Finite Group Databasebeta

← #33094166

Subgroups — #33094166

Order 18688.

730 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620274C211yesmaximal, characteristic
2#22618863C211yesmaximal, characteristic, complemented
3#22618641C211yesmaximal, characteristic
4#22610910C211yesmaximal, characteristic, complemented
5#22610761C211yesmaximal, characteristic
6#22610644C211yesmaximal, characteristic, complemented
7#22610643C211yesmaximal, characteristic, complemented
8#22610640C211yesmaximal, characteristic, complemented
9#22610639C211yesmaximal, characteristic, complemented
10#22610070C211yesmaximal, characteristic, complemented
11#22609770C211yesmaximal, characteristic, complemented
12#22609768C211yesmaximal, characteristic, complemented
13#22609766C211yesmaximal, characteristic, complemented
14#22609617C211yesmaximal, characteristic, complemented
15C73×#1764C211yesmaximal, characteristic, complemented
16C2×#14556597C2211yescharacteristic
17#17989140C2211yescharacteristic
18#17989133C2211yescharacteristic
19#17988954C412yescomplemented
20#17988950C412yescomplemented
21#17988948C412yescomplemented
22#17988945C412yescomplemented
23#17988715—22no—
24C8×Dic146—22no—
25#17988663—22no—
26C8×C22⋊D73—22no—
27#17988615C2211yescharacteristic
28#17988614C2211yescharacteristic
29#17988610C2211yescharacteristic
30#17988610C2211yescharacteristic
31C2×#14556519C2211yescharacteristic
32C2×#14556518C2211yescharacteristic
33C2×#14556517C2211yescharacteristic
34#17988584C2211yescharacteristic
35#17988583C2211yescharacteristic
36#17988581C2211yescharacteristic
37#17988555C2211yescharacteristic
38#17988554C2211yescharacteristic
39#17988542C2211yescharacteristic
40C2×#14556502C2211yescharacteristic
41C2×#14556501C2211yescharacteristic
42C2×#14556501C2211yescharacteristic
43C2×C8×Dic73C2211yescharacteristic
44C2×C8×Dic73C2211yescharacteristic
45#17988433C2211yescharacteristic
46#17988352C2211yescharacteristic
47#17988351C2211yescharacteristic
48#17988351C2211yescharacteristic
49#17988348C2211yescharacteristic
50#17988347C2211yescharacteristic
51#17988346C2211yescharacteristic
52C2×#131×C73C2211yescharacteristic
53C2×#104×C73C2211yescharacteristic
54#416×C73C2211yescharacteristic
55#405×C73C2211yescharacteristic
56C2×C4×C8×C73C2211yescharacteristic
57#341×C73C2211yescharacteristic
58#339×C73C2211yescharacteristic
59C2×#11924028C2311yescharacteristic
60#14556597—22no—
61#14556597—22no—
62C2×#11924012C2311yescharacteristic
63C2×#11924012C2311yescharacteristic
64C2×#11924011—21no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C2×C8×D73—21no—
68#14556590C2×C412yes—
69#14556589C2×C411yescharacteristic
70#14556587C2×C411yescharacteristic
71#14556582C2×C412yes—
72#14556580C2×C411yescharacteristic
73#14556578C2×C411yescharacteristic
74#14556568—22no—
75#14556563—22no—
76C4×Dic146—22no—
77C4×C22⋊D73—22no—
78#14556550C2311yescharacteristic
79C2×C4×Dic73C2311yescharacteristic
80C2×C4×Dic73C2311yescharacteristic
81C4⋊#10596831—22no—
82#14556520—22no—
83#14556520—22no—
84#14556520—22no—
85#14556519—22no—
86#14556518—22no—
87#14556517—22no—
88#14556516C2×C412yes—
89#14556515C2×C412yes—
