Finite Group Databasebeta

← #33056821

Subgroups — #33056821

Order 18688.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620533C211yesmaximal, characteristic
2#22619081C211yesmaximal, characteristic
3#22619027C211yesmaximal, characteristic, complemented
4#22608810C211yesmaximal, characteristic, complemented
5#22608801C211yesmaximal, characteristic, complemented
6#22608800C211yesmaximal, characteristic, complemented
7#22608788C211yesmaximal, characteristic, complemented
8#22608783C211yesmaximal, characteristic, complemented
9#22608778C211yesmaximal, characteristic, complemented
10#22608777C211yesmaximal, characteristic, complemented
11#22608695C211yesmaximal, characteristic, complemented
12#22608388C211yesmaximal, characteristic
13#22608384C211yesmaximal, characteristic, complemented
14#22608219C211yesmaximal, characteristic, complemented
15C73×#1582C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17#17989119C2211yescharacteristic
18#17988994C411yescharacteristic
19#17988978C411yescharacteristic
20#17988954C411yescharacteristic
21#17988945C411yescharacteristic
22#17988846C411yescharacteristic
23#17988844C411yescharacteristic
24#17988832C411yescharacteristic
25#17988830C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988715—21no—
28#17988714—21no—
29#17988714C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31C8×Dic146C2211yescharacteristic
32#17988711C2211yescharacteristic
33C4×Dic292C2211yescharacteristic
34C4×#11924018C2211yescharacteristic
35C4×#11924016C2211yescharacteristic
36#17988665C2211yescharacteristic
37#17988662—21no—
38#17988658—21no—
39#17988649—21no—
40#17988647—21no—
41#17988645—21no—
42#17988643C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988613—21no—
45#17988609C2211yescharacteristic
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988319C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988317C2211yescharacteristic
56D4⋊#10596831C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988309C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×Dic292C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924012—21no—
71C2×#11924011—21no—
72C2×#11924011C2×C411yescharacteristic
73C2×#11924011C2×C411yescharacteristic
74C2×C8×D73—21no—
75#14556590C2×C411yescharacteristic
76#14556589C2×C411yescharacteristic
77#14556584—21no—
78#14556582C2×C411yescharacteristic
79#14556581—21no—
80#14556578C2×C411yescharacteristic
81#14556573—21no—
82#14556571C2×C411yescharacteristic
83#14556571C2×C411yescharacteristic
84#14556569—21no—
85#14556567C2×C411yescharacteristic
86#14556562C2×C411yescharacteristic
87C4×Dic146—21no—
88C4×Dic146C2311yescharacteristic
89C4×Dic146C2311yescharacteristic
90C4×C22⋊D73—21no—
91#14556550—21no—
92#14556548—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#14556520D411yescharacteristic
106#14556520D411yescharacteristic
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#14556503D411yescharacteristic
116#14556503D411yescharacteristic
117#14556501—21no—
118#14556501—21no—
119#14556501—21no—
120#14556501C2×C411yescharacteristic
121#14556501C2×C411yescharacteristic
122C4×#10596831—21no—
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
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×Dic146—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×Dic146C22×C411yescharacteristic
147C2×C22⋊D73—21no—
148C2×C4×D73C22×C411yescharacteristic
149C2×C4×D73C2×D411yescharacteristic
150C2×C4×D73#4111yescharacteristic
151Dic292—41no—
152#11924018—41no—
153#11924016—41no—
154#11924012—81no—
155#11924011—41no—
156#11924011—41no—
157#11924011—81no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C2×D411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C8×D73—42no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73C22×C411yescharacteristic
