Finite Group Databasebeta

← #33094178

Subgroups — #33094178

Order 18688.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620274C211yesmaximal, characteristic
2#22618870C211yesmaximal, characteristic, complemented
3#22618646C211yesmaximal, characteristic
4#22610906C211yesmaximal, characteristic, complemented
5#22610757C211yesmaximal, characteristic
6#22610642C211yesmaximal, characteristic, complemented
7#22610638C211yesmaximal, characteristic, complemented
8#22610634C211yesmaximal, characteristic, complemented
9#22610070C211yesmaximal, characteristic, complemented
10#22609776C211yesmaximal, characteristic, complemented
11#22609772C211yesmaximal, characteristic, complemented
12#22609771C211yesmaximal, characteristic, complemented
13#22609767C211yesmaximal, characteristic, complemented
14#97×Dic73C211yesmaximal, characteristic, complemented
15C73×#1938C211yesmaximal, characteristic, complemented
16C2×#14556599C2211yescharacteristic
17C2×#14556598C2211yescharacteristic
18#17989140C2211yescharacteristic
19#17989133C2211yescharacteristic
20#17988954C412yescomplemented
21#17988950C412yescomplemented
22#17988948C412yescomplemented
23#17988945C412yescomplemented
24#17988716—22no—
25#17988714—22no—
26#17988661—22no—
27#17988655—22no—
28#17988613C2211yescharacteristic
29#17988610C2211yescharacteristic
30#17988610C2211yescharacteristic
31C2×#14556519C2211yescharacteristic
32C2×#14556518C2211yescharacteristic
33C2×#14556517C2211yescharacteristic
34#17988584C2211yescharacteristic
35#17988583C2211yescharacteristic
36#17988581C2211yescharacteristic
37#17988553C2211yescharacteristic
38#17988545C2211yescharacteristic
39#17988543C2211yescharacteristic
40C2×#14556502C2211yescharacteristic
41C2×#14556501C2211yescharacteristic
42C2×#14556501C2211yescharacteristic
43C2×C8×Dic73C2211yescharacteristic
44C2×C8×Dic73C2211yescharacteristic
45C42×Dic73C2211yescharacteristic
46#17988352C2211yescharacteristic
47#17988351C2211yescharacteristic
48#17988351C2211yescharacteristic
49#17988348C2211yescharacteristic
50#17988347C2211yescharacteristic
51#17988346C2211yescharacteristic
52#424×C73C2211yescharacteristic
53C2×#104×C73C2211yescharacteristic
54#416×C73C2211yescharacteristic
55#408×C73C2211yescharacteristic
56C2×#97×C73C2211yescharacteristic
57#341×C73C2211yescharacteristic
58#339×C73C2211yescharacteristic
59C2×#11924028C2311yescharacteristic
60#14556599—22no—
61#14556599—22no—
62#14556598—22no—
63#14556598—22no—
64C2×#11924012—21no—
65C2×#11924012C2311yescharacteristic
66C2×#11924012C2311yescharacteristic
67C2×#11924011—21no—
68C22×#10596831—21no—
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C2×C8×D73—21no—
72#14556590C2×C412yes—
73#14556589C2×C411yescharacteristic
74#14556587C2×C411yescharacteristic
75#14556582C2×C412yes—
76#14556580C2×C411yescharacteristic
77#14556578C2×C411yescharacteristic
78#14556568—22no—
79#14556563—22no—
80C4×Dic146—22no—
81C4×C22⋊D73—22no—
82#14556550C2311yescharacteristic
83C2×C4×Dic73—22no—
84C2×C4×Dic73C2311yescharacteristic
85C2×C4×Dic73C2311yescharacteristic
86#14556520—22no—
87#14556520—22no—
88#14556520—22no—
89#14556519—22no—
90#14556518—22no—
91#14556517—22no—
92#14556516C2×C412yes—
