Finite Group Databasebeta

← #33056815

Subgroups — #33056815

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#22620535C211yesmaximal, characteristic
2#22619083C211yesmaximal, characteristic
3#22619022C211yesmaximal, characteristic, complemented
4#22608811C211yesmaximal, characteristic, complemented
5#22608799C211yesmaximal, characteristic, complemented
6#22608791C211yesmaximal, characteristic, complemented
7#22608782C211yesmaximal, characteristic, complemented
8#22608779C211yesmaximal, characteristic, complemented
9#22608774C211yesmaximal, characteristic, complemented
10#22608766C211yesmaximal, characteristic, complemented
11#22608695C211yesmaximal, characteristic, complemented
12#22608390C211yesmaximal, characteristic
13#22608384C211yesmaximal, characteristic, complemented
14#22608217C211yesmaximal, characteristic, complemented
15C73×#1587C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17#17989124C2211yescharacteristic
18#17988995C411yescharacteristic
19#17988980C411yescharacteristic
20#17988954C411yescharacteristic
21#17988948C411yescharacteristic
22#17988844C411yescharacteristic
23#17988842C411yescharacteristic
24#17988836C411yescharacteristic
25#17988834C411yescharacteristic
26#17988718C2211yescharacteristic
27#17988717—21no—
28#17988716—21no—
29#17988714C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31C8×Dic146C2211yescharacteristic
32C4×#11924018C2211yescharacteristic
33C4×#11924017C2211yescharacteristic
34C4×#11924015C2211yescharacteristic
35#17988666C2211yescharacteristic
36#17988664—21no—
37#17988660—21no—
38#17988652C2211yescharacteristic
39#17988649—21no—
40#17988647—21no—
41#17988646—21no—
42#17988643C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988612—21no—
45#17988609C2211yescharacteristic
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52Q8⋊#10596831C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59#17988308C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924017C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924011—21no—
71C2×#11924011—21no—
72C2×#11924011C2×C411yescharacteristic
73C2×#11924011C2×C411yescharacteristic
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76#14556590C2×C411yescharacteristic
77#14556589C2×C411yescharacteristic
78#14556586—21no—
79#14556582C2×C411yescharacteristic
80#14556581—21no—
81#14556580C2×C411yescharacteristic
82#14556576—21no—
83#14556571C2×C411yescharacteristic
84#14556569—21no—
85#14556567C2×C411yescharacteristic
86#14556567C2×C411yescharacteristic
87#14556566C2×C411yescharacteristic
88C4×Dic146—21no—
89C4×Dic146C2311yescharacteristic
90C4×D292—21no—
91C4×D292C2311yescharacteristic
92#14556548—21no—
93#14556548—21no—
94C42×D73C2311yescharacteristic
95#14556524C2×C411yescharacteristic
96#14556523C2×C411yescharacteristic
97#14556522C2×C411yescharacteristic
98C4⋊#10596831—21no—
99C4⋊#10596831—21no—
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520D411yescharacteristic
106#14556520D411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556515C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503D411yescharacteristic
117#14556503D411yescharacteristic
118#14556502—21no—
119#14556501—21no—
120#14556501—21no—
121#14556501C2×C411yescharacteristic
122#14556501C2×C411yescharacteristic
123C4×#10596831—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×Q16×C73C2×C411yescharacteristic
130C4×Q8×C73C2311yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132#107×C73C2×C411yescharacteristic
133C4⋊C8×C73—21no—
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#103×C73C2×C411yescharacteristic
139#97×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×D292—21no—
147C2×D292C22×C411yescharacteristic
148C2×C4×D73—21no—
149C2×C4×D73C22×C411yescharacteristic
150C2×C4×D73C2×D411yescharacteristic
151C2×C4×D73#4111yescharacteristic
152#11924018—41no—
153#11924017—41no—
154#11924015—41no—
155#11924011—41no—
156#11924011—41no—
157#11924011—81no—
158#11924011—81no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C8×D73—42no—
167C8×D73—81no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73C22×C411yescharacteristic
171C4⋊Dic73C22×C411yescharacteristic
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924005—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186C4×Dic73—21no—
187C4×Dic73C22×C411yescharacteristic
188C4×Dic73C2×D411yescharacteristic
189C4×Dic73#4111yescharacteristic
190C2×Q8×C73C22×C411yescharacteristic
191C2×Q8×C73C22×C411yescharacteristic
192Q16×C73—41no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73C22×C411yescharacteristic
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73C22×C411yescharacteristic
203C4⋊C4×C73C22×C411yescharacteristic
204C42×C73—21no—
205C42×C73—21no—
206C42×C73C2411yescharacteristic
207C22×D73—21no—
208C22×D73C4×D411yescharacteristic
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73C23×C411yescharacteristic
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C2×Dic73—21no—
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73C4×D411yescharacteristic
224C2×Dic73C4×D411yescharacteristic
225C2×Dic73C4×D411yescharacteristic
226D292—21no—
227D292—21no—
228D292—81no—
