Finite Group Databasebeta

← #33240809

Subgroups — #33240809

Order 18688.

632 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#466×D73C211yesmaximal, characteristic
2#427×D73C211yesmaximal, characteristic, complemented
3#22612123C211yesmaximal, characteristic, complemented
4#22612122C211yesmaximal, characteristic, complemented
5#22612119C211yesmaximal, characteristic, complemented
6#22612118C211yesmaximal, characteristic, complemented
7#22612115C211yesmaximal, characteristic, complemented
8#22612113C211yesmaximal, characteristic, complemented
9#22612110C211yesmaximal, characteristic, complemented
10#22611718C211yesmaximal, characteristic, complemented
11#22611716C211yesmaximal, characteristic, complemented
12#22611645C211yesmaximal, characteristic, complemented
13#22611645C211yesmaximal, characteristic, complemented
14#22611540C211yesmaximal, characteristic, complemented
15C73×#2234C211yesmaximal, characteristic, complemented
16C2×D8×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18#121×D73—21no—
19#117×D73—21no—
20C2×#14556530C2211yescharacteristic
21C2×#14556530C2211yescharacteristic
22#17988824C2211yescharacteristic
23#17988823C2211yescharacteristic
24#17988822—21no—
25#17988821—21no—
26#17988820C2211yescharacteristic
27#17988625C2211yescharacteristic, complemented
28#17988624C2211yescharacteristic
29#17988624C2211yescharacteristic
30#17988623—21no—
31#17988622—21no—
32#107×D73C2211yescharacteristic
33#107×D73C2211yescharacteristic, complemented
34#107×D73C2211yescharacteristic, complemented
35#106×D73—21no—
36#102×D73—21no—
37#17988415C2211yescharacteristic, complemented
38#17988414C2211yescharacteristic, complemented
39#17988414C2211yescharacteristic, complemented
40#17988413C2211yescharacteristic, complemented
41#17988412C2211yescharacteristic, complemented
42#17988412C2211yescharacteristic, complemented
43#17988389C2211yescharacteristic, complemented
44#17988389C2211yescharacteristic, complemented
45#17988388C2211yescharacteristic, complemented
46#17988388C2211yescharacteristic, complemented
47#17988387C2211yescharacteristic, complemented
48#17988387C2211yescharacteristic, complemented
49C22⋊#11924003C2211yescharacteristic, complemented
50#17988366C2211yescharacteristic, complemented
51#17988366C2211yescharacteristic, complemented
52#466×C73C2211yescharacteristic
53#427×C73C2211yescharacteristic, complemented
54#367×C73C2211yescharacteristic, complemented
55#366×C73C2211yescharacteristic, complemented
56#357×C73C2211yescharacteristic, complemented
57#357×C73C2211yescharacteristic, complemented
58C22⋊C16×C73C2211yescharacteristic, complemented
59C2×D4×D73—21no—
60C2×D4×D73—41no—
61C22×C4×D73D411yescharacteristic
62C2×D584C2311yescharacteristic
63C2×#11924013—21no—
64D8×D73—22no—
65D8×D73—22no—
66C22×#10596831D411yescharacteristic
67C2×C8×D73—22no—
68C2×C8×D73—22no—
69C2×C8×D73D411yescharacteristic
70C2×C8×D73D411yescharacteristic
71C2×C8×D73C2311yescharacteristic
72C2×C8×D73C2311yescharacteristic
73#14556566—21no—
74#14556565—21no—
75#14556564—41no—
76#14556563—41no—
77#14556562—21no—
78#14556550—21no—
79#14556549—21no—
80#14556549—21no—
81#14556548—41no—
82#14556547—41no—
83C4⋊C4×D73—21no—
84C4⋊C4×D73—21no—
85C4⋊C4×D73—21no—
86C22⋊C4×D73—41no—
87C22⋊C4×D73—41no—
88C42×D73—41no—
89#14556530—22no—
90#14556530—22no—
91C2×#11924003C2311yescharacteristic
92C2×#11924003C2311yescharacteristic