93#14556515C2×C412yes—
94#14556514C2×C412yes—
95#14556513C2×C412yes—
96#14556512C2×C412yes—
97#14556511C2×C412yes—
98#14556503—22no—
99#14556502—21no—
100#14556502—22no—
101#14556501—21no—
102#14556501C2×C412yes—
103#14556501C2×C412yes—
104#14556501D412yes—
105#14556501D412yes—
106C4×#10596831—21no—
107C8×Dic73—21no—
108C8×Dic73—22no—
109C8×Dic73—22no—
110C2×#41×C73C2311yescharacteristic
111C2×M16×C73C2311yescharacteristic
112C2×M16×C73C2311yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C22×C8×C73C2311yescharacteristic
115#117×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117C4⋊C8×C73—22no—
118#104×C73—22no—
119#103×C73C2×C412yes—
120#102×C73C2×C412yes—
121C22⋊C8×C73—22no—
122#97×C73—22no—
123#11924028—21no—
124#11924028—21no—
125#11924028—21no—
126#11924028—21no—
127C2×Dic146—22no—
128C2×Dic146C22×C411yescharacteristic
129C2×D292C22×C411yescharacteristic
130C2×C22⋊D73—21no—
131C2×C22⋊D73—22no—
132C22×Dic73—21no—
133C22×Dic73#4112yes—
134C2×C4×D73—21no—
135#11924012—21no—
136#11924012—21no—
137#11924012—21no—
138#11924012—21no—
139#11924012—42no—
140#11924011—42no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—42no—
146C2×#10596831C22×C412yes—
147C2×#10596831C2×D411yescharacteristic
148C2×#10596831C2×D411yescharacteristic
149C2×#10596831#4112yes—
150C2×#10596831#4112yes—
151C8×D73—42no—
152C4⋊Dic73—22no—
153C4⋊Dic73C22×C412yes—
154#11924007—22no—
155#11924007—22no—
156#11924007—22no—
157C22⋊Dic73—21no—
158C22⋊Dic73—22no—
159#11924005—22no—
160C4×Dic73—21no—
161C4×Dic73—21no—
162C4×Dic73—44no—
163C4×Dic73C22×C411yescharacteristic
164C4×Dic73C22×C411yescharacteristic
165C4×Dic73C2×D412yes—
166C4×Dic73#4112yes—
167#41×C73—21no—
168#41×C73—21no—
169#41×C73—21no—
170#41×C73—21no—
171C2×Q8×C73C22×C411yescharacteristic
172C2×D4×C73—21no—
173C2×D4×C73C22×C411yescharacteristic
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73C2411yescharacteristic
177M16×C73—21no—
178M16×C73—21no—
179M16×C73—21no—
180M16×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73C22×C412yes—
188C2×C8×C73C2×D412yes—
189C4⋊C4×C73C22×C412yes—
190C22⋊C4×C73—21no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73#4112yes—
194C23×C73—21no—
195C23×C73C2×#4111yescharacteristic
196C22×D73—21no—
197Q8×C73—21no—
198Q8×C73—21no—
199D4×C73—21no—
200D4×C73—21no—
201D4×C73—41no—
202D4×C73—41no—
203C2×C4×C73—22no—
204C2×C4×C73—21no—
205C2×C4×C73—22no—
206C2×C4×C73—42no—
207C2×C4×C73—41no—
208C2×C4×C73—41no—
209C2×C4×C73C23×C411yescharacteristic
210C2×C4×C73C22×D411yescharacteristic
211C2×C4×C73C2×#4111yescharacteristic
212C2×C4×C73C2×#4111yescharacteristic
213C2×C4×C73C2×#4111yescharacteristic
214C2×C4×C73C2×#4111yescharacteristic
215C22⋊D73—41no—
216C22⋊D73—41no—
217C22⋊D73—82no—
218C2×Dic73—24no—
219C2×Dic73—22no—
220C2×Dic73—22no—
221C2×Dic73—21no—
222C2×Dic73—42no—
223C2×Dic73C4×D412yes—
224C2×Dic73C4×D412yes—
225D292—21no—
226D292—21no—
227C4×D73—41no—
228C4×D73—41no—
229Dic146—21no—
230Dic146—21no—
231Dic146—82no—
232C8×C73—22no—
233C8×C73—22no—
234C8×C73—41no—
235C8×C73—41no—
236#10596831—22no—
237#10596831—41no—
238#10596831—41no—
239#10596831#12412yes—
240#10596831#12412yes—
241C22×C73—22no—
242C22×C73—42no—
243C22×C73—41no—
