Finite Group Databasebeta

← #33056006

Subgroups — #33056006

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#22620009C211yesmaximal, characteristic
2#22618909C211yesmaximal, characteristic
3C8×Q8×D73C211yesmaximal, characteristic, complemented
4#22608783C211yesmaximal, characteristic, complemented
5#22608781C211yesmaximal, characteristic, complemented
6#22608772C211yesmaximal, characteristic, complemented
7#22608749C211yesmaximal, characteristic, complemented
8#22608747C211yesmaximal, characteristic, complemented
9SD16⋊#10596831C211yesmaximal, characteristic, complemented
10#22608740C211yesmaximal, characteristic, complemented
11#22608713C211yesmaximal, characteristic, complemented
12#22608376C211yesmaximal, characteristic, complemented
13#22608341C211yesmaximal, characteristic
14#22608217C211yesmaximal, characteristic, complemented
15C73×#1583C211yesmaximal, characteristic, complemented
16#17989119C2211yescharacteristic
17C4×Q8×D73C2211yescharacteristic
18#17988919C411yescharacteristic
19#17988899C411yescharacteristic
20#17988897C411yescharacteristic
21#17988896C411yescharacteristic
22#17988808C411yescharacteristic
23#17988807C411yescharacteristic
24#17988744C411yescharacteristic
25#17988724C411yescharacteristic
26#17988717C2211yescharacteristic
27Q8×#10596831C2211yescharacteristic
28C8×Dic146—21no—
29C8×Dic146C2211yescharacteristic
30#17988711—21no—
31#17988711C2211yescharacteristic
32#17988711C2211yescharacteristic
33C4×Dic292C2211yescharacteristic
34C4×#11924018C2211yescharacteristic
35C4×#11924016C2211yescharacteristic
36#17988656—21no—
37D4×#10596831C2211yescharacteristic
38#17988650—21no—
39#17988645—21no—
40#17988643C2211yescharacteristic
41#17988638C2211yescharacteristic
42C4⋊C8×D73—21no—
43C4⋊C8×D73C2211yescharacteristic
44#17988545—21no—
45C4×#11924011C2211yescharacteristic
46C4×C8×D73—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
60C8×Q8×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62#436×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×Q8×D73C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924011—21no—
72C22×#10596831—21no—
73C2×C8×D73—21no—
74C2×C8×D73D411yescharacteristic
75C2×C8×D73D411yescharacteristic
76#14556584—21no—
77#14556582C2×C411yescharacteristic
78#14556578C2×C411yescharacteristic
79#14556573—21no—
80#14556571C2×C411yescharacteristic
81#14556562C2×C411yescharacteristic
82Q8×Dic73C2×C411yescharacteristic
83C4×Dic146—21no—
84C4×Dic146C2311yescharacteristic
85C4×Dic146C2311yescharacteristic
86#14556556—21no—
87#14556556C2×C411yescharacteristic
88C4×C22⋊D73—21no—
89#14556550—21no—
90C4⋊C4×D73—21no—
91C4⋊C4×D73C2×C411yescharacteristic
92C42×D73—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—
119#14556501—21no—
120C4×#10596831—21no—
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C8×Dic73D411yescharacteristic
128C8×Dic73D411yescharacteristic
129C2×SD16×C73C2×C411yescharacteristic
130C2×M16×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—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×Dic146C22×C411yescharacteristic
147Q8×D73—22no—
148Q8×D73—22no—
149C2×C22⋊D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×C4×D73C22×C411yescharacteristic
153C2×C4×D73C2×D411yescharacteristic
154C2×C4×D73#4111yescharacteristic
155Dic292—22no—
156#11924018—22no—
157#11924016—22no—
158#11924011—42no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—42no—
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C8×D73—22no—
168C8×D73—41no—
169C8×D73—42no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73C22×C411yescharacteristic
174C4⋊Dic73C22×C411yescharacteristic
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180C22⋊Dic73—21no—
181C22⋊Dic73—21no—
182C22⋊Dic73—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—
195M16×C73—42no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
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#13112yes—
213D4×C73—21no—
214D4×C73—21no—
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—42no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73C4×D411yescharacteristic
229C2×Dic73C4×D411yescharacteristic
230C2×Dic73C4×D411yescharacteristic
231C4×D73—24no—
232C4×D73—22no—
233C4×D73—21no—
234C4×D73—21no—
235C4×D73—21no—
236C4×D73—21no—
237C4×D73—42no—
238Dic146—24no—
239Dic146—21no—
240Dic146—21no—
241Dic146—21no—