90#14556514C2×C412yes—
91#14556513C2×C412yes—
92#14556512C2×C412yes—
93#14556511C2×C412yes—
94C22⋊#10596831—22no—
95#14556503—22no—
96#14556502—22no—
97#14556501—22no—
98#14556501—21no—
99#14556501C2×C412yes—
100#14556501C2×C412yes—
101C8×Dic73—21no—
102C8×Dic73—22no—
103C8×Dic73D412yes—
104C8×Dic73D412yes—
105#14556498—22no—
106C2×#41×C73C2311yescharacteristic
107#131×C73—22no—
108#131×C73—22no—
109C2×M16×C73—21no—
110C2×M16×C73C2311yescharacteristic
111C2×M16×C73C2311yescharacteristic
112C22×C8×C73—21no—
113C22×C8×C73C2311yescharacteristic
114C22×C8×C73C2311yescharacteristic
115#117×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117#104×C73—22no—
118#103×C73C2×C412yes—
119#102×C73C2×C412yes—
120#97×C73—21no—
121C4×C8×C73—21no—
122C4×C8×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#11924011—42no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831C22×C412yes—
147C2×#10596831C2×D412yes—
148C8×D73—42no—
149C4⋊Dic73—22no—
150C4⋊Dic73C22×C412yes—
151#11924007—22no—
152#11924007—22no—
153#11924007—22no—
154C22⋊Dic73—21no—
155C22⋊Dic73—22no—
156#11924005—22no—
157C4×Dic73—21no—
158C4×Dic73—21no—
159C4×Dic73C22×C411yescharacteristic
160C4×Dic73C22×C411yescharacteristic
161C4×Dic73C2×D412yes—
162C4×Dic73#4112yes—
163#41×C73—21no—
164#41×C73—21no—
165#41×C73—21no—
166#41×C73—21no—
167C2×Q8×C73C22×C411yescharacteristic
168C2×D4×C73—21no—
169C2×D4×C73C22×C411yescharacteristic
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73C2411yescharacteristic
173M16×C73—21no—
174M16×C73—21no—
175M16×C73—21no—
176M16×C73—21no—
177M16×C73—42no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—42no—
183C2×C8×C73C22×C412yes—
184C2×C8×C73C2×D411yescharacteristic
185C2×C8×C73C2×D411yescharacteristic
186C2×C8×C73#4112yes—
187C2×C8×C73#4112yes—
188C4⋊C4×C73C22×C412yes—
189C22⋊C4×C73—21no—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73#4112yes—
193C23×C73—21no—
194C23×C73C2×#4111yescharacteristic
195C22×D73—21no—
196Q8×C73—21no—
197Q8×C73—21no—
198D4×C73—21no—
199D4×C73—21no—
200D4×C73—41no—
201D4×C73—41no—
202C2×C4×C73—22no—
203C2×C4×C73—21no—
204C2×C4×C73—22no—
205C2×C4×C73—42no—
206C2×C4×C73—41no—
207C2×C4×C73—41no—
208C2×C4×C73C23×C411yescharacteristic
209C2×C4×C73C22×D411yescharacteristic
210C2×C4×C73C2×#4111yescharacteristic
211C2×C4×C73C2×#4111yescharacteristic
212C2×C4×C73C2×#4111yescharacteristic
213C2×C4×C73C2×#4111yescharacteristic
214C22⋊D73—44no—
215C22⋊D73—41no—
216C22⋊D73—41no—
217C2×Dic73—22no—
218C2×Dic73—21no—
219C2×Dic73—22no—
220C2×Dic73—42no—
221C2×Dic73—42no—
222C2×Dic73C4×D412yes—
223C2×Dic73C4×D412yes—
224D292—21no—
225D292—21no—
226C4×D73—41no—
227C4×D73—41no—
228Dic146—21no—
229Dic146—21no—
230Dic146—44no—
231C8×C73—22no—
232C8×C73—41no—
233C8×C73—41no—
234C8×C73#12412yes—
235C8×C73#12412yes—
236#10596831—22no—
237#10596831—22no—
238#10596831—41no—
239#10596831—41no—
240C22×C73—22no—
241C22×C73—42no—
242C22×C73—41no—
243C22×C73C2×C4×D411yescharacteristic
244C22×C73#52911yescharacteristic
245C22×C73#52911yescharacteristic
246C2×D73—42no—
247C2×D73—41no—
248C4×C73—42no—
249C4×C73—42no—
250C4×C73—41no—
251C4×C73C4×#4111yescharacteristic