93#14556525C2311yescharacteristic
94#14556525C2311yescharacteristic
95#14556525C2311yescharacteristic
96#14556524—21no—
97#14556524—21no—
98#14556524—21no—
99#14556523—21no—
100#14556522—21no—
101#14556522—21no—
102#14556513—21no—
103#14556512—21no—
104#14556511—21no—
105C2×D8×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107#121×C73—21no—
108#117×C73—21no—
109C2×C16×C73C2311yescharacteristic
110C2×C16×C73C2311yescharacteristic
111#107×C73C2311yescharacteristic
112#107×C73C2311yescharacteristic
113#107×C73C2311yescharacteristic
114#106×C73—21no—
115#102×C73—21no—
116C23×D73—41no—
117C23×D73D811yescharacteristic
118C2×D292—21no—
119C2×D292—41no—
120C2×C22⋊D73—41no—
121C2×C22⋊D73—41no—
122C2×C22⋊D73—41no—
123D4×D73—42no—
124D4×D73—42no—
125D4×D73—84no—
126C22×Dic73D811yescharacteristic
127C2×C4×D73—22no—
128C2×C4×D73—22no—
129C2×C4×D73—41no—
130C2×C4×D73—41no—
131C2×C4×D73—41no—
132C2×C4×D73D811yescharacteristic
133C2×C4×D73D811yescharacteristic
134C2×C4×D73C2×D411yescharacteristic
135C2×C4×D73C2×D411yescharacteristic
136D584—21no—
137D584—21no—
138#11924013—42no—
139C2×#10596831—22no—
140C2×#10596831C2×D411yescharacteristic
141C2×#10596831C2×D411yescharacteristic
142C8×D73—22no—
143C8×D73—21no—
144C8×D73—21no—
145C8×D73—22no—
146C8×D73#4112yes—
147C8×D73#4112yes—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151#11924007—41no—
152#11924007—41no—
153#11924007—41no—
154C22⋊Dic73—41no—
155C22⋊Dic73—41no—
156#11924005—41no—
157#11924005—41no—
158#11924005—41no—
159#11924005—41no—
160C4×Dic73—41no—
161C4×Dic73—41no—
162C4×Dic73—41no—
163#11924003—21no—
164#11924003—21no—
165C2×D4×C73—21no—
166C2×D4×C73—41no—
167C22×C4×C73C2×D411yescharacteristic
168D8×C73—21no—
169D8×C73—21no—
170C2×C8×C73—21no—
171C2×C8×C73—21no—
172C2×C8×C73C2×D411yescharacteristic
173C2×C8×C73C2411yescharacteristic
174C4⋊C4×C73—21no—
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C22⋊C4×C73—41no—
178C22⋊C4×C73—41no—
179C42×C73—41no—
180C16×C73—21no—
181C16×C73—21no—
182C23×C73—41no—
183C23×C73C2×D811yescharacteristic
184C22×D73—22no—
185C22×D73—22no—
186C22×D73—41no—
187C22×D73—41no—
188C22×D73—82no—
189C22×D73—82no—
190C22×D73—82no—
191C22×D73C2×D811yescharacteristic
192C22×D73C2×D811yescharacteristic
193D4×C73—41no—
194D4×C73—41no—
195D4×C73—82no—
196C2×C4×C73—21no—
197C2×C4×C73—21no—
198C2×C4×C73—41no—
199C2×C4×C73—41no—
200C2×C4×C73—41no—
201C2×C4×C73C2×D811yescharacteristic
202C2×C4×C73C22×D411yescharacteristic
203C22⋊D73—82no—
204C22⋊D73—82no—
205C22⋊D73—82no—
206C2×Dic73—22no—
207C2×Dic73—41no—
208C2×Dic73—41no—
209C2×Dic73—41no—
210C2×Dic73C2×D811yescharacteristic
211C2×Dic73C2×D811yescharacteristic
212D292—41no—
213D292—41no—
214D292—82no—
215C4×D73—22no—
216C4×D73—21no—
217C4×D73—21no—
218C4×D73—22no—
219C4×D73—82no—
220C4×D73—82no—
221C4×D73—82no—
222C4×D73#12312yes—
223C4×D73#13712yes—
224C8×C73—21no—
225C8×C73C2×#4111yescharacteristic
226C8×C73C2×#4111yescharacteristic
227#10596831—21no—
228#10596831#12312yes—
229C22×C73—21no—
230C22×C73—21no—
231C22×C73—21no—
232C22×C73—81no—
233C22×C73—81no—
234C22×C73—81no—
235C22×C73C22×D811yescharacteristic
236C2×D73—21no—
237C2×D73—21no—
238C2×D73—21no—
239C2×D73—21no—
240C2×D73—44no—
241C2×D73—81no—
242C2×D73—81no—
243C2×D73—81no—
244C2×D73—164no—
245C2×D73#48012yes—
246C2×D73#50912yes—
247C4×C73—21no—
248C4×C73—81no—
249C4×C73—81no—
250C4×C73—81no—
251C4×C73C2×#12311yescharacteristic