170C4⋊Dic73C22×C411yescharacteristic
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
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—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73C22×C411yescharacteristic
187C4×Dic73C2×D411yescharacteristic
188C4×Dic73#4111yescharacteristic
189C2×Q8×C73C22×C411yescharacteristic
190C2×D4×C73C22×C411yescharacteristic
191C22×C4×C73—21no—
192SD16×C73—41no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—81no—
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C4⋊C4×C73—21no—
202C4⋊C4×C73C22×C411yescharacteristic
203C4⋊C4×C73C22×C411yescharacteristic
204C22⋊C4×C73—21no—
205C42×C73—21no—
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208C22×D73C4×D411yescharacteristic
209Q8×C73—21no—
210Q8×C73—21no—
211D4×C73—21no—
212D4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73C23×C411yescharacteristic
219C2×C4×C73C22×D411yescharacteristic
220C2×C4×C73C2×#4111yescharacteristic
221C22⋊D73—81no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73C4×D411yescharacteristic
227C2×Dic73C4×D411yescharacteristic
228C2×Dic73C4×D411yescharacteristic
229C4×D73—21no—
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—41no—
234Dic146—21no—
235Dic146—21no—
236Dic146—21no—
237Dic146—21no—
238Dic146—81no—
239C8×C73—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—41no—
244C8×C73—41no—
245C8×C73—41no—
246#10596831—22no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—41no—
252#10596831—41no—
253C22×C73—41no—
254C22×C73—41no—
255C22×C73—41no—
256C22×C73C2×C4×D411yescharacteristic
257C2×D73—21no—
258C2×D73—21no—
259C2×D73—21no—
260C4×C73—21no—
261C4×C73—41no—
262C4×C73—41no—
263C4×C73—41no—
264C4×C73#56811yescharacteristic
265C4×C73#56811yescharacteristic
266C4×C73#57711yescharacteristic
267C4×C73#57811yescharacteristic
268Dic73—21no—
269Dic73—21no—
270Dic73—21no—
271Dic73—41no—
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275#17988—731nomaximal, Sylow
276C2×C73—81no—
277C2×C73#293211yescharacteristic
278C2×C73#294711yescharacteristic
279C2×C73#295611yescharacteristic
280D73—41no—
281#3172—731no—
282#2993—731no—
283#2985—731no—
284#1588—731no—
285#1587—731no—
286#1587—731no—
287#1585—731no—
288#1584—731no—
289#1584—731no—
290#1583—731no—
291#1582D7311yescharacteristic, complemented
292#1569—731no—
293#1494—731no—
294#1493—731no—
295#1451—731no—
296C73#1798811yescharacteristic, complemented, Sylow
297#533—731no—
298#529—731no—
299#501—731no—
300#497—731no—
301#491—731no—
302#489—731no—
303#470—731no—
304#470—731no—
305#468—731no—
306#468—731no—
307#446—731no—
308#446—731no—
309#446—1461no—
310#446—1461no—
311#446C2×D7311yescharacteristic
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8—731no—
315C4×Q16—731no—
316C4×Q16—731no—
317C4×SD16—731no—
318C4×SD16C2×D7311yescharacteristic
319#436—731no—
320#436—1461no—
321#435—1461no—
322C8×D4C2×D7311yescharacteristic
323#433—1461no—
324#433—1461no—
325#433—1461no—
326#432—731no—
327#431—731no—
328#424—1461no—
329#423—731no—
330C4×M16—731no—
331C2×C4×C8—731no—
332#335—731no—
333#335—731no—
334#334—731no—
335#334C2×D7311yescharacteristic
336Q8⋊C8—731no—
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8C2×D7311yescharacteristic
342D4⋊C8—731no—
343D4⋊C8C2×D7311yescharacteristic
344#322—731no—
345#322—731no—
346#322—731no—
347#322C2×D7311yescharacteristic
348C2×Q16—731no—
349C2×Q16—731no—
350C2×SD16—731no—
351C2×SD16C4×D7311yescharacteristic
352C2×M16—731no—
353C2×M16—731no—
354C2×M16—1461no—
355C2×M16—1461no—
356C22×C8—21no—
357C22×C8—1461no—
358C4⋊Q8—731no—
359C4⋊Q8—731no—
360#126—1461no—
361#125—731no—
362#125—1461no—
363#124—731no—
364#123—1461no—
365C22⋊Q8—731no—
366C22⋊Q8—731no—
367C22⋊Q8—731no—
368C22⋊Q8—1461no—
369#121—731no—
370C4×Q8—731no—
371C4×Q8—731no—
372C4×Q8—1461no—
373C4×Q8C22×D7311yescharacteristic
374C4×D4—1461no—