252C4×C73C4×#4111yescharacteristic
253C4×C73C2×#12411yescharacteristic
254C4×C73#53211yescharacteristic
255Dic73—22no—
256Dic73—22no—
257Dic73—42no—
258Dic73—42no—
259Dic73—41no—
260#21661—731nomaximal, Sylow
261C2×C73—21no—
262C2×C73—21no—
263C2×C73—81no—
264C2×C73C4×#12411yescharacteristic
265C2×C73#295512yes—
266D73—81no—
267#3135—731no—
268#2960—731no—
269#2931—731no—
270#1995—731no—
271#1963—731no—
272#1938—731no—
273#1938—731no—
274#1938—731no—
275#1938—731no—
276#1838—731no—
277#1764—731no—
278#1764—731no—
279#1764—731no—
280#1764D7311yescharacteristic, complemented
281#1726—731no—
282C73#2166111yescharacteristic, complemented, Sylow
283C2×#131—731no—
284C2×#131C2×D7311yescharacteristic
285#533—731no—
286#532—731no—
287#491—732no—
288#490—732no—
289#489—732no—
290#489—732no—
291#446—1462no—
292C8×Q8—1462no—
293#436—1462no—
294C8×D4—1462no—
295#424—731no—
296#424—731no—
297#423—731no—
298#423—731no—
299C2×#104—731no—
300C2×#104—731no—
301C2×#104—731no—
302C2×#104C2×D7311yescharacteristic
303#416—731no—
304#416—731no—
305#416—731no—
306#416C2×D7311yescharacteristic
307#408—731no—
308#408—731no—
309#405—731no—
310#405C2×D7311yescharacteristic
311C2×#97—731no—
312C2×#97—731no—
313C2×#97—731no—
314C2×C4×C8—731no—
315C2×C4×C8—731no—
316C2×C4×C8C2×D7311yescharacteristic
317#376—731no—
318#341—731no—
319#341—731no—
320#341—731no—
321#341C2×D7311yescharacteristic
322#339—731no—
323#339—731no—
324#339—731no—
325#339C2×D7311yescharacteristic
326C2×#41—731no—
327C2×#41C22×D7311yescharacteristic
328#131—22no—
329#131—22no—
330#131—1462no—
331#131—1462no—
332C2×M16—21no—
333C2×M16—731no—
334C2×M16—731no—
335C2×M16—1461no—
336C2×M16C22×D7311yescharacteristic
337C2×M16C22×D7311yescharacteristic
338C22×C8—21no—
339C22×C8—731no—
340C22×C8—731no—
341C22×C8—1461no—
342C22×C8C22×D7311yescharacteristic
343C22×C8C22×D7311yescharacteristic
344C4⋊Q8—732no—
345C4⋊Q8—731no—
346#127—731no—
347#125—732no—
348#124—731no—
349#124—731no—
350C22⋊Q8—1462no—
351#121—1462no—
352C4×Q8—1462no—
353C4×D4—1462no—
354#117—731no—
355#117C22×D7311yescharacteristic
356C2×C42—731no—
357C2×C42—731no—
358C2×C42C22×D7311yescharacteristic
359C4⋊C8—1462no—
360C4⋊C8—1462no—
361C4⋊C8—1462no—
362C4⋊C8—1462no—
363#104—22no—
364#104—1462no—
365#104—1462no—
366#104—1462no—
367#103—732no—
368#103—732no—
369#103—732no—
370#103C4×D7312yes—
371#102—732no—
372#102—732no—
373#102—732no—
374#102C4×D7312yes—
375C22⋊C8—1462no—
376C22⋊C8—1462no—
377#97—21no—
378#97—732no—
379#97—732no—
380#97—1462no—
381#97—1461no—
382#97—1462no—
383C4×C8—21no—
384C4×C8—22no—
385C4×C8—732no—
386C4×C8—732no—
387C4×C8—1461no—
388C4×C8—1462no—
389#95—1462no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—1461no—
395#41—1461no—
396#41—1461no—
397#41—1461no—
398C2×Q8—731no—
399C2×Q8—1462no—
400C2×Q8C2×C4×D7311yescharacteristic
401C2×D4—21no—
402C2×D4—731no—
403C2×D4—1462no—
404C2×D4—1461no—
405C2×D4C2×C4×D7311yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—732no—
409C22×C4—1461no—
410C22×C4—1461no—
411C22×C4C23×D7311yescharacteristic
412M16—21no—
413M16—21no—
414M16—21no—
415M16—21no—
416M16—42no—
417M16—2922no—