252C4×C73C2×#13711yescharacteristic
253Dic73—21no—
254Dic73—81no—
255Dic73—81no—
256Dic73—81no—
257Dic73#48012yes—
258#33648—731nomaximal, Sylow
259C2×C73—41no—
260C2×C73—161no—
261C2×C73C2×#48011yescharacteristic
262C2×C73C2×#50911yescharacteristic
263C2×C73#341411yescharacteristic
264D73—22no—
265D73—22no—
266D73—161no—
267C2×#466—731no—
268C2×#427—731no—
269#2234—731no—
270#2234—731no—
271#2234—731no—
272#2234D7311yescharacteristic, complemented
273#2233—731no—
274#2233—731no—
275#2232—731no—
276#2232—731no—
277#2159—731no—
278#2159—731no—
279#2140—731no—
280#2140—731no—
281#2112—731no—
282C73#3364811yescharacteristic, complemented, Sylow
283C22×D8—731no—
284C23×C8—731no—
285C2×#121—1461no—
286C2×#117—1461no—
287C2×M32—731no—
288C2×M32—731no—
289#466—731no—
290#466—731no—
291#466—731no—
292#466—1461no—
293#466—1461no—
294#466C2×D7311yescharacteristic
295#427—731no—
296#427—731no—
297#427—731no—
298#427—1461no—
299#427—1461no—
300#427C2×D7311yescharacteristic, complemented
301C2×#107—731no—
302C2×#107—731no—
303C2×#107—731no—
304C2×#106—1461no—
305C2×#102—1461no—
306#367—731no—
307#367—731no—
308#367—731no—
309#367C2×D7311yescharacteristic, complemented
310#366—731no—
311#366—731no—
312#366—731no—
313#366C2×D7311yescharacteristic, complemented
314#357—731no—
315#357—731no—
316#357—731no—
317#357—731no—
318#357—731no—
319#357—731no—
320#357C2×D7311yescharacteristic, complemented
321#357C2×D7311yescharacteristic, complemented
322C22⋊C16—731no—
323C22⋊C16—731no—
324C22⋊C16—731no—
325C22⋊C16C2×D7311yescharacteristic, complemented
326C22×D4—2921no—
327C22×D4—1461no—
328C23×C4—731no—
329C2×D8—731no—
330C2×D8—1462no—
331C2×D8—1462no—
332C2×D8—1461no—
333C2×D8C22×D7311yescharacteristic
334C22×C8—731no—
335C22×C8—731no—
336C22×C8—731no—
337C22×C8—731no—
338C22×C8—731no—
339C22×C8—1462no—
340C22×C8—1462no—
341C22×C8C22×D7311yescharacteristic
342#121—21no—
343#121—2921no—
344#121—2921no—
345#121—1461no—
346#121—1461no—
347#121—1461no—
348#117—21no—
349#117—2921no—
350#117—2921no—
351#117—1461no—
352#117—1461no—
353#117—1461no—
354C2×C4⋊C4—1461no—
355C2×C4⋊C4—1461no—
356C2×C4⋊C4—1461no—
357C2×C22⋊C4—2921no—
358C2×C22⋊C4—2921no—
359C2×C42—2921no—
360M32—1462no—
361M32—1462no—
362C2×C16—731no—
363C2×C16—731no—
364C2×C16C22×D7311yescharacteristic
365C2×C16C22×D7311yescharacteristic
366#107—731no—
367#107—731no—
368#107—731no—
369#107—1461no—
370#107—1461no—
371#107—1461no—
372#107C22×D7311yescharacteristic
373#107C22×D7311yescharacteristic
374#107C22×D7311yescharacteristic
375#106—21no—
376#106—1461no—
377#106—1461no—
378#106—1461no—
379#102—21no—
380#102—1461no—
381#102—1461no—
382#102—1461no—
383C24—2921no—
384C24—731no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—2921no—
388C2×D4—2921no—
389C2×D4—2921no—
390C2×D4—2922no—
391C2×D4—2922no—
392C2×D4—2921no—
393C2×D4—5844no—
394C2×D4—1461no—
395C22×C4—2921no—
396C22×C4—2921no—
397C22×C4—2921no—
398C22×C4—731no—
399C22×C4—731no—
400C22×C4—731no—
401C22×C4—731no—
402C22×C4—731no—
403C22×C4—1462no—
404C22×C4—1462no—
405C22×C4D4×D7311yescharacteristic
406D8—21no—
407D8—21no—
408D8—2922no—
409D8—1461no—
410D8—1461no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—731no—
414C2×C8—732no—
415C2×C8—732no—
416C2×C8—731no—
417C2×C8—1462no—
418C2×C8—1462no—
419C2×C8—1462no—
420C2×C8—1461no—
421C2×C8—1461no—
422C2×C8D4×D7311yescharacteristic
423C2×C8C23×D7311yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—2921no—