375C4×D4C22×D7311yescharacteristic
376#117—1461no—
377#117—1461no—
378C2×C42—731no—
379#107—731no—
380#107—731no—
381#106—731no—
382#106C4×D7311yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—1461no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8C22×D7311yescharacteristic
395C4⋊C8C22×D7311yescharacteristic
396#103—731no—
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103C4×D7311yescharacteristic
402#102—731no—
403#102C4×D7311yescharacteristic
404C22⋊C8—21no—
405C22⋊C8—731no—
406C22⋊C8—731no—
407C22⋊C8—1461no—
408C22⋊C8—1461no—
409#97—21no—
410#97—731no—
411#97—731no—
412#97—1461no—
413#97—1461no—
414#97—1461no—
415C4×C8—731no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—1461no—
419C4×C8—1461no—
420C4×C8—1461no—
421C4×C8—1461no—
422C4×C8C22×D7311yescharacteristic
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C2×Q8—731no—
426C2×Q8—731no—
427C2×Q8—1461no—
428C2×Q8C2×C4×D7311yescharacteristic
429C2×D4—1461no—
430C2×D4C2×C4×D7311yescharacteristic
431C22×C4—21no—
432C22×C4—731no—
433C22×C4—731no—
434C22×C4—731no—
435Q16—2921no—
436Q16—2921no—
437SD16—41no—
438SD16—2921no—
439M16—2921no—
440M16—2921no—
441M16—5841no—
442M16—5841no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—2922no—
448C2×C8—731no—
449C2×C8—731no—
450C2×C8—731no—
451C2×C8—731no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8C2×C4×D7311yescharacteristic
456C2×C8C2×C4×D7311yescharacteristic
457C2×C8D4×D7311yescharacteristic
458C2×C8D4×D7311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—731no—
461C4⋊C4—731no—
462C4⋊C4—1461no—
463C4⋊C4—1461no—
464C4⋊C4—1461no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4C2×C4×D7311yescharacteristic
473C4⋊C4C2×C4×D7311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—21no—
482C42—731no—
483C42—731no—
484C42—731no—
485C42—1461no—
486C42—1461no—
487C42C23×D7311yescharacteristic
488C23—21no—
489C23—731no—
490Q8—21no—
491Q8—21no—
492Q8—5841no—
493Q8—1461no—
494Q8—1461no—
495Q8—1461no—
496Q8—1461no—
497D4—21no—
498D4—21no—
499D4—5841no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—2921no—
506C2×C4—731no—
507C2×C4—731no—
508C2×C4—731no—
509C2×C4—1461no—
510C2×C4—1461no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4C22×C4×D7311yescharacteristic
518C2×C4C2×D4×D7311yescharacteristic
519C2×C4#41×D7311yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—2921no—
528C8—2921no—
529C8—1462no—
530C8—1461no—
531C8—1461no—
532C8—1461no—
533C8—1461no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—1461no—
538C22—1461no—
539C22—1461no—
540C22C4×D4×D7311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—2921no—
546C4—2921no—
547C4—2921no—
548C4—2921no—
549C4—1461no—
550C4—1461no—
551C4—1461no—
552C4#1798935211yescharacteristic
553C4#1798935311yescharacteristic
554C4#1798939311yescharacteristic
555C4#1798940111yescharacteristic
556C2—81no—
557C2—2921no—
558C2#2261864511yescharacteristic
559C2#2261876711yescharacteristic
560C2#2261883911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1582C2
socleC22×C73C2×C4×D4
prime radical#14556562C2×C4
cosocleC42×C73C24
hypercenter#1582D73
hypocenterC73#17988
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. #22619027C2semidirect
4. #22608810C2semidirect
5. #22608801C2semidirect
6. #22608800C2semidirect
7. #22608788C2semidirect
8. #22608783C2semidirect
9. #22608778C2semidirect
10. #22608777C2semidirect
11. #22608695C2semidirect
13. #22608384C2semidirect
14. #22608219C2semidirect
15. C73×#1582C2semidirect
291. #1582D73semidirect
296. C73#17988semidirect

Maximal subgroups

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

subgroupindex
#226205332
#226190812
#226190272
#226088102
#226088012
#226088002
#226087882
#226087832
#226087782
#226087772
#226086952
#226083882
#226083842
#226082192
C73×#15822
#1798873