274Dic73—21no—
275Dic73—41no—
276Dic73—41no—
277Dic73—41no—
278Dic73#44412yes—
279#17916—731nomaximal, Sylow
280C2×C73—42no—
281C2×C73#292911yescharacteristic
282C2×C73C4×#13711yescharacteristic
283C2×C73C2×#44411yescharacteristic
284D73—41no—
285#3107—731no—
286C8×#41—731no—
287#2960—731no—
288#1584—731no—
289#1584—731no—
290#1582—731no—
291#1582D7311yescharacteristic, complemented
292#1579—731no—
293#1579—731no—
294SD16⋊C8—731no—
295SD16⋊C8—731no—
296#1574—731no—
297#1489—731no—
298#1485—731no—
299#1451—731no—
300C73#1791611yescharacteristic, complemented, Sylow
301#533—731no—
302C4×#41—731no—
303#485—731no—
304#485—731no—
305#475—731no—
306#474—731no—
307#462—731no—
308#461—731no—
309#452—731no—
310#452—731no—
311#446—731no—
312#446—1461no—
313#446C2×D7311yescharacteristic
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—731no—
317C8×Q8—731no—
318C8×Q8—1461no—
319C4×Q16—731no—
320C4×Q16—731no—
321C4×SD16—731no—
322C4×SD16C2×D7311yescharacteristic
323C8×D4—731no—
324C8×D4—1461no—
325C8×D4—1461no—
326C8×D4C2×D7311yescharacteristic
327#431—731no—
328#431—731no—
329#431—1461no—
330#424—1461no—
331#423—731no—
332#405—1461no—
333C4×M16—731no—
334C2×C4×C8—731no—
335C2×C4×C8—1461no—
336#335—731no—
337#335—731no—
338#334—731no—
339#334C2×D7311yescharacteristic
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343Q8⋊C8—731no—
344Q8⋊C8—731no—
345Q8⋊C8C2×D7311yescharacteristic
346D4⋊C8—731no—
347D4⋊C8C2×D7311yescharacteristic
348#322—731no—
349#322—731no—
350#322—731no—
351#322C2×D7311yescharacteristic
352C2×#41—731no—
353C2×Q16—731no—
354C2×Q16—731no—
355C2×SD16—731no—
356C2×SD16C4×D7311yescharacteristic
357C2×M16—1461no—
358C2×M16—1461no—
359C22×C8—21no—
360C22×C8—731no—
361C22×C8—731no—
362C22×C8—1461no—
363C4⋊Q8—731no—
364C4⋊Q8—731no—
365#125—1461no—
366C22⋊Q8—731no—
367C22⋊Q8—731no—
368C22⋊Q8—1461no—
369C4×Q8—731no—
370C4×Q8—731no—
371C4×Q8—731no—
372C4×Q8—1461no—
373C4×Q8C22×D7311yescharacteristic
374C4×D4—731no—
375C4×D4—1461no—
376C4×D4—1461no—
377C4×D4C22×D7311yescharacteristic
378#117—731no—
379#117—1461no—
380#117—1461no—
381C2×C42—731no—
382C2×C42—1461no—
383#107—731no—
384#107—731no—
385#106—731no—
386#106C4×D7311yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—731no—
391C4⋊C8—731no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8—1461no—
398C4⋊C8C22×D7311yescharacteristic
399C4⋊C8C22×D7311yescharacteristic
400#103—731no—
401#103—731no—
402#103—731no—
403#103—731no—
404#103—731no—
405#103C4×D7311yescharacteristic
406#102—731no—
407#102C4×D7311yescharacteristic
408C22⋊C8—21no—
409C22⋊C8—731no—
410C22⋊C8—731no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—21no—
414#97—1461no—
415#97—1461no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8—1461no—
426C4×C8C22×D7311yescharacteristic
427C4×C8C22×D7311yescharacteristic
428C4×C8C22×D7311yescharacteristic
429#41—1462no—
430#41—1462no—
431C2×Q8—731no—
432C2×Q8—731no—
433C2×Q8—1461no—
434C2×Q8C2×C4×D7311yescharacteristic
435C2×D4—1461no—
436C2×D4C2×C4×D7311yescharacteristic
437C22×C4—21no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—1461no—
442C22×C4—1461no—
443Q16—1462no—
444Q16—1462no—
445SD16—22no—
446SD16—1462no—
447M16—2922no—
448M16—2922no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—2921no—
454C2×C8—2922no—
455C2×C8—731no—
456C2×C8—731no—
457C2×C8—731no—
458C2×C8—731no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1462no—
463C2×C8C2×C4×D7311yescharacteristic
464C2×C8C2×C4×D7311yescharacteristic
465C2×C8D4×D7311yescharacteristic
466C2×C8D4×D7311yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—731no—
469C4⋊C4—731no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4C2×C4×D7311yescharacteristic
479C4⋊C4C2×C4×D7311yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—1461no—
482C22⋊C4—1461no—
483C22⋊C4—1461no—
484C22⋊C4—1461no—
485C42—21no—
486C42—731no—
487C42—731no—
488C42—731no—
489C42—1461no—
490C42—1461no—
491C42—1461no—
492C42—1461no—
493C42C23×D7311yescharacteristic
494C23—21no—
495C23—731no—
496Q8—21no—
497Q8—21no—
498Q8—2922no—
499Q8—732no—
500Q8—1461no—
501Q8—1461no—
502Q8—1461no—
503D4—21no—
504D4—1464no—
505D4#1455659912yes—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—2922no—
512C2×C4—731no—
513C2×C4—731no—
514C2×C4—731no—
515C2×C4—1462no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1464no—
520C2×C4—1461no—
521C2×C4—1461no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4C22×C4×D7311yescharacteristic
526C2×C4C2×D4×D7311yescharacteristic
527C2×C4#41×D7311yescharacteristic
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—2921no—
535C8—2921no—
536C8—2921no—
537C8—1461no—
538C8—1461no—
539C8—1461no—
540C8—1461no—
541C8#1455662012yes—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—1461no—
546C22—1461no—
547C22—1461no—
548C22C4×D4×D7311yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—2921no—
554C4—2921no—
555C4—2921no—
556C4—732no—
557C4—1461no—
558C4—1461no—
559C4—1462no—
560C4#131×D7311yescharacteristic
561C4C2×#1455659911yescharacteristic
562C4C2×#1455662011yescharacteristic
563C4#1798938411yescharacteristic
564C2—42no—
565C2—2921no—
566C2#2261862211yescharacteristic
567C2C4×#1455662011yescharacteristic
568C2#444×D7311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1582C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924027C2×C4
cosocleC42×C73C24
hypercenter#1582D73
hypocenterC73#17916
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
3. #22618862C2semidirect
4. #22608783C2semidirect
5. #22608779C2semidirect
6. #22608767C2semidirect
7. #22608749C2semidirect
8. #22608747C2semidirect
9. SD16⋊#10596831C2semidirect
10. #22608740C2semidirect
11. #22608718C2semidirect
13. #22608350C2semidirect
14. #22608217C2semidirect
15. C73×#1582C2semidirect
291. #1582D73semidirect
300. C73#17916semidirect

Maximal subgroups

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

subgroupindex
#226199982
C8×#119240272
#226188622
#226087832
#226087792
#226087672
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SD16⋊#105968312
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C73×#15822
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