229C4×D73—21no—
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—41no—
234C4×D73—41no—
235C4×D73—41no—
236Dic146—21no—
237Dic146—21no—
238Dic146—81no—
239C8×C73—22no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—41no—
245C8×C73—41no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—41no—
251#10596831—41no—
252#10596831—41no—
253C22×C73C2×C4×D411yescharacteristic
254C2×D73—21no—
255C2×D73—21no—
256C2×D73—21no—
257C2×D73—41no—
258C2×D73—41no—
259C2×D73—41no—
260C4×C73—21no—
261C4×C73—41no—
262C4×C73—41no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73#56811yescharacteristic
266C4×C73#56811yescharacteristic
267C4×C73#57711yescharacteristic
268C4×C73#57811yescharacteristic
269Dic73—21no—
270Dic73—21no—
271Dic73—21no—
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275#17988—731nomaximal, Sylow
276C2×C73#293211yescharacteristic
277C2×C73#294711yescharacteristic
278C2×C73#295611yescharacteristic
279D73—41no—
280D73—81no—
281#3172—731no—
282#2993—731no—
283#2985—731no—
284#1588—731no—
285#1587—731no—
286#1587D7311yescharacteristic, complemented
287#1585—731no—
288#1584—731no—
289#1584—731no—
290#1583—731no—
291#1582—731no—
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×Q8C2×D7311yescharacteristic
315C4×Q16—731no—
316C4×Q16C2×D7311yescharacteristic
317C4×SD16—731no—
318C4×SD16—731no—
319#436—731no—
320#436—1461no—
321#435—1461no—
322C8×D4—731no—
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⋊C8C2×D7311yescharacteristic
341Q8⋊C8C2×D7311yescharacteristic
342D4⋊C8—731no—
343D4⋊C8—731no—
344#322—731no—
345#322—731no—
346#322—731no—
347#322C2×D7311yescharacteristic
348C2×Q16—731no—
349C2×Q16C4×D7311yescharacteristic
350C2×SD16—731no—
351C2×SD16—731no—
352C2×M16—731no—
353C2×M16—731no—
354C2×M16—1461no—
355C2×M16—1461no—
356C22×C8—1461no—
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—1461no—
372C4×Q8C22×D7311yescharacteristic
373C4×Q8C22×D7311yescharacteristic
374C4×D4—731no—
375C4×D4—1461no—
376#117—1461no—
377#117—1461no—
378C2×C42—731no—
379#107—731no—
380#107C4×D7311yescharacteristic
381#106—731no—
382#106—731no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
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#103C4×D7311yescharacteristic
401#103C4×D7311yescharacteristic
402#102—731no—
403#102—731no—
404C22⋊C8—731no—
405C22⋊C8—731no—
406C22⋊C8—1461no—
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—21no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—1461no—
420C4×C8—1461no—
421C4×C8—1461no—
422C4×C8C22×D7311yescharacteristic
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C2×Q8—731no—
426C2×Q8—1461no—
427C2×Q8C2×C4×D7311yescharacteristic
428C2×Q8C2×C4×D7311yescharacteristic
429C2×D4—731no—
430C2×D4—1461no—
431C22×C4—731no—
432C22×C4—731no—
433C22×C4—731no—
434C22×C4—1461no—
435Q16—41no—
436Q16—2921no—
437SD16—2921no—
438SD16—2921no—
439M16—2921no—
440M16—2921no—
441M16—5841no—
442M16—5841no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—2922no—
447C2×C8—5841no—
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—21no—
461C4⋊C4—731no—
462C4⋊C4—731no—
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—1461no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—21no—
482C42—21no—
483C42—731no—
484C42—731no—
485C42—731no—
486C42—1461no—
487C42C23×D7311yescharacteristic
488C23—731no—
489C23—1461no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—5841no—
495Q8—1461no—
496Q8—1461no—
497D4—5841no—
498D4—1461no—
499D4—1461no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—2921no—
505C2×C4—2921no—
506C2×C4—2921no—
507C2×C4—731no—
508C2×C4—731no—
509C2×C4—731no—
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—22no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—2921no—
528C8—2921no—
529C8—2921no—
530C8—1461no—
531C8—1461no—
532C8—1461no—
533C8—1461no—
534C22—2921no—
535C22—2921no—
536C22—2921no—
537C22—1461no—
538C22—1461no—
539C22—1461no—
540C22C4×D4×D7311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—2921no—
547C4—2921no—
548C4—2921no—
549C4—1461no—
550C4—1461no—
551C4—1461no—
552C4#1798935211yescharacteristic
553C4#1798935311yescharacteristic
554C4#1798939611yescharacteristic
555C4#1798940311yescharacteristic
556C2—2921no—
557C2—5841no—
558C2#2261864511yescharacteristic
559C2#2261877311yescharacteristic
560C2#2261883611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1587C2
socleC22×C73C2×C4×D4
prime radical#14556566C2×C4
cosocleC42×C73C24
hypercenter#1587D73
hypocenterC73#17988
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
3. #22619022C2semidirect
4. #22608811C2semidirect
5. #22608799C2semidirect
6. #22608791C2semidirect
7. #22608782C2semidirect
8. #22608779C2semidirect
9. #22608774C2semidirect
10. #22608766C2semidirect
11. #22608695C2semidirect
13. #22608384C2semidirect
14. #22608217C2semidirect
15. C73×#1587C2semidirect
286. #1587D73semidirect
296. C73#17988semidirect

Maximal subgroups

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

subgroupindex
#226205352
#226190832
#226190222
#226088112
#226087992
#226087912
#226087822
#226087792
#226087742
#226087662
#226086952
#226083902
#226083842
#226082172
C73×#15872
#1798873