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—41no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73C2×C4×D411yescharacteristic
261C2×D73—21no—
262C2×D73—21no—
263C2×D73#44412yes—
264C4×C73—22no—
265C4×C73—21no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73C2×#13111yescharacteristic
269C4×C73C2×#13111yescharacteristic
270C4×C73C2×#13711yescharacteristic
271C4×C73#57511yescharacteristic
272Dic73—21no—
273Dic73—22no—
274Dic73—21no—
275Dic73—21no—
276Dic73—41no—
277Dic73—41no—
278Dic73—41no—
279#17915—731nomaximal, Sylow
280C2×C73—81no—
281C2×C73#292911yescharacteristic
282C2×C73C4×#13711yescharacteristic
283C2×C73C2×#44411yescharacteristic
284D73—22no—
285#3108—731no—
286#2966—731no—
287C2×C8×Q8—731no—
288#1584—731no—
289#1584—731no—
290#1583—731no—
291#1583D7311yescharacteristic, complemented
292#1579—731no—
293#1579—731no—
294SD16⋊C8—731no—
295SD16⋊C8—731no—
296#1573—731no—
297#1491—731no—
298#1483—731no—
299#1451—731no—
300C73#1791511yescharacteristic, complemented, Sylow
301#529—731no—
302C2×C4×Q8—731no—
303#483—731no—
304#480—731no—
305#479—731no—
306#479—731no—
307#464—731no—
308#464—731no—
309#451—731no—
310#448—731no—
311#446—731no—
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—1461no—
317C8×Q8—1461no—
318C8×Q8C2×D7311yescharacteristic
319C4×Q16—731no—
320C4×Q16—731no—
321C4×SD16—731no—
322C4×SD16C2×D7311yescharacteristic
323#436C2×D7311yescharacteristic
324#435—1461no—
325C8×D4—731no—
326C8×D4—1461no—
327#433—1461no—
328#432—731no—
329#431—731no—
330C2×C4⋊C8—731no—
331C2×C4⋊C8—1461no—
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
352C22×Q8—731no—
353C2×Q16—731no—
354C2×Q16—731no—
355C2×SD16—731no—
356C2×SD16C4×D7311yescharacteristic
357C2×M16—21no—
358C2×M16—1461no—
359C22×C8—731no—
360C22×C8—731no—
361C22×C8—1461no—
362C22×C8—1461no—
363#126—1461no—
364#125—731no—
365#124—731no—
366#123—1461no—
367C22⋊Q8—731no—
368#121—731no—
369C4×Q8—731no—
370C4×Q8—731no—
371C4×Q8—731no—
372C4×Q8—731no—
373C4×Q8—1461no—
374C4×Q8—1461no—
375C4×Q8C22×D7311yescharacteristic
376C4×D4—1461no—
377C4×D4C22×D7311yescharacteristic
378#117—1461no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—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—1461no—
414#97—1461no—
415#97—1461no—
416C4×C8—21no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8—1461no—
426C4×C8C22×D7311yescharacteristic
427C4×C8C22×D7311yescharacteristic
428C4×C8C22×D7311yescharacteristic
429C2×Q8—731no—
430C2×Q8—731no—
431C2×Q8—1461no—
432C2×Q8—1462no—
433C2×Q8—1462no—
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—42no—
448M16—2922no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—2921no—
453C2×C8—2922no—
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—732no—
498Q8—1464no—
499Q8—1461no—
500Q8—1461no—
501Q8—1461no—
502Q8#1455659912yes—
503D4—21no—
504D4—21no—
505D4—2922no—
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—1464no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
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—41no—
543C22—41no—
544C22—41no—
545C22—732no—
546C22—1461no—
547C22—1461no—
548C22C4×D4×D7311yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—2921no—
554C4—2921no—
555C4—2921no—
556C4—1461no—
557C4—1461no—
558C4—1461no—
559C4—1462no—
560C4#131×D7311yescharacteristic
561C4C2×#1455659911yescharacteristic
562C4C2×#1455662011yescharacteristic
563C4#1798938411yescharacteristic
564C2—81no—
565C2—1462no—
566C2#2261862211yescharacteristic
567C2C4×#1455662011yescharacteristic
568C2#444×D7311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1583C2
socleC22×C73C2×C4×D4
prime radical#14556562C2×C4
cosocleC42×C73C24
hypercenter#1583D73
hypocenterC73#17915
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
3. C8×Q8×D73C2semidirect
4. #22608783C2semidirect
5. #22608781C2semidirect
6. #22608772C2semidirect
7. #22608749C2semidirect
8. #22608747C2semidirect
9. SD16⋊#10596831C2semidirect
10. #22608740C2semidirect
11. #22608713C2semidirect
12. #22608376C2semidirect
14. #22608217C2semidirect
15. C73×#1583C2semidirect
291. #1583D73semidirect
300. C73#17915semidirect

Maximal subgroups

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

subgroupindex
#226200092
#226189092
C8×Q8×D732
#226087832
#226087812
#226087722
#226087492
#226087472
SD16⋊#105968312
#226087402
#226087132
#226083762
#226083412
#226082172
C73×#15832
#1791573