418M16—1461no—
419M16—1461no—
420M16—1461no—
421M16—1461no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—42no—
427C2×C8—2922no—
428C2×C8—732no—
429C2×C8—732no—
430C2×C8—1461no—
431C2×C8—1461no—
432C2×C8—1461no—
433C2×C8—1461no—
434C2×C8—1461no—
435C2×C8—1461no—
436C2×C8C2×C4×D7312yes—
437C2×C8D4×D7311yescharacteristic
438C2×C8D4×D7311yescharacteristic
439C2×C8#1192402712yes—
440C2×C8#1192402812yes—
441C4⋊C4—732no—
442C4⋊C4—1462no—
443C4⋊C4—1462no—
444C4⋊C4—1462no—
445C4⋊C4—1462no—
446C4⋊C4C2×C4×D7312yes—
447C22⋊C4—21no—
448C22⋊C4—1462no—
449C22⋊C4—1462no—
450C22⋊C4—1461no—
451C42—21no—
452C42—21no—
453C42—731no—
454C42—731no—
455C42—732no—
456C42—732no—
457C42—1461no—
458C42—1461no—
459C42#1192402812yes—
460C23—21no—
461C23—1461no—
462C23#41×D7311yescharacteristic
463Q8—21no—
464Q8—21no—
465Q8—2924no—
466Q8—1461no—
467Q8—1461no—
468D4—21no—
469D4—21no—
470D4—41no—
471D4—41no—
472D4—2921no—
473D4—2921no—
474D4—2924no—
475D4—1461no—
476D4—1461no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—2922no—
484C2×C4—2921no—
485C2×C4—2921no—
486C2×C4—2922no—
487C2×C4—732no—
488C2×C4—732no—
489C2×C4—1462no—
490C2×C4—1461no—
491C2×C4—1462no—
492C2×C4C22×C4×D7311yescharacteristic
493C2×C4C2×D4×D7311yescharacteristic
494C2×C4#41×D7311yescharacteristic
495C2×C4C2×#1192402711yescharacteristic
496C2×C4C2×#1192402811yescharacteristic
497C2×C4C2×#1192402811yescharacteristic
498C8—22no—
499C8—41no—
500C8—41no—
501C8—2921no—
502C8—2921no—
503C8—1462no—
504C8—1462no—
505C8#1455657712yes—
506C8#1455657712yes—
507C22—22no—
508C22—42no—
509C22—41no—
510C22—2922no—
511C22—2921no—
512C22C4×D4×D7311yescharacteristic
513C22#1798911511yescharacteristic
514C22#1798911711yescharacteristic
515C4—42no—
516C4—42no—
517C4—41no—
518C4—2922no—
519C4—2922no—
520C4—2921no—
521C4—1462no—
522C4—1462no—
523C4C4×#1192402711yescharacteristic
524C4C4×#1192402811yescharacteristic
525C4C2×#1455657711yescharacteristic
526C4#1798913411yescharacteristic
527C2—21no—
528C2—21no—
529C2—81no—
530C2—5841no—
531C2C4×#1455657711yescharacteristic
532C2#2261882912yes—
subgroupG/H
centerC2×C8D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1764C2
socleC22×C73C2×C4×D4
prime radical#17989133C22
cosocleC22×C4×C73C24
hypercenter#1764D73
hypocenterC73#21661
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1764

Complements

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

NH ≅ G/Ntype
2. #22618863C2semidirect
4. #22610910C2semidirect
6. #22610644C2semidirect
7. #22610643C2semidirect
8. #22610640C2semidirect
9. #22610639C2semidirect
10. #22610070C2semidirect
11. #22609770C2semidirect
12. #22609768C2semidirect
13. #22609766C2semidirect
14. #22609617C2semidirect
15. C73×#1764C2semidirect
19. #17988954C4semidirect
20. #17988950C4semidirect
21. #17988948C4semidirect
22. #17988945C4semidirect
280. #1764D73semidirect
282. C73#21661semidirect

Maximal subgroups

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

subgroupindex
#226202742
#226188632
#226186412
#226109102
#226107612
#226106442
#226106432
#226106402
#226106392
#226100702
#226097702
#226097682
#226097662
#226096172
C73×#17642
#2166173