244C22×C73C2×C4×D411yescharacteristic
245C22×C73#52911yescharacteristic
246C22×C73#52911yescharacteristic
247C2×D73—42no—
248C2×D73—41no—
249C4×C73—42no—
250C4×C73—42no—
251C4×C73—41no—
252C4×C73C4×#4111yescharacteristic
253C4×C73C4×#4111yescharacteristic
254C4×C73C2×#12411yescharacteristic
255C4×C73#53211yescharacteristic
256Dic73—24no—
257Dic73—22no—
258Dic73—22no—
259Dic73—42no—
260Dic73—41no—
261#21662—731nomaximal, Sylow
262C2×C73—21no—
263C2×C73—21no—
264C2×C73—81no—
265C2×C73C4×#12411yescharacteristic
266C2×C73#295612yes—
267D73—81no—
268#3135—731no—
269#2961—731no—
270#2932—731no—
271#1994—731no—
272#1962—731no—
273#1938—731no—
274#1938D7311yescharacteristic, complemented
275#1937—731no—
276#1937—731no—
277#1838—731no—
278#1765—731no—
279#1765—731no—
280#1764—731no—
281#1764—731no—
282C4×#97—731no—
283C73#2166211yescharacteristic, complemented, Sylow
284C2×#131—731no—
285C2×#131—731no—
286#533—731no—
287#532—731no—
288#491—732no—
289#490—732no—
290#489—732no—
291#489—732no—
292#446—1462no—
293#446—1462no—
294#435—1462no—
295#435—1462no—
296#424—731no—
297#424C2×D7311yescharacteristic
298#423—731no—
299#423—731no—
300C2×#104—731no—
301C2×#104—731no—
302C2×#104—731no—
303C2×#104C2×D7311yescharacteristic
304#416—731no—
305#416—731no—
306#416—731no—
307#416C2×D7311yescharacteristic
308#408—731no—
309#408C2×D7311yescharacteristic
310#405—731no—
311#405—731no—
312C2×#97—731no—
313C2×#97—731no—
314C2×#97—731no—
315C2×#97C2×D7311yescharacteristic
316C2×C4×C8—731no—
317C2×C4×C8—731no—
318C43—731no—
319#341—731no—
320#341—731no—
321#341—731no—
322#341C2×D7311yescharacteristic
323#339—731no—
324#339—731no—
325#339—731no—
326#339C2×D7311yescharacteristic
327C2×#41—731no—
328C2×#41C22×D7311yescharacteristic
329#131—1462no—
330#131—1462no—
331#131—1462no—
332#131—1462no—
333C2×M16—731no—
334C2×M16—731no—
335C2×M16—1461no—
336C2×M16—1461no—
337C2×M16C22×D7311yescharacteristic
338C2×M16C22×D7311yescharacteristic
339C22×C8—731no—
340C22×C8—731no—
341C22×C8—1461no—
342C22×C8—1461no—
343C22×C8C22×D7311yescharacteristic
344C22×C8C22×D7311yescharacteristic
345C4⋊Q8—732no—
346C4⋊Q8—731no—
347#127—731no—
348#125—732no—
349#124—731no—
350#124—731no—
351C22⋊Q8—1462no—
352#121—1462no—
353C4×Q8—1462no—
354C4×D4—1462no—
355#117—731no—
356#117C22×D7311yescharacteristic
357C2×C42—731no—
358C2×C42—731no—
359C2×C42—1462no—
360C2×C42C22×D7311yescharacteristic
361C4⋊C8—22no—
362C4⋊C8—1462no—
363C4⋊C8—1462no—
364C4⋊C8—1462no—
365#104—22no—
366#104—1462no—
367#104—1462no—
368#104—1462no—
369#103—732no—
370#103—732no—
371#103—732no—
372#103C4×D7312yes—
373#102—732no—
374#102—732no—
375#102—732no—
376#102C4×D7312yes—
377C22⋊C8—22no—
378C22⋊C8—1462no—
379#97—22no—
380#97—732no—
381#97—732no—
382#97—732no—
383#97—732no—
384#97—1462no—
385#97—1461no—
386#97—1461no—
387C4×C8—1461no—
388C4×C8—1462no—
389C4×C8—1462no—
390C4×C8—1461no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—1461no—
396#41—1461no—
397#41—1461no—
398#41—1461no—
399C2×Q8—731no—
400C2×Q8—1462no—
401C2×Q8C2×C4×D7311yescharacteristic
402C2×D4—21no—
403C2×D4—731no—
404C2×D4—1462no—
405C2×D4—1461no—
406C2×D4C2×C4×D7311yescharacteristic
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—732no—