428C4⋊C4—2921no—
429C4⋊C4—2921no—
430C4⋊C4—1461no—
431C4⋊C4—1461no—
432C4⋊C4—1461no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—2921no—
436C22⋊C4—2921no—
437C22⋊C4—2921no—
438C22⋊C4—2921no—
439C22⋊C4—2921no—
440C22⋊C4—2921no—
441C42—41no—
442C42—2921no—
443C42—2921no—
444C42—2921no—
445C16—21no—
446C16—21no—
447C16—1461no—
448C16—1461no—
449C23—41no—
450C23—2921no—
451C23—2921no—
452C23—5842no—
453C23—5842no—
454C23—5842no—
455C23—731no—
456C23—731no—
457C23—1462no—
458C23—1462no—
459C23D8×D7311yescharacteristic
460D4—41no—
461D4—41no—
462D4—82no—
463D4—2921no—
464D4—2921no—
465D4—5842no—
466D4—5842no—
467D4—5842no—
468D4—5842no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—2921no—
475C2×C4—2921no—
476C2×C4—2921no—
477C2×C4—5842no—
478C2×C4—5842no—
479C2×C4—5842no—
480C2×C4—731no—
481C2×C4—732no—
482C2×C4—732no—
483C2×C4—731no—
484C2×C4—1462no—
485C2×C4—1462no—
486C2×C4—1462no—
487C2×C4—1461no—
488C2×C4—1461no—
489C2×C4D8×D7311yescharacteristic
490C2×C4C2×D4×D7311yescharacteristic
491C8—21no—
492C8—732no—
493C8—1461no—
494C8#41×D7311yescharacteristic
495C8#41×D7311yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—2924no—
503C22—5841no—
504C22—5841no—
505C22—5841no—
506C22—732no—
507C22—732no—
508C22—11684no—
509C22—1461no—
510C22—1461no—
511C22—1461no—
512C22—1461no—
513C22C2×D8×D7311yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—5841no—
519C4—5841no—
520C4—5841no—
521C4—732no—
522C4—1461no—
523C4#123×D7311yescharacteristic
524C4#137×D7311yescharacteristic
525C2—41no—
526C2—161no—
527C2—11681no—
528C2—1462no—
529C2—1462no—
530C2#480×D7311yescharacteristic
531C2#509×D7311yescharacteristic
532C2#2262306411yescharacteristic
subgroupG/H
centerC22C2×D8×D73
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#2234C2
socleC22×C73C22×D8
prime radical#466×D73C2
hypercenter#2234D73
hypocenterC73#33648
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
2. #427×D73C2semidirect
3. #22612123C2semidirect
4. #22612122C2semidirect
5. #22612119C2semidirect
6. #22612118C2semidirect
7. #22612115C2semidirect
8. #22612113C2semidirect
9. #22612110C2semidirect
10. #22611718C2semidirect
11. #22611716C2semidirect
12. #22611645C2semidirect
13. #22611645C2semidirect
14. #22611540C2semidirect
15. C73×#2234C2semidirect
27. #17988625C22semidirect
33. #107×D73C22semidirect
34. #107×D73C22semidirect
37. #17988415C22semidirect
38. #17988414C22semidirect
39. #17988414C22semidirect
40. #17988413C22semidirect
41. #17988412C22semidirect
42. #17988412C22semidirect
43. #17988389C22semidirect
44. #17988389C22semidirect
45. #17988388C22semidirect
46. #17988388C22semidirect
47. #17988387C22semidirect
48. #17988387C22semidirect
49. C22⋊#11924003C22semidirect
50. #17988366C22semidirect
51. #17988366C22semidirect
53. #427×C73C22semidirect
54. #367×C73C22semidirect
55. #366×C73C22semidirect
56. #357×C73C22semidirect
57. #357×C73C22semidirect
58. C22⋊C16×C73C22semidirect
272. #2234D73semidirect
282. C73#33648semidirect
300. #427C2×D73semidirect
309. #367C2×D73semidirect
313. #366C2×D73semidirect
320. #357C2×D73semidirect
321. #357C2×D73semidirect
325. C22⋊C16C2×D73semidirect

Maximal subgroups

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

subgroupindex
#466×D732
#427×D732
#226121232
#226121222
#226121192
#226121182
#226121152
#226121132
#226121102
#226117182
#226117162
#226116452
#226115402
C73×#22342
#3364873