410C22×C4—1461no—
411C22×C4—1461no—
412C22×C4C23×D7311yescharacteristic
413M16—21no—
414M16—21no—
415M16—21no—
416M16—21no—
417M16—2922no—
418M16—2922no—
419M16—1461no—
420M16—1461no—
421M16—1461no—
422M16—1461no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—2922no—
430C2×C8—2922no—
431C2×C8—731no—
432C2×C8—731no—
433C2×C8—732no—
434C2×C8—732no—
435C2×C8—732no—
436C2×C8—1461no—
437C2×C8—1461no—
438C2×C8—1461no—
439C2×C8—1461no—
440C2×C8C2×C4×D7312yes—
441C2×C8D4×D7312yes—
442C4⋊C4—732no—
443C4⋊C4—1462no—
444C4⋊C4—1462no—
445C4⋊C4—1462no—
446C4⋊C4—1462no—
447C4⋊C4C2×C4×D7312yes—
448C22⋊C4—21no—
449C22⋊C4—1462no—
450C22⋊C4—1462no—
451C22⋊C4—1461no—
452C42—21no—
453C42—21no—
454C42—2924no—
455C42—731no—
456C42—731no—
457C42—732no—
458C42—732no—
459C42—1461no—
460C42—1461no—
461C42#1192402712yes—
462C23—21no—
463C23—1461no—
464C23#41×D7311yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—5842no—
468Q8—1461no—
469Q8—1461no—
470D4—21no—
471D4—21no—
472D4—41no—
473D4—41no—
474D4—2921no—
475D4—2921no—
476D4—5842no—
477D4—1461no—
478D4—1461no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—2921no—
486C2×C4—2921no—
487C2×C4—2922no—
488C2×C4—732no—
489C2×C4—732no—
490C2×C4—1462no—
491C2×C4—1461no—
492C2×C4—1464no—
493C2×C4—1462no—
494C2×C4C22×C4×D7311yescharacteristic
495C2×C4C2×D4×D7311yescharacteristic
496C2×C4#41×D7311yescharacteristic
497C2×C4#41×D7311yescharacteristic
498C2×C4#41×D7311yescharacteristic
499C2×C4C2×#1192402711yescharacteristic
500C8—22no—
501C8—22no—
502C8—41no—
503C8—41no—
504C8—2921no—
505C8—2921no—
506C8—732no—
507C8—732no—
508C8—1462no—
509C22—22no—
510C22—42no—
511C22—41no—
512C22—2922no—
513C22—2921no—
514C22C4×D4×D7311yescharacteristic
515C22#1798911411yescharacteristic
516C22#1798912011yescharacteristic
517C4—42no—
518C4—42no—
519C4—41no—
520C4—2922no—
521C4—2921no—
522C4—1464no—
523C4—1462no—
524C4—1462no—
525C4C4×#1192402711yescharacteristic
526C4#1798905511yescharacteristic
527C4#124×D7311yescharacteristic
528C4#1798913211yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—5841no—
533C2#2261247211yescharacteristic
534C2#2261883912yes—
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1938C2
socleC22×C73C2×C4×D4
prime radical#17989133C22
cosocleC22×C4×C73C24
hypercenter#1938D73
hypocenterC73#21662
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1938

Complements

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

NH ≅ G/Ntype
2. #22618870C2semidirect
4. #22610906C2semidirect
6. #22610642C2semidirect
7. #22610638C2semidirect
8. #22610634C2semidirect
9. #22610070C2semidirect
10. #22609776C2semidirect
11. #22609772C2semidirect
12. #22609771C2semidirect
13. #22609767C2semidirect
14. #97×Dic73C2semidirect
15. C73×#1938C2semidirect
20. #17988954C4semidirect
21. #17988950C4semidirect
22. #17988948C4semidirect
23. #17988945C4semidirect
274. #1938D73semidirect
283. C73#21662semidirect

Maximal subgroups

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

subgroupindex
#226202742
#226188702
#226186462
#226109062
#226107572
#226106422
#226106382
#226106342
#226100702
#226097762
#226097722
#226097712
#226097672
#97×Dic732
C73×#19382
#2166273